120 results back to index

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The Concepts and Practice of Mathematical Finance
** by
Mark S. Joshi

Black-Scholes formula, Brownian motion, correlation coefficient, Credit Default Swap, delta neutral, discrete time, Emanuel Derman, fixed income, implied volatility, incomplete markets, interest rate derivative, interest rate swap, London Interbank Offered Rate, martingale, millennium bug, quantitative trading / quantitative ﬁnance, short selling, stochastic process, stochastic volatility, the market place, time value of money, transaction costs, value at risk, volatility smile, yield curve, zero-coupon bond

The general case follows from approximating by piecewise constant functions. 8.6 The joint distribution of minimum and terminal value for a Brownian motion with drift In Section 8.4, we derived the joint law of the minimum and terminal value for a Brownian motion without drift. In this section, we combine that result with our results on Girsanov's theorem to derive the joint law for a Brownian motion with drift. Let Wt be a Brownian motion. Let Yt = aWt, and my be the minimum of Yt up to time t. We then have for y < 0 and x > y that ?(Yt > x, m ' < y) = I1(Yt < 2y - x). (8.37) This follows from the result for Brownian motion, (8.20), as the volatility term makes no real difference. We wish to prove an analogous result for a Brownian motion with drift. Let Zt = vdt + 6dWt (8.38) and mZ denotes its minimum up to time t. Our main result is Theorem 8.2 If y < 0 and x > y, then IED(Zt > x, mZ < y) = e2vy6-2IED(Zt < 2y - x + 2vt) = e2vyv-2N (2y - x + Vt 1 0- "It .

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A quanto option is an option that whose pay-off is transformed into another currency at pre-determined rate. A multi-dimensional Brownian motion is a vector of processes which have jointly normal increments and is a Brownian motion in each dimension. Correlated Brownian motions can be constructed by adding together multiples of one-dimensional Brownian motions. The Ito calculus goes over to higher dimensions with the additional rule dWjdWk = pjkdt where Pjk is the correlation between Wj and Wk. When adding correlation Brownian motions we can find the volatility of the new process by treating the original processes as vectors. We can change the drift of a multi-dimensional Brownian motion by using Girsanov's theorem. 11.11 Exercises 281 No arbitrage will occur if and only if the discounted price processes can be made driftless by a change of measure.

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If we interpret the correlation coefficient as being the cosine of the angle between the two Brownian motions, then this means that the new volatility is just the length of the vector obtained by summing the vectors for each Brownian motion. 266 Multiple sources of risk More generally, we could construct a Brownian motion from any vector a=(a1,...,ak) Ek=1 ajX( ). with a? = 1, by taking When we have a process driven by k > 2 Brownian motions, we obtain a similar expression to (11.20). The volatility becomes n Y" Ors 6j Pig N i,J=1 and we can write dYt = µdt + adW, (11.22) for a Brownian motion W constructed from the old one. We can similarly regard our processes as vectors in 1R which add according to their directions. Example 11.1 Suppose the stocks Xt and Yt follow correlated geometric Brownian motions. Show that XtYt also follows a geometric Brownian motion and compute its drift and volatility. Solution We write dXt = aXtdt + o XtdWW 1), dYt = ,BYtdt + vYdWt(2), and take the correlation coefficient to be p. We compute d(XtYt) = XtdYt + YtdXt + dXt.dYt, = XtYt (f3dt + vdW 2) + adt + vdWr 1) + avpdt) , = XtYt ((a +,B + QVp)dt + o'dW(1) + vdWr2)) .

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Monte Carlo Simulation and Finance
** by
Don L. McLeish

Black-Scholes formula, Brownian motion, capital asset pricing model, compound rate of return, discrete time, distributed generation, finite state, frictionless, frictionless market, implied volatility, incomplete markets, invention of the printing press, martingale, p-value, random walk, Sharpe ratio, short selling, stochastic process, stochastic volatility, survivorship bias, the market place, transaction costs, value at risk, Wiener process, zero-coupon bond, zero-sum game

To motivate this family of distributions, let us GENERATING RANDOM NUMBERS FROM NON-UNIFORM CONTINUOUS DISTRIBUTIONS159 250 200 150 100 50 0 -50 -100 -150 -200 -250 0 1000 2000 3000 4000 5000 6000 7000 8000 9000 10000 Figure 3.18: A Symmetric Stable Random Walk with index α = 1.7 suppose that stock returns follow a Brownian motion process but with respect to a random time scale possibly dependent on volume traded and other external factors independent of the Brownian motion itself. After one day, say, the return on the stock is the value of the Brownian motion process at a random time, τ, independent of the Brownian motion. Assume that this random time has the Inverse Gaussian distribution having probability density function (θ − t)2 θ exp{− } g(t) = √ 2c2 t c 2πt3 (3.21) for parameters θ > 0, c > 0. This is the distribution of a first passage time for Brownian motion. In particular consider a Brownian motion process B(t) having drift 1 and diﬀusion coeﬃcient c. Such a process is the solution to the stochastic diﬀerential equation dB(t) = dt + cdW (t), B(0) = 0.

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The high dm is generated by moving horizontally to the right an even number of steps until just before exiting the histogram. This is above the value d2m−u and dm is between du and d2m−u . A similar result is available for Brownian motion and Geometric Brownian motion. A justification of these results can be made by taking a limit in the discrete case as the time steps and the distances dj − dj−1 all approach zero. If we do this, the parameter θ is analogous to the drift of the Brownian motion. The result for Brownian motion is as follows: Theorem 44 Suppose St is a Brownian motion process dSt = µdt + σdWt , S0 = 0, ST = C, H = max{St ; 0 · t · T } and L = min{St ; 0 · t · T }. If f0 denotes the Normal(0,σ 2 T ) probability density function, the distribution of SIMULATING BARRIER AND LOOKBACK OPTIONS 277 C under drift µ = 0, then f0 (2H − C) is distributed as U [0, 1] independently of C, f0 (C) f0 (2L − C) UL = is distributed as U [0, 1] independently of C. f0 (C) 1 ZH = H(H − C) is distributed as Exponential ( σ 2 T ) independently of C, 2 1 2 ZL = L(L − C) is distributed as Exponential ( σ T )independently of C. 2 UH = We will not prove this result since it is a special case of Theorem 46 below.

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The vertical √ scale is to be decreased by a factor 1/ n and the horizontal scale by a factor n−1 . The theorem concludes that the sequence of processes 1 Yn (t) = √ Snt n converges weakly to a standard Brownian motion process as n → ∞. In practice this means that a process with independent stationary increments tends to look like a Brownian motion process. As we shall see, there is also a wide variety of non-stationary processes that can be constructed from the Brownian motion process by integration. Let us use the above limiting result to render some of the properties of the Brownian motion more plausible, since a serious proof is beyond our scope. Consider the question of continuity, for example. Since Pn(t+h) |Yn (t + h) − Yn (t)| ≈ | √1n i=nt Xi | and this is the absolute value of an asymptotically normally(0, h) random variable by the central limit theorem, it is plausible that the limit as h → 0 is zero so the function is continuous at t.

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Mathematical Finance: Theory, Modeling, Implementation
** by
Christian Fries

Black-Scholes formula, Brownian motion, continuous integration, discrete time, fixed income, implied volatility, interest rate derivative, martingale, quantitative trading / quantitative ﬁnance, random walk, short selling, Steve Jobs, stochastic process, stochastic volatility, volatility smile, Wiener process, zero-coupon bond

q y Definition 27 (Canonical Setup): The space (C([0, ∞)), B(C([0, ∞)), P∗ ) q (as defined in Theorem 25) is called the canonical setup for a Brownian motion W defined by W(t, ω) := ω(t), ω ∈ C([0, ∞)). y Remark 28: A more detailed discussion of Theorem 25 may be found in [18]. A less formal discussion of properties of the Brownian motion may be found in [12]. 2.6. Itô Calculus Motivation: The Brownian motion W is our first encounter with an important continuous stochastic process. The Brownian motion may be viewed as the limit of a scaled random walk.11 If we interpret the Brownian motion W in this sense as a model for the movement of a particle, then W(T ) denotes the position of the particle at time T and W(T + ∆T ) − W(T ) the position change that occurs from T to T + ∆T ; to be precise W(T ) models the probability distribution of the particle position. The model of a Brownian motion√is that position changes are normal distributed with mean 0 and standard deviation ∆T .

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For the discrete case this is not the case. E.g. consider (X(ti ) + ∆X(ti ))3 in the example above. C| 2.7. Brownian Motion with Instantaneous Correlation In Definition 23 Brownian motion was defined through normal distributed increments W(t) − W(s), t > s having covariance matrix (t − s)In . In other words we have that for W = (W1 , . . . , Wn ) the components are one dimensional Brownian motions with pairwise independent increments, i.e. for i , j we have that Wi (t) − Wi (s) and W j (t) − W j (s) are independent (thus uncorrelated). We define the Brownian motion with instantaneously correlated increments as a special Itô process: Definition 45 (Brownian Motion with instantaneous correlated Increments): q Let U denote an m-dimensionale Brownian motion as defined in Definition 23. Let 50 This work is licensed under a Creative Commons License. http://creativecommons.org/licenses/by-nc-nd/2.5/deed.en Comments welcome. ©2004, 2005, 2006 Christian Fries Version 1.3.19 [build 20061210]- 13th December 2006 http://www.christian-fries.de/finmath/ 2.7.

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LIBOR MARKET MODEL 17.1.4.3. Choice of the Correlations Factors We assumed in (17.1) a models in which (potentially) each forward rate Li Brownian motion Wi . The model is driven by an n-dimensional8 Brownian motion W0 W 1 . W = . . . Wn−1 The effective number of factors, i.e. the number of independent Brownian motions, that are driving the model is determines by the correlation ρi, j (t)dt = dWi (t) · dW j (t). By an eigenvector decomposition (PCA) of the correlation matrix R = (ρi, j )i, j=1...n we may represent dW as dW(t) = F(t)dU(t), where U := (U1 , . . . , Um )T und U1 , . . . , Um denote independent Brownian motions and F = ( fi, j ) denotes a n × m-matrix. In other words we have dWi (t) = m X ρi, j (t) = fi, j (t)dU j (t), j=1 m X fi,k (t) · f j,k (t).

pages: 364 words: 101,286

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The Misbehavior of Markets: A Fractal View of Financial Turbulence
** by
Benoit Mandelbrot,
Richard L. Hudson

Albert Einstein, asset allocation, Augustin-Louis Cauchy, Benoit Mandelbrot, Big bang: deregulation of the City of London, Black-Scholes formula, British Empire, Brownian motion, business cycle, buy and hold, buy low sell high, capital asset pricing model, carbon-based life, discounted cash flows, diversification, double helix, Edward Lorenz: Chaos theory, Elliott wave, equity premium, Eugene Fama: efficient market hypothesis, Fellow of the Royal Society, full employment, Georg Cantor, Henri Poincaré, implied volatility, index fund, informal economy, invisible hand, John Meriwether, John von Neumann, Long Term Capital Management, Louis Bachelier, mandelbrot fractal, market bubble, market microstructure, Myron Scholes, new economy, paper trading, passive investing, Paul Lévy, Paul Samuelson, plutocrats, Plutocrats, price mechanism, quantitative trading / quantitative ﬁnance, Ralph Nelson Elliott, RAND corporation, random walk, risk tolerance, Robert Shiller, Robert Shiller, short selling, statistical arbitrage, statistical model, Steve Ballmer, stochastic volatility, transfer pricing, value at risk, Vilfredo Pareto, volatility smile

Instead, it is best to go beyond cartoons. My current best model of how a market works is fractional Brownian motion of multifractal time. It has been called the Multifractal Model of Asset Returns. The basic ideas are similar to the cartoon versions above—though far more intricate, mathematically. The cartoon of Brownian motion gets replaced by an equation that a computer can calculate. The trading-time process is expressed by another mathematical function, called f(α), that can be tuned to fit a wide range of market behavior. My model redistributes time. It compresses it in some places, stretches it out in others. The result appears very wild, very random. The two functions, of time and Brownian motion, work together in what mathematicians call a compound manner: Price is a function of trading time, which in turn is a function of clock time.

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Here, major news—approval of a medicine by the Food and Drug Administration, an unexpected takeover offer, or a windfall legal victory—caused market indigestion; sell and buy orders did not match, and market-makers had to raise or lower their price quotes until they did. To cope, some exchanges license “specialist” broker-dealers to step into the breach and trade when others will not. These specialists, while risking much, also profit greatly. Discontinuity, far from being an anomaly best ignored, is an essential ingredient of markets that helps set finance apart from the natural sciences. 4. Assumption: Price changes follow a Brownian motion. Theory: Brownian motion, again, is a term borrowed from physics for the motion of a molecule in a uniformly warm medium. Bachelier had suggested that this process can also describe price variation. Several critical assumptions come together in this idea. First, independence: Each change in price—whether a five-cent uptick or a $26 collapse—appears independently from the last, and price changes last week or last year do not influence those today.

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By repeating this process over and over, a jagged, complex chart gradually appeared. By careful design, the specific kind of chart shown before was of a Brownian motion—the standard model underlying conventional financial theory. What made it so was the specific shape of the generator: Starting at the point (0, 0), it rose to the point (4/9, 2/3), fell to the point (5/9, 1/3), and ended up at (1, 1). A key observation regards the size of the three segments of the generator. Their widths were 4/9, 1/9, 4/9. The heights: 2/3, -1/3 (minus, because the line falls), and 2/3. Look closely at those six numbers. Each width is the square of each height. It is a nice, tidy relationship—just the kind of thing you would expect from a well-mannered Brownian motion. A cartoon of discontinuity. There are many ways to illustrate the crucial concepts of fat tails and discontinuity—and this one employs the kind of fractal process used earlier in this book.

pages: 443 words: 51,804

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Handbook of Modeling High-Frequency Data in Finance
** by
Frederi G. Viens,
Maria C. Mariani,
Ionut Florescu

algorithmic trading, asset allocation, automated trading system, backtesting, Black-Scholes formula, Brownian motion, business process, buy and hold, continuous integration, corporate governance, discrete time, distributed generation, fixed income, Flash crash, housing crisis, implied volatility, incomplete markets, linear programming, mandelbrot fractal, market friction, market microstructure, martingale, Menlo Park, p-value, pattern recognition, performance metric, principal–agent problem, random walk, risk tolerance, risk/return, short selling, statistical model, stochastic process, stochastic volatility, transaction costs, value at risk, volatility smile, Wiener process

In this chapter, we consider the continuous-time long-memory stochastic volatility (LMSV) model by Comte and Renault (1998): If Xt are the log-returns of the price process St and Yt is the volatility process, then ⎧ ⎨ dXt ⎩ dYt σ 2 (Yt ) = μ− dt + σ (Yt ) dWt , 2 = α Yt dt + β dBtH , (8.1) where Wt is a standard Brownian motion and BtH is a fractional Brownian motion with Hurst index H ∈ (0, 1]. The fractional Brownian motion (fBm) with Hurst parameter H ∈ (0, 1] is a Gaussian process with almost surely continuous paths and covariance structure given by Cov(BtH , BsH ) = 1 2H |t| + |s|2H − |t − s|2H . 2 For H = 1/2 the process is the well-known standard Brownian motion. Formally, we say that a process exhibits long-range dependence when the series of the autocorrelation function is nonsummable, that is +∞ ρ(n) = +∞. n=1 8.1 Introduction 221 From the covariance function of the fractional Brownian motion, we can easily deduce that the autocorrelation function of the increments of fBm is of order n2H −2 .

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Dayanik and Karatzas (2003), Proposition 5.7 STANDING ASSUMPTION 11.15 l0 = x ↓ 0 h+ (x) h+ (x) < ∞, and l = x ↑ ∞ . ∞ x ρ− x ρ+ Let us denote by τx inf {t ≥ 0 / Y (t) = x}, x > 0, the ﬁrst hitting time of level x. The reduction of the optimal stopping problem to the Brownian motion case has been studied by Dayanik and Karatzas in the case when the diffusion was driven by one-dimensional Brownian motion. Their results hold also for the case in which we have a m-dimensional Brownian motion with the only modiﬁcation in the equation solved by the Green functions ψ and ϕ. Still, the problem is solved explicitly for the Brownian motion case by using a graphical method. By taking advantage of the theory developed in Dayanik and Karatzas (2003), in terms of the existence of an optimal stopping time and provided that we can either solve or determine the shape of intervals that form C0 {y > 0/Lg(y) > 0}, (11.59) then the value function is the supremum over stopping times which are exit times from open intervals that contain C0 .

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In fact, the parameter α of the Levy distribution is inversely proportional to the Hurst parameter. The Hurst parameter is an indicator of the memory effects coming from the fractional Brownian motion, which has correlated increments. Furthermore, the TLF maintains statistical properties that are indistinguishable from the Levy ﬂights [15]. 6.2.2 RESCALED RANGE ANALYSIS Hurst [27] initially developed the Rescaled range analysis (R/S analysis). He observed many natural phenomena that followed a biased random walk, that is, every phenomenon showed a pattern. He measured the trend using an exponent now called the Hurst exponent. Mandelbrot [28,29] later introduced a generalized form of the Brownian motion model, the fractional Brownian motion to model the Hurst effect. The numerical procedure to estimate the Hurst exponent H by using the R/S analysis is presented next (for more details, please see [27] and references therein). 1.

pages: 313 words: 34,042

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Tools for Computational Finance
** by
Rüdiger Seydel

bioinformatics, Black-Scholes formula, Brownian motion, commoditize, continuous integration, discrete time, implied volatility, incomplete markets, interest rate swap, linear programming, London Interbank Offered Rate, mandelbrot fractal, martingale, random walk, stochastic process, stochastic volatility, transaction costs, value at risk, volatility smile, Wiener process, zero-coupon bond

. — The Example 1.15 with a system of three SDEs is taken from [HPS92]. [KP92] in Section 4.4 gives a list of SDEs that are analytically solvable or reducible. The model of a geometric Brownian motion of equation (1.33) is the classical model describing the dynamics of stock prices. It goes back to Samuelson (1965; Nobel Prize in economics in 1970). Already in 1900 Bachelier had suggested to model stock prices with Brownian motion. Bachelier used the arithmetic version, which can be characterized by replacing the lefthand side of (1.33) by the absolute change dS. This amounts to the process St = S0 + µt + σWt . Here the stock price can become negative. Main advantages of the geometric Brownian motion are the success of the approaches of Black, Merton and Scholes, which is based on that motion, and the existence of moments (as the expectation).

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. = equal except for rounding errors ≡ identical =⇒ implication ⇐⇒ equivalence Landau-symbol: for h → 0 O(hk ) is bounded f (h) = O(hk ) ⇐⇒ fh(h) k normal distributed with expectation µ and variance σ 2 ∼ N (µ, σ 2 ) ∼ U[0, 1] uniformly distributed on [0, 1] XVIII Notations ∆t tr C 0 [a, b] ∈ C k [a, b] D ∂D L2 H [0, 1]2 Ω f + := max{f, 0} u̇ small increment in t transposed; Atr is the matrix where the rows and columns of A are exchanged. set of functions that are continuous on [a, b] k-times continuously diﬀerentiable set in IRn or in the complex plane, D̄ closure of D, D◦ interior of D boundary of D set of square-integrable functions Hilbert space, Sobolev space (Appendix C3) unit square sample space (in Appendix B1) time derivative du dt of a function u(t) integers: i, j, k, l, m, n, M, N, ν various variables: Xt , X, X(t) Wt y(x, τ ) w h ϕ ψ 1D random variable Wiener process, Brownian motion (Deﬁnition 1.7) solution of a partial diﬀerential equation for (x, τ ) approximation of y discretization grid size basis function (Chapter 5) test function (Chapter 5) indicator function: = 1 on D, = 0 elsewhere. abbreviations: BDF CFL Dow FTBS FTCS GBM MC ODE OTC PDE PIDE PSOR QMC SDE SOR Backward Diﬀerence Formula, see Section 4.2.1 Courant-Friedrichs-Lewy, see Section 6.5.1 Dow Jones Industrial Average Forward Time Backward Space, see Section 6.5.1 Forward Time Centered Space, see Section 6.4.2 Geometric Brownian Motion, see (1.33) Monte Carlo Ordinary Diﬀerential Equation Over The Counter Partial Diﬀerential Equation Partial Integro-Diﬀerential Equation Projected Successive Overrelaxation Quasi Monte Carlo Stochastic Diﬀerential Equation Successive Overrelaxation Notations TVD i.i.d. inf sup supp(f ) XIX Total Variation Diminishing independent and identical distributed inﬁmum, largest lower bound of a set of numbers supremum, least upper bound of a set of numbers support of a function f : {x ∈ D : f (x) = 0} hints on the organization: (2.6) (A4.10) −→ number of equation (2.6) (The ﬁrst digit in all numberings refers to the chapter.) equation in Appendix A; similarly B, C, D hint (for instance to an exercise) Chapter 1 Modeling Tools for Financial Options 1.1 Options What do we mean by option?

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The ∆ of (1.16) is the hedge parameter delta, which eliminates the risk exposure of our portfolio caused by the written option. In multi-period models and continuous models ∆ must be adapted dynamically. The general deﬁnition is ∂V (S, t) ; ∆ = ∆(S, t) = ∂S the expression (1.16) is a discretized version. 1.6 Stochastic Processes Brownian motion originally meant the erratic motion of a particle (pollen) on the surface of a ﬂuid, caused by tiny impulses of molecules. Wiener suggested a mathematical model for this motion, the Wiener process. But earlier Bachelier had applied Brownian motion to model the motion of stock prices, which instantly respond to the numerous upcoming informations similar as pollen react to the impacts of molecules. The illustration of the Dow in Figure 1.14 may serve as motivation. A stochastic process is a family of random variables Xt , which are deﬁned for a set of parameters t (−→ Appendix B1).

pages: 819 words: 181,185

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Derivatives Markets
** by
David Goldenberg

Black-Scholes formula, Brownian motion, capital asset pricing model, commodity trading advisor, compound rate of return, conceptual framework, correlation coefficient, Credit Default Swap, discounted cash flows, discrete time, diversification, diversified portfolio, en.wikipedia.org, financial innovation, fudge factor, implied volatility, incomplete markets, interest rate derivative, interest rate swap, law of one price, locking in a profit, London Interbank Offered Rate, Louis Bachelier, margin call, market microstructure, martingale, Myron Scholes, Norbert Wiener, Paul Samuelson, price mechanism, random walk, reserve currency, risk/return, riskless arbitrage, Sharpe ratio, short selling, stochastic process, stochastic volatility, time value of money, transaction costs, volatility smile, Wiener process, yield curve, zero-coupon bond, zero-sum game

11.7 Further Implications of European Put-Call Parity 11.7.1 Synthesizing Forward Contract from Puts and Calls 11.8 Financial Innovation using European Put-Call Parity 11.8.1 Generalized Forward Contracts 11.8.2 American Put-Call Parity (No Dividends) 11.9 Postscript on ROP CHAPTER 12 OPTION TRADING STRATEGIES, PART 2 12.1 Generating Synthetic Option Strategies from European Put-Call Parity 12.2 The Covered Call Hedging Strategy 12.2.1 Three Types Of Covered Call Writes 12.2.2 Economic Interpretation of the Covered Call Strategy 12.3 The Protective Put Hedging Strategy 12.3.1 Puts as Insurance 12.3.2 Economic Interpretation of the Protective Put Strategy CHAPTER 13 MODEL-BASED OPTION PRICING IN DISCRETE TIME, PART 1: THE BINOMIAL OPTION PRICING MODEL (BOPM, N=1) 13.1 The Objective of Model-Based Option Pricing (MBOP) 13.2 The Binomial Option Pricing Model, Basics 13.2.1 Modeling Time in a Discrete Time Framework 13.2.2 Modeling the Underlying Stock Price Uncertainty 13.3 The Binomial Option Pricing Model, Advanced 13.3.1 Path Structure of the Binomial Process, Total Number of Price Paths 13.3.2 Path Structure of the Binomial Process, Total Number of Price Paths Ending at a Specific Terminal Price 13.3.3 Summary of Stock Price Evolution for the N-Period Binomial Process 13.4 Option Valuation for the BOPM (N=1) 13.4.1 Step 1, Pricing the Option at Expiration 13.4.2 Step 2, Pricing the Option Currently (time t=0) 13.5 Modern Tools for Pricing Options 13.5.1 Tool 1, The Principle of No-Arbitrage 13.5.2 Tool 2, Complete Markets or Replicability, and a Rule of Thumb 13.5.3 Tool 3, Dynamic and Static Replication 13.5.4 Relationships between the Three Tools 13.6 Synthesizing a European Call Option 13.6.1 Step 1, Parameterization 13.6.2 Step 2, Defining the Hedge Ratio and the Dollar Bond Position 13.6.3 Step 3, Constructing the Replicating Portfolio 13.6.4 Step 4, Implications of Replication 13.7 Alternative Option Pricing Techniques 13.8 Appendix: Derivation of the BOPM (N=1) as a Risk-Neutral Valuation Relationship CHAPTER 14 OPTION PRICING IN DISCRETE TIME, PART 2: DYNAMIC HEDGING AND THE MULTI-PERIOD BINOMIAL OPTION PRICING MODEL, N>1 14.1 Modeling Time and Uncertainty in the BOPM, N>1 14.1.1 Stock Price Behavior, N=2 14.1.2 Option Price Behavior, N=2 14.2 Hedging a European Call Option, N=2 14.2.1 Step 1, Parameterization 14.2.2 Step 2, Defining the Hedge Ratio and the Dollar Bond Position 14.2.3 Step 3, Constructing the Replicating Portfolio 14.2.4 The Complete Hedging Program for the BOPM, N=2 14.3 Implementation of the BOPM for N=2 14.4 The BOPM, N>1 as a RNVR Formula 14.5 Multi-period BOPM, N>1: A Path Integral Approach 14.5.1 Thinking of the BOPM in Terms of Paths 14.5.2 Proof of the BOPM Model for general N CHAPTER 15 EQUIVALENT MARTINGALE MEASURES: A MODERN APPROACH TO OPTION PRICING 15.1 Primitive Arrow–Debreu Securities and Option Pricing 15.1.1 Exercise 1, Pricing B(0,1) 15.1.2 Exercise 2, Pricing ADu(ω) and ADd(ω) 15.2 Contingent Claim Pricing 15.2.1 Pricing a European Call Option 15.2.2 Pricing any Contingent Claim 15.3 Equivalent Martingale Measures (EMMs) 15.3.1 Introduction and Examples 15.3.2 Definition of a Discrete-Time Martingale 15.4 Martingales and Stock Prices 15.4.1 The Equivalent Martingale Representation of Stock Prices 15.5 The Equivalent Martingale Representation of Option Prices 15.5.1 Discounted Option Prices 15.5.2 Summary of the EMM Approach 15.6 The Efficient Market Hypothesis (EMH), A Guide To Modeling Prices 15.7 Appendix: Essential Martingale Properties CHAPTER 16 OPTION PRICING IN CONTINUOUS TIME 16.1 Arithmetic Brownian Motion (ABM) 16.2 Shifted Arithmetic Brownian Motion 16.3 Pricing European Options under Shifted Arithmetic Brownian Motion with No Drift (Bachelier) 16.3.1 Theory (FTAP1 and FTAP2) 16.3.2 Transition Density Functions 16.3.3 Deriving the Bachelier Option Pricing Formula 16.4 Defining and Pricing a Standard Numeraire 16.5 Geometric Brownian Motion (GBM) 16.5.1 GBM (Discrete Version) 16.5.2 Geometric Brownian Motion (GBM), Continuous Version 16.6 Itô’s Lemma 16.7 Black–Scholes Option Pricing 16.7.1 Reducing GBM to an ABM with Drift 16.7.2 Preliminaries on Generating Unknown Risk-Neutral Transition Density Functions from Known Ones 16.7.3 Black–Scholes Options Pricing from Bachelier 16.7.4 Volatility Estimation in the Black–Scholes Model 16.8 Non-Constant Volatility Models 16.8.1 Empirical Features of Volatility 16.8.2 Economic Reasons for why Volatility is not Constant, the Leverage Effect 16.8.3 Modeling Changing Volatility, the Deterministic Volatility Model 16.8.4 Modeling Changing Volatility, Stochastic Volatility Models 16.9 Why Black–Scholes is Still Important CHAPTER 17 RISK-NEUTRAL VALUATION, EMMS, THE BOPM, AND BLACK–SCHOLES 17.1 Introduction 17.1.1 Preliminaries on FTAP1 and FTAP2 and Navigating the Terminology 17.1.2 Pricing by Arbitrage and the FTAP2 17.1.3 Risk-Neutral Valuation without Consensus and with Consensus 17.1.4 Risk-Neutral Valuation without Consensus, Pricing Contingent Claims with Unhedgeable Risks 17.1.5 Black–Scholes’ Contribution 17.2 Formal Risk-Neutral Valuation without Replication 17.2.1 Constructing EMMs 17.2.2 Interpreting Formal Risk-Neutral Probabilities 17.3 MPRs and EMMs, Another Version of FTAP2 17.4 Complete Risk-Expected Return Analysis of the Riskless Hedge in the (BOPM, N=1) 17.4.1 Volatility of the Hedge Portfolio 17.4.2 Direct Calculation of σS 17.4.3 Direct Calculation of σC 17.4.4 Expected Return of the Hedge Portfolio 17.5 Analysis of the Relative Risks of the Hedge Portfolio’s Return 17.5.1 An Initial Look at Risk Neutrality in the Hedge Portfolio 17.5.2 Role of the Risk Premia for a Risk-Averse Investor in the Hedge Portfolio 17.6 Option Valuation 17.6.1 Some Manipulations 17.6.2 Option Valuation Done Directly by a Risk-Averse Investor 17.6.3 Option Valuation for the Risk-Neutral Investor Index FIGURES 1.1 Canada/US Foreign Exchange Rate 1.2 Intermediation by the Clearing House 1.3 Offsetting Trades 1.4 Gold Fixing Price in London Bullion Market (USD$) 2.1 Graphical Method to Get Hedged Position Profits 2.2 Payoff Per Share to a Long Forward Contract 2.3 Payoff Per Share to a Short Forward Contract 2.4 Profits per bu. for the Unhedged Position 3.1 Profits Per Share to a Naked Long Spot Position 3.2 Payoffs Per Share to a Naked Long Spot Position 3.3 Payoffs (=Profits) Per Share to a Naked Long Forward Position 3.4 Payoffs Per Share to a Naked Long Spot Position and to a Naked Long Forward Position 5.1 Order Flow Process (Pit Trading) 5.2 The Futures Clearing House 5.3 Offsetting Trades 5.4 Overall Profits for Example 2 6.1 Long vs.

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■ SELECTED CONCEPT CHECK SOLUTIONS Concept Check 3 We used the fact that X1(ω) is independent of W0 in the fourth equality. Our conclusion is that the property E(W1(ω)|W0)=W0 holds. CHAPTER 16 OPTION PRICING IN CONTINUOUS TIME 16.1 Arithmetic Brownian Motion (ABM) 16.2 Shifted Arithmetic Brownian Motion 16.3 Pricing European Options under Shifted Arithmetic Brownian Motion with No Drift (Bachelier) 16.3.1 Theory (FTAP1 and FTAP2) 16.3.2 Transition Density Functions 16.3.3 Deriving the Bachelier Option Pricing Formula 16.4 Defining and Pricing a Standard Numeraire 16.5 Geometric Brownian Motion (GBM) 16.5.1 GBM (Discrete Version) 16.5.2 Geometric Brownian Motion (GBM), Continuous Version 16.6 Itô’s Lemma 16.7 Black–Scholes Option Pricing 16.7.1 Reducing GBM to an ABM with Drift 16.7.2 Preliminaries on Generating Unknown Risk-Neutral Transition Density Functions from Known Ones 16.7.3 Black–Scholes Options Pricing from Bachelier 16.7.4 Volatility Estimation in the Black–Scholes Model 16.8 Non-Constant Volatility Models 16.8.1 Empirical Features of Volatility 16.8.2 Economic Reasons for why Volatility is not Constant, the Leverage Effect 16.8.3 Modeling Changing Volatility, the Deterministic Volatility Model 16.8.4 Modeling Changing Volatility, Stochastic Volatility Models 16.9 Why Black–Scholes is Still Important In this chapter we are going to give an introduction to continuous-time finance.

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Black–Scholes (1973), which is a continuous time, continuous state space model even shows up in some jump option pricing models, such as Merton’s (1976) jump model. Thus, Black–Scholes may indeed survive as a component of some option pricing models. We should probably keep it around for these reasons. ■ KEY CONCEPTS 1. Arithmetic Brownian Motion (ABM). 2. Shifted Arithmetic Brownian Motion. 3. Pricing European Options under Shifted Arithmetic Brownian Motion (Bachelier). 4. Theory (FTAP1 and FTAP2). 5. Transition Density Functions. 6. Deriving the Bachelier Option Pricing Formula. 7. Defining and Pricing a Standard Numeraire. 8. Geometric Brownian Motion (GBM). 9. GBM (Discrete Version). 10. Geometric Brownian Motion (GBM), Continuous Version. 11. Itô’s Lemma. 12. Black–Scholes Option Pricing. 13. Reducing GBM to an ABM with Drift. 14. Preliminaries on Risk-Neutral Transition Density Functions. 15. Black–Scholes Pricing from Bachelier. 16.

pages: 320 words: 33,385

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Market Risk Analysis, Quantitative Methods in Finance
** by
Carol Alexander

asset allocation, backtesting, barriers to entry, Brownian motion, capital asset pricing model, constrained optimization, credit crunch, Credit Default Swap, discounted cash flows, discrete time, diversification, diversified portfolio, en.wikipedia.org, fixed income, implied volatility, interest rate swap, market friction, market microstructure, p-value, performance metric, quantitative trading / quantitative ﬁnance, random walk, risk tolerance, risk-adjusted returns, risk/return, Sharpe ratio, statistical arbitrage, statistical model, stochastic process, stochastic volatility, Thomas Bayes, transaction costs, value at risk, volatility smile, Wiener process, yield curve, zero-sum game

The process Wt is called a Wiener process, also called a Brownian motion. It is a continuous process that has independent increments dWt and each increment has a normal distribution with mean 0 and variance dt.19 On adding uncertainty to the exponential price path (I.1.31) the price process (I.1.29) becomes dSt = dt + dWt (I.1.32) St This is an example of a diffusion process. Since the left-hand side has the proportional change in the price at time t, rather than the absolute change, we call (I.1.32) geometric Brownian motion. If the left-hand side variable were dSt instead, the process would be called arithmetic Brownian motion. The diffusion coefficient is the coefficient of dWt, which is a constant in the case of geometric Brownian motion. This constant is called the volatility of the process.

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Probability and Statistics 139 Application of Itô’s lemma with f = ln S shows that a continuous time representation of geometric Brownian motion that is equivalent to the geometric Brownian motion (I.3.143) but is translated into a process for log prices is the arithmetic Brownian motion, d ln St = − 21 2 dt + dWt (I.3.145) We already know what a discretization of (I.3.145) looks like. The change in the log price is the log return, so using the standard discrete time notation Pt for a price at time t we have d ln St → ln Pt Hence the discrete time equivalent of (I.3.145) is ln Pt = + $t where = prices, i.e. − 1 2 2 $t ∼ NID 0 2 (I.3.146) . This is equivalent to a discrete time random walk model for the log ln Pt = + ln Pt−1 + $t $t ∼ NID 0 2 (I.3.147) To summarize, the assumption of geometric Brownian motion for prices in continuous time is equivalent to the assumption of a random walk for log prices in discrete time.

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A Wiener process, also called a Brownian motion, describes the stochastic part when the process does not jump. Thus a Wiener process is a continuous process with stationary, independent normally distributed increments. The increments are normally distributed so we often use any of the notations Wt Bt or Zt for such a process. The increments of the process are the total change in the process over an infinitesimally small time period; these are denoted dWt dBt or dZt, with EdW = 0 and VdW = dt Now we are ready to write the equation for the dynamics of a continuous time stochastic process X t as the following SDE: dXt = dt + dZt (I.3.141) is called the process volatility. The where is called the drift of the process and model (I.3.141) is called arithmetic Brownian motion. Arithmetic Brownian motion is the continuous time version of a random walk.

pages: 345 words: 86,394

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Frequently Asked Questions in Quantitative Finance
** by
Paul Wilmott

Albert Einstein, asset allocation, beat the dealer, Black-Scholes formula, Brownian motion, butterfly effect, buy and hold, capital asset pricing model, collateralized debt obligation, Credit Default Swap, credit default swaps / collateralized debt obligations, delta neutral, discrete time, diversified portfolio, Edward Thorp, Emanuel Derman, Eugene Fama: efficient market hypothesis, fixed income, fudge factor, implied volatility, incomplete markets, interest rate derivative, interest rate swap, iterative process, lateral thinking, London Interbank Offered Rate, Long Term Capital Management, Louis Bachelier, mandelbrot fractal, margin call, market bubble, martingale, Myron Scholes, Norbert Wiener, Paul Samuelson, quantitative trading / quantitative ﬁnance, random walk, regulatory arbitrage, risk/return, Sharpe ratio, statistical arbitrage, statistical model, stochastic process, stochastic volatility, transaction costs, urban planning, value at risk, volatility arbitrage, volatility smile, Wiener process, yield curve, zero-coupon bond

Short Answer Girsanov’s theorem is the formal concept underlying the change of measure from the real world to the risk-neutral world. We can change from a Brownian motion with one drift to a Brownian motion with another. Example The classical example is to start withdS = µS dt + σ S dWt with W being Brownian motion under one measure (the real-world measure) and converting it to under a different, the risk-neutral, measure. Long Answer First a statement of the theorem. Let Wt be a Brownian motion with measure and sample space Ω. If γt is a previsible process satisfying the constraint then there exists an equivalent measure on Ω such that is a Brownian motion. It will be helpful if we explain some of the more technical terms in this theorem. Sample space: All possible future states or outcomes.

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Figure 2-5: Certainty equivalent as a function of the risk-aversion parameter for example in the text. References and Further Reading Ingersoll, JE Jr 1987 Theory of Financial Decision Making. Rowman & Littlefield What is Brownian Motion and What are its Uses in Finance? Short Answer Brownian Motion is a stochastic process with stationary independent normally distributed increments and which also has continuous sample paths. It is the most common stochastic building block for random walks in finance. Example Pollen in water, smoke in a room, pollution in a river, are all examples of Brownian motion. And this is the common model for stock prices as well. Long Answer Brownian motion (BM) is named after the Scottish botanist who first described the random motions of pollen grains suspended in water. The mathematics of this process were formalized by Bachelier, in an option-pricing context, and by Einstein.

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This idea of the random walk has permeated many scientific fields and is commonly used as the model mechanism behind a variety of unpredictable continuous-time processes. The lognormal random walk based on Brownian motion is the classical paradigm for the stock market. See Brown (1827). 1900 Bachelier Louis Bachelier was the first to quantify the concept of Brownian motion. He developed a mathematical theory for random walks, a theory rediscovered later by Einstein. He proposed a model for equity prices, a simple normal distribution, and built on it a model for pricing the almost unheard of options. His model contained many of the seeds for later work, but lay ‘dormant’ for many, many years. It is told that his thesis was not a great success and, naturally, Bachelier’s work was not appreciated in his lifetime. See Bachelier (1995). 1905 Einstein Albert Einstein proposed a scientific foundation for Brownian motion in 1905. He did some other clever stuff as well.

pages: 338 words: 106,936

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The Physics of Wall Street: A Brief History of Predicting the Unpredictable
** by
James Owen Weatherall

Albert Einstein, algorithmic trading, Antoine Gombaud: Chevalier de Méré, Asian financial crisis, bank run, beat the dealer, Benoit Mandelbrot, Black Swan, Black-Scholes formula, Bonfire of the Vanities, Bretton Woods, Brownian motion, business cycle, butterfly effect, buy and hold, capital asset pricing model, Carmen Reinhart, Claude Shannon: information theory, collateralized debt obligation, collective bargaining, dark matter, Edward Lorenz: Chaos theory, Edward Thorp, Emanuel Derman, Eugene Fama: efficient market hypothesis, financial innovation, fixed income, George Akerlof, Gerolamo Cardano, Henri Poincaré, invisible hand, Isaac Newton, iterative process, John Nash: game theory, Kenneth Rogoff, Long Term Capital Management, Louis Bachelier, mandelbrot fractal, martingale, Myron Scholes, new economy, Paul Lévy, Paul Samuelson, prediction markets, probability theory / Blaise Pascal / Pierre de Fermat, quantitative trading / quantitative ﬁnance, random walk, Renaissance Technologies, risk-adjusted returns, Robert Gordon, Robert Shiller, Robert Shiller, Ronald Coase, Sharpe ratio, short selling, Silicon Valley, South Sea Bubble, statistical arbitrage, statistical model, stochastic process, The Chicago School, The Myth of the Rational Market, tulip mania, Vilfredo Pareto, volatility smile

Over the course of the next six years, French physicist Jean-Baptiste Perrin developed an experimental method to track particles suspended in a fluid with enough precision to show that they indeed followed paths of the sort Einstein predicted. These experiments were enough to persuade the remaining skeptics that atoms did indeed exist. Lucretius’s contribution, meanwhile, went largely unappreciated. The kind of paths that Einstein was interested in are examples of Brownian motion, named after Scottish botanist Robert Brown, who noted the random movement of pollen grains suspended in water in 1826. The mathematical treatment of Brownian motion is often called a random walk — or sometimes, more evocatively, a drunkard’s walk. Imagine a man coming out of a bar in Cancun, an open bottle of sunscreen dribbling from his back pocket. He walks forward for a few steps, and then there’s a good chance that he will stumble in one direction or another. He steadies himself, takes another step, and then stumbles once again.

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They get interested in a stock, they make a lot of trades and send the volume of trades way up, and then they gradually stop paying attention and volume decreases. If you allow for variations in volume, you have to change the underlying assumptions of the random walk model, and you get a new, more accurate model of how stock prices evolve, which Osborne called the “extended Brownian motion” model. In the mid-sixties, Osborne and a collaborator showed that at any instant, the chances that a stock will go up are not necessarily the same as the chances that the stock will go down. This assumption, you’ll recall, was an essential part of the Brownian motion model, where a step in one direction is assumed to be just as likely as a step in the other. Osborne showed that if a stock went up a little bit, its next motion was much more likely to be a move back down than another move up. Likewise, if a stock went down, it was much more likely to go up in value in its next change.

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Although discussing such debates is far from the scope of this book, I should note that the arguments offered here for how one should think of the status of mathematical models in finance are closely connected to more general discussions concerning the status of mathematical or physical theories quite generally. “. . . named after Scottish botanist Robert Brown . . .”: Brown’s observations were published as Brown (1828). “The mathematical treatment of Brownian motion . . .”: More generally, Brownian motion is an example of a random or “stochastic” process. For an overview of the mathematics of stochastic processes, see Karlin and Taylor (1975, 1981). “. . . it was his 1905 paper that caught Perrin’s eye”: Einstein published four papers in 1905. One of them was the one I refer to here (Einstein 1905b), but the other three were equally remarkable. In Einstein (1905a), he first suggests that light comes in discrete packets, now called quanta or photons; in Einstein (1905c), he introduces his special theory of relativity; and in Einstein (1905d), he proposes the famous equation e = mc2

pages: 447 words: 104,258

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Mathematics of the Financial Markets: Financial Instruments and Derivatives Modelling, Valuation and Risk Issues
** by
Alain Ruttiens

algorithmic trading, asset allocation, asset-backed security, backtesting, banking crisis, Black Swan, Black-Scholes formula, Brownian motion, capital asset pricing model, collateralized debt obligation, correlation coefficient, Credit Default Swap, credit default swaps / collateralized debt obligations, delta neutral, discounted cash flows, discrete time, diversification, fixed income, implied volatility, interest rate derivative, interest rate swap, margin call, market microstructure, martingale, p-value, passive investing, quantitative trading / quantitative ﬁnance, random walk, risk/return, Satyajit Das, Sharpe ratio, short selling, statistical model, stochastic process, stochastic volatility, time value of money, transaction costs, value at risk, volatility smile, Wiener process, yield curve, zero-coupon bond

Coming back to the starting point of our non-deterministic description of financial products, in Chapter 8, Section 8.2, we have defined the Brownian motion, or standard Wiener process (also called white noise) as per Eq. 8.2: where y(t) is distributed as (E = 0, V = 1), so that Z(t) is distributed as (E = 0, V = t), that is, with STD = √ t. Because of the nature of y(t), successive values of Z are independent; in discrete time, and abandoning the random subscript “∼”, we have where is a so-called “random number”, actually a number randomly selected from a normal density distribution. For two different times t and t′, the covariance between two Brownian motions is necessarily 0, that is (cf. Eq. 8.5), E[dZ(t).dZ(t′)] = 0. Now, we can generalize the Brownian motion to a fractional Brownian motion BH, H ∈ (0, 1) having as covariance function The parameter H is called the Hurst coefficient.5 As a particular case, if H = , covH(t, t′) = 0 and B1/2 is our standard Brownian motion: the corresponding time series is (pure) random.

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Passing from discrete to continuous time, and thus from discrete time (or “finite”) intervals Δt to infinitely short, « infinitesimal » or « instantaneous » time intervals noted dt, Eq. 8.1 becomes (8.2) called a standard Wiener process, or a Brownian process or Brownian motion.1 This process is also called (although improperly2) white noise, by analogy with the very light but permanent scratching behind a sound produced electronically. From Eq. 8.2 we may deduct that the (t)s are independently distributed and stationary. They are normally distributed, with E = 0, V = dt (or STD = dt). Furthermore, (t) is distributed according to a Gaussian distribution of parameters E = 0, V = t (or STD = t). We see now the reason of the presence of a in Eq. 8.1 and 2: the process allows us to consider that it is the variance V of the process that is proportional to time. Formally speaking, a process (X(t), t ≥ 0) is a standard Wiener or Brownian motion if: P[X(0)] = 0: the Brownian motion starts from the origin, in t0 = 0; ∀ s ≤ t, X(t) − X(s) is a real variable, normally distributed, centered on its mean, and with a variance equal to (t − s): the successive increases of the process are stationary; ∀ n, ∀ ti, 0 ≤ t1… ≤ tn, the variables X(tn) − X(tn−1), …, X(t1) − X(t0), X(t0), are independent: the successive increases of the process are independent.

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Contents Cover Series Title Page Copyright Dedication Foreword Main Notations Introduction Part I: The Deterministic Environment Chapter 1: Prior to the yield curve: spot and forward rates 1.1 INTEREST RATES, PRESENT AND FUTURE VALUES, INTEREST COMPOUNDING 1.2 DISCOUNT FACTORS 1.3 CONTINUOUS COMPOUNDING AND CONTINUOUS RATES 1.4 FORWARD RATES 1.5 THE NO ARBITRAGE CONDITION FURTHER READING Chapter 2: The term structure or yield curve 2.1 INTRODUCTION TO THE YIELD CURVE 2.2 THE YIELD CURVE COMPONENTS 2.3 BUILDING A YIELD CURVE: METHODOLOGY 2.4 AN EXAMPLE OF YIELD CURVE POINTS DETERMINATION 2.5 INTERPOLATIONS ON A YIELD CURVE FURTHER READING Chapter 3: Spot instruments 3.1 SHORT-TERM RATES 3.2 BONDS 3.3 CURRENCIES FURTHER READING Chapter 4: Equities and stock indexes 4.1 STOCKS VALUATION 4.2 STOCK INDEXES 4.3 THE PORTFOLIO THEORY FURTHER READING Chapter 5: Forward instruments 5.1 THE FORWARD FOREIGN EXCHANGE 5.2 FRAs 5.3 OTHER FORWARD CONTRACTS 5.4 CONTRACTS FOR DIFFERENCE (CFD) FURTHER READING Chapter 6: Swaps 6.1 DEFINITIONS AND FIRST EXAMPLES 6.2 PRIOR TO AN IRS SWAP PRICING METHOD 6.3 PRICING OF AN IRS SWAP 6.4 (RE)VALUATION OF AN IRS SWAP 6.5 THE SWAP (RATES) MARKET 6.6 PRICING OF A CRS SWAP 6.7 PRICING OF SECOND-GENERATION SWAPS FURTHER READING Chapter 7: Futures 7.1 INTRODUCTION TO FUTURES 7.2 FUTURES PRICING 7.3 FUTURES ON EQUITIES AND STOCK INDEXES 7.4 FUTURES ON SHORT-TERM INTEREST RATES 7.5 FUTURES ON BONDS 7.6 FUTURES ON CURRENCIES 7.7 FUTURES ON (NON-FINANCIAL) COMMODITIES FURTHER READING Part II: The Probabilistic Environment Chapter 8: The basis of stochastic calculus 8.1 STOCHASTIC PROCESSES 8.2 THE STANDARD WIENER PROCESS, OR BROWNIAN MOTION 8.3 THE GENERAL WIENER PROCESS 8.4 THE ITÔ PROCESS 8.5 APPLICATION OF THE GENERAL WIENER PROCESS 8.6 THE ITÔ LEMMA 8.7 APPLICATION OF THE ITô LEMMA 8.8 NOTION OF RISK NEUTRAL PROBABILITY 8.9 NOTION OF MARTINGALE ANNEX 8.1: PROOFS OF THE PROPERTIES OF dZ(t) ANNEX 8.2: PROOF OF THE ITÔ LEMMA FURTHER READING Chapter 9: Other financial models: from ARMA to the GARCH family 9.1 THE AUTOREGRESSIVE (AR) PROCESS 9.2 THE MOVING AVERAGE (MA) PROCESS 9.3 THE AUTOREGRESSION MOVING AVERAGE (ARMA) PROCESS 9.4 THE AUTOREGRESSIVE INTEGRATED MOVING AVERAGE (ARIMA) PROCESS 9.5 THE ARCH PROCESS 9.6 THE GARCH PROCESS 9.7 VARIANTS OF (G)ARCH PROCESSES 9.8 THE MIDAS PROCESS FURTHER READING Chapter 10: Option pricing in general 10.1 INTRODUCTION TO OPTION PRICING 10.2 THE BLACK–SCHOLES FORMULA 10.3 FINITE DIFFERENCE METHODS: THE COX–ROSS–RUBINSTEIN (CRR) OPTION PRICING MODEL 10.4 MONTE CARLO SIMULATIONS 10.5 OPTION PRICING SENSITIVITIES FURTHER READING Chapter 11: Options on specific underlyings and exotic options 11.1 CURRENCY OPTIONS 11.2 OPTIONS ON BONDS 11.3 OPTIONS ON INTEREST RATES 11.4 EXCHANGE OPTIONS 11.5 BASKET OPTIONS 11.6 BERMUDAN OPTIONS 11.7 OPTIONS ON NON-FINANCIAL UNDERLYINGS 11.8 SECOND-GENERATION OPTIONS, OR EXOTICS FURTHER READING Chapter 12: Volatility and volatility derivatives 12.1 PRACTICAL ISSUES ABOUT THE VOLATILITY 12.2 MODELING THE VOLATILITY 12.3 REALIZED VOLATILITY MODELS 12.4 MODELING THE CORRELATION 12.5 VOLATILITY AND VARIANCE SWAPS FURTHER READING Chapter 13: Credit derivatives 13.1 INTRODUCTION TO CREDIT DERIVATIVES 13.2 VALUATION OF CREDIT DERIVATIVES 13.3 CONCLUSION FURTHER READING Chapter 14: Market performance and risk measures 14.1 RETURN AND RISK MEASURES 14.2 VaR OR VALUE-AT-RISK FURTHER READING Chapter 15: Beyond the Gaussian hypothesis: potential troubles with derivatives valuation 15.1 ALTERNATIVES TO THE GAUSSIAN HYPOTHESIS 15.2 POTENTIAL TROUBLES WITH DERIVATIVES VALUATION FURTHER READING Bibliography Index For other titles in the Wiley Finance series please see www.wiley.com/finance This edition first published 2013 Copyright © 2013 Alain Ruttiens Registered office John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, United Kingdom For details of our global editorial offices, for customer services and for information about how to apply for permission to reuse the copyright material in this book please see our website at www.wiley.com.

**
Analysis of Financial Time Series
** by
Ruey S. Tsay

Asian financial crisis, asset allocation, Bayesian statistics, Black-Scholes formula, Brownian motion, business cycle, capital asset pricing model, compound rate of return, correlation coefficient, data acquisition, discrete time, frictionless, frictionless market, implied volatility, index arbitrage, Long Term Capital Management, market microstructure, martingale, p-value, pattern recognition, random walk, risk tolerance, short selling, statistical model, stochastic process, stochastic volatility, telemarketer, transaction costs, value at risk, volatility smile, Wiener process, yield curve

Furthermore, for any given time indexes 0 ≤ t1 < t2 < · · · < tk , the random vector (wt1 , wt2 , . . . , wtk ) follows a multivariate normal distribution. Finally, a Brownian motion is standard if w0 = 0 almost surely, µ = 0, and σ 2 = 1. Remark: An important property of Brownian motions is that their paths are not differentiable almost surely. In other words, for a standard Brownian motion wt , it can be shown that dwt /dt does not exist for all elements of except for elements in a subset 1 ⊂ such that P(1 ) = 0. As a result, we cannot use the usual intergation in calculus to handle integrals involving a standard Brownian motion when we consider the value of an asset over time. Another approach must be sought. This is the purpose of discussing Ito’s calculus in the next section. 6.2.2 Generalized Wiener Processes The Wiener process is a special stochastic process with zero drift and variance proportional to the length of time interval.

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If {et } is a white noise series with finite moments of order slightly greater than 2, then the DF-statistic converges to a function of the standard Brownian motion as T → ∞; see Chan and Wei (1988) and Phillips (1987) for more information. If φ0 is zero but Eq. (2.36) is employed anyway, then the resulting t ratio for testing φ1 = 1 will converge to another nonstandard asymptotic distribution. In either case, simulation is used to obtain critical values of the test statistics; see Fuller (1976, Chapter 8) for selected critical values. Yet if φ0 = 0 and Eq. (2.36) is used, then the t ratio for testing φ1 = 1 is asymptotically normal. However, large sample sizes are needed for the asymptotic normal distribution to hold. Standard Brownian motion is introduced in Chapter 6. 2.8 SEASONAL MODELS Some financial time series such as quarterly earning per share of a company exhibits certain cyclical or periodic behavior.

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Using the notation of the general Ito’s process in Eq. (6.2), we have µ(xt , t) = µxt and σ (xt , t) = σ xt , where xt = Pt . Such a special process is referred to as a geometric Brownian motion. We now apply the Ito’s lemma to obtain a continuous-time model for the logarithm of the stock price Pt . Let G(Pt , t) = ln(Pt ) be the log price of the underlying stock. Then we have ∂G 1 = , ∂ Pt Pt ∂G = 0, ∂t 1 −1 1 ∂2G = . 2 2 ∂ Pt 2 Pt2 Consequently, via Ito’s lemma, we obtain d ln(Pt ) = 1 1 −1 2 2 σ2 1 µPt + σ Pt dt + σ Pt dwt = µ − dt + σ dwt . Pt 2 Pt2 Pt 2 ITO ’ S LEMMA 229 This result shows that the logarithm of a price follows a generalized Wiener Process with drift rate µ − σ 2 /2 and variance rate σ 2 if the price is a geometric Brownian motion. Consequently, the change in logarithm of price (i.e., log return) between current time t and some future time T is normally distributed with mean (µ−σ 2 /2)(T − t) and variance σ 2 (T −t).

pages: 374 words: 114,600

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The Quants
** by
Scott Patterson

Albert Einstein, asset allocation, automated trading system, beat the dealer, Benoit Mandelbrot, Bernie Madoff, Bernie Sanders, Black Swan, Black-Scholes formula, Blythe Masters, Bonfire of the Vanities, Brownian motion, buttonwood tree, buy and hold, buy low sell high, capital asset pricing model, centralized clearinghouse, Claude Shannon: information theory, cloud computing, collapse of Lehman Brothers, collateralized debt obligation, commoditize, computerized trading, Credit Default Swap, credit default swaps / collateralized debt obligations, diversification, Donald Trump, Doomsday Clock, Edward Thorp, Emanuel Derman, Eugene Fama: efficient market hypothesis, fixed income, Gordon Gekko, greed is good, Haight Ashbury, I will remember that I didn’t make the world, and it doesn’t satisfy my equations, index fund, invention of the telegraph, invisible hand, Isaac Newton, job automation, John Meriwether, John Nash: game theory, Kickstarter, law of one price, Long Term Capital Management, Louis Bachelier, mandelbrot fractal, margin call, merger arbitrage, money market fund, Myron Scholes, NetJets, new economy, offshore financial centre, old-boy network, Paul Lévy, Paul Samuelson, Ponzi scheme, quantitative hedge fund, quantitative trading / quantitative ﬁnance, race to the bottom, random walk, Renaissance Technologies, risk-adjusted returns, Robert Mercer, Rod Stewart played at Stephen Schwarzman birthday party, Ronald Reagan, Sergey Aleynikov, short selling, South Sea Bubble, speech recognition, statistical arbitrage, The Chicago School, The Great Moderation, The Predators' Ball, too big to fail, transaction costs, value at risk, volatility smile, yield curve, éminence grise

The formula has many components, one of which is the assumption that the future movement of a stock—its volatility—is random and leaves out the likelihood of large swings (see fat tails). Brownian motion: First described by Scottish botanist Robert Brown in 1827 when observing pollen particles suspended in water, Brownian motion is the seemingly random vibration of molecules. Mathematically, the motion is a random walk in which the future direction of the movement—left, right, up, down—is unpredictable. The average of the motion, however, can be predicted using the law of large numbers, and is visually captured by the bell curve or normal distribution. Quants use Brownian motion mathematics to predict the volatility of everything from the stock market to the risk of a multinational bank’s balance sheet. Credit default swap: Created in the early 1990s, these contracts essentially provide insurance on a bond or a bundle of bonds.

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After testing a range of other plant specimens, even the ground dust of rocks, and observing similar herky-jerky motion, he concluded that he was observing a phenomenon that was completely and mysteriously random. (The mystery remained unsolved for decades, until Albert Einstein, in 1905, discovered that the strange movement, by then known as Brownian motion, was the result of millions of microscopic particles buzzing around in a frantic dance of energy.) The connection between Brownian motion and market prices was made in 1900 by a student at the University of Paris named Louis Bachelier. That year, he’d written a dissertation called “The Theory of Speculation,” an attempt to create a formula that would capture the movement of bonds on the Paris stock exchange. The first English translation of the essay, which had lapsed into obscurity until it resurfaced again in the 1950s, had been included in the book about the market’s randomness that Thorp had read in New Mexico.

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It’s much more likely that the confused drunkard will sway randomly in many directions as the night progresses (samples that would fall in the middle of the curve) than that he will move continuously in a straight line, or spin in a circle (samples that would fall in the ends of the curve, commonly known as the tails of the distribution). In a thousand coin flips, it’s more likely that the sample will contain roughly five hundred heads and five hundred tails (falling in the curve’s middle) than nine hundred heads and one hundred tails (outer edge of the curve). Thorp, already well aware of Einstein’s 1905 discovery, was familiar with Brownian motion and rapidly grasped the connection between bonds and warrants. Indeed, it was in a way the same statistical rule that had helped Thorp win at blackjack: the law of large numbers (the more observations, the more coin flips, the greater the certainty of prediction). While he could never know if he’d win every hand at blackjack, he knew that over time he’d come out on top if he followed his card-counting strategy.

pages: 206 words: 70,924

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The Rise of the Quants: Marschak, Sharpe, Black, Scholes and Merton
** by
Colin Read

"Robert Solow", Albert Einstein, Bayesian statistics, Black-Scholes formula, Bretton Woods, Brownian motion, business cycle, capital asset pricing model, collateralized debt obligation, correlation coefficient, Credit Default Swap, credit default swaps / collateralized debt obligations, David Ricardo: comparative advantage, discovery of penicillin, discrete time, Emanuel Derman, en.wikipedia.org, Eugene Fama: efficient market hypothesis, financial innovation, fixed income, floating exchange rates, full employment, Henri Poincaré, implied volatility, index fund, Isaac Newton, John Meriwether, John von Neumann, Joseph Schumpeter, Kenneth Arrow, Long Term Capital Management, Louis Bachelier, margin call, market clearing, martingale, means of production, moral hazard, Myron Scholes, Paul Samuelson, price stability, principal–agent problem, quantitative trading / quantitative ﬁnance, RAND corporation, random walk, risk tolerance, risk/return, Ronald Reagan, shareholder value, Sharpe ratio, short selling, stochastic process, Thales and the olive presses, Thales of Miletus, The Chicago School, the scientific method, too big to fail, transaction costs, tulip mania, Works Progress Administration, yield curve

He also allowed a drift of zero mean of the security price and assumed that the variance of the price drift is proportional to the length of time of the random walk. In combination, he had described what we now call a Weiner process. The Times 105 While Bachelier was the first to apply Brownian motion to finance, the methodology is now commonplace. The term “Brownian motion” originated in 1828 from the observations of the botanist Robert Brown, who discovered that pollen suspended in water seemed to experience unusual and random jumps when observed under a microscope. The renowned MIT mathematician Norbert Weiner described the mathematics of Brownian motion in his 1918 PhD thesis. Bachelier had already discovered this, though. His statement that stock prices could be modeled as a random walk according to a Weiner process was amenable to empirical verification. Alfred Cowles, who would found the Cowles Commission, and Herbert Jones explored and subsequently vindicated this notion that there is no memory effect in the price of stocks in a 1937 paper together.8 While the notion of the random walk has since been replaced with the less restrictive concept of a martingale process, much of finance pricing theory still retains the random walk because of its simple first and second moment characterization of price movements.

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Alternative approaches Once Black and Scholes’ paper was published in the prestigious Journal of Political Economy, and with the opening of the CBOE, options pricing theory had arrived as the most sophisticated and potentially most valuable tool for financial market analysts. As theorists struggled to understand and interpret their result, and as Merton soon published his complementary work, a renewed interest developed in Bachelier’s work from 70 years earlier, and even Einstein’s theory of Brownian motion. Within a few years, Brownian motion, Markov processes, martingales, and stochastic calculus had begun to be integrated into the finance discipline. The quantitative school of finance had taken root. At that time, those most schooled in stochastic calculus were trained in physics and applied mathematics. With the advent of the statistical approach to physics that arose from theories of thermodynamics and quantum mechanics in the early twentieth century, physicists had become accustomed to the path of processes buffeted by random shocks.

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It too is of a value that follows a Weiner process because all assets the manager uses to fund his or her portfolio would follow a Weiner process. Then, the difference between the proportional drift of the sum of assets S used to fund this portfolio and the portfolio payout V will also follow a Weiner process: dS S − dV V = (μ − α )dt + θdB, The Theory 155 where µ is the mean return on the funding portfolio, ␣ is the mean return on the payout portfolio, and the Brownian motion term at the end is a combination of the standard deviation on the funding portfolio and the underlying stock multiplied by the Brownian motion of the underlying asset. Merton then established that the tracking error on such a funding portfolio made up of market securities is uncorrelated with the tracking error on the underlying security. This is a consequence of the choice of a funding portfolio that minimizes its correlation with the tracking errors so that one could not capitalize on predictable differences.

**
The Fractalist
** by
Benoit Mandelbrot

Albert Einstein, Benoit Mandelbrot, Brownian motion, business cycle, Claude Shannon: information theory, discrete time, double helix, Georg Cantor, Henri Poincaré, Honoré de Balzac, illegal immigration, Isaac Newton, iterative process, Johannes Kepler, John von Neumann, linear programming, Louis Bachelier, Louis Blériot, Louis Pasteur, mandelbrot fractal, New Journalism, Norbert Wiener, Olbers’ paradox, Paul Lévy, Richard Feynman, statistical model, urban renewal, Vilfredo Pareto

Having heard of its curious mathematical properties, I wondered whether it was irremediably theoretical or if it could be removed from pure esoterica and reinterpreted into something intuitive, concrete, and even practical. It can indeed! And the icing on this cake is the story of the Brownian island coastline. Brownian motion’s ups and downs first shined in Bachelier’s ill-inspired but profound model of price variation. Now forget about prices and imagine a point that moves on a piece of paper in such a way that its projections on the left and bottom sides of the sheet are Brownian motions independent of one another. That point is said to perform plane Brownian motion. This concept became widely used in physics and mathematics. But oddly enough, it seemed that no one I ever heard of had examined it on actual samples. So I drew a very long Brownian sample and set myself a challenge. I tried to blend two properties already established by mathematical reasoning and search for new properties that a skilled visual inspection might allow me to observe.

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These two men were the only living proof that my Keplerian dream was not an idle one—that it was possible to put together and develop a new mathematical approach to a very old, very concrete problem that overlapped several disciplines. Matching the sterling quality of their accomplishments was far beyond my ambitions, and I couldn’t think of less exalted advisers. Norbert Wiener of MIT The towering Keplerian achievements of Norbert Wiener (1894–1964) were his mathematical theory of Brownian motion and cybernetics—the word and the book. Isaac Newton knew around 1700 that prisms decompose light into components of different colors. But the mathematical theory was given much later, by Wiener. A related achievement, his theory of Brownian motion, strongly affected me later in my life—as a miserable model of the variation of competitive prices, and as a wiggle with an interesting boundary that forms fractal islands. His own account of early motivations was thrilling. Having become interested in the motion of pollen as seen through a microscope, he decided that the solution must use something called Lebesgue integrals—at that time still novel and the epitome of an esoteric toy.

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In particular, my Brownian intervals were deficient—unnatural—from a certain aesthetic viewpoint, one that is familiar in a far simpler shape, as a straight interval’s end positions differ from its middle portion. My first step was to eliminate this complication by creating a loop—as when the straight interval from 0 to 1 is made into the circumference of a circle. Obliging the Brownian motion to end where it had started yielded a distinctive new shape I called a Brownian cluster. But it still had too much irrelevant detail, and the elimination of this extraneous complexity demanded one more step. After many false starts, I separated the picture into two parts by “painting” white for all the points in the plane one can reach from far away, and black for those points “screened” from far away by one or another piece of Brownian motion. The result was astounding. (Illustration Credit 28.1) Instantly—but not a second before!—an interesting new island emerged. Automatically, my visual memory recognized some actual islands as well as some islands produced by fractal computer models I had previously devised.

pages: 416 words: 39,022

**
Asset and Risk Management: Risk Oriented Finance
** by
Louis Esch,
Robert Kieffer,
Thierry Lopez

asset allocation, Brownian motion, business continuity plan, business process, capital asset pricing model, computer age, corporate governance, discrete time, diversified portfolio, fixed income, implied volatility, index fund, interest rate derivative, iterative process, P = NP, p-value, random walk, risk/return, shareholder value, statistical model, stochastic process, transaction costs, value at risk, Wiener process, yield curve, zero-coupon bond

In ﬁnancial modelling, several speciﬁc cases of Itô process are used, and a geometric Brownian motion is therefore obtained when: at (Xt ) = a · Xt bt (Xt ) = b · Xt An Ornstein–Uhlenbeck process corresponds to: at (Xt ) = a · (c − Xt ) bt (Xt ) = b and the square root process is such that: √ bt (Xt ) = b Xt at (Xt ) = a · (c − Xt ) 2.3.3 Stochastic differential equations Expressions of the type dXt = at (Xt ) · dt + bt (Xt ) · dwt cannot simply be handled in the same way as the corresponding determinist expressions, because wt cannot be derived. It is, however, possible to extend the deﬁnition to a concept of stochastic differential, through the theory of stochastic integral calculus.8 As the stochastic process zt is deﬁned within the interval [a; b], the stochastic integral of zt is deﬁned within [a; b] with respect to the standard Brownian motion wt by: a 7 8 b zt dwt = lim n→∞ δ→0 n−1 ztk (wtk+1 − wtk ) k=0 The root function presents a vertical tangent at the origin.

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We no longer have a stationary random model, such as Sharpe’s example, but a model that combines the random and temporal elements; this is known as a stochastic process. An example of this type of model is the Black–Scholes model for equity options (see Section 5.3.2), where the price p is a function of various variables (price of underlying asset, realisation price, maturity, volatility of underlying asset, risk-free interest rate). In this model, the price of the underlying asset is itself modelled by a stochastic process (standard Brownian motion). 3 Equities 3.1 THE BASICS An equity is a ﬁnancial asset that corresponds to part of the ownership of a company, its value being indicative of the health of the company in question. It may be the subject of a sale and purchase, either by private agreement or on an organised market. The law of supply and demand on this market determines the price of the equity. The equity can also give rise to the periodic payment of dividends. 3.1.1 Return and risk 3.1.1.1 Return on an equity Let us consider an equity over a period of time [t − 1; t] the duration of which may be one day, one week, one month or one year.

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Note that this property is a generalisation for the random case of the determinist formula St = S0 · (1 + i)t . 3.4.2.2 Continuous model The method of equity value change shown in the binomial model is of the random walk type. At each transition, two movements are possible (rise or fall) with unchanged probability. When the period between each transaction tends towards 0, this type of random sequence converges towards a standard Brownian motion or SBM.52 Remember that we are looking at a stochastic process wt (a random variable that is a function of time), which obeys the following processes: • w0 = 0. • wt is a process with independent increments : if s < t < u, then wu − wt is independent of wt − ws . • wt is a process with stationary increments : the random variables wt+h − wt and wh are identically distributed. • Regardless of what t may be, the random variable √ wt is distributed according to a normal law of zero mean and standard deviation t: fwt (x) = √ 1 2πt e−x 2 /2t The ﬁrst use of this process for modelling the development in the value of a ﬁnancial asset was produced by L.

pages: 461 words: 128,421

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The Myth of the Rational Market: A History of Risk, Reward, and Delusion on Wall Street
** by
Justin Fox

activist fund / activist shareholder / activist investor, Albert Einstein, Andrei Shleifer, asset allocation, asset-backed security, bank run, beat the dealer, Benoit Mandelbrot, Black-Scholes formula, Bretton Woods, Brownian motion, business cycle, buy and hold, capital asset pricing model, card file, Cass Sunstein, collateralized debt obligation, complexity theory, corporate governance, corporate raider, Credit Default Swap, credit default swaps / collateralized debt obligations, Daniel Kahneman / Amos Tversky, David Ricardo: comparative advantage, discovery of the americas, diversification, diversified portfolio, Edward Glaeser, Edward Thorp, endowment effect, Eugene Fama: efficient market hypothesis, experimental economics, financial innovation, Financial Instability Hypothesis, fixed income, floating exchange rates, George Akerlof, Henri Poincaré, Hyman Minsky, implied volatility, impulse control, index arbitrage, index card, index fund, information asymmetry, invisible hand, Isaac Newton, John Meriwether, John Nash: game theory, John von Neumann, joint-stock company, Joseph Schumpeter, Kenneth Arrow, libertarian paternalism, linear programming, Long Term Capital Management, Louis Bachelier, mandelbrot fractal, market bubble, market design, Myron Scholes, New Journalism, Nikolai Kondratiev, Paul Lévy, Paul Samuelson, pension reform, performance metric, Ponzi scheme, prediction markets, pushing on a string, quantitative trading / quantitative ﬁnance, Ralph Nader, RAND corporation, random walk, Richard Thaler, risk/return, road to serfdom, Robert Bork, Robert Shiller, Robert Shiller, rolodex, Ronald Reagan, shareholder value, Sharpe ratio, short selling, side project, Silicon Valley, Social Responsibility of Business Is to Increase Its Profits, South Sea Bubble, statistical model, stocks for the long run, The Chicago School, The Myth of the Rational Market, The Predators' Ball, the scientific method, The Wealth of Nations by Adam Smith, The Wisdom of Crowds, Thomas Kuhn: the structure of scientific revolutions, Thomas L Friedman, Thorstein Veblen, Tobin tax, transaction costs, tulip mania, value at risk, Vanguard fund, Vilfredo Pareto, volatility smile, Yogi Berra

Another famous example came in the mid-1920s when the young founder of Moscow’s Business Cycle Institute, Nikolai Kondratiev, proposed that economic activity moved in half-century-long “waves.”35 As the study of statistics progressed and the mathematics of random processes such as Brownian motion became more widely understood, those on the frontier of this work began to question these apparent cycles. In his November 1925 presidential address to Great Britain’s Royal Statistical Society, Cambridge professor George Udny Yule demonstrated that random Brownian motion could, with a little tweaking, produce dramatic patterns that didn’t look random at all.36 A few years later, a mathematician working for Kondratiev in Moscow penned what came to be seen as the definitive debunking of the pattern finders. “Almost all of the phenomena of economic life,” wrote Eugen Slutsky, “occur in sequences of rising and falling movements, like waves.”

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The mathematical expectation of the speculator was the expected return of the stock or of the overall market, around which the actual return would fluctuate randomly. It is conceivable that Bachelier and Poincaré were aware of these flaws in 1900, and didn’t bother correcting them because Bachelier’s formula was meant to look only an “instant” into the future. It didn’t matter that Bachelier’s Brownian motion would eventually lead prices where they could not go, because he had made explicit that it was not to be used for purposes of long-term prediction anyway. Beset by no such qualms, Samuelson revised Bachelier’s formula. He introduced what he variously called “geometric,” “economic,” or “logarithmic” Brownian motion, which avoided negative prices by describing percentage moves of stock prices, not dollars and cents. And he depicted stock market investing as a bet in which the payoffs fluctuated randomly around the expected return. SAMUELSON BEGAN TALKING UP THESE ideas around MIT and in visits to other universities in the late 1950s.

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After some study of the market, he concluded: It was a game of competitive gambling. In it some were smart and some were not so smart, and the players changed sides so often that it was a picture of financial chaos or bedlam. As I had some experience in molecular chaos as a physicist studying statistical mechanics, the analogies were very clear to me indeed.7 The analogy that was clearest to him was that of Brownian motion. As Samuelson had already noticed, straight arithmetic Brownian motion couldn’t possibly fit the data. Instead, Osborne used the same percentage-change version as Samuelson had, then published his findings in the March–April 1959 issue of the journal Operations Research. As soon as the article came out, letters pointing out similarities to the stock market work of Bachelier, Maurice Kendall, and others came pouring in. Osborne hadn’t known about any of that beforehand.

pages: 425 words: 122,223

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Capital Ideas: The Improbable Origins of Modern Wall Street
** by
Peter L. Bernstein

"Robert Solow", Albert Einstein, asset allocation, backtesting, Benoit Mandelbrot, Black-Scholes formula, Bonfire of the Vanities, Brownian motion, business cycle, buy and hold, buy low sell high, capital asset pricing model, corporate raider, debt deflation, diversified portfolio, Eugene Fama: efficient market hypothesis, financial innovation, financial intermediation, fixed income, full employment, implied volatility, index arbitrage, index fund, interest rate swap, invisible hand, John von Neumann, Joseph Schumpeter, Kenneth Arrow, law of one price, linear programming, Louis Bachelier, mandelbrot fractal, martingale, means of production, money market fund, Myron Scholes, new economy, New Journalism, Paul Samuelson, profit maximization, Ralph Nader, RAND corporation, random walk, Richard Thaler, risk/return, Robert Shiller, Robert Shiller, Ronald Reagan, stochastic process, Thales and the olive presses, the market place, The Predators' Ball, the scientific method, The Wealth of Nations by Adam Smith, Thorstein Veblen, transaction costs, transfer pricing, zero-coupon bond, zero-sum game

If stock prices vary according to the square root of time, they bear a remarkable resemblance to molecules randomly colliding with one another as they move in space. An English physicist named Robert Brown discovered this phenomenon early in the nineteenth century, and it is generally known as Brownian motion. Brownian motion was a critical ingredient of Einstein’s theory of the atom. The mathematical formula that describes this phenomenon was one of Bachelier’s crowning achievements. Over time, in the literature on finance, Brownian motion came to be called the random walk, which someone once described as the path a drunk might follow at night in the light of a lamppost. No one knows who first used this expression, but it became increasingly familiar among academics during the 1960s, much to the annoyance of financial practitioners.

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Second, again unaware that he was echoing Bachelier, Osborne argues that prices represent decisions at those moments—and only at those moments—when the buyer expects a stock to rise in price and the seller expects it to fall: Transactions take place only when there is a difference of opinion. This means that, for the market as a whole, the expected price change is zero. The market is as likely to go up x percent as down x percent. Third, Osborne’s mathematical manipulations show that the range within which prices tend to fluctuate will “increase as the square root of the time interval”26—Brownian motion, precisely as Bachelier had prophesied. Fourth, in a set of experiments with actual stock market data, Osborne confirms the hypothesis of Brownian motion, including percentage price changes over intervals of a day, a week, a month, two months, up to twelve years. He also finds that Cowles’s long history of stock prices follows “. . . the square root of time diffusion law very nicely indeed.”27 Finally, he finds that distributions of the monthly changes in the Dow Jones Industrial Average from 1925 to 1956 “are quite comparable.”28 The fifth finding made by Osborne’s imaginary statistician is another example of how Osborne, working all by himself, confirmed the research conclusions of others.

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See also Wells Fargo Bank Barr Rosenberg Associates (BARRA) Battle for Investment Survival, The (Loeb) “Behavior of Stock Prices, The” (Fama) Bell Journal Bell Laboratories Beta: see Risk, systematic “Beta Revolution: Learning to Live with Risk” Black Monday (October, 1987, crash) Black/Scholes formula Block trading Boeing Bond(s) convertible discount rates and government high-grade interest rates international junk liquidity maturity risk treasury: see Bond(s), government zero-coupon Bond market Boston Company Brokerage commissions. See also Transaction costs Brownian motion “Brownian Motion in the Stock Market” (Osborne) Butterfly swaps Buy and hold strategy California Public Employees Retirement System Calls: see Options Capital cost of optimal structure of preserving strategy “Capital Asset Prices: A Theory of Market Equilibrium Under Conditions of Risk” (Sharpe) Capital Asset Pricing Model (CAPM) non-stock applicability risk/return ratio in time analysis and Capital gains tax Capital Guardian Capital markets theory competition and corporate investment and debt/equity ratios and research CAPM: see Capital Asset Pricing Model CDs CEIR Center for Research in Security Prices (CRSP).

pages: 285 words: 78,180

**
Life at the Speed of Light: From the Double Helix to the Dawn of Digital Life
** by
J. Craig Venter

Albert Einstein, Alfred Russel Wallace, Asilomar, Barry Marshall: ulcers, bioinformatics, borderless world, Brownian motion, clean water, discovery of DNA, double helix, epigenetics, experimental subject, global pandemic, Isaac Newton, Islamic Golden Age, John von Neumann, Louis Pasteur, Mars Rover, Mikhail Gorbachev, phenotype, Richard Feynman, stem cell, the scientific method, Thomas Kuhn: the structure of scientific revolutions, Turing machine

Einstein’s notion was eventually confirmed with careful experiments conducted in Paris by Jean Baptiste Perrin (1870–1942), who was rewarded for this and other work with the Nobel Prize in Physics in 1926. Brownian motion has profound consequences when it comes to understanding the workings of living cells. Many of the vital components of a cell, such as DNA, are larger than individual atoms but still small enough to be jostled by the constant pounding of the surrounding sea of atoms and molecules. So while DNA is indeed shaped like a double helix, it is a writhing, twisting, spinning helix as a result of the forces of random Brownian motion. The protein robots of living cells are only able to fold into their proper shapes because their components are mobile chains, sheets, and helices that are constantly buffeted within the cell’s protective membrane. Life is driven by Brownian motion, from the kinesin protein trucks that pull tiny sacks of chemicals along microtubules to the spinning ATP synthase.31 Critically, the amount of Brownian motion depends on temperature: too low and there is not enough motion; too high and all structures become randomized by the violent motion.

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Life is driven by Brownian motion, from the kinesin protein trucks that pull tiny sacks of chemicals along microtubules to the spinning ATP synthase.31 Critically, the amount of Brownian motion depends on temperature: too low and there is not enough motion; too high and all structures become randomized by the violent motion. Thus life can only exist in a narrow temperature range. Within this range, the equivalent of a Richter 9 earthquake rages continuously inside cells. “You would not need to even pedal your bicycle: you would simply attach a ratchet to the wheel preventing it from going backwards and shake yourselves forward,” according to George Oster and Hongyun Wang, of the Department of Molecular and Cellular Biology at the University of California, Berkeley.32 Protein robots accomplish a comparable feat by using ratchets and power strokes to harness the power of Brownian motion. Due to the incessant random movement and vibrations of molecules, diffusion is very rapid over short distances, which enables biological reactions to occur with tiny quantities of reactants in the extremely confined volumes of most cells.

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A protein with one hundred amino acids can fold in myriad ways, such that the number of alternate structures ranges from 2100 to 10100 possible conformations. For each protein to try every possible conformation would require on the order of ten billion years. But built into the linear protein code are the folding instructions, which are in turn determined by the linear genetic code. As a result, with the help of Brownian motion, the incessant molecular movement caused by heat energy, these processes happen very quickly—in a few thousandths of a second. They are driven by the fact that a correctly folded protein has the lowest possible free energy, so that, like water flowing to the lowest point, the protein naturally achieves its favored shape. The correctly folded conformation that ensures that the enzyme can work properly involves moving from a high degree of entropy and free energy to the thermodynamically stable state of decreased entropy and free energy.

pages: 246 words: 16,997

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Financial Modelling in Python
** by
Shayne Fletcher,
Christopher Gardner

Brownian motion, discrete time, interest rate derivative, London Interbank Offered Rate, stochastic volatility, yield curve, zero day, zero-coupon bond

Throughout this section we denote the function of the one-dimensional Brownian motion4 X T by yT := f (X T ) and the filtratio at time t by Ft . A full mathematical definitio of Brownian motion can be found in [16] but for the purposes of what follows all we need to know is that X T − X t is independent of X t for t < T and is normally distributed with zero mean and variance T − t. The aim of this subsection is to explain how to compute the following conditional expectations: yt := E[yT |Ft ] yt+ := E[max(yT , 0)|Ft ] (4.42) (4.43) Because the increments of a Brownian motion are independent of each other, the above conditional expectations can be written as yt (x) = E[ f (x + X T − X t )|xt = x] yt+ (x) = E[max( f (x + X T − X t ), 0)|xt = x] (4.44) (4.45) We donote the discrete grid of states for the Brownian motion increment X T − X t by xtT . If we fi the function f on the discrete grid of X T , denoted by xT , then x + xtT for X t = x will generally lie outside the domain of the discrete grid xT .

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In the case of the rollback method the integrator is simply the integral member function of the distribution class represented by ftT, and in the case of the rollback max method the integrator is the integral max member function of ftT. class semi analytic domain integrator: def 4 create cached moments(self, x, f): In 1828 the Scottish botanist Robert Brown observed that pollen grains suspended in liquid performed an irregular motion – Brownian motion. 58 Financial Modelling in Python n = x.shape[0] self. ys = numpy.zeros([n, 4]) self. ys[2] = f.moments(4, x[2]) # cubic for j in range(2, n-2): self. ys[j+1] = f.moments(4, x[j+1]) # cubic def rollback (self, t, T, xt, xT, xtT, yT, regridder, integrator): if len(xt.shape) <> len(xT.shape) or \ len(xT.shape) <> len(yT.shape) or \ len(xt.shape) <> 1 or len(xtT.shape) <> 1: raise RuntimeError, ’expected one dimensional arrays’ nt = xt.shape[0] nT = xT.shape[0] ntT = xtT.shape[0] if nt <> nT or ntT <> nT: raise RuntimeError, ’expected array to be of same size’ if yT.shape[0] <> nT: raise RuntimeError, \ ‘array yT has different number of points to xT’ yt = numpy.zeros(nt) cT = piecewise cubic fit(xT, yT) for i in range(nt): # regrid regrid xT = numpy.zeros(nT) xti = xt[i] for j in range(nT): regrid xT[j] = xti+xtT[j] regrid yT = regridder(xT, cT, regrid xT) # polynomial fit cs = piecewise cubic fit(xtT, regrid yT) # perform expectation sum = 0 xl = xtT[2] for j in range(2, nT-2): # somehow this should be enscapsulated xh = xtT[j+1] sum = sum + integrator(cs[:, j-2], xl, xh, self. ys[j], self. ys[j+1]) xl = xh yt[i] = sum if t == 0.0: for j in range(1, nt): yt[j] = yt[0] break return yt Basic Mathematical Tools 59 def rollback(self, t, T, xt, xT, xtT, ftT, yT): # create cache of moments self. create cached moments(xtT, ftT) return self. rollback (t, T, xt, xT, xtT, yT, ftT.regrid, ftT.integral) def rollback max(self, t, T, xt, xT, xtT, ftT, yT): # create cache of moments self. create cached moments(xtT, ftT) return self. rollback (t, T, xt, xT, xtT, yT, ftT.regrid, ftT.integral max) Note that we precompute the moments in the function create cached moments() prior to performing the rollback.

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Indeed Boost.Python offers many more features to help the C++ programmer to seamlessly expose C++ classes to Python and embed Python into C++. 218 Financial Modelling in Python Note that, as expected, the stochastic discount factor is a Q-martingale, in fact it is an exponential martingale, whereas the zero coupon bond price is not a Q-martingale because, as can be seen below, its SDE has a non-zero drift. d P(t, T ) = P(t, T ) (r (t)dt + (φ(t) − φ(T )) C(t)dW (t)) . (C.11) For non path-dependent pricing problems it is normally convenient to work in the so-called forward QT -measure. In this measure the numeraire at time t is simply P(t, T) and Girsanov’s theorem implies that W̄ (t), as define below, is a QT -Brownian motion d W̄ (t) = dW (t) + (φ(T ) − φ(t)) C(t)dt. Substitution of equation (C.12) into equation (C.10) yields t P(t, T ) P(0, T ) C(s)d W̄ (s) = exp − φ(T ) − φ(T ) P(t, T ) P(0, T ) 0 t 1 2 − φ(T ) − φ(T ) C(s)2 ds , ∀t ≤ T ≤ T. 2 0 (C.12) (C.13) In other words, the numeraire-rebased zero coupon bond in the forward QT -measure is a QT martingale. This to be expected in complete markets, where all numeraire-rebased tradables are martingales.

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Mathematical Finance: Core Theory, Problems and Statistical Algorithms
** by
Nikolai Dokuchaev

Black-Scholes formula, Brownian motion, buy and hold, buy low sell high, discrete time, fixed income, implied volatility, incomplete markets, martingale, random walk, short selling, stochastic process, stochastic volatility, transaction costs, volatility smile, Wiener process, zero-coupon bond

The initial price S0>0 is a given non-random value, and the evolution of S(t) is described by the following Ito equation: dS(t)=S(t)(a(t)dt+σ(t)dw(t)). (5.1) Here w(t) is a (one-dimensional) Wiener process, and a and σ are market parameters. Sometimes in the literature S(t) is called a geometric Brownian motion (for the case of non-random and constant a, σ), sometimes ln S(t) is also said to be a Brownian motion. Mathematicians prefer to use the term ‘Brownian motion’ for w(t) only (i.e., Brownian motion is the same as a Wiener process). Definition 5.1 In (5.1), a(t) is said to be the appreciation rate, σ(t) is said to be the volatility. Note that, in terms of more general stochastic differential equations, the coefficient for dt (i.e., a(t)S(t)) is said to be the drift (or the drift coefficient), and the coefficient for dw(t) (i.e., σ(t)S(t)) is said to be the diffusion coefficient.

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Prove that there exists an American option (Definition 3.43) such that its fair price is equal to the fair price of the option from Problem 3.44. © 2007 Nikolai Dokuchaev 4 Basics of Ito calculus and stochastic analysis This chapter introduces the stochastic integral, stochastic differential equations, and core results of Ito calculus. 4.1 Wiener process (Brownian motion) Let T>0 be given, Definition 4.1 We say that a continuous time random process w(t) is a (onedimensional) Wiener process (or Brownian motion) if (i) w(0)=0; (ii) w(t) is Gaussian with Ew(t)=0, Ew(t)2=t, i.e., w(t) is distributed as N(0, t); (iii) w(t+τ)−w(t) does not depend on {w(s), s≤t} for all t≥0, τ>0. Theorem 4.2 (N. Wiener). There exists a probability space such that there exists a pathwise continuous process with these properties. This is why we call it the Wiener process.

pages: 695 words: 194,693

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Money Changes Everything: How Finance Made Civilization Possible
** by
William N. Goetzmann

Albert Einstein, Andrei Shleifer, asset allocation, asset-backed security, banking crisis, Benoit Mandelbrot, Black Swan, Black-Scholes formula, Bretton Woods, Brownian motion, business cycle, capital asset pricing model, Cass Sunstein, collective bargaining, colonial exploitation, compound rate of return, conceptual framework, corporate governance, Credit Default Swap, David Ricardo: comparative advantage, debt deflation, delayed gratification, Detroit bankruptcy, disintermediation, diversified portfolio, double entry bookkeeping, Edmond Halley, en.wikipedia.org, equity premium, financial independence, financial innovation, financial intermediation, fixed income, frictionless, frictionless market, full employment, high net worth, income inequality, index fund, invention of the steam engine, invention of writing, invisible hand, James Watt: steam engine, joint-stock company, joint-stock limited liability company, laissez-faire capitalism, Louis Bachelier, mandelbrot fractal, market bubble, means of production, money market fund, money: store of value / unit of account / medium of exchange, moral hazard, Myron Scholes, new economy, passive investing, Paul Lévy, Ponzi scheme, price stability, principal–agent problem, profit maximization, profit motive, quantitative trading / quantitative ﬁnance, random walk, Richard Thaler, Robert Shiller, Robert Shiller, shareholder value, short selling, South Sea Bubble, sovereign wealth fund, spice trade, stochastic process, the scientific method, The Wealth of Nations by Adam Smith, Thomas Malthus, time value of money, too big to fail, trade liberalization, trade route, transatlantic slave trade, tulip mania, wage slave

It also required the time period for which the option is granted (the “maturity” of the option). Bachelier presented his book, Théorie de la Spéculation, as his doctoral thesis in mathematics at the Sorbonne in 1900. In working through the problem of option pricing, Bachelier had to devise a precise definition of how a stock price moved randomly through time. We now refer to this as Brownian motion. Interestingly, Albert Einstein developed a Brownian motion model in 1905, evidently later and independently from Bachelier. Bachelier’s answer to the option pricing problem turned out to be an equation beyond the knowledge of market participants at the time. This presented an interesting philosophical issue. If option prices conformed to a complex, nonlinear multivariate function that was undiscovered until 1900, how then did the invisible hand—the process of speculation—drive them toward efficiency?

…

Evidently none knew of Bachelier, and thus they had to retrace the mathematical logic of fair prices and random walks when they began work on the problem of option pricing in the late 1960s. Like Bachelier, they relied on a model of variation in prices—Brownian motion—although unlike Bachelier, they chose one that did not allow prices to become negative—a limitation of Bachelier’s work. The Black-Scholes formula, as it is now referred to, was mathematically sophisticated, but at its heart it contained a novel economic—as opposed to mathematical—insight. They discovered that the invisible hand setting option prices was risk-neutral. Option payoffs could be replicated risklessly, provided one could trade in an ideal, frictionless market in which stocks behaved according to Brownian motion. Later researchers4 developed a simple framework called a “binomial model” that was able to match the payoff of a put or a call by trading just the stock and a bond through time.

…

Paul Lévy formalized these prior random walk models into a very general family of stochastic processes referred to as Lévy processes. Brownian motion was just one process in the family of Lévy processes—and perhaps the best behaved of them. Other stochastic processes have such things as discontinuous jumps and unusually large shocks (which might, for example, explain the crash of 1987, when the US stock market lost 22.6% of its value in a single day). In the 1960s, Benoit Mandelbrot began to investigate whether Lévy processes described economic time series like cotton prices and stock prices. He found that the ones that generated jumps and extreme events better described financial markets. He developed a mathematics around these unusual Lévy processes that he called “fractal geometry.” He argued that unusual events—Taleb’s black swan—were in fact much more common phenomena than Brownian motion would suggest.

pages: 266 words: 86,324

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The Drunkard's Walk: How Randomness Rules Our Lives
** by
Leonard Mlodinow

Albert Einstein, Alfred Russel Wallace, Antoine Gombaud: Chevalier de Méré, Atul Gawande, Brownian motion, butterfly effect, correlation coefficient, Daniel Kahneman / Amos Tversky, Donald Trump, feminist movement, forensic accounting, Gerolamo Cardano, Henri Poincaré, index fund, Isaac Newton, law of one price, pattern recognition, Paul Erdős, Pepto Bismol, probability theory / Blaise Pascal / Pierre de Fermat, RAND corporation, random walk, Richard Feynman, Ronald Reagan, Stephen Hawking, Steve Jobs, The Wealth of Nations by Adam Smith, The Wisdom of Crowds, Thomas Bayes, V2 rocket, Watson beat the top human players on Jeopardy!

Then, in a deathblow to his wishful interpretation of the discovery, Brown also observed the motion when looking at inorganic particles—of asbestos, copper, bismuth, antimony, and manganese. He knew then that the movement he was observing was unrelated to the issue of life. The true cause of Brownian motion would prove to be the same force that compelled the regularities in human behavior that Quételet had noted—not a physical force but an apparent force arising from the patterns of randomness. Unfortunately, Brown did not live to see this explanation of the phenomenon he observed. The groundwork for the understanding of Brownian motion was laid in the decades that followed Brown’s work, by Boltzmann, Maxwell, and others. Inspired by Quételet, they created the new field of statistical physics, employing the mathematical edifice of probability and statistics to explain how the properties of fluids arise from the movement of the (then hypothetical) atoms that make them up.

…

But actually it did take an Einstein to finally convince the scientific world of the need for that new approach to physics. Albert Einstein did it in 1905, the same year in which he published his first work on relativity. And though hardly known in popular culture, Einstein’s 1905 paper on statistical physics proved equally revolutionary. In the scientific literature, in fact, it would become his most cited work.32 EINSTEIN’S 1905 WORK on statistical physics was aimed at explaining a phenomenon called Brownian motion. The process was named for Robert Brown, botanist, world expert in microscopy, and the person credited with writing the first clear description of the cell nucleus. Brown’s goal in life, pursued with relentless energy, was to discover through his observations the source of the life force, a mysterious influence believed in his day to endow something with the property of being alive. In that quest, Brown was doomed to failure, but one day in June 1827, he thought he had succeeded.

…

But most physicists are practical, and so the most important roadblock to acceptance was that although the theory reproduced some laws that were known, it made few new predictions. And so matters stood until 1905, when long after Maxwell was dead and shortly before a despondent Boltzmann would commit suicide, Einstein employed the nascent theory to explain in great numerical detail the precise mechanism of Brownian motion.34 The necessity of a statistical approach to physics would never again be in doubt, and the idea that matter is made of atoms and molecules would prove to be the basis of most modern technology and one of the most important ideas in the history of physics. The random motion of molecules in a fluid can be viewed, as we’ll note in chapter 10, as a metaphor for our own paths through life, and so it is worthwhile to take a little time to give Einstein’s work a closer look.

pages: 282 words: 89,436

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Einstein's Dice and Schrödinger's Cat: How Two Great Minds Battled Quantum Randomness to Create a Unified Theory of Physics
** by
Paul Halpern

Albert Einstein, Albert Michelson, Arthur Eddington, Brownian motion, clockwork universe, cosmological constant, dark matter, double helix, Ernest Rutherford, Fellow of the Royal Society, Isaac Newton, Johannes Kepler, John von Neumann, lone genius, Murray Gell-Mann, New Journalism, orbital mechanics / astrodynamics, Richard Feynman, Schrödinger's Cat, Solar eclipse in 1919, The Present Situation in Quantum Mechanics

But that result was just the overture of his grand symphony of scientific revelations. Another major paper Einstein published in 1905 concerned a phenomenon called Brownian motion, named after the Scottish botanist Robert Brown, involving tiny random fluctuations of small particles. In 1827, Brown had observed the agitated motion of particles found in pollen grains immersed in water. He failed to find a credible explanation for their erratic behavior. Building upon his doctoral thesis, Einstein decided to model the movements of particles bashed around by water molecules and discovered precisely the kind of haphazard jig seen by Brown. By explaining Brownian motion as the zigzag result of 35 Einstein’s Dice and Schrödinger’s Cat myriad particle collisions, Einstein furnished important evidence for the existence of atoms.

…

Nothing in this practical work would hint at the explosion of ideas about to be ignited. In the spring of that year, Einstein took aim. Staring classical physics straight in the face, he lit the fuses and launched his grenades. He submitted four papers to a prestigious journal, Annalen der Physik. One was a version of his dissertation. The other three articles— addressing the photoelectric effect, Brownian motion, and the special theory of relativity—would shake the foundations of physical science. Einstein’s paper on the photoelectric effect cemented Planck’s quantum idea by making it tangible and eminently measurable. It considers what would happen if a researcher shines a light on a metal, supplying enough energy to release an electron. If light were purely a wave, theory suggested, its amount of energy would depend mainly on its 34 The Clockwork Universe brightness.

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(Schrödinger), 208 Aristotle, 77, 215 Arkani-Hamed, Nima, 232 Ashtekar, Abhay, 232 Aspect, Alain, 210 Assembly of German Natural Scientists and Physicians (Vienna conference of 1913), 44–51 Atomic bomb Einstein and, 168–169, 183 Germany’s efforts to develop, 178–180 Atomic model, 35 Bohr, 46–48, 73, 81, 82, 84–85 Bohr-Sommerfeld, 83, 98 Rutherford, 45 Atomism, 28, 80 Atoms argument over reality of, 22–24 photoelectric effect and, 35 as probabilistic mechanism, 102 Autiero, Dario, 235 Axioms, 18 Aydelotte, Frank, 168 Bailey, Herbert, 204, 205 Ball-in-the-box thought experiment, 139, 141 Balmer series, 48 Bär, Richard, 154, 155 Bargmann, Sonja, 204 Bargmann, Valentine “Valya,” 149, 168, 169 Barnett, Lincoln, 204 Bauer, Alexander, 16 Bauer, Minnie, 16 Bauer-Bohm, Hansi, 143–144 Becquerel, Henri, 28 Bell, John, 210 Berg, Moe, 179 255 Index Heisenberg and, 86–87, 88 probabilistic interpretation and, 105 Schrödinger wave equation and, 5, 6 wavefunction as ghost field and, 99–100 Bose, Satyendra, 90, 92, 225 Bose-Einstein statistics, 90 Bosonic strings, 230–231 Bosons, 225–227, 230 Bottom quarks, 227 Braunizer, Andreas, 217 Braunizer, Arnulf, 217 Braunizer, Ruth, 219–220 Brecht, Bertolt, 109 Brout, Robert, 226 Brown, Robert, 35 Brownian motion, Einstein on, 34, 35–36 Buddhism/Buddha, 77, 80 Bergmann, Peter, 149, 168, 169, 213, 231 Berlin, 109, 131 Bertel, Annemarie “Anny,” 76, 77 Bertolucci, Sergio, 235 Besso, Michele, 29, 55–56 Beta decay, 136 “Big Bang,” 63 Birch, Francis, 192 BKS (Bohr-Kramers-Slater) theory, 103 Blackbody radiation, 31–32, 90 Black holes, 59 Black Mountain College, 169 Bohm, David, 209–210 Bohm-Aharonov version of EPR thought experiment, 209–210 Bohr, Margrethe, 102 Bohr, Niels, 1, 110, 215 atomic model, 35, 46–48, 73, 81, 82, 84–85 Eddington’s theory and, 148 Einstein and, 137, 168, 200 EPR paper and, 138 escape from Denmark, 179 uncertainty principle and, 106 “Bohr Festival,” 82, 84–85 Bohr’s Institute for Theoretical Physics, 88, 100–102 Bohr-Sommerfeld atomic model, 83, 98 Bohr-Sommerfeld quantization rules, 93 Boltzmann, Ludwig, 22–23, 24, 30, 81, 92 Bondi, Hermann, 157 Borges, Jorge Luis, 62 Born, Max, 1, 82, 87, 89, 144 dismissal and exile of, 128, 130 Einstein and, 103–104, 134 as go-between in de Valera offer to Schrödinger, 154, 155 Calabi, Eugenio, 231 Calabi-Yau manifolds, 231 Callaway, Joseph, 208 Caltech, Einstein’s visits to, 122–123 “Can Quantum Mechanical Description of Physical Reality Be Considered Complete?”

pages: 261 words: 86,261

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The Pleasure of Finding Things Out: The Best Short Works of Richard P. Feynman
** by
Richard P. Feynman,
Jeffrey Robbins

Albert Einstein, Brownian motion, impulse control, index card, John von Neumann, Murray Gell-Mann, pattern recognition, Pepto Bismol, Richard Feynman, Richard Feynman: Challenger O-ring, scientific worldview, the scientific method

I speak, of course, “in principle,” and I am not speaking about the actual manufacture of such devices. Let us therefore discuss what happens if we try to make the devices as small as possible. Reducing the Size FIGURE 5 So my third topic is the size of computing elements and now I speak entirely theoretically. The first thing that you would worry about when things get very small is Brownian motion*—everything is shaking about and nothing stays in place. How can you control the circuits then? Furthermore, if a circuit does work, doesn’t it now have a chance of accidentally jumping back? If we use two volts for the energy of this electric system, which is what we ordinarily use (Fig. 5), that is eighty times the thermal energy at room temperature (kT = 1/40 volt) and the chance that something jumps backward against 80 times thermal energy is e, the base of the natural logarithm, to the power minus eighty, or 10-43.

…

If the things flip back and then go forward later it is still all right. It’s very much the same as a particle in a gas which is bombarded by the atoms around it. Such a particle usually goes nowhere, but with just a little pull, a little prejudice that makes a chance to move one way a little higher than the other way, the thing will slowly drift forward and travel from one end to the other, in spite of the Brownian motion that it has made. So our computer will compute provided we apply a drift force to pull the thing across the calculation. Although it is not doing the calculation in a smooth way, nevertheless, calculating like this, forward and backward, it eventually finishes the job. As with the particle in the gas, if we pull it very slightly, we lose very little energy, but it takes a long time to get to one side from the other.

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., 39, 40, 43 Bessel functions, 223 Beta decay, 192 Bethe, Hans, 11, 60–61, 64, 86, 190, 197–198, 235 Bets, 69 Big Bang, 199, 200 Biology, 99, 100, 101, 105, 123–124, 124–125, 126, 241. See also under Chemistry Black holes, 229(n) Bohr, Aage, 86, 87 Bohr, Niels, 86–88, 190, 203 Bongos, 191 Books of the world, 121–122 Bose-Einstein condensate, xvii Brains, 145, 194, 218, 222. See also Computers, analogy with brains Brass, 90 Brave New World (Huxley), 99 Bridgman, Percy, 118 British Museum Library, 121 Brownian motion, 38–39, 38(fig.), 42 Buddhism, 142 Cadmium, 74, 76 Calculus, 6–7, 195 California Institute of Technology (Caltech), 13, 191–192, 205–216, 226, 232–233 Caltech Cosmic Cube, 30 Cargo cults, 187, 242–243. See also Science, Cargo Cult Science Cathode ray oscilloscope, 120 Catholic Church, 7, 98, 111, 112–113 Censorship. See under Los Alamos Certainty. See Uncertainty Challenger. See Space Shuttle Challenger Chemistry and biology, 137, 138 chemical analysis/synthesis, 125, 137–138 chemical reactions, 131, 218 Chess, 48 chess game analogy, 13–14, 14–15 Chicago, 56–57 Children, 21–22, 145–146, 172 Christ, divinity of, 251, 254 Christie, Bob, 62, 73, 83 Communication, 113, 147 Communism, 251–252 Compton, 55, 56 Computers, 27–52, 126–129, 194 analogy with brains, 46–48 central processors, 29, 30–31 on Challenger Orbiter, 164–168 chips in, 28–29, 44 clock time vs. circuit time in, 35 debugging, 28 energy consumption of, 29, 32–37, 38, 42, 43, 44, 50–51 gates, reversible/irreversible, 39–40, 41(fig.), 43, 50.

pages: 287 words: 87,204

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Erwin Schrodinger and the Quantum Revolution
** by
John Gribbin

Albert Einstein, Albert Michelson, All science is either physics or stamp collecting, Arthur Eddington, British Empire, Brownian motion, double helix, Drosophila, Edmond Halley, Ernest Rutherford, Fellow of the Royal Society, Henri Poincaré, Isaac Newton, Johannes Kepler, John von Neumann, lateral thinking, Richard Feynman, Schrödinger's Cat, Solar eclipse in 1919, The Present Situation in Quantum Mechanics, the scientific method, trade route, upwardly mobile

He spent the winter of 1914–15 there, enjoying the beautiful mountain scenery while the conflict on the Western Front settled into the grim trench warfare for which the First World War is best remembered by Britain and the other Western participants. His next posting was to the equally peaceful, but less scenic, garrison town of Komárom, between Vienna and Budapest. There, Schrödinger wrote a paper about the behaviour of small particles being jostled in a fluid (gas or liquid) by the impact of molecules of the fluid. This is known as Brownian motion, after the Scottish physicist Robert Brown (1773–1858), who studied it in the 1820s. In 1905, Albert Einstein had proved that this erratic jittering can be explained statistically as caused by the constant but uneven bombardment that particles such as pollen grains receive from atoms and molecules, and thereby provided compelling evidence for the reality of atoms—just too late for this to be much comfort to Boltzmann.1 In a quite separate investigation, culminating in 1912, the American Robert Andrews Millikan (1868–1953)—who also, incidentally, coined the term “cosmic rays”—had managed to measure the charge on the electron by monitoring the way tiny electrically charged droplets of water or oil drift in an electric field.

…

In 1905, Albert Einstein had proved that this erratic jittering can be explained statistically as caused by the constant but uneven bombardment that particles such as pollen grains receive from atoms and molecules, and thereby provided compelling evidence for the reality of atoms—just too late for this to be much comfort to Boltzmann.1 In a quite separate investigation, culminating in 1912, the American Robert Andrews Millikan (1868–1953)—who also, incidentally, coined the term “cosmic rays”—had managed to measure the charge on the electron by monitoring the way tiny electrically charged droplets of water or oil drift in an electric field. These droplets are small enough to be affected by Brownian motion, and Schrödinger analysed statistically the importance of these effects in Millikan-type experiments. Nothing dramatic came out of the study, but it is important in the context of Schrödinger’s career because it was his first published foray into statistics, which would later loom large in his work. By the time this paper was published, the war, and Schrödinger, had both moved on. Italy was persuaded to join the Triple Entente with promises of large chunks of Austria, and declared war on 23 May 1915.

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.: Addison-Wesley, 1980) Zeilinger, Anton, Dance of the Photons (New York: Farrar, Strauss & Giroux, 2010) Index action at a distance Aharonov, Yakir Aigentler, Henriette von Alpbach American Philosophical Society Anderson, Carl Annalen der Physik Annales de physique anti-particles Arosa Arzberger, Hans Arzberger, Rhoda (née Bauer, aunt) Aspect, Alain atoms: Bohr model; Boltzmann’s work; concept; Copenhagen Interpretation; decoherence; Einstein’s work; entanglement experiments; “green pamphlet”; Mach’s view; Maxwell’s work; nuclear model; Planck’s work; Poincaré’s work; quantum chemistry; quantum computing; quantum physics; quantum spin of electron; quantum teleportation experiments; Rutherford’s work; Schrödinger’s work; structure Austria: Anschluss (1938); army; First World War and aftermath; International Atomic Energy Agency representation; Nazism; religion; Schrödinger’s flight from; Schrödinger’s return to; Second World War aftermath Austria-Hungary Austrian Empire Austrian Physical Society Baird, John Logie Ballot, Christoph Buys Bamberger, Emily (Minnie, née Bauer, aunt) Bamberger, Helga (cousin) Bamberger, Max Bär, Richard Bauer, Alexander (grandfather) Bauer, Alexander (great-grandfather) Bauer, Emily (Minnie, aunt), see Bamberger Bauer, Emily (Minnie, née Russell, grandmother) Bauer, Friedrich (Fritz) Bauer, Georgie, see Schrödinger Bauer, Johanna (Hansi), see Bohm Bauer, Josepha (née Wittmann-Denglass, great-grandmother) Bauer, Rhoda (aunt), see Arzberger BBC Becquerel, Henri Bell, John Bell’s inequality Bennett, Charles Berlin: Academy of Sciences; Kaiser Wilhelm Institute for Chemistry; Schrödinger’s departure; Schrödinger’s professorship; Schrödinger’s work; University of Bernstein, Jeremy Bertel, Annemarie (Anny), see Schrödinger Besso, Michele birds, vision Bitbol, Michel Blackett, Patrick Blair, Linda Bloch, Felix Bohm, David Bohm, Franz Bohm, Johanna (Hansi, née Bauer): escape from Austria to London; escape from Germany to London; marriage; memories of Schrödinger; pregnancy; relationship with Schrödinger; in Vienna Bohr, Niels: on collapse of wave function; on complementarity; Copenhagen Institute; Copenhagen Interpretation; Einstein’s views of his work; Festival; honours; influence; “Light and Life” lecture; model of the atom; Nobel Prize; quantization rules; relationship with Schrödinger; Schrödinger’s views of his work; work with Heisenberg Boltzmann, Ludwig: background; career; depression; education; on entropy; influence on Schrödinger; on international nature of physics; marriage; relationship with Mach; research; statistical approach; Stefan–Boltzmann Law of black body radiation; suicide; work on atoms; work on thermodynamics Born, Max: background and education; in Cambridge; career; on chance and probability; on Copenhagen school; on Dirac’s work; Edinburgh professorship; in Göttingen; Heisenberg’s studies; in Italy; matrix mechanics; Natural Philosophy of Cause and Chance; Nobel controversy; Nobel Prize; on quantum mechanics; quantum revolution; relationship with Schrödinger; retirement; sacked under Nazis; Schrödinger’s response to his work; statistics; on von Neumann’s work; work on wave function Bose, Satyendra Nath Bose–Einstein statistics bosons Bragg, Lawrence Bragg, William Braunizer, Andreas (grandson) Braunizer, Arnulf Braunizer, Ruth (née March, daughter): in Belgium; birth; birth of son; care of Arthur; in Dublin; in Graz; half-sisters; in Innsbruck; marriage; in Oxford; pregnancy; relationship with Anny; relationship with father; relationship with mother Brecht, Bertolt Breslau Bristol University Brown, Robert Browne, Monsignor Paddy Brownian motion Bunsen, Robert Cahill & Company California: Institute of Technology; University of Cambridge: Born in; Cavendish Laboratory; Heisenberg’s lectures; Maxwell at; Newton at; Philosophical Society; Schrödinger’s visits; Tarner Lectures Cambridge University Press (CUP) “Can Quantum Mechanical Description of Physical Reality Be Considered Complete?”(EPR paper) CERN Charles, Emperor Chemical and Engineering News Chemical–Physical Society Chicago chromosomes Clauser, John Clausius, Rudolf cloud chamber Cockcroft, John Cold War colour vision Columbia University Como conference (1927) complementarity Compton, Arthur Compton effect Condon, Edward Congress of Vienna (1913) Copenhagen, Niels Bohr Institute Copenhagen Interpretation; author’s view; Bell’s view; Bohm’s view; Born on; consensus view; Einstein’s view; origins; package; predictions; presentation; probability in; Schrödinger’s view Cosmic Code, The (Pagels) cosmic rays cosmology Cramer, John Crick, Francis cryptography Curie, Marie and Pierre Czernowitz D-Wave Systems Darwin, Charles Darwin, Charles (grandson of above) Davies, Paul Davy, Humphry de Broglie, Louis: background and education; Einstein’s view of his work; influence; pilot wave model; Solvay Congress; thesis de Broglie, Maurice De magnete (Gilbert) De motu corporum in gyrum (Newton) de Valera, Éamon (“Dev”): background and career; Dublin Institute for Advanced Studies; invitation to Schrödinger; Schrödinger’s departure; Schrödinger’s lectures de Valera, Sinéad (née Flanagan) Debye, Peter decoherence Delbrück, Max Descartes, René Deutsch, David Dewar, Katherine Mary Dieks, Dennis diffusion equation Dirac, Paul: appearance and character; in Cambridge; Dirac Equation; Directions in Physics; Dublin colloquium; education; Fermi–Dirac statistics; influence; Nobel Prize; Solvay Congress; transformation theory; view of interpretation; work on quantum mechanics Dirac Equation Directions in Physics (Dirac) DNA Dollfuss, Engelbert Doppler, Johann Christian Doppler effect Dora (cousin) double slit experiment Dublin: Austrian community; Institute for Advanced Studies (DIAS); Schrödinger in; Schrödinger “family life” in; Schrödinger’s arrival; Schrödinger’s departure; Trinity College (TCD); University College Eckart, Carl Eddington, Arthur Edinburgh University Ehrenfest, Paul Einstein, Albert: on “action at a distance”; annus mirabilis; Berlin professorship; Bose–Einstein statistics; Bose’s work; childhood; Congress of Vienna; Cramer’s work; on de Broglie’s work; on double slit experiment; education and career; EPR Paradox; experiences of anti-Semitism; experiences of Nazism; on Feynman’s work; general theory of relativity; influence on Heisenberg’s work; influence on Schrödinger’s work; on Mount Wilson experiment; Nobel Prize; at Princeton; relationship with Schrödinger; on Schrödinger; on Schrödinger’s cat; Solvay Congress; special theory of relativity; on underlying “reality”; view of chance and probability; view of Copenhagen Interpretation; work on Brownian motion; work on light quanta; work on quantum theory of radiation Ekert, Artur electromagnetic oscillators electromagnetism electron(s): Bohr’s work; bond; Born’s work; “collapse of the wave function”; Compton’s work; Copenhagen Interpretation; Copenhagen scientists’ work; de Broglie’s work; Dirac’s work; Einstein’s work; energy; entangled; Fermi–Dirac statistics; Feynman’s work; Heisenberg’s work; interaction between; Lenard’s work; measurement of charge on; Millikan’s work; negative; orbits; pilot wave model; quantum teleportation; quantum “transaction”; radiation resistance; Rutherford’s work; Schrödinger’s work; sharing of; Solvay Congress (1927); spin; “spooky action at a distance”; Thomson’s work; trajectory in cloud chamber; wave equation; waves and particles entanglement: decoherence; experimental confirmation of; FTL signalling; macroscopic; quantum computing; quantum cryptography; quantum teleportation; Rudolph’s work; Schrödinger’s work; term entropy EPR Paradox Epstein, Paul ETH (Eidgenössiche Technische Hochschule), see Zürich Ettinghausen, Andreas Everett, Hugh evolution Exner, Franz Faraday, Michael Farmelo, Graham faster-than-light (FTL) communication (signalling) Fermi, Enrico Fermi–Dirac statistics fermions Feynman, Richard First World War Forster family Fowler, Ralph Franklin, Rosalind Franz Ferdinand, Archduke Franz Josef, Emperor Fraunhofer, Josef von free will Fresnel, Augustin Friedman, Dennis Friedrich Wilhelm III, King of Prussia Frimmel, Franz Galileo Galilei gas in sealed box gases, kinetic theory Geiger, Hans genes: changes in; copying process; Delbrück’s work; DNA; Haldane’s suggestion; molecules; Schrödinger’s work Ghent, University of Gibbs, Willard Gilbert, William Gordon, George Göttingen gravity: Einstein’s work; Newton’s work; Schrödinger’s work Graz: Boltzmann at; Nazism; Schrödinger’s dismissal; Schrödinger’s lectures; Schrödinger’s professorship; Schrödinger’s research “green pamphlet” Greene, Blathnaid Nicolette (Schrödinger’s daughter) Greene, David Habicht, Conrad Habsburg family Haldane, J.

pages: 306 words: 82,765

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Skin in the Game: Hidden Asymmetries in Daily Life
** by
Nassim Nicholas Taleb

availability heuristic, Benoit Mandelbrot, Bernie Madoff, Black Swan, Brownian motion, Capital in the Twenty-First Century by Thomas Piketty, Cass Sunstein, cellular automata, Claude Shannon: information theory, cognitive dissonance, complexity theory, David Graeber, disintermediation, Donald Trump, Edward Thorp, equity premium, financial independence, information asymmetry, invisible hand, knowledge economy, loss aversion, mandelbrot fractal, mental accounting, microbiome, moral hazard, Murray Gell-Mann, offshore financial centre, p-value, Paul Samuelson, Ponzi scheme, price mechanism, principal–agent problem, Ralph Nader, random walk, rent-seeking, Richard Feynman, Richard Thaler, Ronald Coase, Ronald Reagan, Rory Sutherland, Silicon Valley, Steven Pinker, stochastic process, survivorship bias, The Nature of the Firm, transaction costs, urban planning, Yogi Berra

We can show (Briys and Taleb, in progress and private communication) the necessity of logarithmic transformation as simple ruin avoidance, which happens to be a special case of the HARA utility class. Adaptation of Theorem 1 to Brownian Motion The implications of simplified discussion do not change whether one uses richer models, such as a full stochastic process subjected to an absorbing barrier. And of course in a natural setting the eradication of all previous life can happen (i.e., Xt can take extreme negative value), not just a stopping condition. The Peters and Gell-Mann argument also cancels the so-called equity premium puzzle if you add fat tails (hence outcomes vastly more severe pushing some level equivalent to ruin) and absence of the fungibility of temporal and ensemble. There is no puzzle. The problem is invariant in real life if one uses a Brownian-motion-style stochastic process subjected to an absorbing barrier. In place of the simplified representation we would have, for an process subjected to L, an absorbing barrier from below, in the arithmetic version: or, for a geometric process: where Z is a random variable.

…

The Quarterly Journal of Economics 110(3): 551–584. ———, 2015. Capital in the Twenty-first Century. Cambridge, Mass.: Harvard University Press. Pinker, Steven, 2011. The Better Angels of Our Nature: Why Violence Has Declined. Penguin. Pitman, E. 1980. “Subexponential Distribution Functions.” Journal of the Australian Mathematical Society, Series A, 29(3): 337–347. Pitman, J. W., 1975. “One-Dimensional Brownian Motion and the Three-Dimensional Bessel Process.” Advances in Applied Probability 511–526. Pratt, J. W., R. Zeckhauser, and K. J. Arrow, 1985. Principals and Agents: The Structure of Business. Harvard Business Press. Prichard, H. A., 2002. “Duty and Ignorance of Fact.” In Moral Writings, ed. J. MacAdam. Oxford: Oxford University Press. Rank, Mark Robert, and Thomas Hirschl, 2015. “The Likelihood of Experiencing Relative Poverty Over the Life Course.”

…

Kelly and Thorp recovered the logarithm for maximal growth criterion as an optimal gambling strategy. Nothing to do with utility. Samuelson disses logarithm as aggressive, not realizing that semi-logarithm (or partial logarithm), i.e., on partial of wealth, can be done. From Menger to Arrow, via Chernoff and Samuelson, many in decision theory are shown to be making the mistake of ergodicity. Pitman in 1975 shows that a Brownian motion subjected to an absorbing barrier at 0, with censored absorbing paths, becomes a three-dimensional Bessel process. The drift of the surviving paths is which integrates to a logarithm. Peters and Gell-Mann recover the logarithm for ergodicity and, in addition, put the Kelly-Thorpe result on rigorous physical grounds. With Cirillo, this author (Taleb and Cirillo 2015) discovers the log as unique smooth transformation to create a dual of the distribution in order to remove one-tail compact support to allow the use of extreme value theory.

**
What We Cannot Know: Explorations at the Edge of Knowledge
** by
Marcus Du Sautoy

Albert Michelson, Andrew Wiles, Antoine Gombaud: Chevalier de Méré, Arthur Eddington, banking crisis, bet made by Stephen Hawking and Kip Thorne, Black Swan, Brownian motion, clockwork universe, cosmic microwave background, cosmological constant, dark matter, Dmitri Mendeleev, Edmond Halley, Edward Lorenz: Chaos theory, Ernest Rutherford, Georg Cantor, Hans Lippershey, Harvard Computers: women astronomers, Henri Poincaré, invention of the telescope, Isaac Newton, Johannes Kepler, Magellanic Cloud, mandelbrot fractal, MITM: man-in-the-middle, Murray Gell-Mann, music of the spheres, Necker cube, Paul Erdős, Pierre-Simon Laplace, Richard Feynman, Skype, Slavoj Žižek, Solar eclipse in 1919, stem cell, Stephen Hawking, technological singularity, Thales of Miletus, Turing test, wikimedia commons

It was a tragic end, not least because the most convincing evidence that he was right was just emerging. And it was one of the big names of physics who produced ideas that supported the atomistic view and were very hard to ignore. The work that Einstein and others did on Brownian motion would prove extremely difficult to explain for those who, like Mach, believed in a continuous view of the world. POLLEN PING-PONG Although conventional microscopes don’t allow one to see individual atoms, they did allow scientists in the nineteenth century to see the effect that these atoms were having on their surroundings. It’s called Brownian motion after Robert Brown, who in 1827 noticed the random behaviour of small particles of pollen floating on the surface of water. Since pollen was organic, Brown’s first thought was that it might be exhibiting signs of life as it jumped around the surface.

…

What if I try: particle in, particle out? Perhaps the particle nature of the outgoing electron is actually the key to how I should view the incoming electromagnetic radiation. This was Einstein’s great paradigm shift, which he made in 1905, the year many call his annus mirabilis. It is also the year he came up with the special theory of relativity that I tackle in later Edges, and the theory of Brownian motion, which provided the most convincing support for matter made from atoms described in the previous Edge. Einstein suggested that you should think of electromagnetic radiation or light not as a wave but like a machine-gun fire of tiny billiard balls, just as Newton had suggested. The energy of each individual particle depends on the frequency of the radiation. With this new idea we have a model that can perfectly describe what scientists were experiencing in the lab.

…

Acta Mathematica (Royal Swedish Academy of Science journal) 39 aeons 292–6 ageing 5, 8, 258, 269, 318 al-Sufi, Abd al-Rahman 203 algebra 89, 372–3, 374 Alhazen: Book of Optics 198 Allen Institute for Brain Science 347, 348 Allen, Paul G. 347 Allen, Woody 303 Alpha Centauri 188 alpha particles 98–100, 119, 131, 133, 166–7, 171, 172, 173, 176 alpha waves 314–16 American Association for the Advancement of Science 46 Amiot, Lawrence 280 anaesthesia 334–5, 345 Anderson, Carl 104 Andromeda nebula 203, 204 animals: consciousness and 317–19, 322, 325; evolution and 56, 57, 61; mathematics of animal kingdom 393–4; population dynamics 48–51; species classification 107 Aniston, Jennifer 4, 324–7, 347, 359 antimatter 104 Apple 321, 322, 355 Aquinas, Thomas 297, 390–1, 406 Arago, Francois 197 Archimedes 86 Aristarchus of Samos 189–90 Aristotle 22, 32, 82, 86, 87, 95, 101, 198, 306, 368, 369, 390; Metaphysics 1, 2 Armstrong, Karen 181, 410 artificial intelligence 8, 281, 303–4, 313, 317, 322, 337–9, 345–6, 417 asteroids 2, 182 Asteroids (game) 205–6, 207, 209 astronomy 10, 40, 63, 187–211, 213–16, 218, 222, 223, 236–7, 238–9, 271, 280, 296, 413 see also under individual area of astronomy asymmetrical twins 269–72, 283 atom 78–9, 80; atomic number 90; Brownian motion and 92, 93–5; charge and 96, 97, 98, 99–101, 104, 105, 106, 107, 108, 109, 110–11, 117, 118, 119, 125, 136, 142, 230, 356; dice and 64, 78, 79, 80, 91–2, 94, 103; discovery of 79–80, 95–101, 103, 104; discovery of smaller constituents that make up 95–127; electron microscopes and 78, 79; experimental justification for atomistic view of the matter, first 80, 89–92; LHC and 3–4, 98; measuring time and 123, 249, 251–2, 252, 254, 269; periodic table and 86–92; quantum microscopes and 79; strangeness and 108, 109–11, 115–16; symmetry and 111–17, 120, 121, 125; theoretical atomistic view of matter, history of 78–88, 93 atomic clock 123, 252, 254, 269 axioms 52, 367–8, 371, 377, 378–9, 383, 384–6, 387, 388, 397–8, 400, 401, 402, 403, 404, 413 Babylonians 83, 251, 366, 368, 417 Bach 77, 121, 304 Bacon, Francis 399 banking, chaos theory and 54 Barbour, Julian: The End of Time 299–300 Barrow, Professor John 236–40, 242 baryons 107, 108, 109, 110, 115, 119 Beit Guvrin, Israel, archaeological dig in 20–1 Bell, John/Bell’s theorem 170, 171, 173, 174 Berkeley, Bishop: The Analyst 87 Berger, Hans 314 Berlin Academy 382 Berlin Observatory 197 Bessel, Friedrich 201 Besso, Michele 296–7 beta particles 98, 131 Bible 192 Big Bang 237, 377; cosmic microwave background and 226, 228, 289; as creation myth 235; emergence of consciousness and 319, 377, 407; infinite universe and 219–21; singularity 278, 281–2, 284; testing conditions of 234; time before, existence of 7, 9, 248–9, 262–7, 284, 290, 291–6, 407 biology 237, 405, 416; animal see animals; breakthroughs in 4; consciousness see consciousness; emergence concept and 332; evolution of life and 56–62, 230; gene therapy 416; hypothetical theory and 405; limitations of our 406; telomeres, discovery of 5; unknowns in 7–8 Birch–Swinnerton-Dyer conjecture 376 black holes: Big Bang and 293–4; computer simulation of 352; cosmic microwave background and 293–4; Cygnus X–1 276–7; discovery of 274–6; electron creation of tiny, possibility of 126; entropy and 285–7, 288, 290, 293; future of universe and 291, 293; Hawking radiation and 182, 288–90; infinite density and 277–8; information lost inside of 167, 284–5, 287, 288, 289–90, 293, 355; ‘no-hair theorem’ 285; second law of thermodynamics and 285–6, 290; singularity 278, 279, 280, 281–2; time inside 282–4 black swan 239–40 Blair, Tony 52 Bohr, Niels 103, 123, 131, 159, 178, 418 Bois-Reymond, Emil du 382, 383 Boisbaudran, Lecoq de 90–1 Boltzmann, Ludwig 92 Bombelli, Rafael 372 Borges, Jorge Luis: The Library of Babel 187 bottom quark 120, 121 Boyle, Robert 86; The Sceptical Chymist 86–7 Bradwardine, Thomas 391–2 Brady, Nicholas: ‘Ode to Saint Cecilia’ 88 Brahmagupta 371, 372 brain: alpha waves and 314–16; Alzheimer’s disease and 313–14; animal 317–19; artificial 351–3; Broca area 308, 352; cells, different types of 348; cerebellum 306, 307, 344; cerebrum 306; consciousness and see consciousness; corpus callosum/corpus callosotomy 309–11; EEG scanner and 305, 314–16, 323, 340; fMRI scanner and 4, 305, 316, 323, 333–9, 350, 351, 354, 357; free will and 335–9; integrated information theory (IIT) and 342–5; left side of 308, 310; limits of understanding 5, 9, 376, 377, 387, 408–9, 415, 416; mind-body problem and 330–2; music and see music; neurons and 4, 5, 258, 259, 309, 311–14, 323–9, 340, 341, 342, 343–6, 347, 348, 349, 350, 351, 353, 359, 376–7; out-of-body experiences and 328–30; pineal gland 307; right side of 308–9, 310; self-recognition test and 317–19; synapses 5, 313, 314, 324, 376; two hemispheres of 308–11; unconscious 315, 336–7, 339–41; vegetative state/locked in and 333–5; ventricles 306–7, 308; visual data processing 320–30 Braudel, Fernand 54–5 British Association of Science 10 Broca, Paul 308 Bronowski, Jacob: Ascent of Man 2, 420 Brown, Robert/Brownian motion 92, 93, 141 Bruno, Giordano: On the Infinite Universe and Worlds 192, 393 Buddhism 113, 354 C. elegans worm 4, 345, 349 caesium fountain 252 calculus 30–2, 33, 34, 36, 87, 88, 369 Caltech 104, 105–6, 115, 175, 289, 321, 323, 324, 347 Cambrian period 58 Cambridge University 30, 69, 174–5, 179, 236, 275, 334 cancer 8, 204 Candelas, Philip 155 Cantor, Georg 65–6, 393–402, 406 Cardano, Girolamo 23–4, 25; Liber de Ludo Aleae 24 Carroll, Lewis: Alice’s Adventures in Wonderland 159 Carroll, Sean 236 cascade particles 110 Cassini, Giovanni 199 Castro, Patricia 226 cathode rays 96 Catholic Church 192, 235 cello 77, 78, 79, 80–1, 82, 90, 121, 122, 126, 127, 137, 138, 139, 140, 191, 225, 285, 304, 305, 308, 313, 314, 315 celluloid 91 Cepheid star 202–3, 204 Chadwick, James 100–1 Chalmers, David 347 Chandrasekhar, Subrahmanyan 275 Chaos 67 chaos theory 39–41, 43–53, 54, 55, 56, 58–9, 60, 61, 62–4, 68–72, 157, 168, 178, 179, 242, 402–3, 408, 419 charm quark 120, 121 China 15, 344, 371 chemistry: atomistic view of matter and chemical elements 81, 82, 86–8, 89–92 see also periodic table; brain see brain; breakthroughs in 4; elements and 81–2; emergence concept and 332; Greek, ancient 81–2 Chomsky, Noam 388 Christianity 13, 22, 69, 240, 390–1, 398 see also God and religion Church, Alonso 414 Cicero 188 Clairaut, Alexis 29 Cleverbot (app) 303, 313, 317, 332 climate change 6, 53 cloud chambers 100, 104–6 Cohen, Paul 401–2 Compton wavelength 167 computers: chaos theory modelling on 61–2, 64; consciousness/artificial intelligence and 8, 281, 303–4, 313, 317, 322, 325, 336, 337–9, 345–6, 349, 351, 352, 355, 417; growth in power of 8, 53, 281 Comte, Auguste 10, 202, 243, 347, 409 Connes, Alain 300 ‘connectome’ 345 consciousness 303–60, 403; anaesthesia and 334–5, 345; animals and 317–20, 322; brain as location of 306–11; brain cell types and 348; brain switching between perceptions and 320–3; Buddhism and 354; building an artificial brain that has 351–3; Chinese Room experiment and 338–9; Cleverbot app and 303–4, 313, 315–16, 317, 332, 338; computers/machines and 8, 303–4, 313, 315–16, 317, 322, 337–9, 345–6; ‘connectome’ and 345; two sides of brain and 308–11; death and 353–5; Descartes and 304, 350, 359; different qualities of 305–6; EEG/fMRI and 305, 314–16, 323, 333–9, 340, 350, 351, 354, 356–7; emergence in child 319; first emergence in universe 319–20; focus and 327; free will and 334–5; God concept and 319–20, 348–9; hard problem of 304–6, 347, 360; Human Brain Project and 352; humanities and expression of 419; integrated information theory (IIT) and 341, 342–5, 346, 347, 349, 350, 352, 353–4; internet and 345–6; language and 356–8; mathematical formula for 341, 342–5, 346, 347, 349, 352, 353–4; mind-body problem and 330–2; mirror recognition test and 317–19; mysterianism and 349–50, 351; Necker cube and 321, 323; neurons and 311–14, 323–9, 340, 341, 342, 343–6, 347, 348, 349, 350, 351, 353, 359, 376–7; out-of-body experiences and 328–30; perceptronium and 356; qualia and 325, 350; sleep and 339–41, 342, 343; synesthesia and 305, 325–6; thalamocortical system and 343–4; transcranial magnetic stimulation (TMS) and 339–41; unconsciousness and brain activity 334–7, 339–41, 342–3; unknowable nature of 347, 349–50, 353 355–60, 407–8; vegetative state/locked in and 333–4; virtual reality goggles and 330; vision and 322–3; wave function and 156; where is?

pages: 855 words: 178,507

**
The Information: A History, a Theory, a Flood
** by
James Gleick

Ada Lovelace, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Albert Einstein, AltaVista, bank run, bioinformatics, Brownian motion, butterfly effect, citation needed, Claude Shannon: information theory, clockwork universe, computer age, conceptual framework, crowdsourcing, death of newspapers, discovery of DNA, Donald Knuth, double helix, Douglas Hofstadter, en.wikipedia.org, Eratosthenes, Fellow of the Royal Society, Gödel, Escher, Bach, Henri Poincaré, Honoré de Balzac, index card, informal economy, information retrieval, invention of the printing press, invention of writing, Isaac Newton, Jacquard loom, Jaron Lanier, jimmy wales, Johannes Kepler, John von Neumann, Joseph-Marie Jacquard, lifelogging, Louis Daguerre, Marshall McLuhan, Menlo Park, microbiome, Milgram experiment, Network effects, New Journalism, Norbert Wiener, Norman Macrae, On the Economy of Machinery and Manufactures, PageRank, pattern recognition, phenotype, Pierre-Simon Laplace, pre–internet, Ralph Waldo Emerson, RAND corporation, reversible computing, Richard Feynman, Rubik’s Cube, Simon Singh, Socratic dialogue, Stephen Hawking, Steven Pinker, stochastic process, talking drums, the High Line, The Wisdom of Crowds, transcontinental railway, Turing machine, Turing test, women in the workforce

NORBERT WIENER (1956) (Illustration credit 8.1) He was short and rotund, with heavy glasses and a Mephistophelian goatee. Where Shannon’s fire-control work drilled down to the signal amid the noise, Wiener stayed with the noise: swarming fluctuations in the radar receiver, unpredictable deviations in flight paths. The noise behaved statistically, he understood, like Brownian motion, the “extremely lively and wholly haphazard movement” that van Leeuwenhoek had observed through his microscope in the seventeenth century. Wiener had undertaken a thoroughgoing mathematical treatment of Brownian motion in the 1920s. The very discontinuity appealed to him—not just the particle trajectories but the mathematical functions, too, seemed to misbehave. This was, as he wrote, discrete chaos, a term that would not be well understood for several generations. On the fire-control project, where Shannon made a modest contribution to the Bell Labs team, Wiener and his colleague Julian Bigelow produced a legendary 120-page monograph, classified and known to the several dozen people allowed to see it as the Yellow Peril because of the color of its binder and the difficulty of its treatment.

…

.… The night was noisier than the day, and at the ghostly hour of midnight, for what strange reasons no one knows, the babel was at its height.♦ But engineers could now see the noise on their oscilloscopes, interfering with and degrading their clean waveforms, and naturally they wanted to measure it, even if there was something quixotic about measuring a nuisance so random and ghostly. There was a way, in fact, and Albert Einstein had shown what it was. In 1905, his finest year, Einstein published a paper on Brownian motion, the random, jittery motion of tiny particles suspended in a fluid. Antony van Leeuwenhoek had discovered it with his early microscope, and the phenomenon was named after Robert Brown, the Scottish botanist who studied it carefully in 1827: first pollen in water, then soot and powdered rock. Brown convinced himself that these particles were not alive—they were not animalcules—yet they would not sit still.

…

This idea is carried still further in certain commercial codes where common words and phrases are represented by four- or five-letter code groups with a considerable saving in average time. The standardized greeting and anniversary telegrams now in use extend this to the point of encoding a sentence or two into a relatively short sequence of numbers.♦ To illuminate the structure of the message Shannon turned to some methodology and language from the physics of stochastic processes, from Brownian motion to stellar dynamics. (He cited a landmark 1943 paper by the astrophysicist Subrahmanyan Chandrasekhar in Reviews of Modern Physics.♦) A stochastic process is neither deterministic (the next event can be calculated with certainty) nor random (the next event is totally free). It is governed by a set of probabilities. Each event has a probability that depends on the state of the system and perhaps also on its previous history.

**
Mathematics for Finance: An Introduction to Financial Engineering
** by
Marek Capinski,
Tomasz Zastawniak

Black-Scholes formula, Brownian motion, capital asset pricing model, cellular automata, delta neutral, discounted cash flows, discrete time, diversified portfolio, fixed income, interest rate derivative, interest rate swap, locking in a profit, London Interbank Offered Rate, margin call, martingale, quantitative trading / quantitative ﬁnance, random walk, short selling, stochastic process, time value of money, transaction costs, value at risk, Wiener process, zero-coupon bond

N tN As N → ∞, we have tN → t and N tN → ∞, so that wN (tN ) → W (t) √ in distribution, where W (t) = tX. The last equality means that W (t) is normally distributed with mean 0 and variance t. This argument, based on the Central Limit Theorem, works for any single ﬁxed time t > 0. It is possible to extend the result to obtain a limit for all times t ≥ 0 simultaneously, but this is beyond the scope of this book. The limit W (t) is called the Wiener process (or Brownian motion). It inherits many of the properties of the random walk, for example: 1. W (0) = 0, which corresponds to wN (0) = 0. 2. E(W (t)) = 0, corresponding to E(wN (t)) = 0 (see the solution of Exercise 3.25). 3. Var(W (t)) = t, with the discrete counterpart Var(wN (t)) = t (see the solution of Exercise 3.25). 4. The increments W (t3 ) − W (t2 ) and W (t2 ) − W (t1 ) are independent for 0 ≤ t1 ≤ t2 ≤ t3 ; so are the increments wN (t3 ) − wN (t2 ) and wN (t2 ) − wN (t1 ). 2 See, for example, Capiński and Zastawniak (2001). 70 Mathematics for Finance 5.

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Our treatment of continuous time is a compromise lacking full mathematical rigour, which would require a systematic study of Stochastic Calculus, a topic 186 Mathematics for Finance treated in detail in more advanced texts. In place of this, we shall exploit an analogy with the discrete time case. As a starting point we take the continuous time model of stock prices developed in Chapter 3 as a limit of suitably scaled binomial models with time steps going to zero. In the resulting continuous time model the stock price is given by (8.5) S(t) = S(0)emt+σW (t) , where W (t) is the standard Wiener process (Brownian motion), see Section 3.3.2. This means, in particular, that S(t) has the log normal distribution. Consider a European option on the stock expiring at time T with payoﬀ f (S(T )). As in the discrete-time case, see Theorem 8.4, the time 0 price D(0) of the option ought to be equal to the expectation of the discounted payoﬀ e−rT f (S(T )), (8.6) D(0) = E∗ e−rT f (S(T )) , under a risk-neutral probability P∗ that turns the discounted stock price process e−rt S(t) into a martingale.

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Glossary of Symbols A B β c C C CA CE CE Cov delta div div0 D D DA E E∗ f F gamma Φ k K i m ﬁxed income (risk free) security price; money market account bond price beta factor covariance call price; coupon value covariance matrix American call price European call price discounted European call price covariance Greek parameter delta dividend present value of dividends derivative security price; duration discounted derivative security price price of an American type derivative security expectation risk-neutral expectation futures price; payoﬀ of an option; forward rate forward price; future value; face value Greek parameter gamma cumulative binomial distribution logarithmic return return coupon rate compounding frequency; expected logarithmic return 305 306 Mathematics for Finance M m µ N N k ω Ω p p∗ P PA PE PE PA r rdiv re rF rho ρ S S σ t T τ theta u V Var VaR vega w w W x X y z market portfolio expected returns as a row matrix expected return cumulative normal distribution the number of k-element combinations out of N elements scenario probability space branching probability in a binomial tree risk-neutral probability put price; principal American put price European put price discounted European put price present value factor of an annuity interest rate dividend yield eﬀective rate risk-free return Greek parameter rho correlation risky security (stock) price discounted risky security (stock) price standard deviation; risk; volatility current time maturity time; expiry time; exercise time; delivery time time step Greek parameter theta row matrix with all entries 1 portfolio value; forward contract value, futures contract value variance value at risk Greek parameter vega symmetric random walk; weights in a portfolio weights in a portfolio as a row matrix Wiener process, Brownian motion position in a risky security strike price position in a ﬁxed income (risk free) security; yield of a bond position in a derivative security Index admissible – portfolio 5 – strategy 79, 88 American – call option 147 – derivative security – put option 147 amortised loan 30 annuity 29 arbitrage 7 at the money 169 attainable – portfolio 107 – set 107 183 basis – of a forward contract 128 – of a futures contract 140 basis point 218 bear spread 208 beta factor 121 binomial – distribution 57, 180 – tree model 7, 55, 81, 174, 238 Black–Derman–Toy model 260 Black–Scholes – equation 198 – formula 188 bond – at par 42, 249 – callable 255 – face value 39 – ﬁxed-coupon 255 – ﬂoating-coupon 255 – maturity date 39 – stripped 230 – unit 39 – with coupons 41 – zero-coupon 39 Brownian motion 69 bull spread 208 butterﬂy 208 – reversed 209 call option 13, 181 – American 147 – European 147, 188 callable bond 255 cap 258 Capital Asset Pricing Model 118 capital market line 118 caplet 258 CAPM 118 Central Limit Theorem 70 characteristic line 120 compounding – continuous 32 – discrete 25 – equivalent 36 – periodic 25 – preferable 36 conditional expectation 62 contingent claim 18, 85, 148 – American 183 – European 173 continuous compounding 32 continuous time limit 66 correlation coeﬃcient 99 coupon bond 41 coupon rate 249 307 308 covariance matrix 107 Cox–Ingersoll–Ross model 260 Cox–Ross–Rubinstein formula 181 cum-dividend price 292 delta 174, 192, 193, 197 delta hedging 192 delta neutral portfolio 192 delta-gamma hedging 199 delta-gamma neutral portfolio 198 delta-vega hedging 200 delta-vega neutral portfolio 198 derivative security 18, 85, 253 – American 183 – European 173 discount factor 24, 27, 33 discounted stock price 63 discounted value 24, 27 discrete compounding 25 distribution – binomial 57, 180 – log normal 71, 186 – normal 70, 186 diversiﬁable risk 122 dividend yield 131 divisibility 4, 74, 76, 87 duration 222 dynamic hedging 226 eﬀective rate 36 eﬃcient – frontier 115 – portfolio 115 equivalent compounding 36 European – call option 147, 181, 188 – derivative security 173 – put option 147, 181, 189 ex-coupon price 248 ex-dividend price 292 exercise – price 13, 147 – time 13, 147 expected return 10, 53, 97, 108 expiry time 147 face value 39 ﬁxed interest 255 ﬁxed-coupon bond 255 ﬂat term structure 229 ﬂoating interest 255 ﬂoating-coupon bond 255 ﬂoor 259 ﬂoorlet 259 Mathematics for Finance forward – contract 11, 125 – price 11, 125 – rate 233 fundamental theorem of asset pricing 83, 88 future value 22, 25 futures – contract 134 – price 134 gamma 197 Girsanov theorem 187 Greek parameters 197 growth factor 22, 25, 32 Heath–Jarrow–Morton model hedging – delta 192 – delta-gamma 199 – delta-vega 200 – dynamic 226 in the money 169 initial – forward rate 232 – margin 135 – term structure 229 instantaneous forward rate interest – compounded 25, 32 – ﬁxed 255 – ﬂoating 255 – simple 22 – variable 255 interest rate 22 interest rate option 254 interest rate swap 255 261 233 LIBID 232 LIBOR 232 line of best ﬁt 120 liquidity 4, 74, 77, 87 log normal distribution 71, 186 logarithmic return 34, 52 long forward position 11, 125 maintenance margin 135 margin call 135 market portfolio 119 market price of risk 212 marking to market 134 Markowitz bullet 113 martingale 63, 83 Index 309 martingale probability 63, 250 maturity date 39 minimum variance – line 109 – portfolio 108 money market 43, 235 no-arbitrage principle 7, 79, 88 normal distribution 70, 186 option – American 183 – at the money 169 – call 13, 147, 181, 188 – European 173, 181 – in the money 169 – interest rate 254 – intrinsic value 169 – out of the money 169 – payoﬀ 173 – put 18, 147, 181, 189 – time value 170 out of the money 169 par, bond trading at 42, 249 payoﬀ 148, 173 periodic compounding 25 perpetuity 24, 30 portfolio 76, 87 – admissible 5 – attainable 107 – delta neutral 192 – delta-gamma neutral 198 – delta-vega neutral 198 – expected return 108 – market 119 – variance 108 – vega neutral 197 positive part 148 predictable strategy 77, 88 preferable compounding 36 present value 24, 27 principal 22 put option 18, 181 – American 147 – European 147, 189 put-call parity 150 – estimates 153 random interest rates random walk 67 rate – coupon 249 – eﬀective 36 237 – forward 233 – – initial 232 – – instantaneous 233 – of interest 22 – of return 1, 49 – spot 229 regression line 120 residual random variable 121 residual variance 122 return 1, 49 – expected 53 – including dividends 50 – logarithmic 34, 52 reversed butterﬂy 209 rho 197 risk 10, 91 – diversiﬁable 122 – market price of 212 – systematic 122 – undiversiﬁable 122 risk premium 119, 123 risk-neutral – expectation 60, 83 – market 60 – probability 60, 83, 250 scenario 47 security market line 123 self-ﬁnancing strategy 76, 88 short forward position 11, 125 short rate 235 short selling 5, 74, 77, 87 simple interest 22 spot rate 229 Standard and Poor Index 141 state 238 stochastic calculus 71, 185 stochastic diﬀerential equation 71 stock index 141 stock price 47 strategy 76, 87 – admissible 79, 88 – predictable 77, 88 – self-ﬁnancing 76, 88 – value of 76, 87 strike price 13, 147 stripped bond 230 swap 256 swaption 258 systematic risk 122 term structure 229 theta 197 time value of money 21 310 trinomial tree model Mathematics for Finance 64 underlying 85, 147 undiversiﬁable risk 122 unit bond 39 value at risk 202 value of a portfolio 2 value of a strategy 76, 87 VaR 202 variable interest 255 Vasiček model 260 vega 197 vega neutral portfolio volatility 71 weights in a portfolio Wiener process 69 yield 216 yield to maturity 229 zero-coupon bond 39 197 94

pages: 239 words: 69,496

**
The Wisdom of Finance: Discovering Humanity in the World of Risk and Return
** by
Mihir Desai

activist fund / activist shareholder / activist investor, Albert Einstein, Andrei Shleifer, assortative mating, Benoit Mandelbrot, Brownian motion, capital asset pricing model, carried interest, Charles Lindbergh, collective bargaining, corporate governance, corporate raider, discounted cash flows, diversified portfolio, Eugene Fama: efficient market hypothesis, financial innovation, follow your passion, George Akerlof, Gordon Gekko, greed is good, housing crisis, income inequality, information asymmetry, Isaac Newton, Jony Ive, Kenneth Rogoff, longitudinal study, Louis Bachelier, moral hazard, Myron Scholes, new economy, out of africa, Paul Samuelson, Pierre-Simon Laplace, principal–agent problem, Ralph Waldo Emerson, random walk, risk/return, Robert Shiller, Robert Shiller, Ronald Coase, Silicon Valley, Steve Jobs, Thales and the olive presses, Thales of Miletus, The Market for Lemons, The Nature of the Firm, The Wealth of Nations by Adam Smith, Tim Cook: Apple, transaction costs, zero-sum game

As he watched pollen emit particles in water, these particles seemed to move about randomly. Why and how were they moving? Soot particles did the same thing, making it clear that the pollen particles weren’t autonomously doing something. The conventional history of subsequent intellectual developments goes like this: in his annus mirabilis of 1905, when he produced four remarkable breakthroughs, Albert Einstein provided the first understanding of the mechanisms of so-called Brownian motion. He demonstrated that many processes that seem continuous (like the motion of dust or pollen) are in fact the product of many discrete particles moving about. In other words, the pollen particles were moving around in a continuous way because they were reacting to tiny water molecules that were bumping them at random. This foundational idea transformed physics by demonstrating the presence of atoms and also provided the machinery to mathematically describe all kinds of seemingly random processes, ultimately giving rise to quantum mechanics.

…

As such, the idea that finance, a study of markets and inherently social phenomena, lost its way by aping physics, a “hard” science of precision, is plain wrong. Instead, as philosopher and historian Jim Holt has described, “Here, then, is the correct chronology. A theory is proposed to explain a mysterious social institution (the Paris Bourse). It is then used to resolve a mid-level mystery in physics (Brownian motion). Finally, it clears up an even deeper mystery in physics (quantum behavior). The implication is plain: Market weirdness explains quantum weirdness, not the other way around. Think of it this way: If Isaac Newton had worked at Goldman Sachs instead of sitting under an apple tree, he would have discovered the Heisenberg uncertainty principle.” Aside from an interesting reversal of conventional wisdom, the story of Bachelier’s discovery is also the story of the two most important risk management strategies—options and diversification.

…

., 123 Berryman, John, 33 Bessemer Venture Partners, 147 beta. See capital asset pricing model Bewkes, Jeff, 108 Bhagavad Gita, 155 Big Short, The (film), 97 Book of Matthew, 60 Brooks, Mel, 8, 75, 91–96 Critic, The (film), 93 relationship with Anne Bancroft, 95–96 relationship with Gene Wilder, 94 relationship with mother, 93 relationship with Sid Caesar, 94 Brown, Robert, Brownian motion, 38–40 Buck v. Bell (1927), 21 Buffett, Warren, 22 Burroughs, John, 117 Byrne, David, 13–14 C capital asset pricing model, xi, 53–56 advertising company betas, 53–54 gold, 54–55 high-beta and low-beta assets, 53–56 insurance, 54–55 LinkedIn relationships vs. friendship vs. unconditional love, 55–56 negative betas, 54–55 Case, Steve, 108, 109, 112 Cather, Willa, 9, 170, 172, 174 Charles, Ray, 99 Chaucer, Geoffrey, 18, 74 choix du roi, 104 Coase, Ronald, 115 Code of Justinian, Lex Rhodia, 23 commitments, 6, 154–56, 159–60 Confusion de Confusiones (de la Vega), 5, 43–44 Consilience (Wilson), 177 Cook, Tim, 77, 79, 80, 83 corporate finance, 7–9 corporate governance misaligned incentives, 80, 81 stock-based compensation, 81 Corrêa da Serra, José, 140 Cosmopolis (DeLillo), 165 Costa, Dora, 30 Crews, Frederick, 94 Crossroads of Should and Must, The (Luna), 90–92 Curry, Stephen, 51 D Davies, Owen, 25 Dead Poets Society (film), 17 debt overhang, 132–35 “Defence of Usury” (Bentham), 121 de la Vega, Joseph.

pages: 312 words: 35,664

**
The Mathematics of Banking and Finance
** by
Dennis W. Cox,
Michael A. A. Cox

barriers to entry, Brownian motion, call centre, correlation coefficient, fixed income, G4S, inventory management, iterative process, linear programming, meta analysis, meta-analysis, pattern recognition, random walk, traveling salesman, value at risk

Further, a 2 is equally likely to appear on any subsequent roll of the dice. 4.3 ESTIMATION OF PROBABILITIES There are a number of ways in which you can arrive at an estimate of Prob(A) for the event A. Three possible approaches are: r A subjective approach, or ‘guess work’, which is used when an experiment cannot be easily r repeated, even conceptually. Typical examples of this include horse racing and Brownian motion. Brownian motion represents the random motion of small particles suspended in a gas or liquid and is seen, for example, in the random walk pattern of a drunken man. The classical approach, which is usually adopted if all sample points are equally likely (as is the case in the rolling of a dice as discussed above). The probability may be measured with certainty by analysing the event. Using the same mathematical notation, a mathematical definition of this is: Prob(A) = Number of events classifiable as A Total number of possible events A typical example of such a probability is a lottery.

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Index a notation 103–4, 107–20, 135–47 linear regression 103–4, 107–20 slope significance test 112–20 variance 112 abscissa see horizontal axis absolute value, notation 282–4 accuracy and reliability, data 17, 47 adaptive resonance theory 275 addition, mathematical notation 279 addition of normal variables, normal distribution 70 addition rule, probability theory 24–5 additional variables, linear programming 167–70 adjusted cash flows, concepts 228–9 adjusted discount rates, concepts 228–9 Advanced Measurement Approach (AMA) 271 advertising allocation, linear programming 154–7 air-conditioning units 182–5 algorithms, neural networks 275–6 alternatives, decisions 191–4 AMA see Advanced Measurement Approach analysis data 47–52, 129–47, 271–4 Latin squares 131–2, 143–7 linear regression 110–20 projects 190–2, 219–25, 228–34 randomised block design 129–35 sampling 47–52, 129–47 scenario analysis 40, 193–4, 271–4 trends 235–47 two-way classification 135–47 variance 110–20, 121–7 anonimised databases, scenario analysis 273–4 ANOVA (analysis of variance) concepts 110–20, 121–7, 134–47 examples 110–11, 123–7, 134–40 formal background 121–2 linear regression 110–20 randomised block design 134–5, 141–3 tables 110–11, 121–3, 134–47 two-way classification 136–7 appendix 279–84 arithmetic mean, concepts 37–45, 59–60, 65–6, 67–74, 75–81 assets classes 149–57 reliability 17, 47, 215–18, 249–60 replacement of assets 215–18, 249–60 asymptotic distributions 262 ATMs 60 averages see also mean; median; mode concepts 37–9 b notation 103–4, 107–20, 132–5 linear regression 103–4, 107–20 variance 112 back propagation, neural networks 275–7 backwards recursion 179–87 balance sheets, stock 195 bank cashier problem, Monte Carlo simulation 209–12 Bank for International Settlements (BIS) 267–9, 271 banks Basel Accord 262, 267–9, 271 failures 58 loss data 267–9, 271–4 modelling 75–81, 85, 97, 267–9, 271–4 profitable loans 159–66 bar charts comparative data 10–12 concepts 7–12, 54, 56, 59, 205–6, 232–3 discrete data 7–12 examples 9–12, 205–6, 232–3 286 Index bar charts (cont.) narrative explanations 10 relative frequencies 8–12 rules 8–9 uses 7–12, 205–6, 232–3 base rates, trends 240 Basel Accord 262, 267–9, 271 bathtub curves, reliability concepts 249–51 Bayes’theorem, probability theory 27–30, 31 bell-shaped normal distribution see normal distribution bi-directional associative memory 275 bias 1, 17, 47–50, 51–2, 97, 129–35 randomised block design 129–35 sampling 17, 47–50, 51–2, 97, 129–35 skewness 41–5 binomial distribution concepts 55–8, 61–5, 71–2, 98–9, 231–2 examples 56–8, 61–5, 71–2, 98–9 net present value (NPV) 231–2 normal distribution 71–2 Pascal’s triangle 56–7 uses 55, 57, 61–5, 71–2, 98–9, 231–2 BIS see Bank for International Settlements boards of directors 240–1 break-even analysis, concepts 229–30 Brownian motion 22 see also random walks budgets 149–57 calculators, log functions 20, 61 capital Basel Accord 262, 267–9, 271 cost of capital 219–25, 229–30 cash flows adjusted cash flows 228–9 future cash flows 219–25, 227–34, 240–1 net present value (NPV) 219–22, 228–9, 231–2 standard deviation 232–4 central limit theorem concepts 70, 75 examples 70 chi-squared test concepts 83–4, 85, 89, 91–5 contingency tables 92–5 examples 83–4, 85, 89, 91–2 goodness of fit test 91–5 multi-way tables 94–5 tables 84, 91 Chu Shi-Chieh’s Ssu Yuan Y Chien 56 circles, tree diagrams 30–5 class intervals concepts 13–20, 44–5, 63–4, 241–7 histograms 13–20, 44–5 mean calculations 44–5 mid-points 44–5, 241–7 notation 13–14, 20 Sturges’s formula 20 variance calculations 44–5 classical approach, probability theory 22, 27 cluster sampling 50 coin-tossing examples, probability theory 21–3, 53–4 collection techniques, data 17, 47–52, 129–47 colours, graphical presentational approaches 9 combination, probability distribution (density) functions 54–8 common logarithm (base 10) 20 communications, decisions 189–90 comparative data, bar charts 10–12 comparative histograms see also histograms examples 14–19 completed goods 195 see also stock . . . conditional probability, concepts 25–7, 35 confidence intervals, concepts 71, 75–81, 105, 109, 116–20, 190, 262–5 constraining equations, linear programming 159–70 contingency tables, concepts 92–5 continuous approximation, stock control 200–1 continuous case, failures 251 continuous data concepts 7, 13–14, 44–5, 65–6, 251 histograms 7, 13–14 continuous uniform distribution, concepts 64–6 correlation coefficient concepts 104–20, 261–5, 268–9 critical value 105–6, 113–20 equations 104–5 examples 105–8, 115–20 costs capital 219–25, 229–30 dynamic programming 180–82 ghost costs 172–7 holding costs 182–5, 197–201, 204–8 linear programming 167–70, 171–7 sampling 47 stock control 182–5, 195–201 transport problems 171–7 trend analysis 236–47 types 167–8, 182 counting techniques, probability distribution (density) functions 54 covariance see also correlation coefficient concepts 104–20, 263–5 credit cards 159–66, 267–9 credit derivatives 97 see also derivatives Index credit risk, modelling 75, 149, 261–5 critical value, correlation coefficient 105–6, 113–20 cumulative frequency polygons concepts 13–20, 39–40, 203 examples 14–20 uses 13–14 current costs, linear programming 167–70 cyclical variations, trends 238–47 data analysis methods 47–52, 129–47, 271–4 collection techniques 17, 47–52, 129–47 continuous/discrete types 7–12, 13–14, 44–5, 53–5, 65–6, 72, 251 design/approach to analysis 129–47 errors 129–47 graphical presentational approaches 1–20, 149–57 identification 2–5, 261–5 Latin squares 131–2, 143–7 loss data 267–9, 271–4 neural networks 275–7 qualities 17, 47 randomised block design 129–35 reliability and accuracy 17, 47 sampling 17, 47–52 time series 235–47 trends 5, 10, 235–47 two-way classification analysis 135–47 data points, scatter plots 2–5 databases, loss databases 272–4 debentures 149–57 decisions alternatives 191–4 Bayes’theorem 27–30, 31 communications 189–90 concepts 21–35, 189–94, 215–25, 228–34, 249–60 courses of action 191–2 definition 21 delegation 189–90 empowerment 189–90 guesswork 191 lethargy pitfalls 189 minimax regret rule 192–4 modelling problems 189–91 Monty Hall problem 34–5, 212–13 pitfalls 189–94 probability theory 21–35, 53–66, 189–94, 215–18 problem definition 129, 190–2 project analysis guidelines 190–2, 219–25, 228–34 replacement of assets 215–18, 249–60 staff 189–90 287 steps 21 stock control 195–201, 203–8 theory 189–94 degrees of freedom 70–1, 75–89, 91–5, 110–20, 136–7 ANOVA (analysis of variance) 110–20, 121–7, 136–7 concepts 70–1, 75–89, 91–5, 110–20, 136–7 delegation, decisions 189–90 density functions see also probability distribution (density) functions concepts 65–6, 67, 83–4 dependent variables, concepts 2–5, 103–20, 235 derivatives 58, 97–8, 272 see also credit . . . ; options design/approach to analysis, data 129–47 dice-rolling examples, probability theory 21–3, 53–5 differentiation 251 discount factors adjusted discount rates 228–9 net present value (NPV) 220–1, 228–9, 231–2 discrete data bar charts 7–12, 13 concepts 7–12, 13, 44–5, 53–5, 72 discrete uniform distribution, concepts 53–5 displays see also presentational approaches data 1–5 Disraeli, Benjamin 1 division notation 280, 282 dynamic programming complex examples 184–7 concepts 179–87 costs 180–82 examples 180–87 principle of optimality 179–87 returns 179–80 schematic 179–80 ‘travelling salesman’ problem 185–7 e-mail surveys 50–1 economic order quantity see also stock control concepts 195–201 examples 196–9 empowerment, staff 189–90 error sum of the squares (SSE), concepts 122–5, 133–47 errors, data analysis 129–47 estimates mean 76–81 probability theory 22, 25–6, 31–5, 75–81 Euler, L. 131 288 Index events independent events 22–4, 35, 58, 60, 92–5 mutually exclusive events 22–4, 58 probability theory 21–35, 58–66, 92–5 scenario analysis 40, 193–4, 271–4 tree diagrams 30–5 Excel 68, 206–7 exclusive events see mutually exclusive events expected errors, sensitivity analysis 268–9 expected value, net present value (NPV) 231–2 expert systems 275 exponent notation 282–4 exponential distribution, concepts 65–6, 209–10, 252–5 external fraud 272–4 extrapolation 119 extreme value distributions, VaR 262–4 F distribution ANOVA (analysis of variance) 110–20, 127, 134–7 concepts 85–9, 110–20, 127, 134–7 examples 85–9, 110–20, 127, 137 tables 85–8 f notation 8–9, 13–20, 26, 38–9, 44–5, 65–6, 85 factorial notation 53–5, 283–4 failure probabilities see also reliability replacement of assets 215–18, 249–60 feasibility polygons 152–7, 163–4 finance selection, linear programming 164–6 fire extinguishers, ANOVA (analysis of variance) 123–7 focus groups 51 forward recursion 179–87 four by four tables 94–5 fraud 272–4, 276 Fréchet distribution 262 frequency concepts 8–9, 13–20, 37–45 cumulative frequency polygons 13–20, 39–40, 203 graphical presentational approaches 8–9, 13–20 frequentist approach, probability theory 22, 25–6 future cash flows 219–25, 227–34, 240–1 fuzzy logic 276 Garbage In, Garbage Out (GIGO) 261–2 general rules, linear programming 167–70 genetic algorithms 276 ghost costs, transport problems 172–7 goodness of fit test, chi-squared test 91–5 gradient (a notation), linear regression 103–4, 107–20 graphical method, linear programming 149–57, 163–4 graphical presentational approaches concepts 1–20, 149–57, 235–47 rules 8–9 greater-than notation 280–4 Greek alphabet 283 guesswork, modelling 191 histograms 2, 7, 13–20, 41, 73 class intervals 13–20, 44–5 comparative histograms 14–19 concepts 7, 13–20, 41, 73 continuous data 7, 13–14 examples 13–20, 73 skewness 41 uses 7, 13–20 holding costs 182–5, 197–201, 204–8 home insurance 10–12 Hopfield 275 horizontal axis bar charts 8–9 histograms 14–20 linear regression 103–4, 107–20 scatter plots 2–5, 103 hypothesis testing concepts 77–81, 85–95, 110–27 examples 78–80, 85 type I and type II errors 80–1 i notation 8–9, 13–20, 28–30, 37–8, 103–20 identification data 2–5, 261–5 trends 241–7 identity rule 282 impact assessments 21, 271–4 independent events, probability theory 22–4, 35, 58, 60, 92–5 independent variables, concepts 2–5, 70, 103–20, 235 infinity, normal distribution 67–72 information, quality needs 190–4 initial solution, linear programming 167–70 insurance industry 10–12, 29–30 integers 280–4 integration 65–6, 251 intercept (b notation), linear regression 103–4, 107–20 interest rates base rates 240 daily movements 40, 261 project evaluation 219–25, 228–9 internal rate of return (IRR) concepts 220–2, 223–5 examples 220–2 interpolation, IRR 221–2 interviews, uses 48, 51–2 inventory control see stock control Index investment strategies 149–57, 164–6, 262–5 IRR see internal rate of return iterative processes, linear programming 170 j notation 28–30, 37, 104–20, 121–2 JP Morgan 263 k notation 20, 121–7 ‘know your customer’ 272 Kohonen self-organising maps 275 Latin squares concepts 131–2, 143–7 examples 143–7 lead times, stock control 195–201 learning strategies, neural networks 275–6 less-than notation 281–4 lethargy pitfalls, decisions 189 likelihood considerations, scenario analysis 272–3 linear programming additional variables 167–70 concepts 149–70 concerns 170 constraining equations 159–70 costs 167–70, 171–7 critique 170 examples 149–57, 159–70 finance selection 164–6 general rules 167–70 graphical method 149–57, 163–4 initial solution 167–70 iterative processes 170 manual preparation 170 most profitable loans 159–66 optimal advertising allocation 154–7 optimal investment strategies 149–57, 164–6 returns 149–57, 164–6 simplex method 159–70, 171–2 standardisation 167–70 time constraints 167–70 transport problems 171–7 linear regression analysis 110–20 ANOVA (analysis of variance) 110–20 concepts 3, 103–20 equation 103–4 examples 107–20 gradient (a notation) 103–4, 107–20 intercept (b notation) 103–4, 107–20 interpretation 110–20 notation 103–4 residual sum of the squares 109–20 slope significance test 112–20 uncertainties 108–20 literature searches, surveys 48 289 loans finance selection 164–6 linear programming 159–66 risk assessments 159–60 log-normal distribution, concepts 257–8 logarithms (logs), types 20, 61 losses, banks 267–9, 271–4 lotteries 22 lower/upper quartiles, concepts 39–41 m notation 55–8 mail surveys 48, 50–1 management information, graphical presentational approaches 1–20 Mann–Whitney test see U test manual preparation, linear programming 170 margin of error, project evaluation 229–30 market prices, VaR 264–5 marketing brochures 184–7 mathematics 1, 7–8, 196–9, 219–20, 222–5, 234, 240–1, 251, 279–84 matrix plots, concepts 2, 4–5 matrix-based approach, transport problems 171–7 maximum and minimum, concepts 37–9, 40, 254–5 mean comparison of two sample means 79–81 comparisons 75–81 concepts 37–45, 59–60, 65–6, 67–74, 75–81, 97–8, 100–2, 104–27, 134–5 confidence intervals 71, 75–81, 105, 109, 116–20, 190, 262–5 continuous data 44–5, 65–6 estimates 76–81 hypothesis testing 77–81 linear regression 104–20 normal distribution 67–74, 75–81, 97–8 sampling 75–81 mean square causes (MSC), concepts 122–7, 134–47 mean square errors (MSE), ANOVA (analysis of variance) 110–20, 121–7, 134–7 median, concepts 37, 38–42, 83, 98–9 mid-points class intervals 44–5, 241–7 moving averages 241–7 minimax regret rule, concepts 192–4 minimum and maximum, concepts 37–9, 40 mode, concepts 37, 39, 41 modelling banks 75–81, 85, 97, 267–9, 271–4 concepts 75–81, 83, 91–2, 189–90, 195–201, 215–18, 261–5 decision-making pitfalls 189–91 economic order quantity 195–201 290 Index modelling (cont.) guesswork 191 neural networks 275–7 operational risk 75, 262–5, 267–9, 271–4 output reviews 191–2 replacement of assets 215–18, 249–60 VaR 261–5 moments, density functions 65–6, 83–4 money laundering 272–4 Monte Carlo simulation bank cashier problem 209–12 concepts 203–14, 234 examples 203–8 Monty Hall problem 212–13 queuing problems 208–10 random numbers 207–8 stock control 203–8 uses 203, 234 Monty Hall problem 34–5, 212–13 moving averages concepts 241–7 even numbers/observations 244–5 moving totals 245–7 MQMQM plot, concepts 40 MSC see mean square causes MSE see mean square errors multi-way tables, concepts 94–5 multiplication notation 279–80, 282 multiplication rule, probability theory 26–7 multistage sampling 50 mutually exclusive events, probability theory 22–4, 58 n notation 7, 20, 28–30, 37–45, 54–8, 103–20, 121–7, 132–47, 232–4 n!

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Pascal’s triangle, concepts 56–7 payback period, concepts 219, 222–5 PCs see personal computers people costs 167–70 perception 275 permutation, probability distribution (density) functions 55 personal computers (PCs) 7–9, 58–60, 130–1, 198–9, 208–10, 215–18, 253–5 pictures, words 1 pie charts concepts 7, 12 critique 12 examples 12 planning, data collection techniques 47, 51–2 plot, concepts 1, 10 plus or minus sign notation 279 Poisson distribution concepts 58–66, 72–3, 91–2, 200–1, 231–2 examples 58–65, 72–3, 91–2, 200–1 net present value (NPV) 231–2 normal distribution 72–3 stock control 200–1 suicide attempts 62–5 uses 57, 60–5, 72–3, 91–2, 200–1, 231–2 291 population considerations, sampling 47, 49–50, 75–95, 109, 121–7 portfolio investments, VaR 262–5 power notation 282–4 predictions, neural networks 276–7 presentational approaches concepts 1–20 good presentation 1–2 management information 1–20 rules 8–9 trends 5, 10, 235–47 price/earnings ratio (P/E ratio), concepts 222 principle of optimality, concepts 179–87 priors, concepts 28–30 Prob notation 21–35, 68–70, 254–5 probability distribution (density) functions see also normal distribution binomial distribution 55–8, 61–5, 71–2, 98–9, 231–2 combination 54–8 concepts 53–95, 203, 205, 231–2, 257–60 continuous uniform distribution 64–6 counting techniques 54 discrete uniform distribution 53–5, 72 examples 53–5 exponential distribution 65–6, 209–10, 252–5 log-normal distribution 257–8 net present value (NPV) 231–2 permutation 55 Poisson distribution 58–66, 72–3, 91–2, 200–1, 231–2 probability theory addition rule 24–5 Bayes’theorem 27–30, 31 classical approach 22, 27 coin-tossing examples 21–3, 53–4 concepts 21–35, 53–66, 200–1, 203, 215–18, 231–2 conditional probability 25–7, 35 decisions 21–35, 53–66, 189–94, 215–18 definitions 22 dice-rolling examples 21–3, 53–5 estimates 22, 25–6, 32–5, 75–81 event types 22–4 examples 25–35, 53–5 frequentist approach 22, 25–6 independent events 22–4, 35, 58, 60, 92–5 Monty Hall problem 34–5, 212–13 multiplication rule 26–7 mutually exclusive events 22–4, 58 notation 21–2, 24–30, 54–5, 68–9, 75–6, 79–81, 83–5, 99–104, 121–2, 131–5, 185–7, 254–5 overlapping probabilities 25 simple examples 21–2 subjective approach 22 292 Index probability theory (cont.) tree diagrams 30–5 Venn diagrams 23–4, 28 problems, definition importance 129, 190–2 process costs 167–70 production runs 184–7 products awaiting shipment 195 see also stock . . . profit and loss accounts, stock 195 profitable loans, linear programming 159–66 projects see also decisions alternatives 191–4, 219–25 analysis guidelines 190–2, 219–25, 228–34 break-even analysis 229–30 courses of action 191–2 evaluation methods 219–25, 227, 228–34 finance issues 164–6 guesswork 191 IRR 220–2, 223–5 margin of error 229–30 net present value (NPV) 219–22, 228–9, 231–2 P/E ratio 222 payback period 219, 222–5 returns 164–6, 219–25, 227–34 sponsors 190–2 quality control 61–4 quality needs, information 190–4 quartiles, concepts 39–41 questionnaires, surveys 48, 50–1 questions, surveys 48, 51–2, 97 queuing problems, Monte Carlo simulation 208–10 quota sampling 50 r! notation 54–5 r notation 104–20, 135–47 random numbers, Monte Carlo simulation 207–8 random samples 49–50 random walks see also Brownian motion concepts 22 randomised block design ANOVA (analysis of variance) 134–5, 141–3 concepts 129–35 examples 130–1, 140–3 parameters 132–5 range, histograms 13–20 ranks, U test 99–102 raw materials 195 see also stock . . . reciprocals, numbers 280–4 recursive calculations 56–8, 61–2, 179–87 regrets, minimax regret rule 192–4 relative frequencies, concepts 8–12, 14–20 relevance issues, scenario analysis 272, 273–4 reliability bathtub curves 249–51 concepts 17, 47, 215–18, 249–60 continuous case 251 data 17, 47 definition 251 examples 249 exponential distribution 252–5 obsolescence 215–18 systems/components 215–18, 249–60 Weibull distribution 255–7, 262 reorder levels, stock control 195–201 replacement of assets 215–18, 249–60 reports, formats 1 residual sum of the squares, concepts 109–20, 121–7, 132–47 returns dynamic programming 179–80 IRR 220–2, 223–5 linear programming 149–57, 164–6 net present value (NPV) 219–22, 228–9, 231–2 optimal investment strategies 149–57, 164–6 P/E ratio 222 payback period 219, 222–5 projects 164–6, 219–25, 227–34 risk/uncertainty 227–34 risk adjusted cash flows 228–9 adjusted discount rates 228–9 Basel Accord 262, 267–9, 271 concepts 28–30, 159–66, 227–34, 261–5, 267–9, 271–4 definition 227 loan assessments 159–60 management 28–30, 159–66, 227–34, 261–5, 267–9, 271–4 measures 232–4, 271–4 net present value (NPV) 228–9, 231–2 operational risk 27–8, 75, 262–5, 267–9, 271–4 profiles 268–9 scenario analysis 40, 193–4, 271–4 sensitivity analysis 40, 264–5, 267–9 uncertainty 227–34 VaR 261–5 RiskMetrics 263 rounding 281–4 sample space, Venn diagrams 23–4, 28 sampling see also surveys analysis methods 47–52, 129–47 bad examples 50–1 bias 17, 47–50, 51–2, 97, 129–35 cautionary notes 50–2 Index central limit theorem 70, 75 cluster sampling 50 comparison of two sample means 79–81 concepts 17, 47–52, 70, 75–95, 109, 121–7, 129–47 costs 47 hypothesis testing 77–81, 85–95 mean 75–81 multistage sampling 50 normal distribution 70–1, 75–89 planning 47, 51–2 population considerations 47, 49–50, 75–95, 109, 121–7 problems 50–2 questionnaires 48, 50–1 quota sampling 50 random samples 49–50 selection methods 49–50, 77 size considerations 49, 77–8, 129 stratified sampling 49–50 systematic samples 49–50 units of measurement 47 variables 47 variance 75–81, 83–9, 91–5 scaling, scenario analysis 272 scatter plots concepts 1–5, 103–4 examples 2–3 uses 3–5, 103–4 scenario analysis anonimised databases 273–4 concepts 40, 193–4, 271–4 likelihood considerations 272–3 relevance issues 272, 273–4 scaling 272 seasonal variations, trends 236–40, 242–7 security costs 167–70 selection methods, sampling 49–50, 77 semantics 33–4 sensitivity analysis, concepts 40, 264–5, 267–9 sets, Venn diagrams 23–4, 28 sign test, concepts 98–9 significant digits 281–4 simplex method, linear programming 159–70, 171–2 simulation, Monte Carlo simulation 203–14, 234 size considerations, sampling 49, 77–8, 129 skewness, concepts 41–5 slope significance test see also a notation (gradient) linear regression 112–20 software packages reports 1 stock control 198–9 293 sponsors, projects 190–2 spread, standard deviation 41–5 square root 282–4 SS see sum of the squares SSC see sum of the squares for the causes SST see sum of the squares of the deviations Ssu Yuan Y Chien (Chu Shi-Chieh) 56 staff decision-making processes 189–90 training needs 189 standard deviation see also variance cash flows 232–4 concepts 41–5, 67–81, 83, 97–8, 102, 104–20, 232–4 correlation coefficient 104–20 examples 42–5, 232–4 normal distribution 67–81, 83, 97–8, 102, 232–4 uses 41–5, 104–20, 232–4 standard terms, statistics 37–45 standardisation, linear programming 167–70 statistical terms 1, 37–45 concepts 1, 37–45 maximum and minimum 37–9, 40, 254–5 mean 37–45 median 37, 38–42 mode 37, 39, 41 MQMQM plot 40 skewness 41–5 standard deviation 41–5 standard terms 37–45 upper/lower quartiles 39–41 variance 41–5 statistics, concepts 1, 37–45 std(x) notation (standard deviation) 42–5 stock control concepts 195–201, 203–8 continuous approximation 200–1 costs 182–5, 195–201 economic order quantity 195–201 holding costs 182–5, 197–201, 204–8 lead times 195–201 Monte Carlo simulation 203–8 non-zero lead times 199–201 order costs 197–201 Poisson distribution 200–1 variable costs 197–201 volume discounts 199–201 stock types 195 stratified sampling 49–50 Sturges’s formula 20 subjective approach, probability theory 22 subtraction notation 279 successful products, tree diagrams 30–3 suicide attempts, Poisson distribution 62–5 294 Index sum of the squares for the causes (SSC), concepts 122–5, 133–47 sum of the squares of the deviations (SST), concepts 122–5 sum of the squares (SS) ANOVA (analysis of variance) 110–20, 121–7, 134–5 concepts 109–20, 121–7, 132, 133–47 supply/demand matrix 171–7 surveys see also sampling bad examples 50–1 cautionary notes 50–2 concepts 48–52, 97 interviews 48, 51–2 literature searches 48 previous surveys 48 problems 50–2 questionnaires 48, 50–1 questions 48, 51–2, 97 symmetry, skewness 41–5, 67–9, 75–6, 98–9 systematic errors 130 systematic samples 49–50 systems costs 167–70 t statistic concepts 75–81, 97–8, 114–20, 121, 123, 125, 127 tables 75, 81 tables ANOVA (analysis of variance) 110–11, 121–3, 134–47 chi-squared test 84, 91 contingency tables 92–5 F distribution 85–8 normal distribution 67, 74 t statistic 75, 81 tabular formats, reports 1 telephone surveys 50–2 text surveys 50–1 three-dimensional graphical representations 9 time constraints, linear programming 167–70 time series concepts 235–47 cyclical variations 238–47 mathematics 240–1 moving averages 241–7 seasonal variations 236–40, 242–7 Z charts 245–7 trade finance 164–6 training needs, communications 189 transport problems concepts 171–7 ghost costs 172–7 ‘travelling salesman’ problem, dynamic programming 185–7 tree diagrams examples 30–4 Monty Hall problem 34–5 probability theory 30–5 trends analysis 235–47 concepts 235–47 cyclical variations 238–47 graphical presentational approaches 5, 10, 235–47 identification 241–7 mathematics 240–1 moving averages 241–7 seasonal variations 236–40, 242–7 Z charts 245–7 true rank, U test 99–102 truncated normal distribution, concepts 259, 260 truncation concepts, scatter plots 2–3 Twain, Mark 1 two-tail test, hypothesis testing 77–81, 109 two-way classification analysis 135–47 examples 137–40 type I and type II errors examples 80–1 hypothesis testing 80–1 U test, concepts 99–102 uncertainty concepts 108–20, 227–34 definition 227 linear regression 108–20 net present value (NPV) 228–9, 231–2 risk 227–34 upper/lower quartiles, concepts 39–41 valuations, options 58, 97–8 value at risk (VaR) calculation 264–5 concepts 261–5 examples 262–3 extreme value distributions 262–4 importance 261 variable costs, stock control 197–201 variables bar charts 7–8 concepts 2–3, 7–12, 13–14, 27–35, 70, 103–20, 121–7 continuous/discrete types 7–12, 13–14, 44–5, 53–5, 65–6, 72, 251 correlation coefficient 104–20 data collection techniques 47 dependent/independent variables 2–5, 70, 103–20, 235 histograms 13–20 Index linear programming 149–70 linear regression 3, 103–20 scatter plots 2–5 sensitivity analysis 40, 264–5, 267–9 variance see also standard deviation ANOVA (analysis of variance) 110–20, 121–7, 134–47 chi-squared test 83–4, 85, 89, 91–5 comparisons 83–9 concepts 41–5, 65–6, 67, 75–81, 83–9, 91–5, 102, 104, 107, 110–20, 233–4, 263–5 continuous data 44–5 covariance 104–20, 263–5 examples 42–5 F distribution 85–9, 110–20, 127, 134–7 linear regression 104, 107, 110–20 var(x) notation (variance) 42–5, 233–4 VC see venture capital 295 Venn diagrams, concepts 23–4, 28 venture capital (VC) 149–57 vertical axis bar charts 8–9 histograms 14–20 linear regression 103–4, 107–20 scatter plots 2–5, 103 volume discounts, stock control 199–201 Weibull distribution concepts 255–7, 262 examples 256–7 ‘what/if’ analysis 33 Wilcoxon test see U test words, pictures 1 work in progress 195 Z charts, concepts 245–7 z notation 67–74, 102, 105, 234 zero factorial 54–5 Index compiled by Terry Halliday

pages: 445 words: 105,255

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Radical Abundance: How a Revolution in Nanotechnology Will Change Civilization
** by
K. Eric Drexler

3D printing, additive manufacturing, agricultural Revolution, Bill Joy: nanobots, Brownian motion, carbon footprint, Cass Sunstein, conceptual framework, continuation of politics by other means, crowdsourcing, dark matter, double helix, failed state, global supply chain, industrial robot, iterative process, Mars Rover, means of production, Menlo Park, mutually assured destruction, New Journalism, performance metric, reversible computing, Richard Feynman, Silicon Valley, South China Sea, Thomas Malthus, V2 rocket, Vannevar Bush, zero-sum game

The idea of atoms, of course, had been around since antiquity. In Greece circa 400 BCE Democritus argued that matter must ultimately consist of indivisible particles—as indeed atoms are, barring nuclear reactions. In Rome circa 50 BCE Lucretius argued the same case in considerable depth and suggested that dust motes that could be seen dancing in sunbeams were, in fact, driven by what is now called “Brownian motion,” the effect of collisions with atoms (and for some of the motions he saw, he was right). Today, the most advanced forms of atomically precise fabrication rely on this Brownian dance to move molecules. After classical times, centuries passed before any further progress was achieved in understanding the atomic basis of the material world. Inquiry reached a landmark in England in the early 1800s when John Dalton observed that chemical reactions combined substances in fixed proportions and explained these proportions in terms of atoms.

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PART 5 THE TRAJECTORY OF TECHNOLOGY CHAPTER 12 Today’s Technologies of Atomic Precision HUMAN TECHNOLOGY EVENTUALLY LED to machines, yet it began with wood, hide, stones, and hands—which is to say, with biopolymers (cellulose, collagen) and harder, inorganic materials used to make hand-held tools. AP nanotechnologies are following a similar path, but with AP control of biopolymers and inorganic materials using assembly driven by Brownian motion rather than hands. Once again, advances will lead to machines for making things. Just as an early blacksmith’s hammer and tongs differ from an automated machine in a watch-making factory, today’s early tools differ greatly from advanced APM systems. And just as blacksmith-level technology led to today’s machines, so today’s AP molecular technologies will lead to tomorrow’s nanomachines. Where do we stand today on the road to advanced atomically precise fabrication, the road that leads to APM?

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To understand the next steps and the road ahead, it’s important to understand how self-assembly and stereotactic methods can be combined in complementary ways. Today’s Self-Assembly Methods Self-assembly has one great advantage: Because it employs thermal motion to move parts into place, assembling parts requires no nanoscale machinery. Researchers can use conventional biological or chemical means to make the parts, and if they’re properly designed, thermally driven Brownian motion can do the rest. Self-assembly, however, also brings with it a set of challenges and limitations. To produce complex, non-repetitive structures by self-assembly, each part must bind in just one specific place and position as the structure comes together, and this means that each part must have a unique shape, like a piece of a jigsaw puzzle. These molecular puzzle pieces can’t be too small, or they’d be too simple and too much alike; they can’t bind too strongly, or near-matches would end up in the wrong places and never let go; and like a finished jigsaw puzzle, the end product would be divided by many irregular seams.

pages: 733 words: 179,391

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Adaptive Markets: Financial Evolution at the Speed of Thought
** by
Andrew W. Lo

"Robert Solow", Albert Einstein, Alfred Russel Wallace, algorithmic trading, Andrei Shleifer, Arthur Eddington, Asian financial crisis, asset allocation, asset-backed security, backtesting, bank run, barriers to entry, Berlin Wall, Bernie Madoff, bitcoin, Bonfire of the Vanities, bonus culture, break the buck, Brownian motion, business cycle, business process, butterfly effect, buy and hold, capital asset pricing model, Captain Sullenberger Hudson, Carmen Reinhart, collapse of Lehman Brothers, collateralized debt obligation, commoditize, computerized trading, corporate governance, creative destruction, Credit Default Swap, credit default swaps / collateralized debt obligations, cryptocurrency, Daniel Kahneman / Amos Tversky, delayed gratification, Diane Coyle, diversification, diversified portfolio, double helix, easy for humans, difficult for computers, Ernest Rutherford, Eugene Fama: efficient market hypothesis, experimental economics, experimental subject, Fall of the Berlin Wall, financial deregulation, financial innovation, financial intermediation, fixed income, Flash crash, Fractional reserve banking, framing effect, Gordon Gekko, greed is good, Hans Rosling, Henri Poincaré, high net worth, housing crisis, incomplete markets, index fund, interest rate derivative, invention of the telegraph, Isaac Newton, James Watt: steam engine, job satisfaction, John Maynard Keynes: Economic Possibilities for our Grandchildren, John Meriwether, Joseph Schumpeter, Kenneth Rogoff, London Interbank Offered Rate, Long Term Capital Management, longitudinal study, loss aversion, Louis Pasteur, mandelbrot fractal, margin call, Mark Zuckerberg, market fundamentalism, martingale, merger arbitrage, meta analysis, meta-analysis, Milgram experiment, money market fund, moral hazard, Myron Scholes, Nick Leeson, old-boy network, out of africa, p-value, paper trading, passive investing, Paul Lévy, Paul Samuelson, Ponzi scheme, predatory finance, prediction markets, price discovery process, profit maximization, profit motive, quantitative hedge fund, quantitative trading / quantitative ﬁnance, RAND corporation, random walk, randomized controlled trial, Renaissance Technologies, Richard Feynman, Richard Feynman: Challenger O-ring, risk tolerance, Robert Shiller, Robert Shiller, Sam Peltzman, Shai Danziger, short selling, sovereign wealth fund, Stanford marshmallow experiment, Stanford prison experiment, statistical arbitrage, Steven Pinker, stochastic process, stocks for the long run, survivorship bias, Thales and the olive presses, The Great Moderation, the scientific method, The Wealth of Nations by Adam Smith, The Wisdom of Crowds, theory of mind, Thomas Malthus, Thorstein Veblen, Tobin tax, too big to fail, transaction costs, Triangle Shirtwaist Factory, ultimatum game, Upton Sinclair, US Airways Flight 1549, Walter Mischel, Watson beat the top human players on Jeopardy!, WikiLeaks, Yogi Berra, zero-sum game

The unpredictable nature of this fair game will reveal itself in a precarious two-step dance, as you lurch back and forth like a drunk driver attempting to walk a straight line at a sobriety checkpoint. Any fair game like a martingale will produce wins and losses in a random pattern like a “drunkard’s walk”—and as Bachelier discovered, so do the prices in the stock market. Today, we call Bachelier’s discovery the Random Walk Model of stock prices. Bachelier’s analysis was decades ahead of its time. In fact, Bachelier anticipated Albert Einstein’s very similar work in physics on Brownian motion—the random motion of a tiny particle suspended in fluid, among other things—by five years.14 From an economist’s perspective, however, Bachelier did much more than Einstein.15 Bachelier had come up with a general theory of market behavior, and he did so by arguing that an investor could never profit from past price changes. Because the random price movements in a market were martingales, Bachelier concluded, “the mathematical expectation of the speculator was zero.”

…

The intellectual environment of economics was ripe with problems that could be solved with these ultramathematical techniques. What’s more, this borrowing from physics was also financially profitable. As we saw in chapter 1, the parallels between finance and physics can be very close. For example, the similarities between the movements of an asset’s price and the movements of a particle in Brownian motion led to the Random Walk Hypothesis. This means that financial economists can often use the same mathematics as the physicists: the Black-Scholes/ Merton option pricing formula also happens to be the solution to the heat equation in thermodynamics (heat is also the product of random motion). It shouldn’t be a surprise to learn that Samuelson was also instrumental in the birth of modern financial economics.

…

The rather supercilious references to him, as an unrigorous pioneer in stochastic processes and stimulator of work in that area by more rigorous mathematicians such as Kolmogorov, hardly does Bachelier justice. His methods can hold their own in rigor with the best scientific work of his time, and his fertility was outstanding. Einstein is properly revered for his basic, and independent, discovery of the theory of Brownian motion 5 years after Bachelier. But years ago when I compared the two texts, I formed the judgment (which I have not checked back on) that Bachelier’s methods dominated Einstein’s in every element of the vector. Thus the Einstein-Fokker-Planck Fourier equation for diff usion of probabilities is already in Bachelier, along with subtle uses of the nowstandard method of reflected images. 19. Kendall (1953). 20.

**
Investment: A History
** by
Norton Reamer,
Jesse Downing

activist fund / activist shareholder / activist investor, Albert Einstein, algorithmic trading, asset allocation, backtesting, banking crisis, Berlin Wall, Bernie Madoff, break the buck, Brownian motion, business cycle, buttonwood tree, buy and hold, California gold rush, capital asset pricing model, Carmen Reinhart, carried interest, colonial rule, credit crunch, Credit Default Swap, Daniel Kahneman / Amos Tversky, debt deflation, discounted cash flows, diversified portfolio, dogs of the Dow, equity premium, estate planning, Eugene Fama: efficient market hypothesis, Fall of the Berlin Wall, family office, Fellow of the Royal Society, financial innovation, fixed income, Gordon Gekko, Henri Poincaré, high net worth, index fund, information asymmetry, interest rate swap, invention of the telegraph, James Hargreaves, James Watt: steam engine, joint-stock company, Kenneth Rogoff, labor-force participation, land tenure, London Interbank Offered Rate, Long Term Capital Management, loss aversion, Louis Bachelier, margin call, means of production, Menlo Park, merger arbitrage, money market fund, moral hazard, mortgage debt, Myron Scholes, negative equity, Network effects, new economy, Nick Leeson, Own Your Own Home, Paul Samuelson, pension reform, Ponzi scheme, price mechanism, principal–agent problem, profit maximization, quantitative easing, RAND corporation, random walk, Renaissance Technologies, Richard Thaler, risk tolerance, risk-adjusted returns, risk/return, Robert Shiller, Robert Shiller, Sand Hill Road, Sharpe ratio, short selling, Silicon Valley, South Sea Bubble, sovereign wealth fund, spinning jenny, statistical arbitrage, survivorship bias, technology bubble, The Wealth of Nations by Adam Smith, time value of money, too big to fail, transaction costs, underbanked, Vanguard fund, working poor, yield curve

He became quite ﬂuent in ﬁnance as a result of this experience, and soon Bachelier found himself back in academia working under the polymath Henri Poincaré.1 He defended the ﬁrst portion of his thesis, entitled “Theory of Speculation,” in March 1900. In it, he showed how to value complicated French derivatives using advanced mathematics. In fact, his approach bore some similarity to that of Fischer Black and Myron Scholes many years later. Bachelier’s work was the ﬁrst use of formal models of randomness to describe and evaluate markets. In his paper, Bachelier used a form of what is called Brownian motion.2 Brownian motion was named after Robert Brown, who studied the random motions of pollen in water. Albert Einstein would describe this same phenomenon in one of his famous 1905 papers. The mathematical underpinnings of this description of randomness could be applied not only to the motions of small particles but also to the movements of markets. Bachelier’s work did not seem to have an immediate and profound inﬂuence on those markets, however.

…

Savage wrote postcards to a group of economists asking if any economists were familiar with Bachelier.16 And Samuelson did rethink many of the assumptions Bachelier made, such as noting that the expected return of the speculator should not be zero, as Bachelier suggested, but should rather be positive and commensurate with the risk the speculator is enduring. Otherwise, the investor would simply either not invest or own the risk-free security (short-dated Treasury debt). He also redeﬁned Bachelier’s equations to have the returns in lieu of the actual stock prices move in accordance with a slightly different form of Brownian motion because Bachelier’s form of Brownian motion implied that a stock could potentially have a negative price, which is not sensible, as the concept of limited liability for shareholders implies that the ﬂoor of value is zero.17 The Emergence of Investment Theory 235 Samuelson helped motivate the work on derivatives pricing with a 1965 paper on warrants and a 1969 paper with Robert Merton on the same subject—although he did, as he would later note, miss one crucial assumption that Black and Scholes were able to make in their formulation of options prices.18 Samuelson can be considered an intermediary in calling attention to the subﬁeld of derivatives pricing, even if the cornerstone of the most famous ﬁnal theory was not his own.

…

See also commercial banks; merchant banks Barbarians at the Gate, 276 Bardi bank, 43–44 Barings Bank, 170–72 behavioral ﬁnance, 251–54 bell curve, 239 Benartzi, Shlomo, 252 benchmarking, 328–30 Benedict XIV (pope), 37 Bent, Bruce, 143 Bentham, Jeremy, 36 Index 417 Bergen Tunnel construction project, 178 Berlin Wall, fall of, 96 Bernanke, Ben, 9, 197, 208, 226 beta, 243–45; alpha and, 248–49, 254, 308–9 Bible, 34, 239 Bierman, Harold, 204 bills of exchange, 83–84 Birds, The (Aristophanes), 24 Bismarck, Otto von, 108–9 Black, Fischer, 230, 235–36 BlackRock, 299 Black Thursday (October 24, 1929), 164 Blunt, John, 67–68 Bocchoris, 23 Boesky, Ivan, 147, 181, 184–86 Bogle, Jack, 284–85 bond index funds, 285 bonds: convertible, 178; fabrication of Italian, 163; government, 6, 135, 176; high-yield, 276; holding, 93; investment in, 257, 259, 297, 301; management of, 102 Boness, James, 236 bookkeeping, double-entry, 41 borrower, reputation of, 22–23 Borsa Italiana, 95 Boston, 100 Boston Consulting Group, 194 Boston Post, 157 bourses, 84 Breitowitz, Yitzhok, 150 Bristol-Myers Squibb, 188 Britain: beggar-thy-neighbor policies in, 202; colonial rule of India, 49–50, 61; supplies contract, after American Revolution, 175 British Bankers’ Association, 182 British East India Company, 66, 326 Brookings Institution, 91 Brown, Henry, 143 Brown, Robert, 230 Brownian motion, 230, 234 Brumberg, Richard, 121–22 Brush, Charles, 81 Bubble Act of 1720, 68, 87 bubbles: causes of, 5; housing bubble of 2004–2006, 213–14; South Sea Bubble, 68–69; technology (dot-com bubble of 1999-2000), 187, 213, 223–24, 246, 263, 276, 287 bubonic plague, 75 bucket shops, 90 Buddhist temples, 29–30 budget deﬁcit projections, 218 Buffett, Warren: American Express and, 169; earnings of, 305; on efficient market hypothesis, 250–51; ﬁnancial leverage and, 6; on real ownership, 4; resource allocation and, 7; as value manager, 140 bullet payments, 321 bull market: in 1920s, 91; of 1990s, 269, 285; after World War II, 92, 143 burghers, 42 Bush, George W., 218, 225 BusinessWeek, 143, 188 Buttonwood Agreement, 88, 97 Byzantines, 52 Cabot, Paul, 141 Cady, Roberts decision, 192 Caesar, 28 Calahan, Edward, 90 California Public Employees Retirement System (CalPERS), 129 418 Investment: A History call option: performance fee as, 310–11; sale of, 151 CalPERS.

pages: 252 words: 73,131

**
The Inner Lives of Markets: How People Shape Them—And They Shape Us
** by
Tim Sullivan

"Robert Solow", Airbnb, airport security, Al Roth, Alvin Roth, Andrei Shleifer, attribution theory, autonomous vehicles, barriers to entry, Brownian motion, business cycle, buy and hold, centralized clearinghouse, Chuck Templeton: OpenTable:, clean water, conceptual framework, constrained optimization, continuous double auction, creative destruction, deferred acceptance, Donald Trump, Edward Glaeser, experimental subject, first-price auction, framing effect, frictionless, fundamental attribution error, George Akerlof, Goldman Sachs: Vampire Squid, Gunnar Myrdal, helicopter parent, information asymmetry, Internet of things, invisible hand, Isaac Newton, iterative process, Jean Tirole, Jeff Bezos, Johann Wolfgang von Goethe, John Nash: game theory, John von Neumann, Joseph Schumpeter, Kenneth Arrow, late fees, linear programming, Lyft, market clearing, market design, market friction, medical residency, multi-sided market, mutually assured destruction, Nash equilibrium, Occupy movement, Pareto efficiency, Paul Samuelson, Peter Thiel, pets.com, pez dispenser, pre–internet, price mechanism, price stability, prisoner's dilemma, profit motive, proxy bid, RAND corporation, ride hailing / ride sharing, Robert Shiller, Robert Shiller, Ronald Coase, school choice, school vouchers, sealed-bid auction, second-price auction, second-price sealed-bid, sharing economy, Silicon Valley, spectrum auction, Steve Jobs, Tacoma Narrows Bridge, technoutopianism, telemarketer, The Market for Lemons, The Wisdom of Crowds, Thomas Malthus, Thorstein Veblen, trade route, transaction costs, two-sided market, uber lyft, uranium enrichment, Vickrey auction, Vilfredo Pareto, winner-take-all economy

When we looked at that list of papers and thought about what we could do with the information, it occurred to us that these relatively esoteric academic papers had had, like their counterparts in physics, an outsized influence. That seemed worth exploring, not by reprinting the original papers but by examining how those ideas have lived in the world. This half-century’s worth of economic thought—often as incomprehensible to outsiders in its original formulations as Einstein’s investigations into the theory of Brownian motion is to non-physicists—has been used to make markets work better and, in an ever-widening set of applications, has helped them reach more deeply into our lives. The Inner Lives of Markets explores the intersection of those economic ideas and our lives. INTRODUCTION TERMS OF SERVICE At 109 Lincoln Street in Rutland, Vermont, stands a dilapidated yellow clapboard building. Rutland was incorporated in the late nineteenth century, flush with money from the marble quarries just outside town.

…

His thesis was the beginning of his lifelong project to bring “unification—and clarification—in mathematics” to the profession. Nobel prize winners are generally associated with a particular theory, insight or cohesive set of insights, or even a single specific paper. For Samuelson, rewriting economics in the new language of math was the contribution itself, often borrowing ideas already developed by physicists and mathematicians. He introduced, for example, the idea of Brownian motion (which he borrowed from physics) as a way of understanding financial markets, and a version of Henry-Louis Le Chatelier’s principle (developed by chemists in the nineteenth century) as a tool for understanding market equilibrium. Samuelson didn’t undertake this project alone but was responsible for many of its central contributions. We also see in Samuelson the sense that the discipline imposed by mathematics made economics no less relevant to understanding real-world problems.

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INDEX Abidjan, Ivory Coast, 167–168 Adfibs.com, 69 adverse selection, 48, 51–55, 57, 59 advertising, as money burning, 70–71 Super Bowl advertising, 70–71 AdWords, 14, 101 Airbnb, 3, 6, 50, 109, 125, 170–172 Akerlof, George, 43–51, 58–59, 64, 112 Alaskoil experiment, 55–57, 58–59 algebraic topology, 44–45 Amazon, 2, 3, 16, 50, 51, 52, 59, 74, 91, 95, 97, 108, 110, 119, 126, 128–129 American Express, 115–116 America’s Second Harvest, 154–160 Amoroso, Luigi, 21 Angie’s List, 120 “animal spirits,” 50 applied theory in economics, 45, 50, 75–76 Arnold, John, 156–158, 160 Arrow, Kenneth, 30–34, 36–37, 40, 76, 117, 180 ascending price English auctions, 83, 100 asymmetric information, 41, 44–55 attribution theory, 177–178 auctions AdWords, 14, 101 auction theory, 82–84 coat hooks, 151–152, 174 design, 14, 101–102 first-price sealed-bid, 86–87, 99–100 first-price (live), 84 internet, 94–97 types of, 81–82 wireless spectrum, 102–103 See also eBay; Vickrey auctions AuctionWeb, 40 Ausubel, Larry, 98 Azoulay, Pierre, 112 Bank of America, 113–115 barriers to entry, in marketplace, 173 baseball posting system, 79–81 Bazerman, Max, 55–57 Becker, Gary, 35, 161–162 Berman, Eli, 67 Berners-Lee, Tim, 41–42 Big Data, Age of, 15 Blu-ray-HD DVD format war, Sony, 125–126 Book Stacks Unlimited, 42–43 Boston public schools, 144–149 Boston University MBA students experiment (Bazerman and Samuelson), 55–57, 58–59 See also Alaskoil experiment bridge design, 141–142 Brown, William P., 83–84 Brownian motion, 28–29 cab drivers, Uber vs., 169–170, 172 Camp, Garrett, 170 candle auctions, 82 capitalism, free-market, 172–173 car service platform, 169–171 cash-back bonus, 116 cash-for-sludge transactions, 167–169 See also Summers, Larry centralized clearinghouses, 140–141 Champagne fairs, 105–106, 126–128 Changi POW camp, 175–177 Le Chatelier, Henry Louis, 29 Le Chatelier’s principle, 29 cheap talk, 62–66, 69 chess, difference between Cold War and, 26 See also poker, bluffing in child labor, 180 cigarettes, as currency in German POW camp, 8–9 Clarke, Edward, 93 Clavell, James, 175 clerkship offers, with federal judges, 140 coat hook, 151–152, 174 Codes of the Underworld (Gambetta), 68 Cold War, difference between chess and, 26 See also poker, bluffing in Collectible Supplies, 128–129 “College Admissions and the Stability of Marriage” (Gale and Shapley), 137 commitment, signs of, 62–63, 69–71, 72–75 community game, 178–179 competition models of, 35, 166, 172–173 platform, 124–126 unethical conduct with, 180–181 “Competition is for Losers” (Thiel), 173 competitive equilibrium, existence of, 29, 31–34, 36–37, 40, 45, 76 competitive markets, 35, 124–126, 172–174, 180–181 See also platforms competitive signaling, 70–71 congestion pricing model, 86, 94 constrained optimization, 85–86, 133 contractorsfromhell.com, 120 copycat competitors, 172–173 corporate philanthropy, 72–75 Cowles, Alfred, 25, 27 Cowles Commission for Research in Economics, 25, 27, 31, 134 “creative destruction,” 50 credit card platforms, 113–116, 123–124 criminal organizations, informational challenges of, 68 currency, at Stalag VII-A POW camp, 8–9 customer feedback, 52, 74–75 Davis, Harry, 154, 157 Debreu, Gérard, 20, 24, 25, 32–33, 36–37 decentralized match, 139–140 deferred acceptance algorithm, 137–141, 145–149 Delmonico, Frank, 164 descending price auctions, 81–82 design, auction, 14, 101–102 Digital Dealing (Hall), 94 Discover card, 115–116 distribution of income, 22 Domar, Evsey, 36–37 Dorosin, Neil, 142–144 Douglas Aircraft Company, 25 Dow, Bob, 1–2 Dow, Edna, 1–2 Drèze, Jacques, 85–86 dumping toxic waste, transactions for, 167–169 Dutch auctions, 81–82 dysfunction, market, 36, 75–77, 143 eBay adverse selection on, 51–55, 57 auction listings, 94–97 concerns on model for, 43, 46, 48 on seller motivation for giving to charities, 73–75 start of, 39–41 as two-sided market, 109, 119 e-commerce, 41–43, 52–55 “The Economic Organization of a P.O.W.

pages: 189 words: 48,180

**
Elemental: How the Periodic Table Can Now Explain Everything
** by
Tim James

Albert Einstein, Brownian motion, Dmitri Mendeleev, en.wikipedia.org, Ernest Rutherford, Harvard Computers: women astronomers, Isaac Newton, Murray Gell-Mann, Silicon Valley

It would be foolish to summarize his many achievements in a few paragraphs, so we’ll focus on the one most relevant to chemistry: a paper he published on July 18, 1905, in which he made the atomic hypothesis testable rather than speculative. While working at the Swiss patent office, Einstein stumbled across some research from 1827 by the Scottish botanist Robert Brown. Brown had noticed that grains of pollen floating on water appeared to jiggle in random patterns. Originally, he had assumed the grains were alive but found the same thing happened with sand or dust. The phenomenon was known as Brownian motion and, although unexplained, it was nothing more than a curiosity. Einstein decided to model the pollen’s trajectory through the water and found it could only be explained as the result of bombardment from water particles. To accurately describe how the pollen moved, you had to factor in the friction of pollen against water, which meant you had to accept the existence of “water atoms.” Despite the persistent rumors that he failed math in school, Albert Einstein was a mathematician par excellence and drew up an equation that related water temperature to the pollen grain’s likely movement.

…

Index 3M ability absolute zero acids actinium adenosine triphosphate (ATP) age-related diseases air al-Sufi, Abd al-Rahman alchemy alkahest allotropes alloys alpha particles alpha decay aluminum aluminum oxide Amagat, Émile American Chemical Society americum ammonia amperes amygdalin ancient Egypt ancient Greece Andromeda constellation anti-bacterials anti-neutrinos antimony argon argyria Aristotle arsenic astatine astrochemistry atomic bonds Atomic Energy Authority atomic hypothesis atomic sponge atoms electrical and elemental differences instability interior large non-metals nucleus orbital arrangement origins and proton numbers and the Schrödinger wave equation splitting and star formation of unstable substances uranium ATP see adenosine triphosphate azidoazide azide Babbage’s difference engine Banana Equivalent Dose (BED) barium Becquerel, Henri bell metal berkelium beryllium beta radiation beta decay big bang biology bismuth black holes, super-massive bohrium bone Boomerang Nebula borax crystals boron bosons bottom-up approaches botulinum toxin Boyle, Robert brain Brandt, Hennig bridges bromine bronze Bronze Age Brownian motion Bunsen, Robert cadmium cesium caffeine calcium californium calxes cancer carbon conductivity and diamonds as fuel and graphite of human DNA and making elements and nitroglycerine and sugar carbon charcoal carbon dioxide (CO2) carbon monoxide catfish causation Cavendish, Henry Celsius scale centigrade cerium Chadwick, James chalk charcoal charge Charles’s law chemical bonds chemical reactions chemicals classification see also specific chemicals chemotherapy child mortality figures China chloride chlorination chlorine chlorine gas chlorine trifluoride (CIF3) cholera Chow Tai Fook Enterprises chromic acid chromium climate change, human-made Clostridium botulinum coal cobalt Cold Atom Laboratory Cold War compounds conductors copernicium copper corrosive resistance corundum cosmic rays crematoria critical mass crust crystals see also specific crystals Curie, Marie and Pierre curium current cyanide cytochrome c oxidase Dalton, John darmstadtium Davy, Humphry de Haan, John Democritus density deoxy ribonucleic acid (DNA) “dephlogisticated air” diamond dimethyl cadmium diphosphane (P2H4) Döbereiner, Johann Donkin, Bryan dubnium dynamite dysprosium E = mc2 Earth earths Edison, Thomas Einstein, Albert einsteinium electric chair electric current electric shocks electrical atoms electrical conductivity electrical fields electrical resistance electricity electron orbitals (electron clouds) and chemical reactions effect of increasing numbers of protons on and electricity large and mercury and metals predicting the position of electron sea electrons and acids and carbon charge and chemical reactions and electricity and fluorine and molecular orbitals movement and new element formation of non-metals and the periodic table predicting the position of and the Schrödinger wave equation and static electricity substructure and turning neutrons into protons and W- bosons wavy movement elements abundant and atoms changing one into another classification construction of artificial new cyclical pattern discovery Empedocles on formation in stars hidden most crucial to human development most expensive naming poisonous and the Schrödinger wave equation and the shape of the periodic table see also specific elements elixir of life Empedocles energy erbium essences ether europium execution explosives Fahrenheit scale fat, body fermium Feshbach resonance fire fireworks fission “flammable air” flammable substances Flamsteed, John flavor flerovium fluidity fluoride fluorine fluoroantimonic acid food force fields fossil fuels francium Fraunhofer, Joseph von fructose fundamental particles fusion gadolinium galaxies galinstan gallium gamma rays gases compression inert noble Geiger, Hans Geiger counter Geim, Andre germanium glass global warming glucose glucuronic acid gluons God gods Godzilla gold gold-foil experiments graphene graphite gravity Gray, Stephen Group 17/Group 18 gunmetal gunpowder Gutenberg, Johannes H (Hamiltonian) Haber, Fritz hafnium Haigh, John George hardness hassium hat industry heart heat see also fire heat sensors helium and lasers liquid non-reactivity and the periodic table helium hydride Heraclitus Hertz, Heinrich Higgs bosons holmium Hubble telescope human body chemical formula electrical conductivity Hurricane, Omar hydrochloric acid hydrogen and acid of human DNA and nitroglycerine and the periodic table and plastic and sugar and water hydrogen bomb hydrogen chloride (HCl) hyperdiamond hypochlorous acid (HOCL) i numbers IBM indium infectious diseases insulators International Space Station (ISS) International Union of Pure and Applied Chemistry (IUPAC) iodine ions iridium Irifune, Tetsuo iron Iron Age Ka ket vector (|>) Klapötke, Thomas Krebs, Hans krypton lanthanum lattices Lavoisier, Antoine lawrencium lead Lecoq, Paul-Émile lethal dose (LD50) life expectancy LifeGem light blue and electrons infrared red splitting lightbulbs lightning liquids lithium Litvinenko, Alexander livermorium living things logarithms, laws of lugduname lutetium McMillan, Edwin magic acid “magic numbers” magnesium magnetic fields magnetism malleability mammograms manganese Manhattan Project mantle Marsden, Ernest medicine Meitner, Lise meitnerium Mendeleev, Dmitri mendelevium Menghini, Vincenzo mercury metal chemistry metal oxides metallurgy metals and calxes conductivity definition heavy Lavoisier on opacity reactivity meteorites methane (CH4) microwaves Milky Way Mohs value molecular orbitals molecules molybdenum money mortality rates moscovium musical theory, Western National Helium Reserve National Ignition Facility Nazis neodymium neon neptunium neutrinos neutrons and forging new elements and nuclear decay and nuclear stability and quarks substructure turning into protons uranium Newlands, John Newton, Sir Isaac nickel Niépce, Joseph “Nicéphore” nihonium niobium nitrogen nitroglycerine Nobel, Alfred Nobel Prizes nobelium non-metals non-reactivity Novoselov, Kostya nuclear explosions, of stars nuclear reactors nuclear weapons nuclear-plants, fusion-based nucleus (atomic) and chemical reactions decay and electricity and electron orbitals and forging new elements fusing and the Schrödinger wave equation stability substructure unstable nature uranium octaves oganesson ohms Oppenheimer, Robert osmium oxalic acid oxides oxygen and carbon and crystals discovery and element generation and fluorine of human DNA and metals and nitroglycerine and respiration and sugar and water ozone palladium panacea Paracelcus principle partial differential (∂) particle theory particles, speed pathogens Pauling, Linus Payne-Gaposchkin, Cecilia perchloric acid periodic table architectural simplicity and carbon completion and Empedocles groups and Lavoisier and Mendeleev and Newlands and quantum mechanics and Risenfeld and Seaborg shape and silicon and White periods perpetual motion machines pH scale philosopher’s stone phlogiston phosphane (PH3) phosphorus photography photons pitch (asphalt) pKalow scale Planck’s constant (ħ) planetary formation plant life plastic platinum Plum-Pudding Hypothesis, The plumbing plutonium poison polonium polymer chemistry potassium potassium uranyl sulfate potassium-40 potenz power stations praseodynium Priestly, John printing press prisms promethium protactinium protons and acids charge and making new elements and nuclear decay and nuclear stability and quarks repulsion rogue and the Schrödinger wave equation substructure uranium psi (Ψ) pyrolusite Pythagorean order quantum field theory quantum leaps quantum theory quarks radiation exposure measurement poisoning sickness radiograms radium radon rainbows rat studies reactivity relativy theory, special resiniferatoxin resistance respiration rhenium rhodium Richter scale roentgenium Romans Royal Navy Royal Society rubber rubidium Russia rust ruthenium Rutherford, Ernest rutherfordium salt (sodium chloride) Salvarsan samarium sapphire scandium scanning tunneling microscope Scheele, Carl Scheelite (calcium tungstate) Schrödinger, Erwin Schrödinger wave equation generalized time-dependent version Schulze, Johann science Scoville Heat Units (SHUs) Seaborg, Glenn seaborgium Second World War selenium semi-conductors senses shells Shockley, William siemens per meter sieverts silicon silver silver fulminate silver nitrate silver screen smelting Smith, Mike smoke-detectors smoking Sörensen, Sören sodium sodium chloride sodium-potassium solar systems solder solids space spectroscopy spiciness spontaneous human combustion stability Stahl, Georg stardust stars death formation super-giant static electricity steel Stone Age stop-motion films strontium sucrose sugar sulfate sulfur sulfuric acid Sun suns superacids supernovas sweet syphilis tantalum technetium teflon Telford’s suspension bridge tellurium tennessine terbium terne tetrahedral arrays Thales thallium theobromine thermometers Thomson, Joseph John “J.

**
Risk Management in Trading
** by
Davis Edwards

asset allocation, asset-backed security, backtesting, Black-Scholes formula, Brownian motion, business cycle, computerized trading, correlation coefficient, Credit Default Swap, discrete time, diversified portfolio, fixed income, implied volatility, intangible asset, interest rate swap, iterative process, John Meriwether, London Whale, Long Term Capital Management, margin call, Myron Scholes, Nick Leeson, p-value, paper trading, pattern recognition, random walk, risk tolerance, risk/return, selection bias, shareholder value, Sharpe ratio, short selling, statistical arbitrage, statistical model, stochastic process, systematic trading, time value of money, transaction costs, value at risk, Wiener process, zero-coupon bond

(See Equation 3.6, A Simple Random Process, continued.) 73 Financial Mathematics Simulating price of some asset, abbreviated P, but with a change in notation: n Pn = ∑ ΔPt (3.6) t =1 where Pn Price at time n ΔPt The price change between time t and time t – 1 n ∑ ΔP t =1 t The sum of price changes between time t =1 (indicated below the sigma) to time n (indicated above the sigma) A common type of random process is called Brownian motion. Brownian motion may also be called the Wiener process. In this process, the percent change in price (ΔP) is a random number described by a normal distribution. The end result of this process is equal to the sum of normally distributed movements. Brownian motion is commonly used to model how something might disperse over time. In finance, it is most commonly used to model price movements. At the start of the process, prices will be close to the starting point (called the initial condition). However, as time passes, a greater range of possible values becomes possible.

pages: 385 words: 98,015

**
Einstein's Unfinished Revolution: The Search for What Lies Beyond the Quantum
** by
Lee Smolin

Albert Einstein, Brownian motion, Claude Shannon: information theory, cosmic microwave background, cosmological constant, Ernest Rutherford, Isaac Newton, Jane Jacobs, Jaron Lanier, John von Neumann, Murray Gell-Mann, mutually assured destruction, Richard Feynman, Richard Florida, Schrödinger's Cat, Stephen Hawking, the scientific method, Turing machine

If we want to find an analogue of what Einstein achieved in that single year, we can only look at Newton. Einstein launched two revolutions—relativity and the quantum. Of the latter he had wrested from nature two precious insights: the dual nature of light, and the relation between the energy of the particle and the frequency of the wave, which ties together the two sides of the duality. FIGURE 6. BROWNIAN MOTION Brownian motion is the random motion of molecules and other small particles found in nature. Einstein explained that the motion results from the frequent collisions of molecules making up the air or water, and was able to predict how the magnitude of the effects depends on the density of the atoms. Einstein’s fourth paper, which proved the existence of atoms, said nothing about the quantum nature of light.

…

See pilot wave theory Bohr, Niels, xxi–xxii, xxvii, xxix, 75 anti-realism of, 106 on atoms, 93 Bohm and, 113 complementarity and, 85–86, 90 education of, 77 Einstein and, 8, 78, 102 electrons and, 84 EPR and, 47–48 family and background of, 76 Heisenberg and, 90–91 leadership and inspiration of, 117–18 pilot wave theory and, 102–3 quantum theories and, xxii, 7–8, 9 splitting and, 193–94 Boltzmann, Ludwig, 71, 71n, 72n Born, Max, 8, 34, 81–83, 86, 88–91, 100 Born’s rule, 34, 61, 83, 99–100, 109, 150, 151n, 177 decision theory and, 167–69 definition, 206 probabilities and, 164, 200, 218 Rule 1 and, 171 boundary splits, 197 Brownian motion of molecules, 73 Bub, Jeffrey, 130 buckyballs, 24 causal completeness principle, 232, 247 causal future, 254–55, 266–67 causality, 134, 204, 216–17, 217, 236, 298 causal links, 255 causal loops, 255, 255n causal past, 254, 261, 266–67, 301 causal relations, 254–57, 260–61, 270 causal sets, 260–61, 264–69 causal set theory, 257–58, 298 causal structure, 256, 260, 298 causal theory of views, 269–71 circular motion, 77 classical mechanics, 111, 193–95, 196 classical physics, xx, 30, 298 classical state, 30 classical worlds, 219–20 climate change, xxiv, 178 codes, 48, 185, 186 collapses.

pages: 240 words: 60,660

**
Models. Behaving. Badly.: Why Confusing Illusion With Reality Can Lead to Disaster, on Wall Street and in Life
** by
Emanuel Derman

Albert Einstein, Asian financial crisis, Augustin-Louis Cauchy, Black-Scholes formula, British Empire, Brownian motion, capital asset pricing model, Cepheid variable, creative destruction, crony capitalism, diversified portfolio, Douglas Hofstadter, Emanuel Derman, Eugene Fama: efficient market hypothesis, fixed income, Henri Poincaré, I will remember that I didn’t make the world, and it doesn’t satisfy my equations, Isaac Newton, Johannes Kepler, law of one price, Mikhail Gorbachev, Myron Scholes, quantitative trading / quantitative ﬁnance, random walk, Richard Feynman, riskless arbitrage, savings glut, Schrödinger's Cat, Sharpe ratio, stochastic volatility, the scientific method, washing machines reduced drudgery, yield curve

I showed that expected return is proportional to risk by using just two principles: (1) you should expect equal returns from equal risks, and (2) a stock’s risk is solely the volatility of the diffusion illustrated in Figure 5.3. The first principle is pure theory and hard to argue with: If two securities truly have the same risk, how could you not expect the same return from them? But that’s an expectation. In life, expectations aren’t necessarily fulfilled. The second assumption is pure model. The EMM’s picture of price movements goes by several names: a random walk, diffusion, and Brownian motion. One of its origins is in the description of the drift of pollen particles through a liquid as they collide with its molecules. Einstein used the diffusion model to successfully predict the square root of the average distance the pollen particles move through the liquid as a function of temperature and time, thus lending credence to the existence of hypothetical molecules and atoms too small to be seen.

…

See evil bailouts bare electrons Barfield, Owen Bedazzled (film) Begin, Menachem behavior, human: adequate knowledge and EMM as assumption about explanations for and humans as responsible for their actions and idolatry of models Law of One Price and laws of pragmamorphism and Ben-Gurion, David Bernoulli, Daniel Bernstein, Jeremy beta: CAPM and Betar (Brit Yosef Trumpeldor) binocular diplopia birds Black, Fischer Black-Scholes Model Merton and Blake, William Bnei Akiva (Sons of Akiva) Bnei Zion (Sons of Zion) body-mind relationship Bohr, Aage Bohr, Niels bonds: financial models and See also type of bond Boyle’s Law Brahe, Tycho brain Brave New World (Huxley) Brownian motion bundling of complex products cage: moth in perfect calibration Cape Flats Development Association (South Africa) Capital Asset Pricing Model (CAPM) capitalism caricatures: models as cash. See currency/cash Cauchy, Augustin-Louis causes Cepheid variable stars chalazion chaver (comrade) Chekhov, Anton chemistry: electromagnetic theory and Chesterton, G. K. Chinese choice chromatography Churchill, Winston Coetzee, J.

**
Turing's Cathedral
** by
George Dyson

1919 Motor Transport Corps convoy, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Albert Einstein, anti-communist, Benoit Mandelbrot, British Empire, Brownian motion, cellular automata, cloud computing, computer age, Danny Hillis, dark matter, double helix, fault tolerance, Fellow of the Royal Society, finite state, Georg Cantor, Henri Poincaré, housing crisis, IFF: identification friend or foe, indoor plumbing, Isaac Newton, Jacquard loom, John von Neumann, mandelbrot fractal, Menlo Park, Murray Gell-Mann, Norbert Wiener, Norman Macrae, packet switching, pattern recognition, Paul Erdős, Paul Samuelson, phenotype, planetary scale, RAND corporation, random walk, Richard Feynman, SETI@home, social graph, speech recognition, Thorstein Veblen, Turing complete, Turing machine, Von Neumann architecture

Similar ideas were formalized by Claude Shannon (working in consultation with Wiener) and Andrey Kolmogorov (working independently in the Soviet Union) at about the same time. “The transmission of a single fixed item of information is of no communicative value,” Wiener explained in his report to Weaver in 1942. “We must have a repertory of possible messages, and over this repertory a measure determining the probability of these messages.”9 Wiener had launched his mathematical career with a theory of Brownian motion—the random trajectory followed by a microscopic particle in response to background thermodynamic noise. He was thus prepared for the worst case possible: an aircraft that changes course at random from one moment to the next. Wiener’s theory, strengthened by Bigelow’s experience as a pilot, held that the space of possible trajectories (equivalent to the space of possible messages in communications theory) was constrained by the performance envelope of the aircraft and the physical limitations of the human being at the controls.

…

Maxims 2–4 advised separating the available information into that needed immediately and that needed later, while Maxim 5 added that “if noise is ever to be filtered from signal, it must be done at the earliest possible stage rather than after the two are tangled with other noises and signals, for the same reason that repeater stations are used on a signal line rather than filters and amplifiers at the ends.” Maxim 7 advised “Never estimate what may be accurately computed”; Maxim 8 advised “Never guess what may be estimated”; and, if a guess was absolutely necessary, “Never guess blindly” was Maxim 9. Maxims 10 through 14 specified how to implement optimal prediction when the target “has the character of a Brownian motion impressed upon a resonator system.” Existing methods of tracking a target’s changing position “of necessity refers it to an irrelevant point of observation thus destroying its fundamental symmetry,” while an ideal predictor should assume that the target obeys the conservation laws of physics “upon which is superimposed a random modulation symmetrical in time.”15 The Wiener-Bigelow debomber would model the behavior of the airplane within the frame of reference belonging to the airplane, rather than referring it to that of the observer on the ground.

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Desmond (1901–1971), 8.1, 8.2 BESK (Binär Elektronisk Sekvens Kalkylator), 15.1, 17.1 BESM (Bol’shaya Ehlektronno-Schetnaya Mashina) Bethe, Hans (1906–2005), ack.1, 4.1, 11.1, 11.2, 11.3, 12.1, 16.1 Bigelow, Alice Bigelow, Julian H. (1913–2003), ack.1, 5.1, 7.1, 8.1, 8.2, 8.3, 8.4, 8.5, 8.6, 8.7, 9.1, 11.1, 14.1, 14.2, 15.1, 16.1, 18.1, 18.2, 18.3 on alternative models of computation, 14.1, 14.2, 18.1 and analog computing on antiaircraft fire control, with Norbert Wiener on Barricelli and artificial intelligence on computational inefficiency, 6.1, 16.1 and Cybernetics movement and delays in ECP Guggenheim fellowship (1951) and IAS housing project on processors as organisms receives Q clearance (1950, 1956), 11.1, 14.1 on reliability, 7.1, 8.1, 8.2 and termination of the ECP, 14.1, 18.1, 18.2 on time (vs. sequence), 16.1, 16.2 on Universal Turing Machine, 8.1, 14.1 visits Manchester (1948) on von Neumann, 5.1, 5.2, 7.1, 8.1, 8.2, 14.1, 14.2 on von Neumann, Gödel, and Turing, 6.1, 13.1 Bigelow, Mary, 7.1, 8.1, 14.1 Bigelow, Richard Bikini (Marshall Islands), prf.1, 1.1, 18.1 BINAC (Binary Automatic Computer) binary coding, see codes and coding Birch, Frank Birkbeck College Birkhoff, Garrett (1911–1996) Birkhoff, George David (1884–1944) bit (contraction of binary digit) origins of, ack.1, 1.1 two species of, 1.1, 7.1, 16.1 Bjerknes, Jacob (1897–1975), 9.1, 9.2, 9.3 Bjerknes, Vilhelm (1862–1951) Blake, Gwen Bletchley Park, 13.1, 13.2, 13.3, 18.1 Bliss, Ames Bliss, Gilbert (1876–1951), 5.1, 7.1 Bluetooth (local wireless) B-mathematics (Barricelli), 12.1, 18.1 Bochner, Salomon (1899–1982) Bohr, Harald (1887–1951), 10.1, 10.2 Bohr, Niels (1885–1962), 10.1, 10.2, 10.3 Bolshevik Revolution Bombe (cryptanalytic machine) Boolean logic, 12.1, 13.1, 15.1 Booth, Andrew (1918–2009), 8.1, 8.2, 12.1, 18.1 and Turing Booth, Kathleen (Britten), 8.1, 8.2, 18.1 Boston Herald Bott, Raoul (1923–2005), 4.1, 9.1 Boyle, Robert (1627–1691) Bradbury, Norris (1909–1997), 10.1, 11.1, 11.2 Brin, Sergey British Rubber Producers Research Association (BRPRA), 8.1, 8.2 British Tabulating Machine Company Brookhaven National Laboratory, 10.1, 12.1 Brown, George Brownian motion Brueckner, Keith Budapest, 4.1, 4.2, 10.1, 15.1, 18.1 Bureau of Standards, U.S., 10.1, 11.1, 18.1, 18.2 Bureau of the Census (U.S.) Burks, Arthur W. (1915–2008), 5.1, 6.1, 6.2, 7.1, 7.2, 7.3, 8.1, 8.2, 8.3, 11.1, 12.1, 15.1, 18.1 and ENIAC on von Neumann, Gödel, and Turing Bush, Vannevar (1890–1974), 5.1, 7.1, 11.1, 11.2 Byllynge, Edward calculus ratiocinator (Leibniz), 6.1, 6.2, 18.1 Caldwell, Samuel H. (1904–1960), 5.1, 5.2 California Institute of Technology (Caltech), 9.1, 15.1 California, University of, at Los Angeles (UCLA), 9.1, 9.2, 9.3, 9.4, 10.1, 14.1, 14.2, 18.1, 18.2 Cambridge University, 3.1, 6.1, 8.1, 8.2, 13.1, 13.2, 13.3, 16.1 Cantor, George (1845–1918) capacitors, 5.1, 5.2, 8.1, 8.2, 8.3 carbon dioxide, effect on climate Carteret, Sir George (1610–1680) Casino-on-the-Park (New York) Castle Bravo (hydrogen bomb test, 1952), 1.1, 18.1 cathode-ray tube (CRT), 1.1, 5.1, 8.1, 14.1 proposed as memory (1945) see also Williams (memory) tubes cell phones cellular automata, 8.1, 11.1, 11.2, 11.3, 15.1 central arithmetic unit, 5.1, 8.1, 8.2, 8.3, 12.1 Central Park (New York) central processing unit (CPU) Chandrasekhar, Subrahmanyan (1910–1995) Charles II (1630–1685) Charney, Elinor, 9.1, 14.1 Charney, Jule (1917–1981), 9.1, 9.2, 14.1, 14.2, 18.1, 18.2 on Bigelow on von Neumann on Zworykin Chicago, University of, 3.1, 3.2, 5.1, 9.1 Church, Alonzo (1903–1995), 13.1, 13.2, 13.3 Church, George Church-Turing thesis Clarke, Benjamin classification (secrecy), 5.1, 5.2, 13.1, 18.1, 18.2, 18.3 Clippinger, Richard (1913–1997) cloud computing Cocktail Party, The (Eliot, 1950) codes and coding apps (applications), 14.1, 17.1, 18.1 asynchronous “background” vs.

pages: 761 words: 231,902

**
The Singularity Is Near: When Humans Transcend Biology
** by
Ray Kurzweil

additive manufacturing, AI winter, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Albert Einstein, anthropic principle, Any sufficiently advanced technology is indistinguishable from magic, artificial general intelligence, Asilomar, augmented reality, autonomous vehicles, Benoit Mandelbrot, Bill Joy: nanobots, bioinformatics, brain emulation, Brewster Kahle, Brownian motion, business cycle, business intelligence, c2.com, call centre, carbon-based life, cellular automata, Claude Shannon: information theory, complexity theory, conceptual framework, Conway's Game of Life, coronavirus, cosmological constant, cosmological principle, cuban missile crisis, data acquisition, Dava Sobel, David Brooks, Dean Kamen, disintermediation, double helix, Douglas Hofstadter, en.wikipedia.org, epigenetics, factory automation, friendly AI, George Gilder, Gödel, Escher, Bach, informal economy, information retrieval, invention of the telephone, invention of the telescope, invention of writing, iterative process, Jaron Lanier, Jeff Bezos, job automation, job satisfaction, John von Neumann, Kevin Kelly, Law of Accelerating Returns, life extension, lifelogging, linked data, Loebner Prize, Louis Pasteur, mandelbrot fractal, Marshall McLuhan, Mikhail Gorbachev, Mitch Kapor, mouse model, Murray Gell-Mann, mutually assured destruction, natural language processing, Network effects, new economy, Norbert Wiener, oil shale / tar sands, optical character recognition, pattern recognition, phenotype, premature optimization, randomized controlled trial, Ray Kurzweil, remote working, reversible computing, Richard Feynman, Robert Metcalfe, Rodney Brooks, scientific worldview, Search for Extraterrestrial Intelligence, selection bias, semantic web, Silicon Valley, Singularitarianism, speech recognition, statistical model, stem cell, Stephen Hawking, Stewart Brand, strong AI, superintelligent machines, technological singularity, Ted Kaczynski, telepresence, The Coming Technological Singularity, Thomas Bayes, transaction costs, Turing machine, Turing test, Vernor Vinge, Y2K, Yogi Berra

.: Landes Bioscience, 1999), pp. 309–12, http://www.nanomedicine.com/NMI/9.4.2.5.htm. 154. George Whitesides, "Nanoinspiration: The Once and Future Nanomachine," Scientific American 285.3 (September 16,2001): 78–83. 155. "According to Einstein's approximation for Brownian motion, after 1 second has elapsed at room temperature a fluidic water molecule has, on average, diffused a distance of ~50 microns (~400,000 molecular diameters) whereas a l-rnicron nanorobot immersed in that same fluid has displaced by only ~0.7 microns (only ~0.7 device diameter) during the same time period. Thus Brownian motion is at most a minor source of navigational error for motile medical nanorobots," See K. Eric Drexler et al., "Many Future Nanomachines: A Rebuttal to Whitesides' Assertion That Mechanical Molecular Assemblers Are Not Workable and Not a Concern," a Debate about Assemblers, Institute for Molecular Manufacturing, 2001, http://www.imm.org/SciAmDebate2/whitesides.html. 156.

…

George Whitesides complained in Scientific American that "for nanoscale objects, even if one could fabricate a propeller, a new and serious problem would emerge: random jarring by water molecules. These water molecules would be smaller than a nanosubmarine but not much smaller."154 Whitesides's analysis is based on misconceptions. All medical nanobot designs, including those of Freitas, are at least ten thousand times larger than a water molecule. Analyses by Freitas and others show the impact of the Brownian motion of adjacent molecules to be insignificant. Indeed, nanoscale medical robots will be thousands of times more stable and precise than blood cells or bacteria.155 It should also be pointed out that medical nanobots will not require much of the extensive overhead biological cells need to maintain metabolic processes such as digestion and respiration. Nor do they need to support biological reproductive systems.

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It's simple enough, but consider the diverse and beautiful ways it manifests itself: the endlessly varying patterns as it cascades past rocks in a stream, then surges chaotically down a waterfall (all viewable from my office window, incidentally); the billowing patterns of clouds in the sky; the arrangement of snow on a mountain; the satisfying design of a single snowflake. Or consider Einstein's description of the entangled order and disorder in a glass of water (that is, his thesis on Brownian motion). Or elsewhere in the biological world, consider the intricate dance of spirals of DNA during mitosis. How about the loveliness of a tree as it bends in the wind and its leaves churn in a tangled dance? Or the bustling world we see in a microscope? There's transcendence everywhere. A comment on the word "transcendence" is in order here. "To transcend" means "to go beyond," but this need not compel us to adopt an ornate dualist view that regards transcendent levels of reality (such as the spiritual level) to be not of this world.

pages: 634 words: 185,116

**
From eternity to here: the quest for the ultimate theory of time
** by
Sean M. Carroll

Albert Einstein, Albert Michelson, anthropic principle, Arthur Eddington, Brownian motion, cellular automata, Claude Shannon: information theory, Columbine, cosmic microwave background, cosmological constant, cosmological principle, dark matter, dematerialisation, double helix, en.wikipedia.org, gravity well, Harlow Shapley and Heber Curtis, Henri Poincaré, Isaac Newton, Johannes Kepler, John von Neumann, Lao Tzu, Laplace demon, lone genius, low earth orbit, New Journalism, Norbert Wiener, pets.com, Pierre-Simon Laplace, Richard Feynman, Richard Stallman, Schrödinger's Cat, Slavoj Žižek, Stephen Hawking, stochastic process, the scientific method, wikimedia commons

This was problematic, as the Temperance movement was strong in America at the time, and Berkeley in particular was completely dry; a recurring theme in Boltzmann’s account is his attempts to smuggle wine into various forbidden places.193 We will probably never know what mixture of failing health, depression, and scientific controversy contributed to his ultimate act. On the question of the existence of atoms and their utility in understanding the properties of macroscopic objects, any lingering doubts that Boltzmann was right were rapidly dissipating when he died. One of Albert Einstein’s papers in his “miraculous year” of 1905 was an explanation of Brownian motion (the seemingly random motion of small particles suspended in air) in terms of collisions with individual atoms; most remaining skepticism on the part of physicists was soon swept away. Questions about the nature of entropy and the Second Law remain with us, of course. When it comes to explaining the low entropy of our early universe, we won’t ever be able to say, “Boltzmann was right,” because he suggested a number of different possibilities without ever settling on one in particular.

…

TIME IS PERSONAL 53 On the other hand, the achievements for which Paris Hilton is famous are also pretty mysterious. 54 Einstein’s “miraculous year” was 1905, when he published a handful of papers that individually would have capped the career of almost any other scientist: the definitive formulation of special relativity, the explanation of the photoelectric effect (implying the existence of photons and laying the groundwork for quantum mechanics), proposing a theory of Brownian motion in terms of random collisions at the atomic level, and uncovering the equivalence between mass and energy. For most of the next decade he concentrated on the theory of gravity; his ultimate answer, the general theory of relativity, was completed in 1915, when Einstein was thirty-six years old. He died in 1955 at the age of seventy-six. 55 We should also mention Dutch physicist Hendrik Antoon Lorentz, who beginning in 1892 developed the idea that times and distances were affected when objects moved near the speed of light, and derived the “Lorentz transformations,” relating measurements obtained by observers moving with respect to each other.

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See also event horizons; singularities and arrow of time and baby universes model and closed timelike curves and entropy evaporation of and growth of structure and Hawking radiation and holographic principle and information and Laplace and particle accelerators and quantum tunneling and quasars and the real world and redshift and spacetime and string theory thermodynamic analogy and uncertainty principle uniformity of The Black Hole Wars (Susskind) block time/block universe perspective Bohr, Niels Boltzmann, Emma Boltzmann, Ludwig and anthropic principle and arrow of time and atomic theory and black holes death and de Sitter space and entropy and the H-Theorem and initial conditions of the universe and kinetic theory and Loschmidt’s reversibility objection and Past Hypothesis and Principle of Indifference and recurrence theorem and the Second Law of Thermodynamics and statistical mechanics Boltzmann brains Boltzmann-Lucretius scenario Bondi, Hermann boost. bosons bouncing-universe cosmology boundary conditions and cause and effect described and initial conditions of the universe and irreversibility and Maxwell’s Demon and recurrence theorem and time symmetry Bousso, Raphael Brahe, Tycho branes Brillouinéon brown dwarfs Brownian motion Bruno, Giordano bubbles of vacuum Buddhism Bureau of Longitude Callender, Craig Callisto caloric Calvin, John Calvino, Italo Carnot, Lazare Carnot, Nicolas Léonard Sadi Carrey, Jim Carroll, Lewis cause and effect celestial mechanics cellular automata CERN C-field Chandrasekhar Limit chaotic dynamics The Character of Physical Law (Feynman) charge charge conjugation checkerboard world exercise and arrow of time background of and conservation of information and Hawking radiation and holographic principle and information loss and interaction effects and irreversibility and Principle of Indifference and symmetry and testing hypotheses chemistry Chen, Jennifer choice Chronology Protection Conjecture circles in time.

pages: 654 words: 204,260

**
A Short History of Nearly Everything
** by
Bill Bryson

Albert Einstein, Albert Michelson, Alfred Russel Wallace, All science is either physics or stamp collecting, Arthur Eddington, Barry Marshall: ulcers, Brownian motion, California gold rush, Cepheid variable, clean water, Copley Medal, cosmological constant, dark matter, Dava Sobel, David Attenborough, double helix, Drosophila, Edmond Halley, Ernest Rutherford, Fellow of the Royal Society, Harvard Computers: women astronomers, Isaac Newton, James Watt: steam engine, John Harrison: Longitude, Kevin Kelly, Kuiper Belt, Louis Pasteur, luminiferous ether, Magellanic Cloud, Menlo Park, Murray Gell-Mann, out of africa, Richard Feynman, Stephen Hawking, supervolcano, Thomas Malthus, Wilhelm Olbers

Partly it was to do with the limitations of equipment—there were, for instance, no centrifuges until the second half of the century, severely restricting many kinds of experiments—and partly it was social. Chemistry was, generally speaking, a science for businesspeople, for those who worked with coal and potash and dyes, and not gentlemen, who tended to be drawn to geology, natural history, and physics. (This was slightly less true in continental Europe than in Britain, but only slightly.) It is perhaps telling that one of the most important observations of the century, Brownian motion, which established the active nature of molecules, was made not by a chemist but by a Scottish botanist, Robert Brown. (What Brown noticed, in 1827, was that tiny grains of pollen suspended in water remained indefinitely in motion no matter how long he gave them to settle. The cause of this perpetual motion—namely the actions of invisible molecules—was long a mystery.) Things might have been worse had it not been for a splendidly improbable character named Count von Rumford, who, despite the grandeur of his title, began life in Woburn, Massachusetts, in 1753 as plain Benjamin Thompson.

…

(An application to be promoted to technical examiner second class had recently been rejected.) His name was Albert Einstein, and in that one eventful year he submitted to Annalen der Physik five papers, of which three, according to C. P. Snow, “were among the greatest in the history of physics”—one examining the photoelectric effect by means of Planck's new quantum theory, one on the behavior of small particles in suspension (what is known as Brownian motion), and one outlining a special theory of relativity. The first won its author a Nobel Prize and explained the nature of light (and also helped to make television possible, among other things).*17 The second provided proof that atoms do indeed exist—a fact that had, surprisingly, been in some dispute. The third merely changed the world. Einstein was born in Ulm, in southern Germany, in 1879, but grew up in Munich.

…

“Atoms cannot be perceived by the senses . . . they are things of thought,” he wrote. The existence of atoms was so doubtfully held in the German-speaking world in particular that it was said to have played a part in the suicide of the great theoretical physicist, and atomic enthusiast, Ludwig Boltzmann in 1906. It was Einstein who provided the first incontrovertible evidence of atoms' existence with his paper on Brownian motion in 1905, but this attracted little attention and in any case Einstein was soon to become consumed with his work on general relativity. So the first real hero of the atomic age, if not the first personage on the scene, was Ernest Rutherford. Rutherford was born in 1871 in the “back blocks” of New Zealand to parents who had emigrated from Scotland to raise a little flax and a lot of children (to paraphrase Steven Weinberg).

pages: 291 words: 81,703

**
Average Is Over: Powering America Beyond the Age of the Great Stagnation
** by
Tyler Cowen

Amazon Mechanical Turk, Black Swan, brain emulation, Brownian motion, business cycle, Cass Sunstein, choice architecture, complexity theory, computer age, computer vision, computerized trading, cosmological constant, crowdsourcing, dark matter, David Brooks, David Ricardo: comparative advantage, deliberate practice, Drosophila, en.wikipedia.org, endowment effect, epigenetics, Erik Brynjolfsson, eurozone crisis, experimental economics, Flynn Effect, Freestyle chess, full employment, future of work, game design, income inequality, industrial robot, informal economy, Isaac Newton, Johannes Kepler, John Markoff, Khan Academy, labor-force participation, Loebner Prize, low skilled workers, manufacturing employment, Mark Zuckerberg, meta analysis, meta-analysis, microcredit, Myron Scholes, Narrative Science, Netflix Prize, Nicholas Carr, P = NP, pattern recognition, Peter Thiel, randomized controlled trial, Ray Kurzweil, reshoring, Richard Florida, Richard Thaler, Ronald Reagan, Silicon Valley, Skype, statistical model, stem cell, Steve Jobs, Turing test, Tyler Cowen: Great Stagnation, upwardly mobile, Yogi Berra

Larry Kaufman, who developed the evaluation function for the Rybka program, and who is the mastermind of the Komodo program, graduated from MIT with an undergraduate degree in economics in 1968. He went to work on Wall Street as a broker and soon started developing his own form of options-pricing theory, working independently of Fischer Black and Myron Scholes; Scholes later won a Nobel Prize for that contribution. Kaufman’s theory was based on ideas of Brownian motion and the logistic function, the latter of which he took from formulas for calculating chess ratings. In the 1970s he made money by applying his options-pricing work through a trading firm and stopped when the profits went away, and he has since dedicated his life to chess and computer chess, including his work on Rybka and Komodo. He lives in a fine house in one of the nicest parts of suburban Maryland, with his beautiful wife and young daughter.

…

., 37, 164 Babbage, Charles, 6 Banerjee, Abhijit, 222 BBC, 144 Becker, Gary, 226–27 behavioral economics, 75–76, 99, 105, 110, 149, 227 Belle (chess program), 46 benefit costs, 36, 59, 113 Benjamin, Joel, 47 Berlin, Germany, 246 Berra, Yogi, 229 biases, cognitive, 99–100 Bierce, Ambrose, 134 “Big Data,” 185, 221 Black, Fischer, 203 blogs, 180–81 Bonaparte, Napoleon, 148 Borjas, George, 162 “bots,” 144–45 “brain emulation,” 137–38. See also artificial intelligence (AI) branes, 214 Brazil, 20 Breedlove, Philip M., 20 Bresnahan, Timothy F., 33 Brookings Institution, 53 Brooklyn, New York, 172, 240 Brownian motion, 203 Brynjolfsson, Erik, 6, 33 Burks, John, 62 business cycles, 45 business negotiations, 73, 158 California, 8, 241 Campbell, Howard, 246 Canada, 20, 171, 177 Candidates Match, 156 Capablanca, Jose Raoul, 150 capital flows, 166 capitalism, 258 careers, 41–44, 119–25, 126, 202 Carlsen, Magnus, 104, 156, 189 Carr, Nicholas, 153–54 Caterpillar, 38 cell phone service, 118 CEOs, 100 Chen, Yingheng, 79 chess and cheating, 146–51 Chess Olympiad, 147, 189 computer’s influence on quality of play, 106–8 and decision making, 98–99, 101–2, 104–5, 129 early computer chess, 7, 46–47, 67–70 and face-to-face instruction, 195 and gender issues, 31, 106–8 and globalization of competition, 168 and intuition, 68–70, 72, 97, 99, 101, 105–6, 109–10, 114–15 machine and human styles contrasted, 75–76, 77–86 machine vs. machine matches, 70–75 as model for education, 185–88, 191–92, 202–3 and opening books, 83–85, 86–87, 107, 135, 203 and player ratings, 120 simplicity of rules, 48–49 spectator interest in, 156–57 See also Freestyle chess Chess Tiger (chess program), 78 children and wealth inequality, 249 China chess players from, 108, 189 and demographic trends, 230 and geographic trends, 177 and global competition, 171 and labor competition, 5, 163–64, 167, 169–70 and political trends, 252 and scientific specialization, 216 choice.

**
The Golden Ratio: The Story of Phi, the World's Most Astonishing Number
** by
Mario Livio

Albert Einstein, Albert Michelson, Alfred Russel Wallace, Benoit Mandelbrot, Brownian motion, Buckminster Fuller, cosmological constant, Elliott wave, Eratosthenes, Gödel, Escher, Bach, Isaac Newton, Johann Wolfgang von Goethe, Johannes Kepler, mandelbrot fractal, music of the spheres, Nash equilibrium, Ralph Nelson Elliott, Ralph Waldo Emerson, random walk, Richard Feynman, Ronald Reagan, Thales of Miletus, the scientific method

There were also many cases of feedback between physics and mathematics, where a physical phenomenon inspired a mathematical model that later proved to be the explanation of an entirely different physical phenomenon. An excellent example is provided by the phenomenon known as Brownian motion. In 1827, British botanist Robert Brown (1773–1858) observed that when pollen particles are suspended in water, they get into a state of agitated motion. This effect was explained by Einstein in 1905 as resulting from the collisions that the colloidal particles experience with the molecules of the surrounding fluid. Each single collision has a negligible effect, because the pollen grains are millions of times more massive than the water molecules, but the persistent bombardment has a cumulative effect. Amazingly, the same model was found to apply to the motions of stars in star clusters. There the Brownian motion is produced by the cumulative effect of many stars passing by any given star, with each passage altering the motion (through gravitational interaction) by a tiny amount.

pages: 70 words: 22,682

**
Einstein's Dreams
** by
Alan Lightman

For one, perhaps The Old One is not interested in getting close to his creations, intelligent or not. For another, it is not obvious that knowledge is closeness. For yet another, this time project could be too big for a twenty-six-year-old. On the other hand, Besso thinks that his friend might be capable of anything. Already this year, Einstein has completed his Ph.D. thesis, finished one paper on photons and another on Brownian motion. The current project actually began as an investigation of electricity and magnetism, which, Einstein suddenly announced one day, would require a reconception of time. Besso is dazzled by Einstein’s ambition. For a while, Besso leaves Einstein alone with his thoughts. He wonders what Anna has cooked for dinner and looks down a side street where a silver boat on the Aare glints in the low sun.

pages: 88 words: 25,047

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The Mathematics of Love: Patterns, Proofs, and the Search for the Ultimate Equation
** by
Hannah Fry

Brownian motion, John Nash: game theory, linear programming, Nash equilibrium, Pareto efficiency, recommendation engine, Skype, statistical model

To me, these failings reflect a false impression of mathematics that’s as grave an error as a mistrust of it all together. But beyond its limitations, for me, mathematics has a beauty that encapsulates the realistic, the idiosyncratic and the abstract. And I’ll never get tired of finding more hidden patterns and counter-intuitive results in the real world, regardless of the assumptions it took to get there. Endnotes 1. Breaking the problem down makes the estimate like Brownian motion. An estimate with steps would have an error that diffused like √n. 2. And this is my book. 3. Just so we’re clear, we’re talking about reflection symmetry here. Rotational symmetry in a face is generally considered a bad thing. 4. See, for example, In Your Face by David Perrett for a well-written and comprehensive overview. 5. For n questions, the formula becomes: . 6. This is all true. 7.

pages: 315 words: 92,151

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Ten Billion Tomorrows: How Science Fiction Technology Became Reality and Shapes the Future
** by
Brian Clegg

Albert Einstein, anthropic principle, Brownian motion, call centre, Carrington event, combinatorial explosion, don't be evil, Ernest Rutherford, experimental subject, game design, gravity well, hive mind, invisible hand, Isaac Newton, Johannes Kepler, John von Neumann, Kickstarter, nuclear winter, pattern recognition, RAND corporation, Ray Kurzweil, RFID, Richard Feynman, Schrödinger's Cat, Search for Extraterrestrial Intelligence, silicon-based life, speech recognition, stem cell, Stephen Hawking, Steve Jobs, Turing test

The researchers at the Australian National Laboratory in Canberra made small hollow glass spheres heat up at particular points around their surface with the laser. Where the surface was heated, air molecules that come into contact with the glass gain extra energy. As air molecules push away from the surface, the recoil moves the sphere in the opposite direction. In effect, this is controlled Brownian motion. This is the mechanism that causes small particles like pollen grains to dance around in water, as if they are alive. Albert Einstein explained the effect as being caused by impact from the unseen water molecules on the tiny grains. The interesting aspect of the laser “tractor beam” is that the position heated on the surface of the glass spheres can be modified by changing the polarization of the laser light, so that the effect can be used to move the spheres in any desired direction.

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See also particle gun; phaser; ray guns Archimedes as inventor of light and mirrors in projectile compared to SF use of “Beep” (Blish) Bell, Alexander Graham Bell, Jocelyn Bell Aircraft Corporation Bell Labs laser development by speech recognition and de Bergerac, Cyrano Berkeley Lower Extremity Exoskeleton (BLEEX) The Bionic Woman Blade Runner BLEEX. See Berkeley Lower Extremity Exoskeleton Blish, James AI governments by instantaneous transmitter by virtual learning and Borg (fictional characters) Bose-Einstein condensate Bostrom, Nick The Boys from Brazil (Levin) Bradbury, Ray brain to brain link to computer link electrodes in implants interface to programming BrainGate Brownian motion Brunner, John Bulwer-Lytton, Edward Campbell, John W. Campbell, Murray S. A Canticle for Leibowitz (Miller) Čapek, Karel carbon aliens and artificial muscles and Moon’s lack of nanotubes Carmack, John Carrington event (1859) Casimir effect Cayley, George cell phones Cernan, Eugene chaos theory chess computerized invention of mechanical Chiao, Raymond The Chrysalids (Wyndham) Cities in Flight series (Blish) Clarke, Arthur C.

pages: 389 words: 109,207

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Fortune's Formula: The Untold Story of the Scientific Betting System That Beat the Casinos and Wall Street
** by
William Poundstone

Albert Einstein, anti-communist, asset allocation, beat the dealer, Benoit Mandelbrot, Black-Scholes formula, Brownian motion, buy and hold, buy low sell high, capital asset pricing model, Claude Shannon: information theory, computer age, correlation coefficient, diversified portfolio, Edward Thorp, en.wikipedia.org, Eugene Fama: efficient market hypothesis, high net worth, index fund, interest rate swap, Isaac Newton, Johann Wolfgang von Goethe, John Meriwether, John von Neumann, Kenneth Arrow, Long Term Capital Management, Louis Bachelier, margin call, market bubble, market fundamentalism, Marshall McLuhan, Myron Scholes, New Journalism, Norbert Wiener, offshore financial centre, Paul Samuelson, publish or perish, quantitative trading / quantitative ﬁnance, random walk, risk tolerance, risk-adjusted returns, Robert Shiller, Robert Shiller, Ronald Reagan, Rubik’s Cube, short selling, speech recognition, statistical arbitrage, The Predators' Ball, The Wealth of Nations by Adam Smith, transaction costs, traveling salesman, value at risk, zero-coupon bond, zero-sum game

As we’ve already seen, the fluctuations of a bettor’s bankroll in a game of chance constitute a random walk (a one-dimensional random walk, since wealth can only move up or down). With time, the gambler’s wealth strays further and further from its original value, and this eventually leads to ruin. At about the time Bachelier was writing, Albert Einstein was puzzling over Brownian motion, the random jitter of microscopic particles suspended in a fluid. The explanation, Einstein surmised, was that the particles were being hit on all sides by invisible molecules. These random collisions cause the visible motion. The mathematical treatment of Brownian motion that Einstein published in 1905 was similar to, but less advanced than, the one that Bachelier had already derived for stock prices. Einstein, like practically everyone else, had never heard of Bachelier. The Random Walk Cosa Nostra SAMUELSON ADOPTED Bachelier’s ideas into his own thinking.

pages: 626 words: 181,434

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I Am a Strange Loop
** by
Douglas R. Hofstadter

Albert Einstein, Andrew Wiles, Benoit Mandelbrot, Brownian motion, double helix, Douglas Hofstadter, Georg Cantor, Gödel, Escher, Bach, Isaac Newton, James Watt: steam engine, John Conway, John von Neumann, mandelbrot fractal, pattern recognition, Paul Erdős, place-making, probability theory / Blaise Pascal / Pierre de Fermat, publish or perish, random walk, Ronald Reagan, self-driving car, Silicon Valley, telepresence, Turing machine

Think of how the water in a glass sitting on a table seems completely still to us. If our eyes could shift levels (think of the twist that zooms binoculars in or out) and allow us to peer at the water at the micro-level, we would realize that it is not peaceful at all, but a crazy tumult of bashings of water molecules. In fact, if colloidal particles are added to a glass of water, then it becomes a locus of Brownian motion, which is an incessant random jiggling of the colloidal particles, due to a myriad of imperceptible collisions with the water molecules, which are far tinier. (The colloidal particles here play the role of simmballs, and the water molecules play the role of simms.) The effect, which is visible under a microscope, was explained in great detail in 1905 by Albert Einstein using the theory of molecules, which at the time were only hypothetical entities, but Einstein’s explanation was so far-reaching (and, most crucially, consistent with experimental data) that it became one of the most important confirmations that molecules do exist.

…

On a skiing vacation in the Sierra Nevada, far away from home, my children and I took advantage of the “doggie cam” at the Bloomington kennel where we had boarded our golden retriever Ollie, and thanks to the World Wide Web, we were treated to a jerky sequence of stills of a couple of dozen dogs meandering haphazardly in a fenced-in play area outdoors, looking a bit like particles undergoing random Brownian motion, and although each pooch was rendered by a pretty small array of pixels, we could often recognize our Ollie by subtle features such as the angle of his tail. For some reason, the kids and I found this act of visual eavesdropping on Ollie quite hilarious, and although we could easily describe this droll scene to our human friends, and although I would bet a considerable sum that these few lines of text have vividly evoked in your mind both the canine scene at the kennel and the human scene at the ski resort, we all realized that there was not a hope in hell that we could ever explain to Ollie himself that we had been “spying” on him from thousands of miles away.

…

James) Bloomington, Indiana blue humpback blueprint used in self-replicating machine blurriness of everyday concepts boat with endless succession of leaks bodies vs. souls body parts initiate self-representation Bohr atom, as stepping stone en route to quantum mechanics Bohr, Niels boiling water, reliability of Bonaparte, see Napoleon bon mots: by Carol Hofstadter; by David Moser “Book of nature written in mathematics” (Galileo) Boole, George boot-removal analogy boundaries between souls, blurriness of boundaries, macroscopic, as irrelevant to particles box with flaps making loop Brabner, George brain activity: hiddenness of substrate of; modeled computationally; need for high-level view of; obviousness of high-level view of brain-in-vat scenario brain research, nature of brain-scanning gadgets brain structures brains: compared to hearts; complexity of, as relevant to consciousness; controlling bodies directly vs. indirectly; eerieness of; evolution of; as fusion of two half-brains; as inanimate; inhabited by more than one “I”; interacting via ideas; main; as multi-level systems; not responsible for color qualia; perceiving multiple environments simultaneously; receiving sensory input directly or indirectly; resembling inert sponges; unlikely substrate for interiority Braitenberg, Valentino bread becoming a gun Brown, Charlie Brownian motion Brünn, Austria (birthplace of Kurt Gödel) buck stopping at “I” Bugeaud, Yann bunnies as edible beings “burstwise advance in evolution” (Sperry) Bushmiller, Ernie butterflies: not respecting precinct boundaries; in orchard, as metaphor for human soul Buzzaround Betty C caged-bird metaphor; as analogous to Newtonian physics; hints at wrongness of; as ingrained habit; at level of countries and cultures; metaphors opposed to; normally close to correct; as reinforced by language; temptingness of Cagey’s doubly-hearable line cake whose pieces all taste bad, as inferrred by analogy candles cantata aria Cantor, Georg capital punishment Capitalized Essences; canceled careenium; growing up; self-image of; two views of; unsatisfactory to skeptics Carnap, Rudolf Carol-and-Doug: as higher-level entity; joint mind of; shared dreads and dreams of Carolness, survival of Carol-symbol in Doug’s brain: being vs. representing a person; triggerability of cars: as high-level objects; pushed around by desires Cartesian Eggo Cartesian Ego; as commonsensical view; fading of Cartesian Ergo Cartier-Bresson, Henri Caspian Gemstones, allegory of casual façade as Searlian ploy Catcher in the Rye, The (Salinger) categories and symbols; see also repertoires categorization mechanisms: converting complexity into simplicity; as determining size of self; efficiency of Caulfield, Holden causality: bottoming out in “I”; buck of, stopping at “I”; of dogmas in triggering wars; and insight; schism between two types of; stochasticity of in everyday life; tradeoffs in; upside-down; see also downward causality causal potency: of ideas in brain; of meanings of PM strings; of patterns “causal powers of the brain”, semantic cell phones as universal machines Center for Research into Consciousness and Cognetics Central Consciousness Bank central loop of cognition cerulean sardine chain of command in brain chainium (dominos), causality in Chaitin, Greg Chalmers, David; zombie twin of chameleonic nature: of integers; of universal machines Chantal Duplessix, seeing pixel-patterns as events; missing second level of Aimable’s remarks chaos, potential, in number theory Chaplin twins, (Freda and Greta) character structure of an individual Chávez, César chemistry: bypassed in explanation of heredity and reproduction; of carbon as supposed key to consciousness; reduced to physics; virtual, inside computers “chemistry” (interpersonal); enabling people to live inside each other; as function of musical taste alignment; as highly real causal agent; as “hooked atoms”; lack of, between people “chicken” (meat) vs. chickens chickens as edible creatures children: as catalysts to soul merger of parents; as having fewer hunekers than adults; self-awareness of chimpanzees chinchillas Chinese people, as spread-out entity Chinese Room chirpy notes and deep notes interchanged Chopin, Frédéric; étude Op. 25 no. 4 in A minor; étude Op. 25 no. 11 in A minor; nostalgia of; pieces by, as soul-shards of; survival of chord–angle theorem Christiansen, Winfield church bells Church’s theorem cinnamon-roll aroma in airport corridor circular reasoning, validity of, in video feedback circumventing bans by exploiting flexible substrates clarity as central goal Class A vs.

pages: 153 words: 12,501

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Mathematics for Economics and Finance
** by
Michael Harrison,
Patrick Waldron

Brownian motion, buy low sell high, capital asset pricing model, compound rate of return, discrete time, incomplete markets, law of one price, market clearing, Myron Scholes, Pareto efficiency, risk tolerance, riskless arbitrage, short selling, stochastic process

It follows very naturally from the stuff in Section 5.4. 7.2.2 The Black-Scholes option pricing model Fischer Black died in 1995. In 1997, Myron Scholes and Robert Merton were awarded the Nobel Prize in Economics ‘for a new method to determine the value of derivatives.’ See http://www.nobel.se/announcement-97/economy97.html Black and Scholes considered a world in which there are three assets: a stock, whose price, S̃t , follows the stochastic differential equation: dS̃t = µS̃t dt + σ S̃t dz̃t , where {z̃t }Tt=0 is a Brownian motion process; a bond, whose price, Bt , follows the differential equation: dBt = rBt dt; and a call option on the stock with strike price X and maturity date T . Revised: December 2, 1998 138 7.2. ARBITRAGE AND PRICING DERIVATIVE SECURITIES They showed how to construct an instantaneously riskless portfolio of stocks and options, and hence, assuming that the principle of no arbitrage holds, derived the Black-Scholes partial differential equation which must be satisfied by the option price.

pages: 119 words: 10,356

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Topics in Market Microstructure
** by
Ilija I. Zovko

Brownian motion, computerized trading, continuous double auction, correlation coefficient, financial intermediation, Gini coefficient, information asymmetry, market design, market friction, market microstructure, Murray Gell-Mann, p-value, quantitative trading / quantitative ﬁnance, random walk, stochastic process, stochastic volatility, transaction costs

Models of spread, starting withDemsetz (1968); Tinic (1972); Stoll (1978); Amihud and Mendelson (1980); Ho and Stoll (1981), have examined the possible determinants of spreads as a result of rational, utilitymaximizing problem faced by the market makers. Models providing insight into the utility-maximizing response of agents to other various measures of market conditions such as volatility are for example Lo (2002) who investigate a simple model in which the log stock price is modeled as a Brownian motion diffusion process. Provided agents prefer a lower expected execution time, their model predicts a positive relationship between volatility and limit order placement. Copeland and Galai (1983); Glosten and Milgrom (1985); Easley and O’Hara (1987); Glosten (1995); Foucault (1999); Easley et al. (2001) examine asymmetric information effects on order placement. Andersen (1996) modifies the Glosten and Milgrom (1985) model with the stochastic volatility and information flow perspective.

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Hollow City
** by
Rebecca Solnit,
Susan Schwartzenberg

blue-collar work, Brownian motion, dematerialisation, Golden Gate Park, Haight Ashbury, housing crisis, informal economy, Jane Jacobs, Loma Prieta earthquake, low skilled workers, new economy, New Urbanism, pets.com, rent control, Silicon Valley, South of Market, San Francisco, The Death and Life of Great American Cities, union organizing, upwardly mobile, urban planning, urban renewal, wage slave

Before elevators, the top floor Parisian buildings were was designed as a sort of residential hotel rooms, called ckambres de bonne, maids' in my day, dents and African immigrants filled them; they usually and a communal sink stove; refrigeration stu- a cold-water hallway (one cooked on a camping toilet in the was the windowsill ated a sort of integrated housing: a —the rooms when poor had of in winter). This building style cre- famous of the nineteenth illustration century shows a cross-section of an apartment house with the bourgeoisie in armchairs just above the ground-floor concierge and the inhabi- tants getting progressively poorer as it ascended to the wretches huddled under the rooftop. Bohemia was the brownian motion of urban brought together people of different who would rise classes, was the incubator life; it for those through talent or sink through addiction, poverty, mad- A Paris street Gallery, ness; was where the new would be palatable in the mainstream; tried out long before it would be found was where memory was kept alive as paint- ings, stories, politics. George Sand's novel Horace gives at the time of the 1830 revolution; cated painters and dilettantes, a provincial family's funds were working-class tions with the varying slumming law-student squandering few sympathetically drawn were seldom participants his grisettes.

pages: 349 words: 134,041

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Traders, Guns & Money: Knowns and Unknowns in the Dazzling World of Derivatives
** by
Satyajit Das

accounting loophole / creative accounting, Albert Einstein, Asian financial crisis, asset-backed security, beat the dealer, Black Swan, Black-Scholes formula, Bretton Woods, BRICs, Brownian motion, business process, buy and hold, buy low sell high, call centre, capital asset pricing model, collateralized debt obligation, commoditize, complexity theory, computerized trading, corporate governance, corporate raider, Credit Default Swap, credit default swaps / collateralized debt obligations, cuban missile crisis, currency peg, disintermediation, diversification, diversified portfolio, Edward Thorp, Eugene Fama: efficient market hypothesis, Everything should be made as simple as possible, financial innovation, fixed income, Haight Ashbury, high net worth, implied volatility, index arbitrage, index card, index fund, interest rate derivative, interest rate swap, Isaac Newton, job satisfaction, John Meriwether, locking in a profit, Long Term Capital Management, mandelbrot fractal, margin call, market bubble, Marshall McLuhan, mass affluent, mega-rich, merger arbitrage, Mexican peso crisis / tequila crisis, money market fund, moral hazard, mutually assured destruction, Myron Scholes, new economy, New Journalism, Nick Leeson, offshore financial centre, oil shock, Parkinson's law, placebo effect, Ponzi scheme, purchasing power parity, quantitative trading / quantitative ﬁnance, random walk, regulatory arbitrage, Right to Buy, risk-adjusted returns, risk/return, Satyajit Das, shareholder value, short selling, South Sea Bubble, statistical model, technology bubble, the medium is the message, the new new thing, time value of money, too big to fail, transaction costs, value at risk, Vanguard fund, volatility smile, yield curve, Yogi Berra, zero-coupon bond

The daily price change is scaled to an annual volatility by multiplying the daily price changes by the square root of time; that is, 1% per day translates into an annual volatility of 15.81% (1% × √250 days in the year). In the world of precise high finance the business year is almost always assumed to be roughly 250 days (52 weeks × 5 days –, say, 10 public holidays). This is the root mean square rule, a common statistical trick, based on Geometric Brownian Motion (GBM). GBM describes how something like the stock price moves randomly over time from its current price in such a way that the daily price changes are distributed normally. The average price change is proportional to the square root of the elapsed time. GBM derives from the work of a botanist, Robert Brown. Brown wrote a paper entitled ‘A Brief Account of Microscopical Observations Made in the Months of June, July and August 1827, on the Particles Contained in the Pollen of Plants’.

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However, the text is different. 6 ‘What Worries Warren’ (3 March 2003) Fortune. 13_INDEX.QXD 17/2/06 4:44 pm Page 325 Index accounting rules 139, 221, 228, 257 Accounting Standards Board 33 accrual accounting 139 active fund management 111 actuaries 107–10, 205, 289 Advance Corporation Tax 242 agency business 123–4, 129 agency theory 117 airline profits 140–1 Alaska 319 Allen, Woody 20 Allied Irish Bank 143 Allied Lyons 98 alternative investment strategies 112, 308 American Express 291 analysts, role of 62–4 anchor effect 136 Anderson, Rolf 92–4 annuities 204–5 ANZ Bank 277 Aquinas, Thomas 137 arbitrage 33, 38–40, 99, 114, 137–8, 171–2, 245–8, 253–5, 290, 293–6 arbitration 307 Argentina 45 arithmophobia 177 ‘armpit theory’ 303 Armstrong World Industries 274 arrears assets 225 Ashanti Goldfields 97–8, 114 Asian financial crisis (1997) 4, 9, 44–5, 115, 144, 166, 172, 207, 235, 245, 252, 310, 319 asset consultants 115–17, 281 ‘asset growth’ strategy 255 asset swaps 230–2 assets under management (AUM) 113–4, 117 assignment of loans 267–8 AT&T 275 attribution of earnings 148 auditors 144 Australia 222–4, 254–5, 261–2 back office functions 65–6 back-to-back loans 35, 40 backwardation 96 Banca Popolare di Intra 298 Bank of America 298, 303 Bank of International Settlements 50–1, 281 Bank of Japan 220 Bankers’ Trust (BT) 59, 72, 101–2, 149, 217–18, 232, 268–71, 298, 301, 319 banking regulations 155, 159, 162, 164, 281, 286, 288 banking services 34; see also commercial banks; investment banks bankruptcy 276–7 Banque Paribas 37–8, 232 Barclays Bank 121–2, 297–8 13_INDEX.QXD 17/2/06 326 4:44 pm Page 326 Index Baring, Peter 151 Baring Brothers 51, 143, 151–2, 155 ‘Basel 2’ proposal 159 basis risk 28, 42, 274 Bear Stearns 173 bearer eurodollar collateralized securities (BECS) 231–3 ‘behavioural finance’ 136 Berkshire Hathaway 19 Bermudan options 205, 227 Bernstein, Peter 167 binomial option pricing model 196 Bismarck, Otto von 108 Black, Fischer 22, 42, 160, 185, 189–90, 193, 195, 197, 209, 215 Black–Scholes formula for option pricing 22, 185, 194–5 Black–Scholes–Merton model 160, 189–93, 196–7 ‘black swan’ hypothesis 130 Blair, Tony 223 Bogle, John 116 Bohr, Niels 122 Bond, Sir John 148 ‘bond floor’ concept 251–4 bonding 75–6, 168, 181 bonuses 146–51, 244, 262, 284–5 Brady Commission 203 brand awareness and brand equity 124, 236 Brazil 302 Bretton Woods system 33 bribery 80, 303 British Sky Broadcasting (BSB) 247–8 Brittain, Alfred 72 broad index secured trust offerings (BISTROs) 284–5 brokers 69, 309 Brown, Robert 161 bubbles 210, 310, 319 Buconero 299 Buffet, Warren 12, 19–20, 50, 110–11, 136, 173, 246, 316 business process reorganization 72 business risk 159 Business Week 130 buy-backs 249 ‘call’ options 25, 90, 99, 101, 131, 190, 196 callable bonds 227–9, 256 capital asset pricing model (CAPM) 111 capital flow 30 capital guarantees 257–8 capital structure arbitrage 296 Capote, Truman 87 carbon trading 320 ‘carry cost’ model 188 ‘carry’ trades 131–3, 171 cash accounting 139 catastrophe bonds 212, 320 caveat emptor principle 27, 272 Cayman Islands 233–4 Cazenove (company) 152 CDO2 292 Cemex 249–50 chaos theory 209, 312 Chase Manhattan Bank 143, 299 Chicago Board Options Exchange 195 Chicago Board of Trade (CBOT) 25–6, 34 chief risk officers 177 China 23–5, 276, 302–4 China Club, Hong Kong 318 Chinese walls 249, 261, 280 chrematophobia 177 Citibank and Citigroup 37–8, 43, 71, 79, 94, 134–5, 149, 174, 238–9 Citron, Robert 124–5, 212–17 client relationships 58–9 Clinton, Bill 223 Coats, Craig 168–9 collateral requirements 215–16 collateralized bond obligations (CBOs) 282 collateralized debt obligations (CDOs) 45, 282–99 13_INDEX.QXD 17/2/06 4:44 pm Page 327 Index collateralized fund obligations (CFOs) 292 collateralized loan obligations (CLOs) 283–5, 288 commercial banks 265–7 commoditization 236 commodity collateralized obligations (CCOs) 292 commodity prices 304 Commonwealth Bank of Australia 255 compliance officers 65 computer systems 54, 155, 197–8 concentration risk 271, 287 conferences with clients 59 confidence levels 164 confidentiality 226 Conseco 279–80 contagion crises 291 contango 96 contingent conversion convertibles (co-cos) 257 contingent payment convertibles (co-pays) 257 Continental Illinois 34 ‘convergence’ trading 170 convertible bonds 250–60 correlations 163–6, 294–5; see also default correlations corruption 303 CORVUS 297 Cox, John 196–7 credit cycle 291 credit default swaps (CDSs) 271–84, 293, 299 credit derivatives 129, 150, 265–72, 282, 295, 299–300 Credit Derivatives Market Practices Committee 273, 275, 280–1 credit models 294, 296 credit ratings 256–7, 270, 287–8, 297–8, 304 credit reserves 140 credit risk 158, 265–74, 281–95, 299 327 credit spreads 114, 172–5, 296 Credit Suisse 70, 106, 167 credit trading 293–5 CRH Capital 309 critical events 164–6 Croesus 137 cross-ruffing 142 cubic splines 189 currency options 98, 218, 319 custom repackaged asset vehicles (CRAVEs) 233 daily earning at risk (DEAR) concept 160 Daiwa Bank 142 Daiwa Europe 277 Danish Oil and Natural Gas 296 data scrubbing 142 dealers, work of 87–8, 124–8, 133, 167, 206, 229–37, 262, 295–6; see also traders ‘death swap’ strategy 110 decentralization 72 decision-making, scientific 182 default correlations 270–1 defaults 277–9, 287, 291, 293, 296, 299 DEFCON scale 156–7 ‘Delta 1’ options 243 delta hedging 42, 200 Deming, W.E. 98, 101 Denmark 38 deregulation, financial 34 derivatives trading 5–6, 12–14, 18–72, 79, 88–9, 99–115, 123–31, 139–41, 150, 153, 155, 175, 184–9, 206–8, 211–14, 217–19, 230, 233, 257, 262–3, 307, 316, 319–20; see also equity derivatives Derman, Emmanuel 185, 198–9 Deutsche Bank 70, 104, 150, 247–8, 274, 277 devaluations 80–1, 89, 203–4, 319 13_INDEX.QXD 17/2/06 4:44 pm Page 328 328 Index dilution of share capital 241 DINKs 313 Disney Corporation 91–8 diversification 72, 110–11, 166, 299 dividend yield 243 ‘Dr Evil’ trade 135 dollar premium 35 downsizing 73 Drexel Burnham Lambert (DBL) 282 dual currency bonds 220–3; see also reverse dual currency bonds earthquakes, bonds linked to 212 efficient markets hypothesis 22, 31, 111, 203 electronic trading 126–30, 134 ‘embeddos’ 218 emerging markets 3–4, 44, 115, 132–3, 142, 212, 226, 297 Enron 54, 142, 250, 298 enterprise risk management (ERM) 176 equity capital management 249 equity collateralized obligations (ECOs) 292 equity derivatives 241–2, 246–9, 257–62 equity index 137–8 equity investment, retail market in 258–9 equity investors’ risk 286–8 equity options 253–4 equity swaps 247–8 euro currency 171, 206, 237 European Bank for Reconstruction and Development 297 European currency units 93 European Union 247–8 Exchange Rate Mechanism, European 204 exchangeable bonds 260 expatriate postings 81–2 expert witnesses 310–12 extrapolation 189, 205 extreme value theory 166 fads of management science 72–4 ‘fairway bonds’ 225 Fama, Eugene 22, 111, 194 ‘fat tail’ events 163–4 Federal Accounting Standards Board 266 Federal Home Loans Bank 213 Federal National Mortgage Association 213 Federal Reserve Bank 20, 173 Federal Reserve Board 132 ‘Ferraris’ 232 financial engineering 228, 230, 233, 249–50, 262, 269 Financial Services Authority (FSA), Japan 106, 238 Financial Services Authority (FSA), UK 15, 135 firewalls 235–6 firing of staff 84–5 First Interstate Ltd 34–5 ‘flat’ organizations 72 ‘flat’ positions 159 floaters 231–2; see also inverse floaters ‘flow’ trading 60–1, 129 Ford Motors 282, 296 forecasting 135–6, 190 forward contracts 24–33, 90, 97, 124, 131, 188 fugu fish 239 fund management 109–17, 286, 300 futures see forward contracts Galbraith, John Kenneth 121 gamma risk 200–2, 294 Gauss, Carl Friedrich 160–2 General Motors 279, 296 General Reinsurance 20 geometric Brownian motion (GBM) 161 Ghana 98 Gibson Greeting Cards 44 Glass-Steagall Act 34 gold borrowings 132 13_INDEX.QXD 17/2/06 4:44 pm Page 329 Index gold sales 97, 137 Goldman Sachs 34, 71, 93, 150, 173, 185 ‘golfing holiday bonds’ 224 Greenspan, Alan 6, 9, 19–21, 29, 43, 47, 50, 53, 62, 132, 159, 170, 215, 223, 308 Greenwich NatWest 298 Gross, Bill 19 Guangdong International Trust and Investment Corporation (GITIC) 276–7 guaranteed annuity option (GAO) contracts 204–5 Gutenfreund, John 168–9 gyosei shido 106 Haghani, Victor 168 Hamanaka, Yasuo 142 Hamburgische Landesbank 297 Hammersmith and Fulham, London Borough of 66–7 ‘hara-kiri’ swaps 39 Hartley, L.P. 163 Hawkins, Greg 168 ‘heaven and hell’ bonds 218 hedge funds 44, 88–9, 113–14, 167, 170–5, 200–2, 206, 253–4, 262–3, 282, 292, 296, 300, 308–9 hedge ratio 264 hedging 24–8, 31, 38–42, 60, 87–100, 184, 195–200, 205–7, 214, 221, 229, 252, 269, 281, 293–4, 310 Heisenberg, Werner 122 ‘hell bonds’ 218 Herman, Clement (‘Crem’) 45–9, 77, 84, 309 Herodotus 137, 178 high net worth individuals (HNWIs) 237–8, 286 Hilibrand, Lawrence 168 Hill Samuel 231–2 329 The Hitchhiker’s Guide to the Galaxy 189 Homer, Sidney 184 Hong Kong 9, 303–4 ‘hot tubbing’ 311–12 HSBC Bank 148 HSH Nordbank 297–8 Hudson, Kevin 102 Hufschmid, Hans 77–8 IBM 36, 218, 260 ICI 34 Iguchi, Toshihude 142 incubators 309 independent valuation 142 indexed currency option notes (ICONs) 218 India 302 Indonesia 5, 9, 19, 26, 55, 80–2, 105, 146, 219–20, 252, 305 initial public offerings 33, 64, 261 inside information and insider trading 133, 241, 248–9 insurance companies 107–10, 117, 119, 150, 192–3, 204–5, 221, 223, 282, 286, 300; see also reinsurance companies insurance law 272 Intel 260 intellectual property in financial products 226 Intercontinental Hotels Group (IHG) 285–6 International Accounting Standards 33 International Securities Market Association 106 International Swap Dealers Association (ISDA) 273, 275, 279, 281 Internet stock and the Internet boom 64, 112, 259, 261, 310, 319 interpolation of interest rates 141–2, 189 inverse floaters 46–51, 213–16, 225, 232–3 13_INDEX.QXD 17/2/06 4:44 pm Page 330 330 Index investment banks 34–8, 62, 64, 67, 71, 127–8, 172, 198, 206, 216–17, 234, 265–7, 298, 309 investment managers 43–4 investment styles 111–14 irrational decisions 136 Italy 106–7 Ito’s Lemma 194 Japan 39, 43, 82–3, 92, 94, 98–9, 101, 106, 132, 142, 145–6, 157, 212, 217–25, 228, 269–70 Jensen, Michael 117 Jett, Joseph 143 JP Morgan (company) 72, 150, 152, 160, 162, 249–50, 268–9, 284–5, 299; see also Morgan Guaranty junk bonds 231, 279, 282, 291, 296–7 JWM Associates 175 Kahneman, Daniel 136 Kaplanis, Costas 174 Kassouf, Sheen 253 Kaufman, Henry 62 Kerkorian, Kirk 296 Keynes, J.M. 167, 175, 198 Keynesianism 5 Kidder Peabody 143 Kleinwort Benson 40 Korea 9, 226, 278 Kozeny, Viktor 121 Krasker, William 168 Kreiger, Andy 319 Kyoto Protocol 320 Lavin, Jack 102 law of large numbers 192 Leeson, Nick 51, 131, 143, 151 legal opinions 47, 219–20, 235, 273–4 Leibowitz, Martin 184 Leland, Hayne 42, 202 Lend Lease Corporation 261–2 leptokurtic conditions 163 leverage 31–2, 48–50, 54, 99, 102–3, 114, 131–2, 171–5, 213–14, 247, 270–3, 291, 295, 305, 308 Lewis, Kenneth 303 Lewis, Michael 77–8 life insurance 204–5 Lintner, John 111 liquidity options 175 liquidity risk 158, 173 litigation 297–8 Ljunggren, Bernt 38–40 London Inter-Bank Offered Rate (LIBOR) 6, 37 ‘long first coupon’ strategy 39 Long Term Capital Management (LTCM) 44, 51, 62, 77–8, 84, 114, 166–75, 187, 206, 210, 215–18, 263–4, 309–10 Long Term Credit Bank of Japan 94 LOR (company) 202 Louisiana Purchase 319 low exercise price options (LEPOs) 261 Maastricht Treaty and criteria 106–7 McLuhan, Marshall 134 McNamara, Robert 182 macro-economic indicators, derivatives linked to 319 Mahathir Mohammed 31 Malaysia 9 management consultants 72–3 Manchester United 152 mandatory convertibles 255 Marakanond, Rerngchai 302 margin calls 97–8, 175 ‘market neutral’ investment strategy 114 market risk 158, 173, 265 marketable eurodollar collateralized securities (MECS) 232 Markowitz, Harry 110 mark-to-market accounting 10, 100, 139–41, 145, 150, 174, 215–16, 228, 244, 266, 292, 295, 298 Marx, Groucho 24, 57, 67, 117, 308 13_INDEX.QXD 17/2/06 4:44 pm Page 331 Index mathematics applied to financial instruments 209–10; see also ‘quants’ matrix structures 72 Meckling, Herbert 117 Melamed, Leo 34, 211 merchant banks 38 Meriwether, John 167–9, 172–5 Merrill Lynch 124, 150, 217, 232 Merton, Robert 22, 42, 168–70, 175, 185, 189–90, 193–7, 210 Messier, Marie 247 Metallgesellschaft 95–7 Mexico 44 mezzanine finance 285–8, 291–7 MG Refining and Marketing 95–8, 114 Microsoft 53 Mill, Stuart 130 Miller, Merton 22, 101, 194 Milliken, Michael 282 Ministry of Finance, Japan 222 misogyny 75–7 mis-selling 238, 297–8 Mitchell, Edison 70 Mitchell & Butler 275–6 models financial 42–3, 141–2, 163–4, 173–5, 181–4, 189, 198–9, 205–10 of business processes 73–5 see also credit models Modest, David 168 momentum investment 111 monetization 260–1 monopolies in financial trading 124 moral hazard 151, 280, 291 Morgan Guaranty 37–8, 221, 232 Morgan Stanley 76, 150 mortgage-backed securities (MBSs) 282–3 Moscow, City of 277 moves of staff between firms 150, 244 Mozer, Paul 169 Mullins, David 168–70 multi-skilling 73 331 Mumbai 3 Murdoch, Rupert 247 Nabisco 220 Napoleon 113 NASDAQ index 64, 112 Nash, Ogden 306 National Australia Bank 144, 178 National Rifle Association 29 NatWest Bank 144–5, 198 Niederhoffer, Victor 130 ‘Nero’ 7, 31, 45–9, 60, 77, 82–3, 88–9, 110, 118–19, 125, 128, 292 NERVA 297 New Zealand 319 Newman, Frank 104 news, financial 133–4 News Corporation 247 Newton, Isaac 162, 210 Nippon Credit Bank 106, 271 Nixon, Richard 33 Nomura Securities 218 normal distribution 160–3, 193, 199 Northern Electric 248 O’Brien, John 202 Occam, William 188 off-balance sheet transactions 32–3, 99, 234, 273, 282 ‘offsites’ 74–5 oil prices 30, 33, 89–90, 95–7 ‘omitted variable’ bias 209–10 operational risk 158, 176 opinion shopping 47 options 9, 21–2, 25–6, 32, 42, 90, 98, 124, 197, 229 pricing 185, 189–98, 202 Orange County 16, 44, 50, 124–57, 212–17, 232–3 orphan subsidiaries 234 over-the-counter (OTC) market 26, 34, 53, 95, 124, 126 overvaluation 64 13_INDEX.QXD 17/2/06 4:44 pm Page 332 332 Index ‘overwhelming force’ strategy 134–5 Owen, Martin 145 ownership, ‘legal’ and ‘economic’ 247 parallel loans 35 pari-mutuel auction system 319 Parkinson’s Law 136 Parmalat 250, 298–9 Partnoy, Frank 87 pension funds 43, 108–10, 115, 204–5, 255 People’s Bank of China (PBOC) 276–7 Peters’ Principle 71 petrodollars 71 Pétrus (restaurant) 121 Philippines, the 9 phobophobia 177 Piga, Gustavo 106 PIMCO 19 Plaza Accord 38, 94, 99, 220 plutophobia 177 pollution quotas 320 ‘portable alpha’ strategy 115 portfolio insurance 112, 202–3, 294 power reverse dual currency (PRDC) bonds 226–30 PowerPoint 75 preferred exchangeable resettable listed shares (PERLS) 255 presentations of business models 75 to clients 57, 185 prime brokerage 309 Prince, Charles 238 privatization 205 privity of contract 273 Proctor & Gamble (P&G) 44, 101–4, 155, 298, 301 product disclosure statements (PDSs) 48–9 profit smoothing 140 ‘programme’ issuers 234–5 proprietary (‘prop’) trading 60, 62, 64, 130, 174, 254 publicly available information (PAI) 277 ‘puff’ effect 148 purchasing power parity theory 92 ‘put’ options 90, 131, 256 ‘quants’ 183–9, 198, 208, 294 Raabe, Matthew 217 Ramsay, Gordon 121 range notes 225 real estate 91, 219 regulatory arbitrage 33 reinsurance companies 288–9 ‘relative value’ trading 131, 170–1, 310 Reliance Insurance 91–2 repackaging (‘repack’) business 230–6, 282, 290 replication in option pricing 195–9, 202 dynamic 200 research provided to clients 58, 62–4, 184 reserves, use of 140 reset preference shares 254–7 restructuring of loans 279–81 retail equity products 258–9 reverse convertibles 258–9 reverse dual currency bonds 223–30 ‘revolver’ loans 284–5 risk, financial, types of 158 risk adjusted return on capital (RAROC) 268, 290 risk conservation principle 229–30 risk management 65, 153–79, 184, 187, 201, 267 risk models 163–4, 173–5 riskless portfolios 196–7 RJ Reynolds (company) 220–1 rogue traders 176, 313–16 Rosenfield, Eric 168 Ross, Stephen 196–7, 202 Roth, Don 38 Rothschild, Mayer Amshel 267 Royal Bank of Scotland 298 Rubinstein, Mark 42, 196–7 13_INDEX.QXD 17/2/06 4:44 pm Page 333 Index Rumsfeld, Donald 12, 134, 306 Rusnak, John 143 Russia 45, 80, 166, 172–3, 274, 302 sales staff 55–60, 64–5, 125, 129, 217 Salomon Brothers 20, 36, 54, 62, 167–9, 174, 184 Sandor, Richard 34 Sanford, Charles 72, 269 Sanford, Eugene 269 Schieffelin, Allison 76 Scholes, Myron 22, 42, 168–71, 175, 185, 189–90, 193–7, 263–4 Seagram Group 247 Securities and Exchange Commission, US 64, 304 Securities and Futures Authority, UK 249 securitization 282–90 ‘security design’ 254–7 self-regulation 155 sex discrimination 76 share options 250–1 Sharpe, William 111 short selling 30–1, 114 Singapore 9 single-tranche CDOs 293–4, 299 ‘Sisters of Perpetual Ecstasy’ 234 SITCOMs 313 Six Continents (6C) 275–6 ‘smile’ effect 145 ‘snake’ currency system 203 ‘softing’ arrangements 117 Solon 137 Soros, George 44, 130, 253, 318–19 South Sea Bubble 210 special purpose asset repackaging companies (SPARCs) 233 special purpose vehicles (SPVs) 231–4, 282–6, 290, 293 speculation 29–31, 42, 67, 87, 108, 130 ‘spinning’ 64 333 Spitzer, Eliot 64 spread 41, 103; see also credit spreads stack hedges 96 Stamenson, Michael 124–5 standard deviation 161, 193, 195, 199 Steinberg, Sol 91 stock market booms 258, 260 stock market crashes 42–3, 168, 203, 257, 259, 319 straddles or strangles 131 strategy in banking 70 stress testing 164–6 stripping of convertible bonds 253–4 structured investment products 44, 112, 115, 118, 128, 211–39, 298 structured note asset packages (SNAPs) 233 Stuart SC 18, 307, 316–18 Styblo Bleder, Tanya 153 Suharto, Thojib 81–2 Sumitomo Corporation 100, 142 Sun Tzu 61 Svensk Exportkredit (SEK) 38–9 swaps 5–10, 26, 35–40, 107, 188, 211; see also equity swaps ‘swaptions’ 205–6 Swiss Bank Corporation (SBC) 248–9 Swiss banks 108, 305 ‘Swiss cheese theory’ 176 synthetic securitization 284–5, 288–90 systemic risk 151 Takeover Panel 248–9 Taleb, Nassim 130, 136, 167 target redemption notes 225–6 tax and tax credits 171, 242–7, 260–3 Taylor, Frederick 98, 101 team-building exercises 76 team moves 149 technical analysis 60–1, 135 television programmes about money 53, 62–3 Thailand 9, 80, 302–5 13_INDEX.QXD 17/2/06 4:44 pm Page 334 334 Index Thatcher, Margaret 205 Thorp, Edward 253 tobashi trades 105–7 Tokyo Disneyland 92, 212 top managers 72–3 total return swaps 246–8, 269 tracking error 138 traders in financial products 59–65, 129–31, 135–6, 140, 148, 151, 168, 185–6, 198; see also dealers trading limits 42, 157, 201 trading rooms 53–4, 64, 68, 75–7, 184–7, 208 Trafalgar House 248 tranching 286–9, 292, 296 transparency 26, 117, 126, 129–30, 310 Treynor, Jack 111 trust investment enhanced return securities (TIERS) 216, 233 trust obligation participating securities (TOPS) 232 TXU Europe 279 UBS Global Asset Management 110, 150, 263–4, 274 uncertainty principle 122–3 unique selling propositions 118 unit trusts 109 university education 187 unspecified fund obligations (UFOs) 292 ‘upfronting’ of income 139, 151 Valéry, Paul 163 valuation 64, 142–6 value at risk (VAR) concept 160–7, 173 value investing 111 Vanguard 116 vanity bonds 230 variance 161 Vietnam War 182, 195 Virgin Islands 233–4 Vivendi 247–8 volatility of bond prices 197 of interest rates 144–5 of share prices 161–8, 172–5, 192–3, 199 Volcker, Paul 20, 33 ‘warehouses’ 40–2, 139 warrants arbitrage 99–101 weather, bonds linked to 212, 320 Weatherstone, Dennis 72, 268 Weil, Gotscal & Manges 298 Weill, Sandy 174 Westdeutsche Genosenschafts Zentralbank 143 Westminster Group 34–5 Westpac 261–2 Wheat, Allen 70, 72, 106, 167 Wojniflower, Albert 62 World Bank 4, 36, 38 World Food Programme 320 Worldcom 250, 298 Wriston, Walter 71 WTI (West Texas Intermediate) contracts 28–30 yield curves 103, 188–9, 213, 215 yield enhancement 112, 213, 269 ‘yield hogs’ 43 zaiteku 98–101, 104–5 zero coupon bonds 221–2, 257–8

pages: 532 words: 133,143

**
To Explain the World: The Discovery of Modern Science
** by
Steven Weinberg

Albert Einstein, Alfred Russel Wallace, Astronomia nova, Brownian motion, Commentariolus, cosmological constant, dark matter, Dava Sobel, double helix, Edmond Halley, Eratosthenes, Ernest Rutherford, fudge factor, invention of movable type, Isaac Newton, James Watt: steam engine, Johannes Kepler, music of the spheres, On the Revolutions of the Heavenly Spheres, Pierre-Simon Laplace, probability theory / Blaise Pascal / Pierre de Fermat, retrograde motion, Thomas Kuhn: the structure of scientific revolutions

This step toward unification was resisted by some physicists, including Pierre Duhem, who doubted the existence of atoms and held that the theory of heat, thermodynamics, was at least as fundamental as Newton’s mechanics and Maxwell’s electrodynamics. But soon after the beginning of the twentieth century several new experiments convinced almost everyone that atoms are real. One series of experiments, by J. J. Thomson, Robert Millikan, and others, showed that electric charges are gained and lost only as multiples of a fundamental charge: the charge of the electron, a particle that had been discovered by Thomson in 1897. The random “Brownian” motion of small particles on the surface of liquids was interpreted by Albert Einstein in 1905 as due to collisions of these particles with individual molecules of the liquid, an interpretation confirmed by experiments of Jean Perrin. Responding to the experiments of Thomson and Perrin, the chemist Wilhelm Ostwald, who earlier had been skeptical about atoms, expressed his change of mind in 1908, in a statement that implicitly looked all the way back to Democritus and Leucippus: “I am now convinced that we have recently become possessed of experimental evidence of the discrete or grained nature of matter, which the atomic hypothesis sought in vain for hundreds and thousands of years.”4 But what are atoms?

…

See also equant black holes, 267 blood, circulation of, 118 Boethius of Dacia, 124–25, 128 Bohr, Niels, 261 Bokhara, sultan of, 111 Bologna, University of, 127, 147 Boltzmann, Ludwig, 259–60, 267 Bonaventure, Saint, 129 Book of the Fixed Stars (al-Sufi), 108 Born, Max, 261–62 bosons, 263, 264 Boyle, Robert, 194, 199–200, 202, 213, 217, 265 Boyle’s law, 200 Bradwardine, Thomas, 138 Brahe, Tycho. See Tycho Brahe Broglie, Louis de, 248, 261 Brownian motion, 260 Bruno, Giordano, 157, 181, 188 Bullialdus, Ismael, 226 Buridan, Jean, 71, 132–35, 137, 161, 212 Burning Sphere, The (al-Haitam), 110 Butterfield, Herbert, 145 Byzantine Empire, 103–4, 116 Caesar, Julius, 31, 50, 60 calculus, 15, 195, 223–26, 231–32, 236, 315, 327 differential, 223–25 integral, 39, 223–25 limits in, 236 calendars Antikythera Mechanism for, 71n Arabs and, 109, 116, 118 Greeks and, 56, 58–61 Gregorian, 61, 158 Julian, 61 Khayyam and, 109 Moon vs.

**
The Trade Lifecycle: Behind the Scenes of the Trading Process (The Wiley Finance Series)
** by
Robert P. Baker

asset-backed security, bank run, banking crisis, Basel III, Black-Scholes formula, Brownian motion, business continuity plan, business process, collapse of Lehman Brothers, corporate governance, credit crunch, Credit Default Swap, diversification, fixed income, hiring and firing, implied volatility, interest rate derivative, interest rate swap, locking in a profit, London Interbank Offered Rate, margin call, market clearing, millennium bug, place-making, prediction markets, short selling, statistical model, stochastic process, the market place, the payments system, time value of money, too big to fail, transaction costs, value at risk, Wiener process, yield curve, zero-coupon bond

It is similar to the way a map is used to condense and represent the geography of a region. Models may arise in many ways; here we illustrate a common progression which is loosely based on the case history of a real model. 1. Someone observing stock prices thought they behaved according to a special pattern in which the logarithm of the random jump in prices followed a process known as Brownian motion (or a Wiener process). (Brownian motion is the mathematical model for the apparently random movement of particles suspended in a fluid.) 2. A crude formula was developed to encapsulate this distribution. 3. The formula was tested and refined using empirical prices and found to be a good approximation to reality. 4. Trading processes could use the model to assess the value of the products. At first few people had implemented the model and those who had, produced very different results, so there was a wide discrepancy in prices being traded. 5.

**
What Kind of Creatures Are We? (Columbia Themes in Philosophy)
** by
Noam Chomsky

Affordable Care Act / Obamacare, Albert Einstein, Arthur Eddington, Brownian motion, conceptual framework, en.wikipedia.org, failed state, Henri Poincaré, Isaac Newton, Jacques de Vaucanson, liberation theology, mass incarceration, means of production, phenotype, Ronald Reagan, The Wealth of Nations by Adam Smith, theory of mind, Turing test, wage slave

Henri Poincaré went so far as to say that we adopt the molecular theory of gases only because we are familiar with the game of billiards. Ludwig Boltzmann’s scientific biographer speculates that he committed suicide because of his failure to convince the scientific community to regard his theoretical account of these matters as more than a calculating system—ironically, shortly after Albert Einstein’s work on Brownian motion and broader issues had convinced physicists of the reality of the entities he postulated. Niels Bohr’s model of the atom was also regarded as lacking “physical reality” by eminent scientists. In the 1920s, America’s first Nobel Prize–winning chemist dismissed talk about the real nature of chemical bonds as metaphysical “twaddle”: they are nothing more than “a very crude method of representing certain known facts about chemical reactions, a mode of representation” only, because the concept could not be reduced to physics.

pages: 1,079 words: 321,718

**
Surfaces and Essences
** by
Douglas Hofstadter,
Emmanuel Sander

affirmative action, Albert Einstein, Arthur Eddington, Benoit Mandelbrot, Brownian motion, cognitive dissonance, computer age, computer vision, dematerialisation, Donald Trump, Douglas Hofstadter, Ernest Rutherford, experimental subject, Flynn Effect, Georg Cantor, Gerolamo Cardano, Golden Gate Park, haute couture, haute cuisine, Henri Poincaré, Isaac Newton, l'esprit de l'escalier, Louis Pasteur, Mahatma Gandhi, mandelbrot fractal, Menlo Park, Norbert Wiener, place-making, Sapir-Whorf hypothesis, Silicon Valley, statistical model, Steve Jobs, Steve Wozniak, theory of mind, upwardly mobile, urban sprawl, yellow journalism, zero-sum game

One other factor that might have contributed to Einstein’s faith in his analogy between the physics of the ideal gas and that of the black body (not just between the mathematical formulas for their spectra) was the fact that only a few months earlier, he had found and deeply exploited an analogy between an ideal gas and another physical system — namely, a liquid containing colloidal particles whose nonstop, apparently random hopping-about could be observed through a microscope. This analogy had allowed him to argue persuasively for the existence of extremely tiny invisible molecules that were incessantly pelting the far larger colloidal particles (like thousands of gnats bashing randomly into hanging lamps) and giving them their mysterious hops, known as “Brownian motion”. It is thus probable that two distinct forces in Einstein’s mind — the mathematical similarity of the formulas and also his recent Brownian-motion analogy — gave him great trust in his analogy between a black body and an ideal gas. In any case, building on the bedrock of his latest analogy, Einstein undertook a series of computations, all based on thermodynamics, the branch of physics that he thought of as the deepest and most reliable of all. First he calculated the entropy of each of the systems and then he transformed the two entropy formulas so that they would look as similar as possible to each other; in fact, at the end of his ingenious manipulations, they wound up exactly identical except for the algebraic form of one simple exponent.

…

INDEX —A— “A”, diversity of members of the category, 4–5, 57; picture, 5 “a”: as naming a category, 76; as vowel recognized in speech without one’s knowing how, 511, 512 “A rolling stone gathers no moss”, opposite interpretations of, 102 Aaron, Henry, 325–326 abc ⇒ abd, see Copycat analogies Abel, Niels Henrik, 446 abstract dog and abstract bite, 104 abstract, grounded in the concrete, 28–29, 286–289, 333–337 abstraction: absurd levels of, 107–108, 166, 354, 448–449; as central to expertise, 245–246; by children, 38, 42–43; defined, 187; drive towards, 288; going hand-in-hand with generalization in math, 449; hierarchies of, 235–246; as impoverishing and enriching, 250; as key to encoding, 172, 174–176; legitimized by physics, 448; as luxury add-on to embodied cognition, 288–289; moving between levels of, 30–31; nature of, 107; opaque legalese as bad form of, see legalese; optimal level of, 108; relentless push towards, in mathematics, 448; streamlined by preplaced pitons, 131; techniques for, in mathematics, 449; unconscious acts of, 150–152, 165–166; in word problems in math, 428; see also category extension accelerating frames of reference, 486, 488 acceleration: as indistinguishable from gravity, 491–492, 493–494, 496; linear versus circular, 497 acronyms, 89–93; catchiness of, 90; early examples of, 89–90; efficiency of, 92; list of, 90–91 actable-upon objects, category of, 253 action errors, caused by analogies, 279–280, 404–407 activated categories seeking instances of themselves, 299 adaptation of word meanings to contexts, 196–198 address, generalization to virtual world, 385–386, 395, 398 ad-hoc categories, 137–138; in metaphor understanding, 228–229, 232 adjectives: as labels for the two types of mass, 485; as names of categories, 272 Æsop, 112, 115, 388 affordances, perceptual, 278, 345, 450 airlines and airports as parts of hub concept, 52 airplanes, undetectabilityof motion of, 466–467 airport scenes: evoking words left and right, 33–34; evoking memories of analogous scenes, 157–158; as transculturation of métro scene, 377–379 Alberic of Monte Cassino, 22 Albert Einstein, Creator and Rebel, 473; see also Banesh Hoffmann Albert’s Auberge, excellent coffee of, 462 algebra of classical categories, 56 Alice in Many Tongues (Weaver), 369–370, 372 alignment of two lives on time axis, 433–434 allegory for strange versus normal mass, 476 ambiguous category-membership, 59, 189–192 America/China frame blend, 367–368 amplification, proverbs about, 109 analogic versus logic, 258, 307–310, 311–312, 338, 393, 410, 439, 452, 453, 474, 499–500, 501; see also esthetics analogical fabric of thought, 127 analogical reasoning, mistaken for analogy’s essence, 16–17, 283 analogies: between analogies, 27, 211–212, 502; between random things, 302; as bridges between mental entities, 181–184; coercing one’s flow of thought, 257, 258, 310–313, 444; as cognitive luxuries, 506; in competition, 260–278, 333; conveying truth despite falsity, 366; to counterfactual situations, 362; deep versus shallow, 337–346, 351–357, 375–376, 454–455, 517; as discardable crutches, 392, 421; down-to-earth, great utility of, 23, 507, 509, 516; by Einstein turning out to be eternal truths, 453–454, 486; engendered by obsessions, 258, 299–305, 524; extremely bland cases of, 155–156, 281–284, 507–509; failure of one as stepping stone en route to a deeper one, 356–357, 481, 490–491; as fallible and misleading, 22–24, 435; formal versus physical, 458; as frilly baubles and bangles, 506; functional and visual, coordinated, 277–278; as gems, 16, 506; high frequency of, 18, 507–510; as icing on cognition’s cake, 506, 508; imposing themselves, 29, 31, 289–307, 310–314; inspired by previous analogies, 211–212; invading minds willy-nilly, 257; involving frame-blending, 359–367; involving grammar patterns, 69–70; irrepressibility of, 104, 155, 157, 297, 305–313, 513–514; jumping unbidden to mind, 513–514; latent in semantic halos, 49, 271; like asparagus tips, 135; at the low end of the creativity spectrum, 450; manipulated by us, 331, 382–383, 513; manipulating our thoughts, 29, 31, 315, 331, 382–383, 501, 514; as mere sparkle and pizzazz, 506; as misleading, 21–23; mundane, by Albert Einstein, 454–455; nonstop deluge of, 155; not necessarily a source of pride, 517; objectivity of, 181–183; partially correct and partially wrong, 361; power of, 331–332, 444; pressures pushing for, 300–301, 355–356, 458; purposeless, 258, 281–286; rarity of, 506; seen as analogous to wild horses, 392; as sources of speech and action errors, 259–280; spicy one-line examples, list of, 136; stereotypes of, 135–136, 392, 486; strength of, as reflecting number of resemblances, 516; as strokes of genius, 16–17; superficial, in machine translation, 373, 375; taboo cases of, 104; as training wheels, 392; trivial and meaningless, ceaseless production of, 282, 284–286; unconscious, 259–281, 282, 285–286, 383, 386, 390, 403–407, 514; as uninvited guests, 31, 257; used in thermodynamics but not in electrodynamics, 337; versus frame blends, 363–364, 366–367; visual and sensory, 277–278, 286–289; wild and implausible, as hypothetical crux of creativity, 452 analogues versus schemas, 336–337 analogy: as analogous to asparagus tips, 135; as analogous to siren songs, 23; as analogous to wild horses, 392 analogy leapfrog, 211–212 analogy-making: addictive nature of, 155; as applying to entities versus applying to relations, 517–519; automaticity of, 513–514; as bridge-building between two items on the same level, 519–522; as a cognitive luxury, 506; as compatible with very few disparities, 515–517; as a conscious process, 510–513; as contrasted with assignment to a schema, 336; as the core of cognition, 3, 18, 25–26, 383, 505, 530; as creative, 508–510; as the crux of intelligence, 127; in decision-making, 330–337; as the Delaware of cognition, 17; delight provided by, 506; dependence on familiarity of source domain, 339–340; described by experts exactly as categorization is described, 436, 506; driven by surface-level cues, 337–346; efficiency of, 346; embodiment and, 287–289; in everyday life versus in wartime, 333–335; evoking symbol-manipulation recipes in mathematics, 450–451; as fallible and misleading, 22–24, 435, 527–529; as formal reasoning, 16; frame-blending and, 357–367; as the fuel and fire of thinking, 3; in getting used to new mathematical concepts, 442–444; going as deep as one can go in, 360; as the heartbeat of thought, 15, 17; identity with categorization, 503–530; illusion of necessary seriousness of, 282; incessant avalanche of, 18, 24, 28; as jumping between two levels of abstraction, 519–522; lack of right answers in, 16, 350, 352; as lacking in computers, 25; as the machinery of categorization, 15, 17, 39–49, 183–184, 309, 336, 399; as making the novel familiar, 436, 506; as making the world predictable, 436; by mathematicians, 439–451; as mediating object recognition, 19; misleading stereotypes of, 15–17; in mundane mathematical manipulations, 449–450; naïve analogy concerning, 451; as noble, 508; not used in domestic politics, 337; as objective, 522–526; opacity of the mechanisms of, 511; at the origin of metaphors, 63–64; in poetry translation, 380–381; as prerequisite to survival, 155, 157; as primarily done in intelligence tests, 16; as a rare luxury, 505–508; in real life as opposed to the lab, 339; as reliable, 527–529; as risky, 527; as routine, 508–510; in scientific discovery, 32, 210–214, 361; as subjective, 522–526; supposedly driven by superficial features only, 337–340; supposedly strengthened by disparities, 515–517; as suspect, 527–529; in translation of this book, 377–382; ubiquity of, 506–508; as an unconscious process, 510–513; underlying all word choices, see word choices; utility of, 135; versus categorization, 434–437; as a voluntary process, 513–514; in wartime decision-making, 17, 331–337; wide range of, 19; wide spectrum of abstraction of, in mathematics, 451 “analogy”, rarity of the word, 135 and-situations as a category, 55, 70–75; contrasted with but-situations, 72–75 Anderson, John, 436 angel stung by bumblebee, see interplanetary bumblebee animal, as highly variegated category, 516 animal words as metaphors, 228–232 animals: conceptual repertoires of, 54; as Platonic categories, 56 Ann, as member of many categories, 59, 190, 191 Anna, as spokesperson for the centrality of analogy-making, 503–529; poofing into thin air, 529; see also Katy, Katyanna annihilating nano-boulders, 482 annus minimus of Ellen Ellenbogen, 463–464 annus mirabilis of Albert Einstein, 453, 467, 468–469 “Ant and the Grasshopper” (Æsop), 388 anti-economy, principle of, as a consequence of the dominance of the superficial in reminding, 341 ants: near Grand Canyon, see Danny at Grand Canyon; on orange, watching eclipse, 204–205, 367 appearances, as deceptive versus revelatory, 345 Arabic language, proverb in, 106 Archimedes, 130, 250–252, 300–301, 509; of minigolf, the, 222 Argentina, role of, in Falkland Islands War, 332 Aristotle, 15–16, 21, 437; of the airwaves, the, 222 arithmetical operations, relative difficulty of, 425 “Arizona Ants” (Kellie Gutman), 160, 380–381 army/thought analogy, 26, 27 Arnaud, Pierre, 259 Ars Magna (Cardano), 438–439 articles (“a” and “the”), as names of categories, 76 artificial intelligence, 20, 25 artistic unity, as goal of Einstein, 477, 495; see also esthetics “as deep as one can go”, in analogy-making, 360 asparagus tip analogies, 19 “atmospheric harbor” as incomprehensible phrase, 86 “atom” as an unsplittable etym in English, 89 atom/solar system analogy, 142–143, 510, 513, 515, 518 atoms: lingering doubts about existence of, 459, 475, 487; vibrating in solids to make heat, 461, 475; vibrating in wall of black body, 456 attic, concept of 48–49, 278 avoidance maneuvers while walking, analogy-making in, 285 —B— Babbage, Charles, 369 Bach, Johann Sebastian, 312; of the vibraphone, the, 222; rapid essence-spotting by, 501; Bachelard, Gaston, 22 bagels belonging to a single batch, 309–310, 529 bait-and-switch as a concept available to anglophones, 123–124 balls, bells, and bowls, 488 Banach, Stefan, 502 banalogies (banal analogies), 143–156, 281–286; certainty of, 529; by Einstein, 454–455; elusiveness of, due to blandness, 152, 282, 285–286; great utility of, 23, 507, 509, 516, 529 bananalogy, of use when seeking bananas, 156 “band”, diverse meanings of, 3–4 Bar-Hillel, Yehoshua, 370 bark worse than bite category, 96 Barsalou, Lawrence, 137–138 baseball-based caricature analogies, 325–326, 383 base-level categories, 190 basketballs as members of the category floating objects, 58 Bassok, Myriam, 345 bassoonist falling off roof as source of me-too analogy, 150–151 “Bayh”/”bye” analogy, 27 “beaucoup”, as compound word in French, broken into two concepts in English, 83 bending over backwards to accommodate contrary evidence, 291–292 Bengali poetry, as perceived by non-speakers, 343 Benserade, Isaac de, 112 betting one’s life at all moments on a myriad of trivial and unconscious analogies, 156 Bezout, Étienne, 413, 415, 420 bibles, category of 220, 229 bike-rental anomaly, explained by analogy, 328–330 bilingual data bases in machine translation, 369, 372–373 biplans: involving actions, 279; linguistic, 268–270 bird: as an example of an imprecise category, 55–56, 58, 59–60; as a platform for making inferences, 102 birds in airport/accordionist in métro analogy, 378, 380 black body: defined, 455; Max Planck and, 456–457; spectrum of, 455–459 black body/ideal gas analogy: as found by Einstein, 457–459, 463; as found by Wilhelm Wien, 458 black body/swimming pool explanatory analogy, 455, 456, 458 blended scenario, see frame blends blending, see frame blends, lexical blending blinders, categorical, 58, 290–296 blindness as result of an inability to categorize, 21 blobs, colored, in conceptual spaces, 78–81 boat in amusement park as member of category trolleycar, 521 boat on tracks as category, 521–522 body-to-body analogies, 155–156 Bohr, Niels, 143; pooh-poohing Einstein’s light quanta, 462 Bolt, Usain, 75; of cognitive science, the, 222 Boltzmann, Ludwig, 457 Bombelli, Raffaello, 440, 442 bongos on savannah in museum, 364–366 books: as abstract, immaterial entities, 7; strange types of, 83 Borges, Jorge Luis, 38, 188 “bosse” (French word), 198–200 bottle, evolution of the concept in a child’s mind, 198–200 bottlecaps on ground, see Dick at Karnak bottles thrown overboard, 284 box canyon, see impasse boxes, as misleading model of categories, 13–14, 20, 52, 54–57, 60–61, 435 brainbows, 182–184 brain tumors, analogy between two, 312–313 “brand”, evolution of meanings of, 202 brand names, genericized, 217–218 Brazilian street vendors’ arithmetic, 414–415, 422 breaking, marginal examples of the category, 41–42 bridge, as surprisingly elusive category, 67 bridges everywhere lighting up when button is pushed, 67 bridges, mental, 183–184, 336; see also analogy-making Brissiaud, Rémi, 424 Brownian motion, 458 “browse”, old-fashioned definition of, 397 “brush”, used zeugmatically, 8 “Brustwarze”, unheard parts inside, 87 bubbling-up of concepts from dormancy, 67, 170–171, 489, 491, 492, 498, 511, 513–514, 525; see also remindings, memory retrieval Buffett, Warren, 320 bumblebee, see angel stung by bumblebee bureaucratic use of acronyms, 92 Buresh, Ellie, 364–366 Buridan’s ass, 454 Bush/Schwarzenegger analogical conflation, 275 but as a category, 55, 70–75; contrasted with and, 72–75; in Russian, 74 “butter for lobster tails” joke, 358 “butterfingers”, as isolated metaphorical usage, 63–64 button #1/button #2 analogy by Monica, 169–170 buzzing interplanetary bumblebee, see randomly buzzing interplanetary bumblebee —C— c, the: in string abc, 349, 355; in string xyz, 354, 356 c2, enormous size of, 471, 482 Cairo, 75, 151, 162, 192 “camel”, marked and unmarked senses of, 199–200 Camille (who undressed the banana), 39, 41, 126 candle problem, Duncker’s, 250, 256 canine concepts, 178–181 canonization of individuals, 221–222 can-opener, universal, 439 Cantor, George, 444 “car”, marked versus unmarked senses of, 197, 230, 232 Cardano, Gerolamo, 438–440, 441, 445, 449 caricature analogies: analyzed, 320–330; blurted out, 323–324, 382–383; cascade of, 323–324; clarity as goal of, 317–318, 326–330; concreteness as force in, 329; creativity of, 324–326; diverse forms of, 320; drastic simplification in, 326; essence-spotting in, 321–322, 324–330; exaggeration as inadequate for, 321; for explaining subtle ideas to others or oneself, 326–330; feeble example of, 320; humorous baseball examples of, 325–326, 383; involving French number-words “cinq” and “six”, 380; list of, 318–320; involving Jan’s liquid and frozen assets, 476, 481, 485; mini-scenarios imagined in creation of, 323–324; mocking the timidity of Einstein’s Nobel Prize citation, 462; non-uniqueness of, 323, 325; rapidity of, 321, 323–324; reasons for concocting, 31, 317–318, 322, 324–328; search processes in, 321–322, 324–325; translation of, 380; used by the authors, 13, 18, 22, 25, 65, 108, 281, 320, 321, 337, 340, 366, 370–371, 411, 454, 462, 468, 476, 485, 497, 527 Carol signing with maiden name, 148–149 cars, blue, analogy between, 283 carving up the world in “the right way”, 14, 77, 522–523 casting pearls before swine, as category, 165 categorical blinders, 290–296, 400 categories: absurdly fine-grained, 83; ad-hoc, 137–138; base-level, 190; as blinders, 290–293, 313; blurriness in, 60, 61, 214–216, 244, 523; as boxes, 13–14, 435–436, 520, 522; of children, 39–43, 45; classical approach to, 13–14, 54–57, 435; competition between, 260–278, 281; defined by fables, 29–30, 113–118; as defining identity, 190; degree of centrality of members of, 57; development over time, 34–38, 43–45, 198–204; in discourse space, 69–76; of dogs, 178–181; dominant, 191; as drawers in a dresser, 13; extended by analogy-making, 34–38, 46, 62, 115–116, 246–248; with extremely intangible flavors, 75; as filters on perception, 292, 298–299; handed out on the silver platter of one’s language and culture, 123–124, 128–131; ideal degree of refinement of, 83–84, 108; imprecision of boundaries of, 55–61; instantly forgotten, 284; jumping unbidden to mind, 513; levels of abstraction of, 188; as the motor and fuel of cognition, 506; natural grain size of, 84; nested in the manner of Russian dolls, 520; non-lexicalized, 137, 139–140, 166–167, 176–180; organization of, as critical for expertise, 187, 237–246, 393; as organs of perception, 257, 299, 314; outnumbering words by far, 85; overly subdivided, 83; people’s frequent conflation with sets of visible objects, 54–55; private repertoire of, 166–168, 283–284; as relational, 517–519; seeming to be objectively there, 110, 111, 132–133; suburbs of, 65, 202, 213; unnoticed at their birth, 167; whose members exhibit great variety, 516; see also concepts categorization: as allowing prediction, 14–15; as applying to entities versus applying to relations, 517–519; as assignment to a schema, 336; automaticity of, 513–514; as bridge-building between two items on the same level, 519–522; carried out by analogy-making, 18–19, 179, 183–184, 309, 336, 399; as compatible with many disparities, 515–517; competition during, 261; as a conscious process, 510–513; as a constant necessity, 505; as the core of cognition, 505, 530; as creative, 508–510; described by experts exactly as analogy-making is described, 436, 506; errors in, 102–103, 527; by experts versus by novices, 342–344, 346; as fallible and misleading, 527–529; growing smoothly out of a single first instance, 182–184, 336, 520, 522; as humdrum, 508–510; identity with analogy-making, 503–530; illusion of automaticity of, 450, 513–514; as a judgment call, 117–118, 126; as jumping between two levels of abstraction, 519–522; as making the novel familiar, 436, 506; as making the world predictable, 436; as the meat and potatoes of cognition, 506; nature of, 13–15; not taught in schools, 60, 65, 126, 127; as objective, 522–526; as often being erroneous, 102–103, 527; opacity of its mechanisms, 511; “pure”, 65; rapid, as crucial for survival, 79, 83, 505–506; as rapid simplification, 505–506; reflecting one’s current perspective, 526; as reliable, 527–529; as risk-free, 527; as routine, 508–510; shades of gray in, 14; as subjective, 522–526; as suspect, 527–529; as an unconscious process, 510–513; as uncreative, 509; versus analogy-making, 434–437; as a voluntary process, 513–514; as weakened by disparities, 515–517 category boundaries, treated as sharp in everyday speech, 61 category/city analogy, 61–62, 522 category extension: via analogy, 187, 254, 395–400, 402–407; applied to proper nouns, 217–223; as an art, 468; as deep human drive, 64, 216; by Einstein, 465–468, 485–486, 495–496; by Ellenbogen, Gelenk, et al, 463–465; guiding role of language in, 465; horizontal, 463–468; as a kind of refinement, 84; and marking, 254; of number, 439–443, 447–448; from the physical world to the virtual world, 394–400; repeated acts of, 150; as revealing hidden conceptual essences, 200–204, 255, 295, 397–398; unconscious, in me-too’s, 150; vertical, 463–468; of very recent concepts, 130, 402–407; from the virtual world to the physical world, 402–407 category membership: context-dependence of, 58, 185–186; hypothetical courses in, 60, 65, 70; illusion of precision of, 59–60; illusion of uniqueness of, 58, 190, 192, 465–466; as intrinsically blurry, 60; measured by strength of analogousness, 399; necessary and sufficient conditions for, 55, 436; not taught in schools, 60, 65, 126, 127; versus playing a role in an analogy, 399 category systems: building of, as education’s goal, 393; rival, 241, 243 cat’s death, as inappropriate reminding, 157 cause–effect naïve analogy for equations, 410–411; see also operation–result centrality versus marginality of members of concepts, 57–58 chair, diversity of members of the category, 4, 5, 107 chance favoring the prepared mind, 300 Char (labrador), analogies by, 180 chat room concept, contaminated by thin wall concept, 406 chess, novices’ lack of skill in, 340 Chi, Michelene, 342 Chiflet, Jean-Loup, 97 “child” concepts modifying “parent” concepts, 53–54 children: abstraction by, 41–43; categorization by, 39–43, 45; inferences by, 391; riskily exploring usage patterns of the word “much”, 70; semantic choices made by, 41–43, 270, 273 Chinese language: concepts different from English-language counterparts, 368; Katy’s dream in, 504; “Once bitten, twice shy” in, 105; zeugmas in, 12 Chinese Pythagoras, 221 Chopin, Frédéric, 312; canonized, 221 Chrysippus, 210 chunking: of concepts over one’s lifetime, 50–54; perceptual, and esthetics, 349–352 chunks: in bilingual data base, 372–373, 375; of light, see light quanta “ciao”: competing with “grazie”, 269; competing with “salve” and “buongiorno”, 45–46 cicada, naïve analogy concerning, 388 “ciel”, vast number of meanings of, as typical, 375, 376 “Cigale et la Fourmi” (La Fontaine), 388 cigarette “melting” in ashtray, 40; as the flip side of chocolates “going up in smoke”, 126 cigarette/penis analogy, 362 “circle”, literal versus metaphorical uses of, 64 circles, non-Euclidean, 498 circular structures in Copycat domain and in real life, 355 circumference/diameter ratio, 498; see also π cities, blurriness of boundaries of, 62 city, as metaphor for concept, 61–62, 522 clairvoyance in encoding, chimera of, 173–174, 353–354 Claro, Francisco and Isabel, 312–313 classical music, category in the mind of a rock-music lover, 241 classical view of concepts, 13–14, 54–57, 435; see also Rosch, Eleanor classification versus categorization, 20 cleanliness/morality analogy, 289–290 Clement, Catherine, 436 Clément, Évelyne, 295 clocks, blocks, and rocks, 481 clothing, fringe members of the category of, 528 clouds: covering up details of sabbatical year, 50; how many in the sky?

…

Martin, 189–191 Glucksberg, Sam, 228 God is a sniper category, 168 Gödel, Kurt, 455 Goldstone, Robert, lexical blend by, 265 golf concepts, typical, 49–50 golf obsession, 301–302 golfer, as example of concept with halo, 49–50 Goodman, Nelson, 302 good taste versus bad taste in the Copycat domain, 349–352, 355–358; see also dizziness Google Translate: performance of, 369, 374, 377; techniques employed in, 368–369, 372–374 “Google” versus “google”, 218 gotta situations, 42 grammar: as a domain for analogy-making, 69–70; mastery of, as crucial to translation, 376–377 “grand”, broken into two concepts in French, 80 Grand Canyon seen solely as color pattern, 163; see also Danny grandmother, as marginal member of category mommy, 36–37 grandparents ⇒grandchildren conceptual slippage, 276, 356 grasshopper/human analogy, 387 gravitation/acceleration analogy, 491–492, 493–494, 496, 499 gravity: bending light, 496; having only relative existence, 494; as indistinguishable from acceleration, 491–492, 493–494, 496; as needing an explanation, yet unnoticed, 18; propagation of, across space, 489–490 gravity/electrostatics analogy, 489–491 gravity/fictitious force analogy, 491–492 “Gray Rectangle on Gray Background”, 296 Greece’s hand re Falkland Islands forced by analogy, 332 Greek letters, irrelevance of, in understanding mathematical ideas, 392–394 Grieg, Edvard, face of, 182–184, 520–522 grocery stores, navigated by analogy, 23, 156 “gros”, broken into two concepts in English, 80 groups (mathematical), 446–447, 448–449; division of one by another, 448–449 “growing smaller”, 196, 249, 413 growth of a category from sequence of instances, 182–184, 336, 520, 522 guilty and innocent as categories, 512, 514, 528–529 Gutman, Kellie, 47–49; parallel poems by, 160, 380–381 Gutman, Richard, 47–49, 159–161, 166, 380–381 Gyro Gearloose, 197 —H— h, see Planck’s constant “hacker”, old-fashioned and new definitions of, 397 halo of concepts surrounding each concept, 49–50, 62, 64, 150–151, 328, 335; constantly moving outwards, 62 hamburger: different ideas of, in American and French cultures, 122; gender of, 427; replaced by soft-drink bottle in caricature analogy, 326; used in Paul Newman’s caricature analogy, 318 hammer: as category (not) involving relationships among parts, 517–518; making everything look like a nail, 301 Hampton, James, 56 hand/foot analogy, 15, 50, 323–324 “happiest thought of my life” (Einstein), 494 Haussdorff, Felix, 444 “He who will steal an egg will steal an ox”, 106–109; upbeat interpretation of, 109 heart: as category involving relationships, 517; as member of category pump, 518 heart/finger analogy, 464–465 heart/pump analogy, 515, 518–519 heat-capacity anomaly explained by Einstein’s sound-quantum hypothesis, 461 Heisenberg, Werner, 453 “here”, as mediating mundane yet subtle analogies, 23, 142 Hertz, Heinrich, 460, 461 Herz, Hartmut, 464–465 hesitations in speech as audible traces of silently seething subterranean competition, 263, 269, 281 heureux versus heureuse, 9 hierarchy of concepts, blurriness of, 52–54 high-level perception, 452 Hilbert spaces, 444 historical precedents in wartime decisions, 17, 331–337 history repeating itself, 313; see also political analogies Hitchcock, Alfred, 59 “hither and skither”, 260, 383 Hitler, Adolf: annexing Sudetenland, 332, 334; as baby, 427; caricature analogy involving, 319; contaminating the name “Adolf”, 514; as hackneyed source for political analogies, 17; pluralized, 335; of snuggling, the, 222 Hoagland, Tony, 132 Hobbes, Thomas, 38; ranting against metaphors, 21–22 Hoffmann, Banesh, 473, 474, 477, 480, 481, 482, 495, 500–501 Hofsander, Dounuel, finishing up book in French and English on the unity of analogy-making and categorization, 529–530 Hofsander, Katyanna, as Katy/Anna fusion, 23, 32, 529–530 Hofstadter, Carol: coming up with caricature analogy, 318; driving across U.S. with family, 160; gawking at random hole, 163; lemon-sized brain tumor of, 312–313; signing with maiden name, 148–149, 174–175 Hofstadter, Danny, 283: eating water, 40; playing with ants and leaves at edge of Grand Canyon, 159–167, 171–174 Hofstadter, Douglas: choosing among greetings in Italian, 45–46; coming up with caricature analogies, 317–318; conflating glass of water with dollar bill, 280; as disillusionee and disillusioner, 171; encoding a significant event in real time, 174; as error collector, 259; falling momentarily for categories = boxes, 436; as father disappointing daughter re button, 169–170; gawking at random hole, 163; given hope by an analogy, 313; lecturing on analogies in physics, 452–453; reminded of an experience forty years later, 169–170; study and office of, 47–49; taking coffee break, 185, 317; two blue cars of, 283; watching son at Grand Canyon, 30, 159–161; as youngster enchanted by number patterns, 169–170 Hofstadter, Monica, 283: enchanted by noises from Dustbuster, 169–170, 174 Hofstadter, Oliver, as neighborhood star, 218 Hofstadter, Robert: as father disappointing son re subscripts, 169–170, 174; study and office of, 47–48 holes in the way a language fills conceptual space, see lacunæ Holyoak, Keith, 330, 436 horizontal versus vertical category extensions, 463–468 Homo sapiens sapiens versus computers, 24–25 homosexual marriage, impact on concept of marriage, 53 hub concept: as broadened from wheel center to central airport, 76, 84; internal structure of, 51–54; picture of, 51 human minds versus computers, 24–25 humor, in Copycat domain, 358, 360, 366 hump, evolution of the concept in a child’s mind, 198–200 Hunting Mister Heartbreak (Raban), 284 Hurricane Helene/lady-with-suitcase analogy, 284–286 Hussein/Hitler analogy, 135 hybrid phrases, see lexical blends hyphenated, spaced, and welded compound words, 88 —I— i (square root of –1), 445; generalized, 448 “I am like you” analogy, pervasiveness of, 156 Icelandic reminding episode, 181–182 idea choice, constrained by conversation, 26 ideal gas: defined, 457; energy spectrum of, 457, 458 ideal gas/black body analogy: found by Wilhelm Wien, 458; refound by Einstein, 457–459, 463 ideal gas/Brownian motion analogy, 458 ideal gas/pool table explanatory analogy, 135, 457–458 identity: confusion of two people’s, 224–225; intrinsic and permanent, 190, 435 idiomatic phrases in American English, list of, 95 idioms: in language A with no counterpart in language B, 119–121; meaning not deducible from constituent words, 96–98 iggfruders versus snuoiqers, 11 ignoring the surface level of word problems, difficulty of, 427–428 illusion: that category labels are mechanically retrieved, 450, 513–514; that category labels are objective, 522–526; that category labels are precise, 59–61; that category labels are unique, 58, 190, 192, 465–466; that category membership is black-and-white, 14; that concepts provided by one’s native language are monolithic, 82–83; that one’s native-language categories cut nature at the joints, 14 image-based search process, 172 imaginary numbers, gradual acceptance of, 442–443 “I’m going to pay for my beer” me-too analogy, 143–144 immaterial objects, interacting with, 252–253 impasse: caused by overhasty categorization, 258; escape from, 248–252, 255–256, 292–292; pinpointing the source of, as crucial in creativity, 256 impoverishment: of overly abstracted concepts, 107–108, 166, 204; possible utility of, 250 “in”: broken into two concepts by the French language, 78, 80; used zeugmatically, 6, 7–8 incoherent analogies in Copycat and in real life, 357–358; see also dizziness index fnger/fourth finger analogy, 464 Indianapolis hospital/Verona hospital analogy, 312 indignation, as frequent cause of caricature analogies, 317, 321 individuals, categories centered on, 221–227 Indonesian language, concept of sibling in, 77 induced structure, 345 induction: as extrapolation via analogy from the past, 307–310; parameters affecting credibility of, 308 inferences: effects of typicality on, 390–391; fallacious, due to frame-blending, 361; flowing from naïve analogies, 386; mediated by categorization, 20–21, 225, 278 infinite-dimensional spaces, 444 inner world of expectations as defining certain categories, 68 insight: incoherently mixed with literal-mindedness, 358; quartet of, found successively and exploited together, 357; thanks to caricature analogies, 326–330 in-situations, subtlety of, 7–8 instant pinpointing of timeless essences, 173–174 intelligence: and analogy-making, 126; as a function of the number of concepts one has, 128; list of various definitions of, 125; nature of, 124–126; as the pinpointing of essence, 125–126, 128–131; possibly rising steadily over time, 130; tests, as the prime venue of analogy-making, 16 intelligent ignoring and forgetfulness, 426–427 intension versus extension of a category, 55, 244 intensity of emotion as a function of strength of analogical mapping onto another person, 155 interfaces, profiting from naïve analogies, 400 interjections as categories, 46 interplanetary bumblebee, see buzzing interplanetary bumblebee intuition, alleged irrationality of, 392, 501 “invite”/”accept” caricature analogy, 319, 380 IQ scores and IQ tests, see intelligence irony, as key in encoding of Danny at the Grand Canyon, 161 irresistible analogies, 104, 155, 157, 297, 305–313 irresistible force meeting immovable object category, 326 Isis, 38 isomorphic word problems perceived differently, 429–434 Italian language: compound words in, 89; greetings in, 45–46; names of pasta types in, 243–244; zeugmas in, 8, 11 italics as a convention for concepts, 34, 110 —J— Jan, allegory of, 476, 481, 485 jargon, made mostly of everyday words, 394–400 javelin caricature of coffee-stirring sticks, 317, 321–322 Jeanine/Ruth analogical conflation, 225 Jeff, pluralization of, 223 Jewish mother category, 93–94 jiggles, ripples, rumbles, tumbles, 475 Joane (who said “Come on!”)

pages: 166 words: 53,103

**
Slack: Getting Past Burnout, Busywork, and the Myth of Total Efficiency
** by
Tom Demarco

Brownian motion, delayed gratification, Frederick Winslow Taylor, interchangeable parts, knowledge worker, new economy, risk tolerance, Silicon Valley, Silicon Valley startup, Steve Jobs, Yogi Berra

They are annoyed when anyone in the organization challenges direction. “We wouldn’t be doing this stuff at all if it weren’t right; now what we need is for everyone to get on board to help us do it as efficiently as possible.” Unfortunately, momentum in some direction or other does not necessarily imply carefully thought-out strategic thinking. A company can begin to move (or be moved) by a process that is more or less drift. The Brownian motion within the company asserts a net force in some direction and “By God we’re moving.” The difference between strategic thinking and drift is a matter of whether the key choices are made mindfully or mindlessly. It may sound like a harsh charge that organizations are setting directions mindlessly, that they’re prone to get their tactics right but not their strategy. But tactics are a lot easier than strategy.

pages: 492 words: 149,259

**
Big Bang
** by
Simon Singh

Albert Einstein, Albert Michelson, All science is either physics or stamp collecting, Andrew Wiles, anthropic principle, Arthur Eddington, Astronomia nova, Brownian motion, carbon-based life, Cepheid variable, Chance favours the prepared mind, Commentariolus, Copley Medal, cosmic abundance, cosmic microwave background, cosmological constant, cosmological principle, dark matter, Dava Sobel, Defenestration of Prague, discovery of penicillin, Dmitri Mendeleev, Edmond Halley, Edward Charles Pickering, Eratosthenes, Ernest Rutherford, Erwin Freundlich, Fellow of the Royal Society, fudge factor, Hans Lippershey, Harlow Shapley and Heber Curtis, Harvard Computers: women astronomers, Henri Poincaré, horn antenna, if you see hoof prints, think horses—not zebras, Index librorum prohibitorum, invention of the telescope, Isaac Newton, Johannes Kepler, John von Neumann, Karl Jansky, Kickstarter, Louis Daguerre, Louis Pasteur, luminiferous ether, Magellanic Cloud, Murray Gell-Mann, music of the spheres, Olbers’ paradox, On the Revolutions of the Heavenly Spheres, Paul Erdős, retrograde motion, Richard Feynman, scientific mainstream, Simon Singh, Solar eclipse in 1919, Stephen Hawking, the scientific method, Thomas Kuhn: the structure of scientific revolutions, unbiased observer, Wilhelm Olbers, William of Occam

Albert and Mileva were married in 1903, and their first son, Hans Albert, was born the next year. In 1905, while juggling the responsibilities of fatherhood and his obligations as a patent clerk, Einstein finally managed to crystallise his thoughts about the universe. His theoretical research climaxed in a burst of scientific papers which appeared in the journal Annalen der Physik. In one paper, he analysed a phenomenon known as Brownian motion and thereby presented a brilliant argument to support the theory that matter is composed of atoms and molecules. In another paper, he showed that a well-established phenomenon called the photoelectric effect could be fully explained using the newly developed theory of quantum physics. Not surprisingly, this paper went on to win Einstein a Nobel prize. The third paper, however, was even more brilliant.

…

Page numbers in italic refer to Figures Abell, George O. 401 absorption 235, 235, 236, 244, 245, 259 abundances, see atomic abundances Accademia del Cimento 89 Aikman, Duncan 276 Alexandria 11, 12, 13 Alfonso VI, King of Spain 33 Alfonso X, King of Castile and León 36, 76 Algol 195, 197, 198,199 al-Haytham (Alhazen) 88 alpha particles 289-92, 291, 295, 296, 297, 298,299 Alpher, Ralph 335, 471, 476, 481-3; Alpha-Beta-Gamma paper 319, 322-3,328,332,435; CMB radiation prediction 332-3,430, 434-7, 456, 473; work on nucleosynthesis 315-23,326, 390,397, 437; work on recombination 326—36, 429 Alphonsine Tables 36, 37 American Association for the Advancement of Science 227 American Astronomical Society 227 American Physical Society 460 American Telephone and Telegraph (AT&T) 402-3, 425; see also Bell Laboratories Anaxagoras 15-16, 17, 195 Anaximander 6, 7, 79 Andromeda Galaxy/Nebula 178, 179, 225; Doppler shift 247; Hubble’s distance measurement 223—6, 374—7; novae in 191-3, 222-3, 224 Annalen der Physik 107 Annates de la Société Scientifique de Bruxelles 160 anthropic principle 395, 396, 487-8 Arabs 32-3,36 Archimedes 22 Arcturus 239 Argonne National Laboratory 317 Aristarchus 15—17, 17; Sun-centred universe 22-7, 23,32, 38,41,44, 46 Aristotle 28,36,61,88 asteroids 145,479 Astrophysical Journal 432, 434, 460 Atkinson, Robert d’Escourt 300-2 atom 107,284-94,299; formation of, see nucleosynthesis; nuclear model 292—3, 294, 296, 299,368; plum pudding model 289, 289, 292, 296,368; primeval 159,269,276, 280,309; size 293-5; stability 297,299-300,310, 324-5,391; structure 292-5, 294; wavelengths 232-5, 234, 420 atomic abundances 305, 308-9, 369 388, 400,Table 4,6; hydrogen/helium 283-5,318-19,323, 327, 397 atomic bomb 311, 317 atomic number 293, 294 atomic physics 285,299 Augustine, St 492-3 Ault, Warren 217 Auteroche, Jean d’ 136 Avicenna, see Ibn Sina Baade, Walter 373-80,381, 382, 384, 414, 416 Babylonians 17-18, 28, 77 Bailey, Solon 206-7 Ball, Robert: The Story of the Heavens 194 Barberini, Francesco 74 Barnard’s Star 240 BBC 351,352 Bell, Jocelyn 167-8, 400 Bell Laboratories 402-3, 406, 422, 424—5, 431—2; horn antenna radio telescope 425-9, 427, 437, 439 Bellarmine, Cardinal 74 beryllium 391-3, 392, 396 Bessel, Friedrich Wilhelm 174-7, 176, 195 Betelgeuse 238 Bethe, Hans 303-5, 310, 319, 322 Bible 76-7, 276, 360, 362, 399 Big Bang model 3-4, 168, 254, 268-70, 336; acceptance of 438, 463; criticism of 277-83, 323, 334, 337, 341, 363-4, 378, 459, 483; forerunners of 152, 158—61; multiple 490-1; naming of 352—3, 483—4; observational evidence 252, 255,258,272, 323,430-38,460; philosophical implications 485—88; scientific method in 469-71; versus Steady State 346,347-9,359,361, 364-73,415-22, 430,432,438, 440-2, Table 4, 6; what came before it 488-92 Big Crunch 146, 480, 490-1 binary stars 145, 197-8 black holes 134, 145, 479 Bohr, Niels 491 Bond, William Cranch 204 Bondi, Hermann 340-1,345-50, 349, 384,418, 421, 438 Bonner, William 361 Born, Max 142, 338 boron 398 Brahe,Tycho 47-52, 53, 54, 71, 89, 119; De mundi ætherei 49, 50 ; model of universe 49-50, 50 Braidwood, Thomas 196 Bronstein, Matvei 363 Brownian motion 107 Bruno, Giordano 39—40; On the Infinite Universe and Worlds 39 Bunsen, Robert 237, 238 Burbidge, Geoffrey 398, 439 Burbidge, Margaret 398 Burke, Bernard 430 Buys-Ballot, Christoph 243 California Institute of Technology 272, 278, 395, 425 Cambridge 134, 412, 413, 416 Cancer,Tropic of 11, 20 Cannon, Annie Jump 206 Capra, Frank 260 carbon 304-5,308; excited state of 393-5; formation 390-5, 392, 394,396-7 Carnegie, Andrew 188,402 Carnegie Institute 187 Cassini, Giovanni Domenico 90,92 catastrophe theory 78, 147 Catholic Church 39, 41, 44, 58, 67, 70, 73-5, 484-5; banned books 70, 74; endorses Big Bang 360-2, 364; Inquisition 39, 70, 73 Cavendish Laboratory 288 centrality, illusion of 272 Cepheid variable stars 199-201, 207-10, 211, 223-6, 224; distance scale 212-13, 225, 376-7, 381; magnitude 211; populations 376-7 Chadwick, James 295-6, 302,312 Chandrasekhar, Subrahmanyan 380 chaos 326 Chicago University 186, 215, 267 Chown, Marcus 389, 457 Christian IV, King of Denmark 51 Churchill, Winston 409 circular perfection 28, 56,58 Clarke Telescope 247 Clerke, Agnes 192 Cleveland, Lemuel 227 COBE (Cosmic Background Explorer) 453-63, 458, 461, 471-3,481 Cockcroft, John 310 colour 230-5, 231 Columbia University 424 comets 147, 170, 180 computers 326 Comte, Auguste 229,237 Copernicus, Nicholas 37-47, 71,129, 367,401,485; Commentariolus 37-9; De revolutionibus 41-4, 42, 46,49,53, 63,70; errors exposed 53-4; planetary phases predicted 63-6; Sun-centred universe 38, 41, 174 cosmic density 228 cosmic microwave background (CMB) radiation 473,476,Table 4,6; detected as noise 430-8; predicted 333-4,336, 430; satellites 453-63, 458, 461,471, 481, 482; variations in 446-62, 452, 461 cosmic-ray physics 158 cosmological constant 148-9, 151-2, 153, 161, 273-4 cosmological principle 146,345; perfect 347 Coulson, Charles 484 creation 180, 261,276,284, 489-90, Table 4,6; continuous 345,347-8, 364; date of 76-7; moment of 158-9, 252-3, 255,269-70,282,344,379, 417,438 creation field (C-field) 347 creation myths 4—6 Curie, Marie and Pierre 285-7,297-8, 312 Curtis, Heber 190, 191,193-4, 224, 227 Daguerre, Louis 201 dark energy 481, 482 dark matter 280,479-80,481, 482 Darwin, Charles 3,77,350 Davis, Elmer 360 Davisson, Clinton J. 402 Dead of Night 341-4 deferents 30, 31,32, 45, 124, 367 Delta Cephei 198-9, 199 Dicke, Robert 431-2,434-5, 491 Dirac, Paul 338 Doppler, Christian 241,243,244 Doppler effect 241-8, 242,365,451; see also redshift Draper, John and Henry 204 Drydenjohn 118 dust, interstellar 193,227,407 Dyson, Frank 135 Dyson, Freeman 487 Earth 10; age of 77-8, 372, 378; composition 283; measuring 11—13, 12, 14,20,Table l; motion 24, 100-1, 405, 451, Table 2, 3; orbit around Sun 22, 119; rotation 22,38; speed through cosmos 451-2 Earth-centred universe 20—7, 23, 29, 58, 63, 72, 124, Table 2, 3; Brahe’s model 49-50, 50; Copernicus on 38-9; phases of Venus 63—5, 66; Ptolemaic model 30-6, 31,44-6, 63, 65 eclipses 197-9; lunar 10, 13, 14; solar 17, 20, 71,132-3, 135, 138-40, 141 Eddington, Arthur 134-41, 144,157, 338,476; expanding universe theory 270,280-3; and Lemaître 268-9,280; The Mathematical Theory of Relativity 135; nucleosynthesis theory 385; on rebounding universe 491; solar eclipse observations 135,137-41,143; Space, Time and Gravitation 138; on tired light theory 280 Ehrenfest, Paul 123 Egyptians 18-19,28 Einstein, Albert 24,105-7, 108, 144,191, 198; and bending of light 130-3, 140-2; and Big Bang 161,273-4,372; constancy of speed of light 103—5, 107; cosmological constant 148—9, 151-3,161,273-4; cosmology 145-9, 167,272-3; E = mc2 formula 298-9, 301; eternal, static model of universe 146-8,161, 273-4; ether thought experiment 98-103, 105, 106; and Friedmann 153-6; general relativity 116-37,143-9,153,273,345-7,471; and Lemaître 160,273-6, 275; spacetime 120—2, 121; special relativity 108-16,298-9 electromagnetic radiation 230,406, 407 electromagnetic spectrum 407, 407 electrons 292-5, 294,299, 314,328, 472 elements: formation, see nucleosynthesis; heavy 309-10,323-6,328, 385-89, 397-8,Table 5; periodic table 286-7, 287; radioactive 285—6; see also atomic abundances ellipses 54-6,55,58,119 epicycles and deferents 30, 31, 32,45, 58, 65, 66,124, 367 Eratosthenes 11-16, 12,17,19,20,177, 195 Eta Aquilae 198-9 ether 93-8, 96,101-3,141-2,145,306, 368 evolution 77,158-9, 258-60,350,360 exponential notation Table 1 Fabricius, David 58 Ferdinand, Archduke of Graz 51 Fermi, Enrico 327,380 Fernie, Donald 378 Fleming, Alexander 409 Fleming, Williamina 204, 205,206,374 Fowler, Willy 395-6,398,425 Franz Ferdinand, Archduke 133 Fraunhofer, Joseph von 237 Frederick II, King of Denmark 47, 50 Frederick Wilhelm III, King of Prussia 174 Frederiks, Vsevolod 363 Freundlich, Erwin 130,132-3 Friedmann, Alexander 150, 167, 306; expanding universe model 149—56, 249, 268; forerunner of Big Bang 254, 258,269,273,363,471,491 Fry, Art 408 galaxies 230, Table 4, 6; age of 378; distances 226, 228,372-3,376-79, 381—3; dwarf 226; expansion 271; formation 369,442-7, 451, 452, 457-62,473,477-8, 480; gravity 279; Hubble’s law 256; as nebulae 180—1, 184, 193, 219, 226; radio galaxies 405, 408, 414-20,425; recessional velocity 247-50,252-60, 253, 259,268,270-3,277, 365,373,377; redshifts 248, 252, 259,260,270,273, 277-80,282; single galaxy theory 190, 191—2,219; in Steady State universe 345, 346,348; young 348,369, 415-17 Galileo Galilei 60-75, 71,129,250,367, 401; astronomical observations 62—6, 62, 64,65-7, 66; Church and 72-4, 361,485; Dialogue Concerning the Two Chief World Systems 72-4,99; relativity principle 99-101,105,110,145; speed of light measurement 88—9; telescope 59,61-2,171,203 Gamow, George 308, 310,312, 335, 336, 364,385,471,473, 476; Alpha-Beta-Gamma paper 319,322-3,328, 332, 435; correspondence with Pope 360-1; Creation of the Universe 361, 489; critics of 323-4,332; humour 319, 325,334-5,349, 398, 399,417, 419, 420; popular science 334,351, 359,361; work on CMB radiation 333-4, 430-1, 435-7, 473; work on nucleosynthesis 306-22,326, 327, 390,397 Gauss, Carl Friedrich 472 Geiger, Hans 290-2, 291, 296 geocentric universe, see Earth-centred universe geology 78,277 George I, King of England 169 George III, King of England 169, 172, 402 George Washington University 308,311, 315,320 Gerard of Cremona 33, 36 Giese, Canon 41 Global Positioning System (GPS) 113 God 76, 79,147,180,360-1,462-3, 484-5, 488,490 gods 7,16,18 Gold, Thomas 349, 349,361, 384; on radio galaxies 413-15,418; and Steady State model 340-7, 421,438 Goodricke, John 196-8,200 gravity 25, 58, 67, 87, 200,488,Table 3; anti-gravity 148, 274; extreme 124—6, 130,144; galactic 279, 443,479; and general relativity 117,119-33,137, 144-6; Greek model 10-11, 24-5; Newtonian 118-19,122-8,137,144 Great Debate 189-94,198,201,206, 213,219-20,223-5 Greeks, Ancient 6-17,19, 33-6,79, 195; on composition of stars 238; measurements 9-17,20; nebulae 178; on planetary orbits 28—32; theory of light and sound 87—8; world-view 22—7 Grossman, Marcel 123 Grote, Harriet 214-15 Guericke, Otto von 93 Guth, Alan 477, 479, 492 H II regions 383 Haldane, J.

pages: 807 words: 154,435

**
Radical Uncertainty: Decision-Making for an Unknowable Future
** by
Mervyn King,
John Kay

"Robert Solow", Airbus A320, Albert Einstein, Albert Michelson, algorithmic trading, Antoine Gombaud: Chevalier de Méré, Arthur Eddington, autonomous vehicles, availability heuristic, banking crisis, Barry Marshall: ulcers, battle of ideas, Benoit Mandelbrot, bitcoin, Black Swan, Bonfire of the Vanities, Brownian motion, business cycle, business process, capital asset pricing model, central bank independence, collapse of Lehman Brothers, correlation does not imply causation, credit crunch, cryptocurrency, cuban missile crisis, Daniel Kahneman / Amos Tversky, David Ricardo: comparative advantage, demographic transition, discounted cash flows, disruptive innovation, diversification, diversified portfolio, Donald Trump, easy for humans, difficult for computers, Edmond Halley, Edward Lloyd's coffeehouse, Edward Thorp, Elon Musk, Ethereum, Eugene Fama: efficient market hypothesis, experimental economics, experimental subject, fear of failure, feminist movement, financial deregulation, George Akerlof, germ theory of disease, Hans Rosling, Ignaz Semmelweis: hand washing, income per capita, incomplete markets, inflation targeting, information asymmetry, invention of the wheel, invisible hand, Jeff Bezos, Johannes Kepler, John Maynard Keynes: Economic Possibilities for our Grandchildren, John Snow's cholera map, John von Neumann, Kenneth Arrow, Long Term Capital Management, loss aversion, Louis Pasteur, mandelbrot fractal, market bubble, market fundamentalism, Moneyball by Michael Lewis explains big data, Nash equilibrium, Nate Silver, new economy, Nick Leeson, Northern Rock, oil shock, Paul Samuelson, peak oil, Peter Thiel, Philip Mirowski, Pierre-Simon Laplace, popular electronics, price mechanism, probability theory / Blaise Pascal / Pierre de Fermat, quantitative trading / quantitative ﬁnance, railway mania, RAND corporation, rent-seeking, Richard Feynman, Richard Thaler, risk tolerance, risk-adjusted returns, Robert Shiller, Robert Shiller, Ronald Coase, sealed-bid auction, shareholder value, Silicon Valley, Simon Kuznets, Socratic dialogue, South Sea Bubble, spectrum auction, Steve Ballmer, Steve Jobs, Steve Wozniak, Tacoma Narrows Bridge, Thales and the olive presses, Thales of Miletus, The Chicago School, the map is not the territory, The Market for Lemons, The Nature of the Firm, The Signal and the Noise by Nate Silver, The Wealth of Nations by Adam Smith, The Wisdom of Crowds, Thomas Bayes, Thomas Davenport, Thomas Malthus, Toyota Production System, transaction costs, ultimatum game, urban planning, value at risk, World Values Survey, Yom Kippur War, zero-sum game

A person may be uncertain which city is the capital of Pennsylvania, or mistakenly believe that it is Philadelphia, but unless he is intending to meet the Governor it probably does not matter much. Sometimes, as in that case, we can resolve uncertainty by consulting a reference book or the internet, or by approaching someone who knows. These resolvable uncertainties represent one pole of uncertainty, at which we can remove our doubt by further investigation. Other resolvable uncertainties are the product of stationary probability distributions – tossing a fair coin, or Brownian motion (the random movement of small particles in a liquid or gas). Everything which can be known about these uncertainties is known and quantified. Probabilistic reasoning was devised for games of chance which are based on randomness – card games, roulette wheels, lotteries. But these problems are artificial. The rules of the game, the composition of the pack of cards, are completely specified and what remains unknown – where the spin of the wheel will take the ball, whether the next card will be an ace – is not capable of being known.

…

INDEX 10 (film, 1979), 97 737 Max aircraft, 228 9/11 terror attacks, 7 , 74–6 , 202 , 230 Abbottabad raid (2011), 9–10 , 20 , 26 , 44 , 71 , 102 , 118–19 , 120 , 174–5 ; reference narrative of, 122–3 , 277 , 298 ; role of luck in, 262–3 ; and unhelpful probabilities, 8–19 , 326 abductive reasoning, 138 , 147 , 211 , 388 , 398 ABN AMRO, 257 Abraham (biblical character), 206 Abrahams, Harold, 273 Abramovich, Roman, 265 accountancy, 409 aeronautics, 227–8 , 352–6 , 383 Agdestein, Simen, 273 AIDS, 57 , 230 , 375–6 Airbus A380, 40 , 274–6 , 408 Akerlof, George, 250–1 , 252 , 253 , 254 , 382 Alchian, Armen, 158 alien invasion narratives, 295–6 Allais, Maurice, 134–5 , 136 , 137 , 437 , 440–3 Allen, Bill, 227–8 Allen, Paul, 28 , 29 Altair desktop, 28 Amazon, 289 , 309 Anderson, Roy, 375 ant colonies, 173 anthropology, 160 , 189–91 , 193–4 , 215–16 antibiotics, 40 , 45 , 284 , 429 Antz (film, 1998), 274 apocalyptic narratives, 331–2 , 335 , 358–62 Appiah, Anthony, 117–18 Apple, 29–30 , 31 , 169 , 309 Applegarth, Adam, 311 arbitrage, 308 Archilochus (Greek poet), 222 Aristotle, 137 , 147 , 303 Arrow, Kenneth, 254 , 343–5 , 440 artificial intelligence (AI), xvi , 39 , 135 , 150 , 173–4 , 175–6 , 185–6 , 387 ; the ‘singularity’, 176–7 Ashtabula rail bridge disaster (1876), 33 Asimov, Isaac, 303 asteroid strikes, 32 , 71–2 , 238 , 402 astrology, 394 astronomical laws, 18–19 , 35 , 70 , 373–4 , 388 , 389 , 391–2 , 394 AT&T, 28 auction theory, 255–7 Austen, Jane, 217 , 224–5 , 383 autism, 394 , 411 aviation, commercial, 23–4 , 40 , 227–8 , 274–6 , 315 , 383 , 414 axiomatic rationality: Allais disputes theory, 134–5 , 136 , 137 ; Arrow– Debreu world, 343–5 ; assumption of transitivity, 437 ; and Becker, 114 , 381–2 ; and behavioural economics, 116 , 135–6 , 141–9 , 154–5 , 167–8 , 386–7 , 401 ; capital asset pricing model (CAPM), 307–8 , 309 , 320 , 332 ; completeness axiom, 437–8 ; consistency of choice axiom, 108–9 , 110–11 ; continuity axiom, 438–40 ; definition of rationality, 133–4 , 137 , 436 ; definition of risk, 305 , 307 , 334 , 420–1 ; efficient market hypothesis, 252 , 254 , 308–9 , 318 , 320 , 332 , 336–7 ; efficient portfolio model, 307–8 , 309 , 318 , 320 , 332–4 , 366 ; and evolutionary rationality, 16 , 152–3 , 154–5 , 157 , 158 , 166–7 , 171–2 , 386–7 , 407 ; and ‘expectations’ concept, 97–8 , 102–3 , 121–2 , 341–2 ; extended to decision-making under uncertainty, xv , 40–2 , 110–14 , 133–7 , 257–9 , 420–1 ; and Friedman, 73–4 , 111–12 , 113–14 , 125 , 257–9 , 307 , 399–400 , 420 , 437 ; hegemony of over radical uncertainty, 40–2 , 110–14 ; implausibility of assumptions, xiv–xv , 16 , 41–4 , 47 , 74–84 , 85–105 , 107–9 , 111 , 116–22 , 344–9 , 435–44 ; independence axiom, 440–4 ; as limited to small worlds, 170 , 309–10 , 320–1 , 342–9 , 382 , 400 , 421 ; and Lucas, 36 , 92 , 93 , 338–9 , 341 , 345 , 346 ; and Markowitz, 307 , 308 , 309–10 , 318 , 322 , 333 ; maximising behaviour, 310 ; ‘pignistic probability’, 78–84 , 438 ; and Popperian falsificationism, 259–60 ; Prescott’s comparison with engineering, 352–6 ; ‘rational expectations theory, 342–5 , 346–50 ; and Samuelson, xv , 42 , 110–11 , 436 ; and Savage, 111–14 , 125 , 257–9 , 309 , 345 , 400 , 435 , 437 , 442–3 ; shocks and shifts discourse, 42 , 346 , 347 , 348 , 406–7 ; Simon’s work on, 134 , 136 , 149–53 ; triumph of probabilistic reasoning, 15–16 , 20 , 72–84 , 110–14 ; Value at risk models (VaR), 366–8 , 405 , 424 ; von Neumann–Morgenstern axioms, 111 , 133 , 435–44 ; see also maximising behaviour Ballmer, Steve, 30 , 227 Bank of England, xiii , 45 , 103–5 , 286 , 311 Barclays Bank, 257 Barings Bank, 411 Basel regulations, 310 , 311 Bay of Pigs fiasco (1961), 278–9 Bayes, Reverend Thomas, 60–3 , 66–7 , 70 , 71 , 358 , 431 Beane, Billy, 273 Bear Stearns, 158–9 Becker, Gary, 114 , 381–2 Beckham, David, 267–8 , 269 , 270 , 272–3 , 414 behavioural economics, 116 , 145–8 , 154 , 386–7 ; and Allais paradox, 442 ; ‘availability heuristic’, 144–5 ; biases in human behaviour, 16 , 136 , 141–8 , 154 , 162 , 165 , 167–8 , 170–1 , 175–6 , 184 , 401 ; and evolutionary science, 154–5 , 165 ; Kahneman’s dual systems, 170–1 , 172 , 271 ; Kahneman–Tversky experiments, 141–7 , 152 , 215 ; ‘noise’ (randomness), 175–6 ; nudge theory, 148–9 Bentham, Jeremy, 110 Berkshire Hathaway, 153 , 319 , 324 , 325–6 Berlin, Isaiah, 222 Bernoulli, Daniel, 114–16 , 199 Bernoulli, Nicolaus, 199 , 442 Bertrand, Joseph, 70 Bezos, Jeff, 289 big data, 208 , 327 , 388–90 billiard players, 257–8 bin Laden, Osama, 7 , 8–10 , 21 , 44 , 71 , 118–19 , 120 , 122–3 , 262–3 , 326 Bismarck, Otto von, 161 Bitcoin, 96 , 316 Black Death, 32 , 39–40 BlackBerry, 30 , 31 blackjack, 38 Blackstone, Sir William, 213 BNP Paribas, 5 , 6 BOAC, 23–4 Boas, Franz, 193 Boeing, 24 , 227–8 Boer War, 168 Bolt, Usain, 273 bonobos, 161–2 , 178 Borges, Jorge Luis, 391 Borodino, battle of (1812), 3–4 , 433 Bortkiewicz, Ladislaus, 235–6 Bower, Tom, 169–70 Bowral cricket team, New South Wales, 264 Box, George, 393 Boycott, Geoffrey, 264–5 Bradman, Don, 237 , 264 Brahe, Tycho, 388–9 Brånemark, Per-Ingvar, 387 , 388 Branson, Richard, 169–70 Brearley, Michael, 140–1 , 264–5 Breslau (now Wrocław), 56 Brexit referendum (June 2016), 241–2 ; lies told during, 404 bridge collapses, 33 , 341 Brownian motion, 37 Brunelleschi, Filippo, 143 , 147 Buffett, Warren, 83 , 152 , 179 , 319–20 , 324 , 335 , 336–7 Burns, Robert, 253 Bush, George W., 295 , 407 , 412 business cycles, 347 business history (academic discipline), 286 business schools, 318 business strategy: approach in 1970s, 183 ; approach in 1980s, 181–2 ; aspirations confused with, 181–2 , 183–4 ; business plans, 223–4 , 228 ; collections of capabilities, 274–7 ; and the computer industry, 27–31 ; corporate takeovers, 256–7 ; Lampert at Sears, 287–9 , 292 ; Henry Mintzberg on, 296 , 410 ; motivational proselytisation, 182–3 , 184 ; quantification mistaken for understanding, 180–1 , 183 ; and reference narratives, 286–90 , 296–7 ; risk maps, 297 ; Rumelt’s MBA classes, 10 , 178–80 ; Shell’s scenario planning, 223 , 295 ; Sloan at General Motors, 286–7 ; strategy weekends, 180–3 , 194 , 296 , 407 ; three common errors, 183–4 ; vision or mission statements, 181–2 , 184 Buxton, Jedediah, 225 Calas, Jean, 199 California, 48–9 Cambridge Growth Project, 340 Canadian fishing industry, 368–9 , 370 , 423 , 424 cancer, screening for, 66–7 Candler, Graham, 352 , 353–6 , 399 Cardiff City Football Club, 265 Carlsen, Magnus, 175 , 273 Carnegie, Andrew, 427 Carnegie Mellon University, 135 Carré, Dr Matt, 267–8 Carroll, Lewis, Through the Looking-Glass , 93–4 , 218 , 344 , 346 ; ‘Jabberwocky’, 91–2 , 94 , 217 Carron works (near Falkirk), 253 Carter, Jimmy, 8 , 119 , 120 , 123 , 262–3 cartography, 391 Casio, 27 , 31 Castro, Fidel, 278–9 cave paintings, 216 central banks, 5 , 7 , 95 , 96 , 103–5 , 285–6 , 348–9 , 350 , 351 , 356–7 Central Pacific Railroad, 48 Centre for the Study of Existential Risk, 39 Chabris, Christopher, 140 Challenger disaster (1986), 373 , 374 Chamberlain, Neville, 24–5 Chandler, Alfred, Strategy and Structure , 286 Chariots of Fire (film, 1981), 273 Charles II, King, 383 Chelsea Football Club, 265 chess, 173 , 174 , 175 , 266 , 273 , 346 Chicago economists, 36 , 72–4 , 86 , 92 , 111–14 , 133–7 , 158 , 257–8 , 307 , 342–3 , 381–2 Chicago Mercantile Exchange, 423 chimpanzees, 161–2 , 178 , 274 China, 4–5 , 419–20 , 430 cholera, 283 Churchill, Winston: character of, 25–6 , 168 , 169 , 170 ; fondness for gambling, 81 , 168 ; as hedgehog not fox, 222 ; on Montgomery, 293 ; restores gold standard (1925), 25–6 , 269 ; The Second World War , 187 ; Second World War leadership, 24–5 , 26 , 119 , 167 , 168–9 , 170 , 184 , 187 , 266 , 269 Citibank, 255 Civil War, American, 188 , 266 , 290 Clapham, John, 253 Clark, Sally, 197–8 , 200 , 202 , 204 , 206 Clausewitz, Carl von, On War , 433 climate systems, 101–2 Club of Rome, 361 , 362 Coase, Ronald, 286 , 342 Cochran, Johnnie, 198 , 217 Cochrane, John, 93 coffee houses, 55–6 cognitive illusions, 141–2 Cohen, Jonathan, 206–7 Colbert, Jean-Baptiste, 411 Cold War, 293–4 , 306–7 Collier, Paul, 276–7 Columbia disaster (2003), 373 Columbia University, 117 , 118 , 120 Columbus, Christopher, 4 , 21 Colyvan, Mark, 225 Comet aircraft, 23–4 , 228 communication: communicative rationality, 172 , 267–77 , 279–82 , 412 , 414–16 ; and decision-making, 17 , 231 , 272–7 , 279–82 , 398–9 , 408 , 412 , 413–17 , 432 ; eusociality, 172–3 , 274 ; and good doctors, 185 , 398–9 ; human capacity for, 159 , 161 , 162 , 172–3 , 216 , 272–7 , 408 ; and ill-defined concepts, 98–9 ; and intelligibility, 98 ; language, 98 , 99–100 , 159 , 162 , 173 , 226 ; linguistic ambiguity, 98–100 ; and reasoning, 265–8 , 269–77 ; and the smartphone, 30 ; the ‘wisdom of crowds’, 47 , 413–14 Community Reinvestment Act (USA, 1977), 207 comparative advantage model, 249–50 , 251–2 , 253 computer technologies, 27–31 , 173–4 , 175–7 , 185–6 , 227 , 411 ; big data, 208 , 327 , 388–90 ; CAPTCHA text, 387 ; dotcom boom, 228 ; and economic models, 339–40 ; machine learning, 208 Condit, Phil, 228 Condorcet, Nicolas de, 199–200 consumer price index, 330 , 331 conviction narrative theory, 227–30 Corinthians (New Testament), 402 corporate takeovers, 256–7 corporations, large, 27–31 , 122 , 123 , 286–90 , 408–10 , 412 , 415 Cosmides, Leda, 165 Cretaceous–Paleogene extinction, 32 , 39 , 71–2 Crick, Francis, 156 cricket, 140–1 , 237 , 263–5 crime novels, classic, 218 crosswords, 218 crypto-currencies, 96 , 316 Csikszentmihalyi, Mihaly, 140 , 264 Cuba, 278–80 ; Cuban Missile Crisis, 279–81 , 299 , 412 Custer, George, 293 Cutty Sark (whisky producer), 325 Daily Express , 242–3 , 244 Damasio, Antonio, 171 Dardanelles expedition (1915), 25 Darwin, Charles, 156 , 157 Davenport, Thomas, 374 Dawkins, Richard, 156 de Havilland company, 23–4 Debreu, Gerard, 254 , 343–4 decision theory, xvi ; critiques of ‘American school’, 133–7 ; definition of rationality, 133–4 ; derived from deductive reasoning, 138 ; Ellsberg’s ‘ambiguity aversion’, 135 ; expected utility , 111–14 , 115–18 , 124–5 , 127 , 128 – 30 , 135 , 400 , 435–44 ; hegemony of optimisation, 40–2 , 110–14 ; as unable to solve mysteries, 34 , 44 , 47 ; and work of Savage, 442–3 decision-making under uncertainty: and adaptation, 102 , 401 ; Allais paradox, 133–7 , 437 , 440–3 ; axiomatic approach extended to, xv , 40–2 , 110–14 , 133–7 , 257–9 , 420–1 ; ‘bounded rationality concept, 149–53 ; as collaborative process, 17 , 155 , 162 , 176 , 411–15 , 431–2 ; and communication, 17 , 231 , 272–7 , 279–82 , 398–9 , 408 , 412 , 413–17 , 432 ; communicative rationality, 172 , 267–77 , 279–82 , 412 , 414–16 ; completeness axiom, 437–8 ; continuity axiom, 438–40 ; Cuban Missile Crisis, 279–81 , 299 , 412 ; ‘decision weights’ concept, 121 ; disasters attributed to chance, 266–7 ; doctors, 184–6 , 194 , 398–9 ; and emotions, 227–9 , 411 ; ‘evidence-based policy’, 404 , 405 ; excessive attention to prior probabilities, 184–5 , 210 ; expected utility , 111–14 , 115–18 , 124–5 , 127 , 128–30 , 135 , 400 , 435–44 ; first-rate decision-makers, 285 ; framing of problems, 261 , 362 , 398–400 ; good strategies for radical uncertainty, 423–5 ; and hindsight, 263 ; independence axiom, 440–4 ; judgement as unavoidable, 176 ; Klein’s ‘primed recognition decision-making’, 399 ; Gary Klein’s work on, 151–2 , 167 ; and luck, 263–6 ; practical decision-making, 22–6 , 46–7 , 48–9 , 81–2 , 151 , 171–2 , 176–7 , 255 , 332 , 383 , 395–6 , 398–9 ; and practical knowledge, 22–6 , 195 , 255 , 352 , 382–8 , 395–6 , 405 , 414–15 , 431 ; and prior opinions, 179–80 , 184–5 , 210 ; ‘prospect theory’, 121 ; public sector processes, 183 , 355 , 415 ; puzzle– mystery distinction, 20–4 , 32–4 , 48–9 , 64–8 , 100 , 155 , 173–7 , 218 , 249 , 398 , 400–1 ; qualities needed for success, 179–80 ; reasoning as not decision-making, 268–71 ; and ‘resulting’, 265–7 ; ‘risk as feelings’ perspective, 128–9 , 310 ; robustness and resilience, 123 , 294–8 , 332 , 335 , 374 , 423–5 ; and role of economists, 397–401 ; Rumelt’s ‘diagnosis’, 184–5 , 194–5 ; ‘satisficing’ (’good enough’ outcomes), 150 , 167 , 175 , 415 , 416 ; search for a workable solution, 151–2 , 167 ; by securities traders, 268–9 ; ‘shock’ and ‘shift’ labels, 42 , 346 , 347 , 348 , 406–7 ; simple heuristics, rules of thumb, 152 ; and statistical discrimination, 207–9 , 415 ; triumph of probabilistic reasoning, 20 , 40–2 , 72–84 , 110–14 ; von Neumann– Morgenstern axioms, 111 , 133 , 435–44 ; see also business strategy deductive reasoning, 137–8 , 147 , 235 , 388 , 389 , 398 Deep Blue, 175 DeepMind, 173–4 The Deer Hunter (film, 1978), 438 democracy, representative, 292 , 319 , 414 demographic issues, 253 , 358–61 , 362–3 ; EU migration models, 369–70 , 372 Denmark, 426 , 427 , 428 , 430 dentistry, 387–8 , 394 Derek, Bo, 97 dermatologists, 88–9 Digital Equipment Corporation (DEC), 27 , 31 dinosaurs, extinction of, 32 , 39 , 71–2 , 383 , 402 division of labour, 161 , 162 , 172–3 , 216 , 249 DNA, 156 , 198 , 201 , 204 ‘domino theory’, 281 Donoghue, Denis, 226 dotcom boom, 316 , 402 Doyle, Arthur Conan, 34 , 224–5 , 253 Drapers Company, 328 Drescher, Melvin, 248–9 Drucker, Peter, Concept of the Corporation (1946), 286 , 287 Duhem–Quine hypothesis, 259–60 Duke, Annie, 263 , 268 , 273 Dulles, John Foster, 293 Dutch tulip craze (1630s), 315 Dyson, Frank, 259 earthquakes, 237–8 , 239 Eco, Umberto, The Name of the Rose , 204 Econometrica , 134 econometrics, 134 , 340–1 , 346 , 356 economic models: of 1950s and 1960s, 339–40 ; Akerlof model, 250–1 , 252 , 253 , 254 ; ‘analogue economies’ of Lucas, 345 , 346 ; artificial/complex, xiv–xv , 21 , 92–3 , 94 ; ‘asymmetric information’ model, 250–1 , 254–5 ; capital asset pricing model (CAPM), 307–8 , 309 , 320 , 332 ; comparative advantage model, 249–50 , 251–2 , 253 ; cost-benefit analysis obsession, 404 ; diversification of risk, 304–5 , 307–9 , 317–18 , 334–7 ; econometric models, 340–1 , 346 , 356 ; economic rent model, 253–4 ; efficient market hypothesis, 252 , 254 , 308–9 , 318 , 320 , 332 , 336–7 ; efficient portfolio model, 307–8 , 309 , 318 , 320 , 332–4 , 366 ; failure over 2007–08 crisis, xv , 6–7 , 260 , 311–12 , 319 , 339 , 349–50 , 357 , 367–8 , 399 , 407 , 423–4 ; falsificationist argument, 259–60 ; forecasting models, 7 , 15–16 , 68 , 96 , 102–5 , 347–50 , 403–4 ; Goldman Sachs risk models, 6–7 , 9 , 68 , 202 , 246–7 ; ‘grand auction’ of Arrow and Debreu, 343–5 ; inadequacy of forecasting models, 347–50 , 353–4 , 403–4 ; invented numbers in, 312–13 , 320 , 363–4 , 365 , 371 , 373 , 404 , 405 , 423 ; Keynesian, 339–40 ; Lucas critique, 341 , 348 , 354 ; Malthus’ population growth model, 253 , 358–61 , 362–3 ; misuse/abuse of, 312–13 , 320 , 371–4 , 405 ; need for, 404–5 ; need for pluralism of, 276–7 ; pension models, 312–13 , 328–9 , 405 , 423 , 424 ; pre-crisis risk models, 6–7 , 9 , 68 , 202 , 246–7 , 260 , 311–12 , 319 , 320–1 , 339 ; purpose of, 346 ; quest for large-world model, 392 ; ‘rational expectations theory, 342–5 , 346–50 ; real business cycle theory, 348 , 352–4 ; role of incentives, 408–9 ; ‘shift’ label, 406–7 ; ‘shock’ label, 346–7 , 348 , 406–7 ; ‘training base’ (historical data series), 406 ; Value at risk models (VaR), 366–8 , 405 , 424 ; Viniar problem (problem of model failure), 6–7 , 58 , 68 , 109 , 150 , 176 , 202 , 241 , 242 , 246–7 , 331 , 366–8 ; ‘wind tunnel’ models, 309 , 339 , 392 ; winner’s curse model, 256–7 ; World Economic Outlook, 349 ; see also axiomatic rationality; maximising behaviour; optimising behaviour; small world models Economic Policy Symposium, Jackson Hole, 317–18 economics: adverse selection process, 250–1 , 327 ; aggregate output and GDP, 95 ; ambiguity of variables/concepts, 95–6 , 99–100 ; appeal of probability theory, 42–3 ; ‘bubbles’, 315–16 ; business cycles, 45–6 , 347 ; Chicago School, 36 , 72–4 , 86 , 92 , 111–14 , 133–7 , 158 , 257–8 , 307 , 342–3 , 381–2 ; data as essential, 388–90 ; division of labour, 161 , 162 , 172–3 , 216 , 249 ; and evolutionary mechanisms, 158–9 ; ‘expectations’ concept, 97–8 , 102–3 , 121–2 , 341–2 ; forecasts and future planning as necessary, 103 ; framing of problems, 261 , 362 , 398–400 ; ‘grand auction’ of Arrow and Debreu, 343–5 ; hegemony of optimisation, 40–2 , 110 – 14 ; Hicks–Samuelson axioms, 435–6 ; market fundamentalism, 220 ; market price equilibrium, 254 , 343–4 , 381–2 ; markets as necessarily incomplete, 344 , 345 , 349 ; Marshall’s definition of, 381 , 382 ; as ‘non-stationary’, 16 , 35–6 , 45–6 , 102 , 236 , 339–41 , 349 , 350 , 394–6 ; oil shock (1973), 223 ; Phillips curve, 340 ; and ‘physics envy’, 387 , 388 ; and power laws, 238–9 ; as practical knowledge, 381 , 382–3 , 385–8 , 398 , 399 , 405 ; public role of the social scientist, 397–401 ; reciprocity in a modern economy, 191–2 , 328–9 ; and reflexivity, 35–6 , 309 , 394 ; risk and volatility, 124–5 , 310 , 333 , 335–6 , 421–3 ; Romer’s ‘mathiness’, 93–4 , 95 ; shift or structural break, 236 ; Adam Smith’s ‘invisible hand’, 163 , 254 , 343 ; social context of, 17 ; sources of data, 389 , 390 ; surge in national income since 1800, 161 ; systems as non-linear, 102 ; teaching’s emphasis on quantitative methods, 389 ; validity of research findings, 245 ‘Economists Free Ride, Does Anyone Else?’

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Quantitative Trading: How to Build Your Own Algorithmic Trading Business
** by
Ernie Chan

algorithmic trading, asset allocation, automated trading system, backtesting, Black Swan, Brownian motion, business continuity plan, buy and hold, compound rate of return, Edward Thorp, Elliott wave, endowment effect, fixed income, general-purpose programming language, index fund, John Markoff, Long Term Capital Management, loss aversion, p-value, paper trading, price discovery process, quantitative hedge fund, quantitative trading / quantitative ﬁnance, random walk, Ray Kurzweil, Renaissance Technologies, risk-adjusted returns, Sharpe ratio, short selling, statistical arbitrage, statistical model, survivorship bias, systematic trading, transaction costs

Handbook of Asset and Liability Management, Volume I, Zenios and Ziemba (eds.). Elsevier 2006. Available at: www.EdwardOThorp.com. Toepke, Jerry. 2004. “Fill ‘Er Up! Benefit from Seasonal Price Patterns in Energy Futures.” Stocks, Futures and Options Magazine. March 3(3). Available at: www.sfomag.com/issuedetail.asp?MonthNameID=March& yearID=2004. Uhlenbeck, George, and Leonard Ornstein. 1930. “On the Theory of Brownian Motion.” Physical Review 36: 823–841. Van Norden, Simon, and Huntley Schaller. 1997. “Regime Switching in Stock Market Returns.” Applied Financial Economics 7: 177–191. P1: JYS bib JWBK321-Chan September 24, 2008 15:5 172 Printer: Yet to come P1: JYS ata JWBK321-Chan August 27, 2008 10:58 Printer: Yet to come About the Author rnest P. Chan is the founder of E. P. Chan & Associates (www.epchan.com), a consulting firm focusing on trading strategy and software development for money managers.

pages: 108 words: 63,808

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The State of the Art
** by
Iain M. Banks

Brownian motion, mutually assured destruction, South China Sea

It was a TV production I'd seen on the BBC while I was in London ... or maybe the ship had repeated it. I couldn't recall. What I did recall was the plot and the setting, both of which seemed so apposite to my little scene with Linter that I started to wonder whether the beast upstairs was watching all this. Probably was, come to think of it. And not much point in looking for anything; the ship could produce bugs so small the main problem with camera stability was Brownian motion. Was The Ambassadors a sign from it then? Whatever; the play was replaced by a commercial for Odor-Eaters. 'I've told you,' Linter brought me back from my musings, speaking quietly, 'I'm prepared to take my chances. Do you think I haven't thought it all through before, many times? This isn't sudden, Sma; I felt like this my first day here, but I waited for months before I said anything, so I'd be sure.

pages: 186 words: 64,267

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A Brief History of Time
** by
Stephen Hawking

Albert Einstein, Albert Michelson, anthropic principle, Arthur Eddington, bet made by Stephen Hawking and Kip Thorne, Brownian motion, cosmic microwave background, cosmological constant, dark matter, Edmond Halley, Ernest Rutherford, Henri Poincaré, Isaac Newton, Johannes Kepler, Magellanic Cloud, Murray Gell-Mann, Richard Feynman, Stephen Hawking

For centuries the argument continued without any real evidence on either side, but in 1803 the British chemist and physicist John Dalton pointed out that the fact that chemical compounds always combined in certain proportions could be explained by the grouping together of atoms to form units called molecules. However, the argument between the two schools of thought was not finally settled in favor of the atomists until the early years of this century. One of the important pieces of physical evidence was provided by Einstein. In a paper written in 1905, a few weeks before the famous paper on special relativity, Einstein pointed out that what was called Brownian motion—the irregular, random motion of small particles of dust suspended in a liquid—could be explained as the effect of atoms of the liquid colliding with the dust particles. By this time there were already suspicions that these atoms were not, after all, indivisible. Several years previously a fellow of Trinity College, Cambridge, J. J. Thomson, had demonstrated the existence of a particle of matter, called the electron, that had a mass less than one thousandth of that of the lightest atom.

pages: 740 words: 161,563

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The Discovery of France
** by
Graham Robb

Brownian motion, deindustrialization, Honoré de Balzac, Louis Pasteur, New Economic Geography, Peace of Westphalia, price stability, trade route, urban sprawl

On the high road, for the twelve miles between Le Bouchet-St-Nicolas and Pradelles, the only other travellers he saw were ‘a cavalcade of stride-legged ladies and a pair of post-runners’, but he also saw some of the million tendrils of the other network that carried most of the traffic: The little green and stony cattle-tracks wandered in and out of one another, split into three or four, died away in marshy hollows, and began again sporadically on hillsides or at the borders of a wood. There was no direct road to Cheylard, and it was no easy affair to make a passage in this uneven country and through this intermittent labyrinth of tracks. This labyrinth is the reason why the towns and villages of France were both cut off and connected. Wares and produce travelled through the system of tracks and tiny roads by something akin to Brownian motion, changing hands slowly over great distances. When the main roads were improved and railways were built, trade was drained from the capillary network, links were broken, and a large part of the population suddenly found itself more isolated than before. Many regions today are experiencing the same effect because of the TGV railway system. * IT WOULD TAKE a thousand separate maps to show the movements of the migrant population through this labyrinth of tracks, but an excellent overall view can be gained from any large–scale relief map or satellite photograph.

…

link Beauvais to Amiens: Goubert, 89; also Malaucène: Saurel, I, 57–60. link fragile capillaries: Braudel, III, 228–32; Peuchet, ‘Calvados’, 10. link ‘My road lay through’: Stevenson (1879), 56. link Voie Regordane: Moch, 49–50. The name may be related to the Gaulish rigo, ‘king’. link Stevenson could have bought: Moch, quoting R. Thinthoin, 49–50. link ‘The little green and stony cattle-tracks’: Stevenson (1879), 38. link Brownian motion: Planhol, 186–7. link south and east of the line: Hufton, 72; Planhol, 242 and 285–9. link ‘Crabas amont, filhas aval’: Moch, 68. link From the . . . Cantal: Weber, 279; Wirth. link army handbook: État-major de l’armée de terre, 118. link processions of young girls: Dureau de la Malle, 250; also Gildea, 10. link loues or louées: N. Parfait, in Les Français, Province, II, 104–5; Masson de Saint-Amand, 129.

pages: 295 words: 66,824

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A Mathematician Plays the Stock Market
** by
John Allen Paulos

Benoit Mandelbrot, Black-Scholes formula, Brownian motion, business climate, business cycle, butter production in bangladesh, butterfly effect, capital asset pricing model, correlation coefficient, correlation does not imply causation, Daniel Kahneman / Amos Tversky, diversified portfolio, dogs of the Dow, Donald Trump, double entry bookkeeping, Elliott wave, endowment effect, Erdős number, Eugene Fama: efficient market hypothesis, four colour theorem, George Gilder, global village, greed is good, index fund, intangible asset, invisible hand, Isaac Newton, John Nash: game theory, Long Term Capital Management, loss aversion, Louis Bachelier, mandelbrot fractal, margin call, mental accounting, Myron Scholes, Nash equilibrium, Network effects, passive investing, Paul Erdős, Paul Samuelson, Ponzi scheme, price anchoring, Ralph Nelson Elliott, random walk, Richard Thaler, Robert Shiller, Robert Shiller, short selling, six sigma, Stephen Hawking, stocks for the long run, survivorship bias, transaction costs, ultimatum game, Vanguard fund, Yogi Berra

Louis Bachelier, whom I mentioned in chapter 4, also devised a formula for options more than one hundred years ago. Bachelier’s formula was developed in connection with his famous 1900 doctoral dissertation in which he was the first to conceive of the stock market as a chance process in which price movements up and down were normally distributed. His work, which utilized the mathematical theory of Brownian motion, was way ahead of its time and hence was largely ignored. His options formula was also prescient, but ultimately misleading. (One reason for its failure is that Bachelier didn’t take account of the effect of compounding on stock returns. Over time this leads to what is called a “lognormal” distribution rather than a normal one.) The Black-Scholes options formula depends on five parameters: the present price of the stock, the length of time until the option expires, the interest rate, the strike price of the option, and the volatility of the underlying stock.

pages: 239 words: 56,531

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The Secret War Between Downloading and Uploading: Tales of the Computer as Culture Machine
** by
Peter Lunenfeld

Albert Einstein, Andrew Keen, anti-globalists, Apple II, Berlin Wall, British Empire, Brownian motion, Buckminster Fuller, Burning Man, business cycle, butterfly effect, computer age, creative destruction, crowdsourcing, cuban missile crisis, Dissolution of the Soviet Union, don't be evil, Douglas Engelbart, Douglas Engelbart, Dynabook, East Village, Edward Lorenz: Chaos theory, Fall of the Berlin Wall, Francis Fukuyama: the end of history, Frank Gehry, Grace Hopper, gravity well, Guggenheim Bilbao, Honoré de Balzac, Howard Rheingold, invention of movable type, Isaac Newton, Jacquard loom, Jane Jacobs, Jeff Bezos, John Markoff, John von Neumann, Kickstarter, Mark Zuckerberg, Marshall McLuhan, Mercator projection, Metcalfe’s law, Mother of all demos, mutually assured destruction, Nelson Mandela, Network effects, new economy, Norbert Wiener, PageRank, pattern recognition, peer-to-peer, planetary scale, plutocrats, Plutocrats, post-materialism, Potemkin village, RFID, Richard Feynman, Richard Stallman, Robert Metcalfe, Robert X Cringely, Schrödinger's Cat, Search for Extraterrestrial Intelligence, SETI@home, Silicon Valley, Skype, social software, spaced repetition, Steve Ballmer, Steve Jobs, Steve Wozniak, Ted Nelson, the built environment, The Death and Life of Great American Cities, the medium is the message, Thomas L Friedman, Turing machine, Turing test, urban planning, urban renewal, Vannevar Bush, walkable city, Watson beat the top human players on Jeopardy!, William Shockley: the traitorous eight

., 123–124 Berners-Lee, Tim, 144, 167–169, 175 Bespoke futures adopting future as client and, 110–113 anticipated technology and, 108–110 crafting, 113–116 design and, 102, 105–106, 110–111, 115–116, 119–120, 124–125, 137 downloading and, 97, 123, 132, 138 dynamic equilibrium and, 117–120 89/11 and, xvi, 97, 100–102, 105, 130 Enlightenment and, xvi, 129–139 information and, 98, 100–101, 124–126 lack of vision and, 106–108 markets and, 97–104, 118, 120, 127, 131–132, 137–138 MaSAI (Massively Synchronous Applications of the Imagination) and, xvi, 112, 120–123, 127, 193n32 199 modernists and, 105–108 mutants and, 105–108 networks and, 98–101, 108, 112–113, 116, 119–126, 133, 137 New Economy and, 97, 99, 104, 131, 138, 144–145, 190n3 participation and, 98–99, 120–121, 129 plutopian meliorism and, xvi, 127–129, 133, 137–138 prosumers and, 120–121 reperceiving and, 112–113 R-PR (Really Public Relations) and, 123–127 scenario planning and, 111–119, 191n19, 192n20 simulation and, 98, 121, 124, 126–127 strange attractors and, xvi, 117–120, 192n27 technology and, 98–104, 107–113, 116, 119, 125–127, 131–133, 136–139 television and, 101, 108, 124, 127–129, 133–137 unﬁnish and, 127–129, 136 uploading and, 97, 120–123, 128–129, 132 Best use, 10, 13–15, 138 Bezos, Jeff, 145 Bible, 28, 137 BitTorrent, 92 Black Album, The (Jay Z), 55 Blade Runner (Scott), 107 Blogger, 177 Blogosphere, xvii bespoke futures and, 101 culture machine and, 175, 177 Facebook and, 81, 145, 180n2 stickiness and, 30, 34 Twitter and, 34, 180n2 unimodernism and, 49, 68 Web n.0 and, 80, 92–93 INDEX Bohème, La (Puccini), 61 Boing Boing magazine, 68–69 Bollywood, 62 Bourgeoisie, 31 Bowie, David, 62 Braque, Georges, 93 Breuer, Marcel, 45 Brillat-Savarin, Jean Anthèlme, 3 Brin, Sergey, 144, 174–176 Broadband technology, 9, 57 Brownian motion, 49 Burroughs, Allie Mae, 40–42 Burroughs, William, 52 Bush, Vannevar, 52, 194n6 culture machine and, 144, 147–152, 157 Engelbart and, 157 Memex and, 108, 149–151 Oppenheimer and, 150 systems theory and, 151 war effort and, 150–151 Business 2.0 magazine, 145 C3I , 146–147 Cabrini Green, 85 Calypso, 25–27 Cambodia, 107 Cambridge, 17, 36 “Can-Can” (“Orpheus in the Underworld”) (Offenbach), 62 Capitalism, 4, 13 bespoke futures and, 97–100, 103–105 Sears and, 103–105 stickiness and, 13 unimodernism and, 66, 75 Web n.0 and, 90 Capitulationism, 7, 24, 30, 182n1 Carnegie, Andrew, 166 Casablanca (ﬁlm), 90 Cassette tapes, 2 CATIA 3–D software, 39 Cell phones, xiii, xvii, 17, 23, 42, 53, 56, 76, 101 Chaos theory, 117–120 Chaplin, Charlie, 45 Cheney, Dick, 99 China, 104, 107 Christians, 135 Cicero, 47 Cinema, 8, 10 micro, 56–60 stickiness and, 15 unimodernism and, 47, 52, 56–60, 63, 71 Clarke, Arthur C., 174 CNN, 58 Cobain, Kurt, 62 Code breaking, 17–18 Cold war, 101 Cole, Nat King, 62 Commercial culture, 4–5, 8 bespoke futures and, 98, 102, 108, 120, 132–134 culture machine and, 153–156, 167, 170, 172, 175–177 copyright and, 54, 88–95, 123, 164, 166, 173, 177 Mickey Mouse Protection Act and, 90 open source and, 36, 61, 69, 74–75, 91–92, 116, 121–126, 144, 170– 173, 177, 189n12 propaganda and, 124 scenario planning and, 111–119 stickiness and, 23, 28–31, 37 unimodernism and, 41, 69 Web n.0 and, 82–86 Commercial syndrome, 85–86 Communism, 97–98, 103 Compact discs (CDs), 2, 48, 53 Complex City (Simon), 39 “Computable Numbers, On” (Turing), 18 Computer Data Systems, 145 Computers, xi.

pages: 667 words: 186,968

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The Great Influenza: The Story of the Deadliest Pandemic in History
** by
John M. Barry

Albert Einstein, Brownian motion, centralized clearinghouse, conceptual framework, coronavirus, discovery of penicillin, double helix, Fellow of the Royal Society, germ theory of disease, index card, Louis Pasteur, Marshall McLuhan, Mason jar, means of production, statistical model, the medium is the message, the scientific method, traveling salesman, women in the workforce

I have never known him to engage in purposeless rivalries or competitive research. But often have I seen him sit calmly, lost in thought, while all around him others with great show of activity were flitting about like particles in Brownian motion; then, I have watched him rouse himself, smilingly saunter to his desk, assemble a few pipettes, borrow a few tubes of media, perhaps a jar of ice, and then do a simple experiment which answered the question.” But now, in the midst of a killing epidemic, everything and everyone around him—including even the pressure from Welch—shouldered thought aside, shouldered perspective and preparation aside, substituting for it what Avery so disdained: Brownian motion—the random movement of particles in a fluid. Others hated influenza for the death it caused. Avery hated it for that, too, but for a more personal assault as well, an assault upon his integrity.

pages: 684 words: 188,584

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The Age of Radiance: The Epic Rise and Dramatic Fall of the Atomic Era
** by
Craig Nelson

Albert Einstein, Brownian motion, Charles Lindbergh, cognitive dissonance, Columbine, continuation of politics by other means, corporate governance, cuban missile crisis, dark matter, Doomsday Clock, El Camino Real, Ernest Rutherford, failed state, Henri Poincaré, hive mind, Isaac Newton, John von Neumann, Louis Pasteur, low earth orbit, Menlo Park, Mikhail Gorbachev, music of the spheres, mutually assured destruction, nuclear winter, oil shale / tar sands, Project Plowshare, Ralph Nader, Richard Feynman, Ronald Reagan, Skype, Stuxnet, technoutopianism, too big to fail, uranium enrichment, William Langewiesche, éminence grise

After they helped her, she danced for them privately at their home and introduced them to sculptor Auguste Rodin; the four became regular friends and perhaps the only two people in the world the Curies saw regularly who weren’t scientists or blood relatives. Their closest friends remained the next-door neighbors at boulevard Kellermann, Jean and Henriette Perrin; he was a physics professor at the Sorbonne who verified Einstein’s explanation of Brownian motion, correctly estimated the size of water molecules and atoms, and established cathode rays as negatively charged particles—electrons. Pierre presented his and Marie’s scientific findings to France’s Academy of Sciences on March 16, 1903, and the Swedish Academy of Sciences then awarded them and Becquerel the Nobel Prize. Behind the scenes, four members of the French Académie had recommended that Becquerel and Pierre alone share the Nobel, leaving out Marie’s work entirely.

…

., 233 DuBridge, Lee, 247 Dulles, John Foster, 283 Dunning, John R., 104–05, 133 DuPont, Robert, 369–70 DuPont and Company, 131, 149, 164, 282 Dyson, Freeman, 225, 231, 262, 265, 267, 305 earthquakes, in Japan, 5, 7, 342–45, 352–53 Ebermayer, Erich, 93 Edison, Thomas, 13 Edmundson, James, 245 Eifler, Carl, 185 Einstein, Albert, 5, 34, 46, 244, 341 on atomic bomb use, 220–21 on Bohr, 94 Brownian motion explanation of, 34 childhood interest in science of, 84–85 Emergency Committee of Concerned Scientists of, 190 emigration to the United States by, 68, 80, 115 Fermi on, 66 German denunciations of, 67–68, 92, 176 on Haber, 373 as hero in popular culture, 369 on Langevin, 44 letters between Roosevelt and, 116–18, 119, 153, 176, 220, 369 Los Alamos consultations by, 153 Manhattan Project and, 83, 122 on Marie Curie, 43, 48 on Meitner, 75, 89 need for atomic bomb research advocated by, 114–15 nuclear energy and, 112, 369 nuclear warfare and 299 Oppenheimer and, 261 Planck’s research and, 87–88 on scientists and war efforts, 89 Szilard and, 77, 78, 127, 163 theory of general relativity of, 67 unified field theory of, 83 US military research and, 122 Eisenhower, Dwight D., 340, 370 arms control (Open Skies) plan of, 284, 287 arms race and, 277, 282, 286, 304 Atomic Energy Commission and, 260, 267 Atoms for Peace and, 304, 305, 331, 363 ballistic missile tracking and, 330 concern about nuclear arms use and, 255, 370 defense policy of, 283 first US nuclear power plant and, 304 military-industrial complex of, 252 missile defense shield concept and, 330 nuclear merchant ship commissioned by, 304–05 Oppenheimer and, 259–60 presidency of, 246, 252, 283 Rosenbergs’ execution and, 242 Soviet threat and, 245, 255, 256, 259 test-ban agreement and, 267 use of atomic bomb in Japan and, 208, 222 Eltenton, George¸ 261 Elugelab atoll, Mike thermonuclear tests on, 250, 251, 252–53 Emergency Committee of Concerned Scientists, 190 ENIAC computer, 248, 249 Eniwetok Island, Mike thermonuclear tests on, 250, 251, 252–53 Environmental Protection Agency (EPA), 128, 308, 310, 363 Esau, Abraham, 105 Ester, Julius, 26 Falk, Jim, 369 fallout shelters, 286, 376 Fate of the Earth, The (Schell), 299, 328 Fat Man bomb, 154, 197–98, 211, 216, 217, 230, 237, 371 FBI Bohr and, 174–75 Einstein and, 122 Fermi and, 123 Manhattan Project and, 149, 155, 171 Oppenheimer and, 155, 170, 257, 258, 260, 261, 262 spying detected by, 238–39, 240, 241, 242, 363 Szilard and, 149 Feather, Norman, 146 Fermi, Enrico, 54, 55–72, 157, 369, 379 atomic bomb design and, 168, 170, 266–67 atomic bomb testing and, 201–02, 206, 207, 229, 266–67 childhood of, 56–57 death of, 265–66, 269 decision to emigrate to the United States by, 64–65, 67, 68–72 education of, 57–58 element discovered by, 84 family life of, 123 German nuclear program and, 185 Hahn’s research on nucleus and, 103–04 Hanford reactor and, 164–65 irradiation research of, 90 legacy of, 55–56, 266, 369 Los Alamos and, 158–59, 160, 225, 228, 247 Manhattan Project and, 148, 154, 155 marriage of, 66–67, 123, 159 need for atomic bomb research advocated by, 114, 119 Nobel Prize to, 69–70, 71, 83, 97, 110, 128 nuclear fission experiment at Columbia and, 104, 105, 133 nuclear reactor design by, 129–39, 149, 160, 163, 172, 185, 233 Oak Ridge reactor and, 163 on Oppenheimer, 261 personality of, 165, 193, 225–26 political campaigns and power of, 251 postwar research at Chicago by, 225 research approach of, 123–25 research secrecy and, 112–13, 254 on scientific advances, 379 subatomic particle research of, 226 Szilard and, 229 Teller and, 147, 157, 158, 227, 228, 229, 247, 253, 265, 330 thermonuclear fusion research and, 228, 235, 247, 254 US military research and, 122–23 University of Rome research on uranium of, 58–64, 91, 266 uranium fission research of, 109–13, 124–25, 129, 266 wartime status as enemy alien, 128–29 Wigner on, 109 Fermi, Giulio, 55, 69, 71–72, 128, 226 Fermi, Laura, 55, 63–64, 65, 66–67, 69, 70, 71–72, 83, 115–16, 123–24, 126, 128, 129, 159, 170, 176, 225–26, 265, 266 Fermi, Nella, 55, 65, 70, 71–72, 123, 128, 226–27, 266, 269 Fermilab, 266 Fermi paradox, 76, 337 fermium, 253, 266 Forsmark nuclear power plant, Sweden, 312 Ferraby, Tom¸ 212 Feynman, Richard (Dick), 151, 152, 164, 166, 202, 205, 247 films, radiation theme in, 274–75, 310–11, 367 First Lightning weapons test, 233–34, 235, 238, 239, 373 Fischer, Emil, 86, 88 fishermen thermonuclear testing affecting, 273, 340 tsunami affecting, 344–45 Fitch, Val, 196, 203 Flerov, Georgi, 171–72, 193–94 Flexible Response strategy, 283, 287, 372 Fokker, Adriaan, 94, 95 Fonda, Jane, 310 France, 351, 364 Franck, James, 89, 91, 93, 207, 225 Frank, Barney, 334–35 Frayn, Michael, 181 French Academy of Sciences (Académie des Sciences), 14, 27, 34, 37, 188, 325 Frisch, David, 150 Frisch, Otto Robert, 91, 121 atomic trigger device designed by, 166–67 background of, 91 Meitner’s relationship with, 97, 189, 190 move to England by, 120 move to Los Alamos by, 152–53 nuclear fission research of Meitner and, 99–102, 103, 105, 144 thermal diffusion and, 162–63 Frisén, Jonas, 378 Fromm, Friedrich, 183 Fuchs, Elizabeth, 170–71 Fuchs, Klaus background of, 170–71 Los Alamos research by, 152, 169–70, 227, 240 spying by, 170, 171, 172, 173, 194, 237, 238, 239, 240, 251, 259 Fukushima Daiichi power plant disaster, Japan, 5, 340–60 deaths from, 360 earthquake causing, 342–45 evacuations after, 346, 349–50, 356 evidence of ancient tsunami near, 342 government regulators and, 352–53, 354 health effects of, 350, 358 heat generation from fission fragments in, 343–44, 345–46, 356 information withheld in, 350–51, 354–55 location of, 341–42 plant damage after, 347–49, 351–52, 356, 359–60 political effects of, 357, 359 private industry’s relationship with government regulators in, 353 radiation released in, 336, 355, 357, 358 rehabilitation of area and resettlement after, 358–59 steam venting in, 346–47, 349 TEPCO’s responsibilities after, 351–52 tsunami damage in, 344–45, 352–53 US consultants on, 349, 351, 355, 356 workers at, 346–48, 349, 352, 353–55, 356–57 Fuller, Loie, 33–34 Gabor, Dennis, 75, 79 Gale, Robert, 319, 349 Gamow, George, 94, 99, 248, 282 Gard, Robert, 334 Gardner, Meredith, 238, 242 Garson, Greer, 51 Garwin, Richard, 225, 247–48, 251 Geiger, Hans, 74, 87, 89, 113 Geitel, Hans Friedrich, 26 genetic abnormalities, and radiation, 326 Giannini, Gabriel Maria, 59–60 Gibertson Company, 375 Giesel, Friedrich, 31, 35, 188 Girshfield, Viktor, 290 Glicksman, Maurice, 265 Gold, Harry, 170, 172–73, 240–41, 242, 251 Goldstine, Herman, 248 Goncharov, German, 255, 275 Goodyear Tire & Rubber Company, 132, 282 Gopnik, Adam, 337 Gorbachev, Mikhail Chernobyl accident and, 318, 359, 361 International Thermonuclear Experimental Reactor (ITER) and, 364 on nuclear weapons, 328 proposed nuclear arms reduction treaty and, 329–30, 332–33 Reagan’s Strategic Defense Initiative and, 331, 332 START treaty and, 333 Göring, Hermann, 183 Goudsmit, Samuel, 186–87 Gore, Albert Sr., 293, 294 Great War (World War I), 32–33, 36, 74, 89, 91, 193, 372 Greenglass, David, 171, 172, 173, 194, 237, 240–41, 251 Greenglass, Ruth, 171, 173, 241 Greenglass, Samuel, 171 Greenewalt, Crawford, 134, 138, 164 Greisen, Kenneth, 204 Groves, Leslie Allied bombing targets recommended by, 186 atomic bomb and, 197, 198, 199, 206, 207, 202, 229 Bohr surveillance ordered by, 174–75 bombing of Japan as signal to Russia and, 222 bombing of Vemork plant, Norway, and, 178 intelligence missions of, 185–86 Los Alamos and, 151, 157, 169, 225, 228 Manhattan Project management by, 147–50, 156, 165, 175, 197–98, 199 Oak Ridge National Laboratory and, 161, 162–63 Oppenheimer and, 262 postwar atomic arms research and, 229, 230 Russian scientists and, 194 silver supply and, 161 Soviet threat and, 227 Szilard and, 127, 150, 207, 208 uranium source and, 154 Grubbe, Emil, 13 Haber, Fritz, 75, 89, 92, 372–73 Hahn, David, 362–63 Hahn, Edith, 93 Hahn, Otto Allied capture and internment of, 186–87, 188–89, 190 atomic bomb research and, 113, 121, 183, 187 awards and recognition of, 190 Hitler’s Jewish laws and, 92, 93 on Meitner, 86, 96, 98, 191 Meitner’s research with, 64, 84, 85–87, 88–90, 98, 99, 100, 102, 103, 121, 189, 190 Meitner’s treatment by, 92, 93, 96–97, 102–03, 189, 190–91 Nobel Prize to, 188–89, 190 as scientist in Nazi Germany, 190–91 Hall, Joan, 242 Hall, Theodore, 171, 194, 237, 242 Hanford, Washington, reactor complex, 159, 160, 164–65, 166, 168, 175, 188, 225, 282 Harding, Warren G., 50 Harris, Michael, 253, 272 Harrison, Richard Stewart, 144 Haukelid, Knut, 178 Havenaar, Johan, 323, 324 Hawkins, David, 192 Hawks, H.

pages: 267 words: 71,941

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How to Predict the Unpredictable
** by
William Poundstone

accounting loophole / creative accounting, Albert Einstein, Bernie Madoff, Brownian motion, business cycle, butter production in bangladesh, buy and hold, buy low sell high, call centre, centre right, Claude Shannon: information theory, computer age, crowdsourcing, Daniel Kahneman / Amos Tversky, Edward Thorp, Firefox, fixed income, forensic accounting, high net worth, index card, index fund, John von Neumann, market bubble, money market fund, pattern recognition, Paul Samuelson, Ponzi scheme, prediction markets, random walk, Richard Thaler, risk-adjusted returns, Robert Shiller, Robert Shiller, Rubik’s Cube, statistical model, Steven Pinker, transaction costs

You don’t know what you’ll spend it on, so you just pick a number from the touch-screen menu of round amounts. When we make up amounts of cash, and aren’t trying to deceive anyone by making them look random, we almost always pick round numbers. The only thing wrong with round numbers is that, in some contexts, they aren’t businesslike. Companies have a responsibility to negotiate the best deals and to buy no more than is needed. Even when a price happens to be a round number, a Brownian motion of discounts, allowances, transportation charges, and taxes tends to move the net amount away from the round number. The discipline of running an honest business exerts a gravitational pull, bringing the associated values into line with Benford’s law. When the money handling is more lax or evasive, the values diverge. HMC’s principals had been using its funds like their own current account.

pages: 232

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Planet of Slums
** by
Mike Davis

barriers to entry, Branko Milanovic, Bretton Woods, British Empire, Brownian motion, centre right, clean water, conceptual framework, crony capitalism, declining real wages, deindustrialization, Deng Xiaoping, edge city, European colonialism, failed state, Gini coefficient, Hernando de Soto, housing crisis, illegal immigration, income inequality, informal economy, Intergovernmental Panel on Climate Change (IPCC), Internet Archive, jitney, jobless men, Kibera, labor-force participation, land reform, land tenure, liberation theology, low-wage service sector, mandelbrot fractal, market bubble, megacity, microcredit, Nelson Mandela, New Urbanism, Pearl River Delta, Ponzi scheme, RAND corporation, rent control, structural adjustment programs, surplus humans, upwardly mobile, urban planning, urban renewal, War on Poverty, Washington Consensus, working poor

Likewise in Bangalore, the urban fringe is where entrepreneurs can most profitably mine cheap labor with minimal oversight by the state.96 Millions of temporary workers and desperate peasants also hover around the edges of such world capitals of super-exploitation as Surat and Shenzhen. These labor nomads lack secure footing in either city or countryside, and often spend their lifetimes in a kind of desperate Brownian motion 93 See Seabrook, In the Cities of the South, p. 187. 94 Mohamadou Abdoul, "The Production of the City and Urban Informalities," in Enwezor et al. Under Siege, p. 342 95 Guy Thuillier, "Gated Communities in the Metropolitan Area of Buenos Aires," Housing Studies 20:2 (March 2005), p. 255. 96 Hans Schenk, "Urban Fringes in Asia: Markets versus Plans," in I. S. A. Baud and J. Post (eds), Realigning Actors in an Urbanising World: Governance and Institutions from a Development Perspective, Aldershot 2002, pp. 121-22, 131.

pages: 312 words: 86,770

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Endless Forms Most Beautiful: The New Science of Evo Devo
** by
Sean B. Carroll

Albert Einstein, Alfred Russel Wallace, Brownian motion, dark matter, Drosophila, Johann Wolfgang von Goethe, the scientific method

There are some excellent tutorials and animations on these authors’ Web site concerning the generation of periodic and spacing patterns: www.eb.tuebingen.mpg.de/dept4/meinhardt/home.html. François Jacob’s quotation of Jean Perrin appears in his essay “Evolution and Tinkering,” Science 196 (1977): 1161–66. Jean Perrin was a Nobel laureate in Physics (1926) who was cited for his work on colloids and Brownian motion. He wrote a very popular book, Les Atomes (1913), from which the quotation is taken. 5. The Dark Matter of the Genome: Operating Instructions for the Tool Kit I first encountered “dark matter” in Brian Greene’s The Elegant Universe (New York: W. W. Norton, 1999), a very engaging book about the structure of the universe from the very smallest to the largest scale, and in Martin Rees’s excellent Just Six Numbers: The Deep Forces That Shape the Universe (New York: Basic Books, 2001).

**
Humble Pi: A Comedy of Maths Errors
** by
Matt Parker

8-hour work day, Affordable Care Act / Obamacare, bitcoin, British Empire, Brownian motion, Chuck Templeton: OpenTable:, collateralized debt obligation, computer age, correlation does not imply causation, crowdsourcing, Donald Trump, Flash crash, forensic accounting, game design, High speed trading, Julian Assange, millennium bug, Minecraft, obamacare, orbital mechanics / astrodynamics, publication bias, Richard Feynman, Richard Feynman: Challenger O-ring, selection bias, Tacoma Narrows Bridge, Therac-25, value at risk, WikiLeaks, Y2K

Nine: A Round-about Way 1 This carefully calculated figure is surprisingly close to merely assuming that each of the three thousand transactions per working day over twenty-two months took 0.00045 off the index on average. 2 I haven’t just split the difference between the two dates; this is the prediction from a line-of-best-fit of all records between the 6 July 1912 record of 10.6 seconds and the 20 June 1936 record of 10.2 seconds. 3 Yes, these are physics problems with this theory. Maybe one day the regulations for wind assistance will also apply to Brownian motion. 9.49: Too Small to Notice 1 Of course, if you start with a solid block of Swiss cheese and slice it, the holes will line up because they were formed by bubbles in the cheese. So assume the Swiss cheese slices have been adequately shuffled. 2 This is the opposite to what we saw with the Apollo fire, where the only exit was a plug seal. Emergency exits should never be plug seals. In this case, the windscreen should never need to open so could be fitted from the inside.

pages: 348 words: 83,490

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More Than You Know: Finding Financial Wisdom in Unconventional Places (Updated and Expanded)
** by
Michael J. Mauboussin

Albert Einstein, Andrei Shleifer, Atul Gawande, availability heuristic, beat the dealer, Benoit Mandelbrot, Black Swan, Brownian motion, butter production in bangladesh, buy and hold, capital asset pricing model, Clayton Christensen, clockwork universe, complexity theory, corporate governance, creative destruction, Daniel Kahneman / Amos Tversky, deliberate practice, demographic transition, discounted cash flows, disruptive innovation, diversification, diversified portfolio, dogs of the Dow, Drosophila, Edward Thorp, en.wikipedia.org, equity premium, Eugene Fama: efficient market hypothesis, fixed income, framing effect, functional fixedness, hindsight bias, hiring and firing, Howard Rheingold, index fund, information asymmetry, intangible asset, invisible hand, Isaac Newton, Jeff Bezos, Kenneth Arrow, Laplace demon, Long Term Capital Management, loss aversion, mandelbrot fractal, margin call, market bubble, Menlo Park, mental accounting, Milgram experiment, Murray Gell-Mann, Nash equilibrium, new economy, Paul Samuelson, Pierre-Simon Laplace, quantitative trading / quantitative ﬁnance, random walk, Richard Florida, Richard Thaler, Robert Shiller, Robert Shiller, shareholder value, statistical model, Steven Pinker, stocks for the long run, survivorship bias, The Wisdom of Crowds, transaction costs, traveling salesman, value at risk, wealth creators, women in the workforce, zero-sum game

Treynor, “Market Efficiency and the Bean Jar Experiment,” Financial Analysts Journal (May-June 1987): -53; Sherry Sontag and Christopher Drew, Blind Man’s Bluff: The Untold Story of American Submarine Espionage (New York: Perseus Books, 1998), 58-59. 6 Kay-Yut Chen, Leslie R. Fine, and Bernardo A. Huberman, “Predicting the Future,” Information Systems Frontiers 5, no. 1 (2003): 47-61, http://www.hpl.hp.com/shl/papers/future/future.pdf. 31. A Tail of Two Worlds 1 This process is know as Brownian motion. Albert Einstein pointed out that this motion is caused by random bombardment of heat-excited water molecules on the pollen. 2 See GloriaMundi, “Introduction to VaR,” http://www.gloriamundi.org/introduction.asp. 3 Edgar E. Peters, Fractal Market Analysis (New York: John Wiley & Sons, 1994), 21-27. 4 Roger Lowenstein, When Genius Failed: The Rise and Fall of Long-Term Capital Management (New York: Random House, 2000), 72.

pages: 301 words: 85,263

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New Dark Age: Technology and the End of the Future
** by
James Bridle

AI winter, Airbnb, Alfred Russel Wallace, Automated Insights, autonomous vehicles, back-to-the-land, Benoit Mandelbrot, Bernie Sanders, bitcoin, British Empire, Brownian motion, Buckminster Fuller, Capital in the Twenty-First Century by Thomas Piketty, carbon footprint, cognitive bias, cognitive dissonance, combinatorial explosion, computer vision, congestion charging, cryptocurrency, data is the new oil, Donald Trump, Douglas Engelbart, Douglas Engelbart, Douglas Hofstadter, drone strike, Edward Snowden, fear of failure, Flash crash, Google Earth, Haber-Bosch Process, hive mind, income inequality, informal economy, Internet of things, Isaac Newton, John von Neumann, Julian Assange, Kickstarter, late capitalism, lone genius, mandelbrot fractal, meta analysis, meta-analysis, Minecraft, mutually assured destruction, natural language processing, Network effects, oil shock, p-value, pattern recognition, peak oil, recommendation engine, road to serfdom, Robert Mercer, Ronald Reagan, self-driving car, Silicon Valley, Silicon Valley ideology, Skype, social graph, sorting algorithm, South China Sea, speech recognition, Spread Networks laid a new fibre optics cable between New York and Chicago, stem cell, Stuxnet, technoutopianism, the built environment, the scientific method, Uber for X, undersea cable, University of East Anglia, uranium enrichment, Vannevar Bush, WikiLeaks

The conspiracy theory is the dominant narrative and the lingua franca of the times: properly read, it really does explain everything. In the gray zone, the contrails are both chemtrails and the early warning signs of global warming: they can be each of these things at the same time. In the gray zone, the exhaust fumes of industrial chimneys mingle with the free molecules of the upper atmosphere, animating the natural and unnatural in Brownian motions of uncertain provenance. The fibrous strands that poke through the skin of Morgellons sufferers are trace elements of fibre-optic cables, and the electromagnetic vibrations of cellphone towers transmitting high-frequency financial data. In the gray zone, the setting sun refracts through the haze of airborne particulates, and the earth really is out of kilter: we’re just prepared to admit it now.

pages: 998 words: 211,235

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A Beautiful Mind
** by
Sylvia Nasar

"Robert Solow", Al Roth, Albert Einstein, Andrew Wiles, Brownian motion, business cycle, cognitive dissonance, Columbine, experimental economics, fear of failure, Gunnar Myrdal, Henri Poincaré, invisible hand, Isaac Newton, John Conway, John Nash: game theory, John von Neumann, Kenneth Arrow, Kenneth Rogoff, linear programming, lone genius, longitudinal study, market design, medical residency, Nash equilibrium, Norbert Wiener, Paul Erdős, Paul Samuelson, prisoner's dilemma, RAND corporation, Ronald Coase, second-price auction, Silicon Valley, Simon Singh, spectrum auction, The Wealth of Nations by Adam Smith, Thorstein Veblen, upwardly mobile, zero-sum game

Einstein had used to complain around the Institute that “Birkhoff is one of the world’s great academic anti-Semites.” Whether or not this was true, Birkhoff’s bias had prevented him from taking advantage of the emigration of the brilliant Jewish mathematicians from Nazi Germany.27 Indeed, Harvard also had ignored Norbert Wiener, the most brilliant American-born mathematician of his generation, the father of cybernetics and inventor of the rigorous mathematics of Brownian motion. Wiener happened to be a Jew and, like Paul Samuelson, the future Nobel Laureate in economics, he sought refuge at the far end of Cambridge at MIT, then little more than an engineering school on a par with the Carnegie Institute of Technology.28 William James, the preeminent American philosopher and older brother of the novelist Henry James, once wrote of a critical mass of geniuses causing a whole civilization to “vibrate and shake.”29 But the man in the street didn’t feel the tremors emanating from Princeton until World War II was practically over and these odd men with their funny accents, peculiar dress, and passion for obscure scientific theories became national heroes.

…

., 261 Brandeis University, 314–22 Brauer, Fred, 146 Brenner, Joseph, 239, 258 Brezhnev, Leonid, 332 Bricker, Jacob Leon, 144, 223, 321 Alicia Larde and, 200–201 Eleanor Stier and, 177, 178, 181, 182, 206–7 Nash’s delusions about, 326 Nash’s relationship with, 180–83, 204, 206–7 bridge, 142 Brieskorn, Egbert, 318 Brod, Max, 278 Brode, Wallace, 279 Bronx High School, 142 Brouwer’s fixed point theorem, 45, 128, 362 Browder, Earl, 153 Browder, Eva, 233–34, 380 Browder, Felix, 73, 142, 154, 157, 229, 244, 246–47 Nashes’ British trip and, 233–34 Nashes’ socializing with, 380, 386 on Nash’s defection effort, 281 Nash’s McLean commitment and, 257 Browder, William, 309, 335 Brown, Douglas, 126, 310, 312 Brownian motion, 55 Buchanan, James, 364 Buchwald, Art, 271 Bulletin de la Société Mathématique de France, 298 Bunker Hill Community College, 344 Burr, Stefan, 299 Bush, Vannevar, 137 Calabi, Eugenio, 64, 68, 72, 232, 244–45 Calabi, Giuliana, 245 calculus, tensor, 380 California Institute of Technology, 375 Camus, Albert, 271 Cantorian set theory, 52 Cappell, Sylvain, 99 Carl XVI Gustav, king of Sweden, 379–80 Carleson, Lennart, 223–24, 226, 227 Carnegie Institute of Technology, 35, 39–45, 129, 362 description of, 40 Carrier Clinic, 304, 305–8, 312–13, 43, 344 Cartan, Elie-Joseph, 157 Cartwright, Mary, 57 Casals, Pablo, 193 Castle, The (Kafka), 273, 278 Cauchy problem, 297–98 Cauvin, Jean-Pierre, 284, 298, 308 Cauvin, Louisa, 308 Central Bank of Sweden Prize in Economic Science in Memory of Alfred Nobel, see Nobel Prize in economics Central Intelligence Agency (CIA), 134 Centre de la Recherches Nationale Scientifiques, 298 Chamberlain, Gary, 354 Charles, Ray, 255 Chern, Shiing-shen, 72, 236, 279 Chiang Kai-shek, 153 Chicago, University of, 45, 132, 236, 237, 244 China, 153 Choate, Hall & Steward, 153 Chung, Kai Lai, 66 Church, Alonzo, 63, 64, 93 CIA (Central Intelligence Agency), 134 City College, 142, 144, 180 John Bates Clark medal for economics, 369 Clark University, 59 C.

pages: 315 words: 93,628

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Is God a Mathematician?
** by
Mario Livio

Albert Einstein, Antoine Gombaud: Chevalier de Méré, Brownian motion, cellular automata, correlation coefficient, correlation does not imply causation, cosmological constant, Dava Sobel, double helix, Edmond Halley, Eratosthenes, Georg Cantor, Gerolamo Cardano, Gödel, Escher, Bach, Henri Poincaré, Isaac Newton, Johannes Kepler, John von Neumann, music of the spheres, Myron Scholes, probability theory / Blaise Pascal / Pierre de Fermat, Russell's paradox, Thales of Miletus, The Design of Experiments, the scientific method, traveling salesman

The Black-Scholes model won its originators (Myron Scholes and Robert Carhart Merton; Fischer Black passed away before the prize was awarded) the Nobel Memorial Prize in economics. The key equation in the model enables the understanding of stock option pricing (options are financial instruments that allow bidders to buy or sell stocks at a future point in time, at agreed-upon prices). Here, however, comes a surprising fact. At the heart of this model lies a phenomenon that had been studied by physicists for decades—Brownian motion, the state of agitated motion exhibited by tiny particles such as pollen suspended in water or smoke particles in the air. Then, as if that were not enough, the same equation also applies to the motion of hundreds of thousands of stars in star clusters. Isn’t this, in the language of Alice in Wonderland, “curiouser and curiouser”? After all, whatever the cosmos may be doing, business and finance are definitely worlds created by the human mind.

pages: 356 words: 95,647

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Sun in a Bottle: The Strange History of Fusion and the Science of Wishful Thinking
** by
Charles Seife

Albert Einstein, anti-communist, Brownian motion, correlation does not imply causation, Dmitri Mendeleev, Ernest Rutherford, Fellow of the Royal Society, Gary Taubes, Isaac Newton, John von Neumann, Mikhail Gorbachev, Norman Macrae, Project Plowshare, Richard Feynman, Ronald Reagan, the scientific method, Yom Kippur War

Physicists soon joined the chemists in their support of atomic theory; they began to provide evidence for the existence of tiny atomic particles. Theorists like Ludwig Boltzmann realized that you could explain the properties of gases simply by imagining matter as a collection of atoms madly bouncing around. Observers even saw the random motion of atoms indirectly: the jostling of water molecules makes a tiny pollen grain swim erratically about. (Albert Einstein helped explain this phenomenon—Brownian motion—in 1905.) Though a few stubborn holdouts absolutely refused to believe in atomic theory,14 by the beginning of the twentieth century the scientific community was convinced. Matter was made of invisible atoms of various kinds: hydrogen atoms, oxygen atoms, carbon atoms, iron atoms, gold atoms, uranium atoms, and a few dozen others. But, as scientists were soon to find out, atoms are not quite as uncuttable as the ancient Greeks thought.

pages: 353 words: 88,376

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The Investopedia Guide to Wall Speak: The Terms You Need to Know to Talk Like Cramer, Think Like Soros, and Buy Like Buffett
** by
Jack (edited By) Guinan

Albert Einstein, asset allocation, asset-backed security, Brownian motion, business cycle, business process, buy and hold, capital asset pricing model, clean water, collateralized debt obligation, computerized markets, correlation coefficient, credit crunch, Credit Default Swap, credit default swaps / collateralized debt obligations, discounted cash flows, diversification, diversified portfolio, dividend-yielding stocks, dogs of the Dow, equity premium, fixed income, implied volatility, index fund, intangible asset, interest rate swap, inventory management, London Interbank Offered Rate, margin call, money market fund, mortgage debt, Myron Scholes, passive investing, performance metric, risk tolerance, risk-adjusted returns, risk/return, shareholder value, Sharpe ratio, short selling, statistical model, time value of money, transaction costs, yield curve, zero-coupon bond

In contrast, less liquid assets such as a small-cap stock will have wider spreads, sometimes as high as 1 to 2% of the asset’s value. Related Terms: • Ask • Market Maker • New York Stock Exchange—NYSE • Bid • Pink Sheets Black Scholes Model What Does Black Scholes Model Mean? A model of price variation over time in financial instruments such as stocks that often is used to calculate the price of a European call option. The model assumes that the price of heavily traded assets follows a geometric Brownian motion with constant drift and volatility. When applied to a stock option, the model incorporates the constant price variation of the stock, the time value of money, the option’s strike price, and the time to the option’s expiration. Also known as the Black-Scholes-Merton Model. Investopedia explains Black Scholes Model The Black Scholes Model is one of the most important concepts in modern financial theory.

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High-Frequency Trading
** by
David Easley,
Marcos López de Prado,
Maureen O'Hara

algorithmic trading, asset allocation, backtesting, Brownian motion, capital asset pricing model, computer vision, continuous double auction, dark matter, discrete time, finite state, fixed income, Flash crash, High speed trading, index arbitrage, information asymmetry, interest rate swap, latency arbitrage, margin call, market design, market fragmentation, market fundamentalism, market microstructure, martingale, natural language processing, offshore financial centre, pattern recognition, price discovery process, price discrimination, price stability, quantitative trading / quantitative ﬁnance, random walk, Sharpe ratio, statistical arbitrage, statistical model, stochastic process, Tobin tax, transaction costs, two-sided market, yield curve

Clark (1973) suggested a related variant, arguing for a volume-based clock. Mandelbrot (1973) explained the difference between them in the following terms: There is – as I have said – no dispute between us about the value of the concept of subordinated process. Clark’s approach is an interesting and natural modification of one described by Mandelbrot and Taylor. The notion is that price change would cease to be erratic and would reduce to the familiar Brownian motion if only it were followed in an appropriate “local time” different from “clock time”. Taylor and I had thought that local time might coincide with transaction time, while Clark links it with volume. He also has the merit of having investigated this hunch empirically…. However, it should be kept in mind that if price variation is to proceed smoothly in local time, then local time itself must flow at random and at a highly variable rate.

pages: 297 words: 91,141

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Market Sense and Nonsense
** by
Jack D. Schwager

3Com Palm IPO, asset allocation, Bernie Madoff, Brownian motion, buy and hold, collateralized debt obligation, commodity trading advisor, computerized trading, conceptual framework, correlation coefficient, Credit Default Swap, credit default swaps / collateralized debt obligations, diversification, diversified portfolio, fixed income, high net worth, implied volatility, index arbitrage, index fund, London Interbank Offered Rate, Long Term Capital Management, margin call, market bubble, market fundamentalism, merger arbitrage, negative equity, pattern recognition, performance metric, pets.com, Ponzi scheme, quantitative trading / quantitative ﬁnance, random walk, risk tolerance, risk-adjusted returns, risk/return, Robert Shiller, Robert Shiller, selection bias, Sharpe ratio, short selling, statistical arbitrage, statistical model, survivorship bias, transaction costs, two-sided market, value at risk, yield curve

The efficient market hypothesis is inextricably linked to an underlying assumption that market price changes follow a random walk process (that is, price changes are normally distributed7). The assumption of a normal distribution allows one to calculate the probability of different-size price moves. Mark Rubinstein, an economist, colorfully described the improbability of the October 1987 stock market crash: Adherents of geometric Brownian motion or lognormally distributed stock returns (one of the foundation blocks of modern finance) must ever after face a disturbing fact: assuming the hypothesis that stock index returns are lognormally distributed with about a 20% annualized volatility (the historical average since 1928), the probability that the stock market could fall 29% in a single day is 10−160. So improbable is such an event that it would not be anticipated to occur even if the stock market were to last for 20 billion years, the upper end of the currently estimated duration of the universe.

pages: 321 words: 92,828

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Late Bloomers: The Power of Patience in a World Obsessed With Early Achievement
** by
Rich Karlgaard

Airbnb, Albert Einstein, Amazon Web Services, Apple's 1984 Super Bowl advert, Bernie Madoff, Bob Noyce, Brownian motion, Captain Sullenberger Hudson, cloud computing, cognitive dissonance, Daniel Kahneman / Amos Tversky, deliberate practice, Electric Kool-Aid Acid Test, Elon Musk, en.wikipedia.org, experimental economics, fear of failure, financial independence, follow your passion, Frederick Winslow Taylor, hiring and firing, Internet of things, Isaac Newton, Jeff Bezos, job satisfaction, knowledge economy, labor-force participation, longitudinal study, low skilled workers, Mark Zuckerberg, meta analysis, meta-analysis, Moneyball by Michael Lewis explains big data, move fast and break things, move fast and break things, pattern recognition, Peter Thiel, Sand Hill Road, science of happiness, shareholder value, Silicon Valley, Silicon Valley startup, Snapchat, Steve Jobs, Steve Wozniak, theory of mind, Tim Cook: Apple, Toyota Production System, unpaid internship, upwardly mobile, women in the workforce, working poor

* * * In 1905 a German-born Swiss patent application examiner—a late bloomer who didn’t speak until age six and now at twenty-five was so easily distracted at work that he was repeatedly rejected for promotion at the patent office—wrote, during his nonwork hours, a series of papers that would profoundly change the world. They included a Ph.D. thesis and four additional papers on the photoelectric effect, Brownian motion, special relativity, and the relationship between mass and energy. The author summarized the last paper with the famous equation E = mc2. And with them, Albert Einstein altered the foundations of the world as we know it. But 1905 was also notable for another series of papers that continue to define our world today. The author, like Einstein, was a self-taught outsider. Born in Nice in 1857, Alfred Binet was educated as a lawyer, but his interests were varied and quirky.

pages: 334 words: 98,950

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Bad Samaritans: The Myth of Free Trade and the Secret History of Capitalism
** by
Ha-Joon Chang

affirmative action, Albert Einstein, Big bang: deregulation of the City of London, bilateral investment treaty, borderless world, Bretton Woods, British Empire, Brownian motion, business cycle, call centre, capital controls, central bank independence, colonial rule, Corn Laws, corporate governance, David Ricardo: comparative advantage, Deng Xiaoping, Doha Development Round, en.wikipedia.org, falling living standards, Fellow of the Royal Society, financial deregulation, fixed income, Francis Fukuyama: the end of history, income inequality, income per capita, industrial robot, Isaac Newton, joint-stock company, Joseph Schumpeter, Kenneth Rogoff, Kickstarter, land reform, liberal world order, liberation theology, low skilled workers, market bubble, market fundamentalism, Martin Wolf, means of production, mega-rich, moral hazard, Nelson Mandela, offshore financial centre, oil shock, price stability, principal–agent problem, Ronald Reagan, South Sea Bubble, structural adjustment programs, The Wealth of Nations by Adam Smith, trade liberalization, transfer pricing, urban sprawl, World Values Survey

Before the Convention went into effect in July 1884, Britain, Ecuador and Tunisia signed up, bringing the number of original member countries to 14. Subsequently, Ecuador, El Salvador and Guatemala denounced the Convention, and did not re-join it until the 1990s. The information is from the WIPO (World Intellectual Property Organization) website: http://www.wipo.int/about-ip/en/iprm/pdf/ch5.pdf#paris. 22 They were on the Brownian motion, the photoelectric effect and, most importantly, special relativity. 23 It was only in 1911, six years after he finished his Ph.D., that he was made a professor of physics in the University of Zürich. 24 For further details on the history of Swiss patent system, see Schiff (1971), Industrialisation without National Patents – the Netherlands, 1869–1912 and Switzerland, 1850–1907 (Princeton University Press, Princeton). 25 Moreover, the 1817 Dutch patent law was rather deficient even by the standards of the time.

pages: 313 words: 101,403

**
My Life as a Quant: Reflections on Physics and Finance
** by
Emanuel Derman

Berlin Wall, bioinformatics, Black-Scholes formula, Brownian motion, buy and hold, capital asset pricing model, Claude Shannon: information theory, Donald Knuth, Emanuel Derman, fixed income, Gödel, Escher, Bach, haute couture, hiring and firing, implied volatility, interest rate derivative, Jeff Bezos, John Meriwether, John von Neumann, law of one price, linked data, Long Term Capital Management, moral hazard, Murray Gell-Mann, Myron Scholes, Paul Samuelson, pre–internet, publish or perish, quantitative trading / quantitative ﬁnance, Sharpe ratio, statistical arbitrage, statistical model, Stephen Hawking, Steve Jobs, stochastic volatility, technology bubble, the new new thing, transaction costs, volatility smile, Y2K, yield curve, zero-coupon bond, zero-sum game

After my experiences in physics, I never again worried too much about sharing credit with collaborators. It almost never did you harm. 1RMS is a common mnemonic for both Risk Management System and Root Mean Square.Volatility-a crucial measure of risk that is defined as the square root of the mean of the squares of the stock's daily returns, or "root mean square" in common statistical parlance. Root mean square is also suggestive of Brownian motion, the process by which a randomly moving stock price diffuses from its initial value in such a way that the average price change is proportional to the square root of the elapsed time. 'A few years later a lady who cut my hair asked for my title at work. When I said I was a Vice President at Goldman Sachs, she congratulated me on having only one person above me. She didn't understand that I was one of probably 3,000 VPs.

pages: 571 words: 105,054

**
Advances in Financial Machine Learning
** by
Marcos Lopez de Prado

algorithmic trading, Amazon Web Services, asset allocation, backtesting, bioinformatics, Brownian motion, business process, Claude Shannon: information theory, cloud computing, complexity theory, correlation coefficient, correlation does not imply causation, diversification, diversified portfolio, en.wikipedia.org, fixed income, Flash crash, G4S, implied volatility, information asymmetry, latency arbitrage, margin call, market fragmentation, market microstructure, martingale, NP-complete, P = NP, p-value, paper trading, pattern recognition, performance metric, profit maximization, quantitative trading / quantitative ﬁnance, RAND corporation, random walk, risk-adjusted returns, risk/return, selection bias, Sharpe ratio, short selling, Silicon Valley, smart cities, smart meter, statistical arbitrage, statistical model, stochastic process, survivorship bias, transaction costs, traveling salesman

Using Roll's estimates, we can derive informative features regarding the market's liquidity conditions. 19.3.3 High-Low Volatility Estimator Beckers [1983] shows that volatility estimators based on high-low prices are more accurate than the standard estimators of volatility based on closing prices. Parkinson [1980] derives that, for continuously observed prices following a geometric Brownian motion, where k1 = 4log[2], , Ht is the high price for bar t, and Lt is the low price for bar t. Then the volatility feature σHL can be robustly estimated based on observed high-low prices. 19.3.4 Corwin and Schultz Building on the work of Beckers [1983], Corwin and Schultz [2012] introduce a bid-ask spread estimator from high and low prices. The estimator is based on two principles: First, high prices are almost always matched against the offer, and low prices are almost always matched against the bid.

pages: 347 words: 99,317

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Bad Samaritans: The Guilty Secrets of Rich Nations and the Threat to Global Prosperity
** by
Ha-Joon Chang

affirmative action, Albert Einstein, banking crisis, Big bang: deregulation of the City of London, bilateral investment treaty, borderless world, Bretton Woods, British Empire, Brownian motion, business cycle, call centre, capital controls, central bank independence, colonial rule, Corn Laws, corporate governance, David Ricardo: comparative advantage, Deng Xiaoping, Doha Development Round, en.wikipedia.org, falling living standards, Fellow of the Royal Society, financial deregulation, fixed income, Francis Fukuyama: the end of history, income inequality, income per capita, industrial robot, Isaac Newton, joint-stock company, Joseph Schumpeter, Kenneth Rogoff, Kickstarter, land reform, liberal world order, liberation theology, low skilled workers, market bubble, market fundamentalism, Martin Wolf, means of production, mega-rich, moral hazard, Nelson Mandela, offshore financial centre, oil shock, price stability, principal–agent problem, Ronald Reagan, South Sea Bubble, structural adjustment programs, The Wealth of Nations by Adam Smith, trade liberalization, transfer pricing, urban sprawl, World Values Survey

Before the Convention went into effect in July 1884, Britain, Ecuador and Tunisia signed up, bringing the number of original member countries to 14. Subsequently, Ecuador, El Salvador and Guatemala denounced the Convention, and did not re-join it until the 1990s. The information is from the WIPO (World Intellectual Property Organization) website: http://www.wipo.int/aboutip/en/iprm/pdf/ch5.pdf#paris. 22 They were on the Brownian motion, the photoelectric effect and, most importantly, special relativity. 23 It was only in 1911, six years after he finished his Ph.D., that he was made a professor of physics in the University of Zürich. 24 For further details on the history of Swiss patent system, see Schiff (1971), Industrialisation without National Patents – the Netherlands, 1869–1912 and Switzerland, 1850–1907 (Princeton University Press, Princeton). 25 Moreover, the 1817 Dutch patent law was rather deficient even by the standards of the time.

pages: 356 words: 102,320

**
Pashazade
** by
Jon Courtenay Grimwood

Brownian motion, music of the spheres

It was, thought Raf, like looking into a deep well and not even knowing if there was water at the bottom. 'Send him over,' said Hu San. 'But tell him to lose that cigar first ...' Around the edge of the room, on black leather banquettes, slouched Seattle's wealthy. Tall and blond or dark, handsome and unfortunately not tall at all, elegantly dressed or expensively dishevelled, both women and men talked intently or stood to shake hands and air-kiss briefly. The Brownian motion of money. The woman with the fox fur was repeating her story of meeting a horrible delivery boy on the way in. She was telling it for the third time and her partner was still pretending to be shocked. Only a few of those in the room showed their age in a surgical tightness around the eyes, the regrettable side effects of having reached middle age before the start of nanetíc surgery. The rest had that youthful permanence which came from being able to afford faces that were constantly rebuilt from the inside.

**
The Art of Computer Programming
** by
Donald Ervin Knuth

Brownian motion, complexity theory, correlation coefficient, Donald Knuth, Eratosthenes, G4S, Georg Cantor, information retrieval, Isaac Newton, iterative process, John von Neumann, Louis Pasteur, mandelbrot fractal, Menlo Park, NP-complete, P = NP, Paul Erdős, probability theory / Blaise Pascal / Pierre de Fermat, RAND corporation, random walk, sorting algorithm, Turing machine, Y2K

Brent, Richard Peirce, 8, 28, 40, 130, 136, 139, 141, 241, 279, 280, 313, 348, 352-353, 355, 356, 382, 386, 403, 501, 529-534, 539-540, 556, 590, 600, 643, 644, 646, 657, 695, 719-721. Brezinski, Claude, 357, 721. Brillhart, John David, 29, 394, 396, 400, 660. Brockett, Roger Ware, 712. Brocot, Achille, 655. Bronte, Emily Jane, 292. Brooks, Frederick Phillips, Jr., 226. Brouwer, Luitzen Egbertus Jan, 179. Brown, David, see Spencer Brown. Brown, George William, 135. Brown, Mark Robbin, 712. Brown, Robert, see Brownian motion. Brown, William Stanley, 419, 428, 438, 454, 686. Brownian motion, 559. Bruijn, Nicolaas Govert de, 181, 212, 568, 653, 664, 686, 694. cycle, 38-40. Brute force, 642. Bshouty, Nader Hanna (^j-i. l^ jjL>), 700. Buchholz, Werner, 202, 2~26. Bunch, James Raymond, 500. Buneman, Oscar, 706. Biirgisser, Peter, 515. Burks, Arthur Walter, 202. Burrus, Charles Sidney, 701. Butler, James Preston, 77. Butler, Michael Charles Richard, 442.

…

The probability that X, < x is F(x), so we have the binomial distribution discussed in Section 1.2.10: Fn(x) = s/n with probability (") F{x)s(l - F(x))n~s; the mean is F(x); the standard deviation is y/F(x)(l - F(x))/n. [See Eq. 1.2.10-(i9). This suggests that a slightly better statistic would be to define max {Fn(x) - F( — oo<x<oo see exercise 22. We can calculate the mean and standard deviation of Fn(y) — Fn(x), for x < y, and obtain the covariance of Fn(x) and Fn(y). Using these facts, it can be shown that for large values of n the function Fn(x) behaves as a "Brownian motion," and techniques from this branch of probability theory may be used to study it. The situation is exploited in articles by J. L. Doob and M. D. Donsker, Annals Math. Stat. 20 A949), 393-403 and 23 A952), 277-281; their approach is generally regarded as the most enlightening way to study the KS tests.] 7. Set j = n in Eq. A3) to see that K? is never negative, and that it can get as high as ^/n- Similarly, set j = 1 to make the same observations about K~. 8.

pages: 354 words: 26,550

**
High-Frequency Trading: A Practical Guide to Algorithmic Strategies and Trading Systems
** by
Irene Aldridge

algorithmic trading, asset allocation, asset-backed security, automated trading system, backtesting, Black Swan, Brownian motion, business cycle, business process, buy and hold, capital asset pricing model, centralized clearinghouse, collapse of Lehman Brothers, collateralized debt obligation, collective bargaining, computerized trading, diversification, equity premium, fault tolerance, financial intermediation, fixed income, high net worth, implied volatility, index arbitrage, information asymmetry, interest rate swap, inventory management, law of one price, Long Term Capital Management, Louis Bachelier, margin call, market friction, market microstructure, martingale, Myron Scholes, New Journalism, p-value, paper trading, performance metric, profit motive, purchasing power parity, quantitative trading / quantitative ﬁnance, random walk, Renaissance Technologies, risk tolerance, risk-adjusted returns, risk/return, Sharpe ratio, short selling, Small Order Execution System, statistical arbitrage, statistical model, stochastic process, stochastic volatility, systematic trading, trade route, transaction costs, value at risk, yield curve, zero-sum game

In mathematical terms, if a linear model can be expressed as shown in equation (8.37), reprinted here for convenience, then nonlinear models are best expressed as shown in equation (8.38) which follows: yt = α + ∞ βi xt−i + εt (8.37) i=0 yt = f (xt , xt−1 , xt−2 , · · ·) (8.38) where {yt } is the time series of random variables that are to be forecasted, {xt } is a factor significant in forecasting {yt }, and α and β are coefficients to be estimated. The one-step-ahead nonlinear forecast conditional on the information available in the previous period is usually specified using a Brownian motion formulation, as shown in equation (8.39): yt+1 = µt+1 + σt+1 ξt+1 (8.39) where µt+1 = Et [yt+1 ] is the one-period-ahead forecast of the mean of the variable being forecasted, σt+1 = vart [xt+1 ] is the one-period-ahead forecast of the volatility of the variable being forecasted, and ξt+1 is an identically and independently distributed random variable with mean 0 and variance 1. The term ξt+1 is often referred to as a standardized shock or innovation.

pages: 407 words: 104,622

**
The Man Who Solved the Market: How Jim Simons Launched the Quant Revolution
** by
Gregory Zuckerman

affirmative action, Affordable Care Act / Obamacare, Albert Einstein, Andrew Wiles, automated trading system, backtesting, Bayesian statistics, beat the dealer, Benoit Mandelbrot, Berlin Wall, Bernie Madoff, blockchain, Brownian motion, butter production in bangladesh, buy and hold, buy low sell high, Claude Shannon: information theory, computer age, computerized trading, Credit Default Swap, Daniel Kahneman / Amos Tversky, diversified portfolio, Donald Trump, Edward Thorp, Elon Musk, Emanuel Derman, endowment effect, Flash crash, George Gilder, Gordon Gekko, illegal immigration, index card, index fund, Isaac Newton, John Meriwether, John Nash: game theory, John von Neumann, Loma Prieta earthquake, Long Term Capital Management, loss aversion, Louis Bachelier, mandelbrot fractal, margin call, Mark Zuckerberg, More Guns, Less Crime, Myron Scholes, Naomi Klein, natural language processing, obamacare, p-value, pattern recognition, Peter Thiel, Ponzi scheme, prediction markets, quantitative hedge fund, quantitative trading / quantitative ﬁnance, random walk, Renaissance Technologies, Richard Thaler, Robert Mercer, Ronald Reagan, self-driving car, Sharpe ratio, Silicon Valley, sovereign wealth fund, speech recognition, statistical arbitrage, statistical model, Steve Jobs, stochastic process, the scientific method, Thomas Bayes, transaction costs, Turing machine

Thorp’s firm based its trading on computer-generated algorithms and economic models, using so much electricity that their office in Southern California was always boiling hot. Thorp’s trading formula was influenced by the doctoral thesis of French mathematician Louis Bachelier, who, in 1900, developed a theory for pricing options on the Paris stock exchange using equations similar to those later employed by Albert Einstein to describe the Brownian motion of pollen particles. Bachelier’s thesis, describing the irregular motion of stock prices, had been overlooked for decades, but Thorp and others understood its relevance to modern investing. In 1974, Thorp landed on the front page of the Wall Street Journal in a story headlined: “Computer Formulas Are One Man’s Secret to Success in Market.” A year later, his fortune swelling, he was driving a new red Porsche 911S.

pages: 518 words: 107,836

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How Not to Network a Nation: The Uneasy History of the Soviet Internet (Information Policy)
** by
Benjamin Peters

Albert Einstein, American ideology, Andrei Shleifer, Benoit Mandelbrot, bitcoin, Brownian motion, Claude Shannon: information theory, cloud computing, cognitive dissonance, computer age, conceptual framework, continuation of politics by other means, crony capitalism, crowdsourcing, cuban missile crisis, Daniel Kahneman / Amos Tversky, David Graeber, Dissolution of the Soviet Union, Donald Davies, double helix, Drosophila, Francis Fukuyama: the end of history, From Mathematics to the Technologies of Life and Death, hive mind, index card, informal economy, information asymmetry, invisible hand, Jacquard loom, John von Neumann, Kevin Kelly, knowledge economy, knowledge worker, linear programming, mandelbrot fractal, Marshall McLuhan, means of production, Menlo Park, Mikhail Gorbachev, mutually assured destruction, Network effects, Norbert Wiener, packet switching, Pareto efficiency, pattern recognition, Paul Erdős, Peter Thiel, Philip Mirowski, RAND corporation, rent-seeking, road to serfdom, Ronald Coase, scientific mainstream, Steve Jobs, Stewart Brand, stochastic process, technoutopianism, The Structural Transformation of the Public Sphere, transaction costs, Turing machine

Aleksandr Bogdanov—old Bolshevik revolutionary, right-hand man to Vladimir Lenin, and philosopher—developed a wholesale theory that analogized between society and political economy, which he published in 1913 as Tektology: A Universal Organizational Science, a proto-cybernetics minus the mathematics, whose work Wiener may have seen in translation in the 1920s or 1930s.39 Stefan Odobleja was a largely ignored Romanian whose pre–World War II work prefaced cybernetic thought.40 John von Neumann, the architect of the modern computer, a founding game theorist, and a Macy Conference participant, was a Hungarian émigré. Szolem Mandelbrojt, a Jewish Polish scientist and uncle of fractal founder Benoit Mandelbrot, organized Wiener’s collaboration on harmonic analysis and Brownian motion in 1950 in Nancy, France. Roman Jakobson, the aforementioned structural linguist, a collaborator in the Macy Conferences, and a Russian émigré, held the chair in Slavic studies at Harvard founded by Norbert Wiener’s father. And finally, Wiener’s own domineering and brilliant father, Leo Wiener, was a self-made polymath, the preeminent translator of Tolstoy into English in the twentieth-century, the founder of Slavic studies in America, an émigré from a Belarusian shtetl, and like his son, a humanist committed to uncovering methods for nearly universal communication.41 Although summarizing the intellectual and international sources for the consolidation of cybernetics as a midcentury science for self-governing systems is beyond the scope of this project, the following statement is probably not too far of a stretch.

pages: 396 words: 117,149

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The Master Algorithm: How the Quest for the Ultimate Learning Machine Will Remake Our World
** by
Pedro Domingos

Albert Einstein, Amazon Mechanical Turk, Arthur Eddington, basic income, Bayesian statistics, Benoit Mandelbrot, bioinformatics, Black Swan, Brownian motion, cellular automata, Claude Shannon: information theory, combinatorial explosion, computer vision, constrained optimization, correlation does not imply causation, creative destruction, crowdsourcing, Danny Hillis, data is the new oil, double helix, Douglas Hofstadter, Erik Brynjolfsson, experimental subject, Filter Bubble, future of work, global village, Google Glasses, Gödel, Escher, Bach, information retrieval, job automation, John Markoff, John Snow's cholera map, John von Neumann, Joseph Schumpeter, Kevin Kelly, lone genius, mandelbrot fractal, Mark Zuckerberg, Moneyball by Michael Lewis explains big data, Narrative Science, Nate Silver, natural language processing, Netflix Prize, Network effects, NP-complete, off grid, P = NP, PageRank, pattern recognition, phenotype, planetary scale, pre–internet, random walk, Ray Kurzweil, recommendation engine, Richard Feynman, scientific worldview, Second Machine Age, self-driving car, Silicon Valley, social intelligence, speech recognition, Stanford marshmallow experiment, statistical model, Stephen Hawking, Steven Levy, Steven Pinker, superintelligent machines, the scientific method, The Signal and the Noise by Nate Silver, theory of mind, Thomas Bayes, transaction costs, Turing machine, Turing test, Vernor Vinge, Watson beat the top human players on Jeopardy!, white flight, zero-sum game

Humans do it all the time: an executive can move from, say, a media company to a consumer-products one without starting from scratch because many of the same management skills still apply. Wall Street hires lots of physicists because physical and financial problems, although superficially very different, often have a similar mathematical structure. Yet all the learners we’ve seen so far would fall flat if we, say, trained them to predict Brownian motion and then asked them to predict the stock market. Stock prices and the velocities of particles suspended in a fluid are just different variables, so the learner wouldn’t even know where to start. But analogizers can do this using structure mapping, an algorithm invented by Dedre Gentner, a psychologist at Northwestern University. Structure mapping takes two descriptions, finds a coherent correspondence between some of their parts and relations, and then, based on that correspondence, transfers further properties from one structure to the other.

pages: 460 words: 122,556

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The End of Wall Street
** by
Roger Lowenstein

Asian financial crisis, asset-backed security, bank run, banking crisis, Berlin Wall, Bernie Madoff, Black Swan, break the buck, Brownian motion, Carmen Reinhart, collateralized debt obligation, credit crunch, Credit Default Swap, credit default swaps / collateralized debt obligations, diversified portfolio, eurozone crisis, Fall of the Berlin Wall, fear of failure, financial deregulation, fixed income, high net worth, Hyman Minsky, interest rate derivative, invisible hand, Kenneth Rogoff, London Interbank Offered Rate, Long Term Capital Management, margin call, market bubble, Martin Wolf, money market fund, moral hazard, mortgage debt, negative equity, Northern Rock, Ponzi scheme, profit motive, race to the bottom, risk tolerance, Ronald Reagan, Rubik’s Cube, savings glut, short selling, sovereign wealth fund, statistical model, the payments system, too big to fail, tulip mania, Y2K

Wall Street adopted quantitative strategies because they afforded more precision than old-fashioned judgment—they seemed to convert financial gambles into hard science. Investment banks stocked risk departments with PhDs. The problem was that homeowners weren’t molecules, and finance wasn’t physics. Merrill hired John Breit, a particle theorist, as a risk manager, and Breit tried to explain to his peers that the laws of Brownian motion didn’t truly describe finance—this wasn’t science, it was pseudoscience. The models said a diversified portfolio of municipal bonds would lose money once every 10,000 years, but as Breit pointed out, such a portfolio had been devastated merely 150 years ago, during the Civil War. With regard to Merrill’s portfolio of CDOs, the firm judged its potential loss to be “$71.3 million.”6 This was absurd—not because the number was high or low, but because of the arrogance and self-delusion embedded in such fine, decimal-point precision.

pages: 571 words: 124,448

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Building Habitats on the Moon: Engineering Approaches to Lunar Settlements
** by
Haym Benaroya

3D printing, biofilm, Black Swan, Brownian motion, Buckminster Fuller, carbon-based life, centre right, clean water, Colonization of Mars, Computer Numeric Control, conceptual framework, data acquisition, Elon Musk, fault tolerance, gravity well, inventory management, Johannes Kepler, low earth orbit, orbital mechanics / astrodynamics, performance metric, RAND corporation, risk tolerance, Ronald Reagan, stochastic process, telepresence, telerobotics, the scientific method, urban planning, X Prize, zero-sum game

But if the largest amplitude force occurs only infrequently, the system would be over-designed. In other words, the system would be designed to be stronger than it needs to be, making it uneconomical. In this book, the structural designs for the Moon use very high factors of safety because of concerns about the unknown unknowns. We distinguish between inherently random molecular forces, such as the Brownian motion experienced by atoms on a molecular scale, and the environmental forces of concern here. Environmental forces may not be inherently random, although they undergo very complex cycles. Natural randomness is called aleatory variability, and scientific uncertainty in the model of a process due to limited data or knowledge is called epistemic uncertainty. Such complex phenomena can only be modeled probabilistically.

pages: 502 words: 124,794

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Nexus
** by
Ramez Naam

artificial general intelligence, bioinformatics, Brownian motion, crowdsourcing, Golden Gate Park, hive mind, low earth orbit, mandatory minimum, Menlo Park, pattern recognition, the scientific method, upwardly mobile

"But there are ways to increase the range." Pieces clicked together for Sam. The "no transmitters" rule. The "repeaters" Rangan had mentioned. These kids had found a way to extend Nexus transmissions. Dear god. "Sounds great," she replied. "I'll take your lead." Her pulse was quick now. Her stomach was a knot. Ilya popped the top of the vial. Sam caught a glimpse of a metallic liquid swirling through the glass. Brownian motion mixed tendrils of grey and silver. For an instant she had the impression of the drug as a living thing, aware, alert, purposeful. The moment passed. Ilya handed her the vial, followed closely by a glass of juice from the table. Sam downed the drug. The liquid tasted strongly metallic, slightly bitter. It felt heavy on her tongue, oily as it flowed down her throat. She sipped the juice.

pages: 478 words: 142,608

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The God Delusion
** by
Richard Dawkins

Albert Einstein, anthropic principle, Any sufficiently advanced technology is indistinguishable from magic, Ayatollah Khomeini, Brownian motion, cosmological principle, David Attenborough, Desert Island Discs, double helix, en.wikipedia.org, experimental subject, Fellow of the Royal Society, gravity well, invisible hand, John von Neumann, luminiferous ether, Menlo Park, meta analysis, meta-analysis, Murray Gell-Mann, Necker cube, Peter Singer: altruism, phenotype, placebo effect, planetary scale, Ralph Waldo Emerson, Richard Feynman, Schrödinger's Cat, scientific worldview, Search for Extraterrestrial Intelligence, stem cell, Stephen Hawking, Steven Pinker, the scientific method, theory of mind, Thorstein Veblen, trickle-down economics, unbiased observer

The very nerve impulses with which we do our thinking and our imagining depend upon activities in Micro World. But no action that our wild ancestors ever had to perform, no decision that they ever had to take, would have been assisted by an understanding of Micro World. If we were bacteria, constantly buffeted by thermal movements of molecules, it would be different. But we Middle Worlders are too cumbersomely massive to notice Brownian motion. Similarly, our lives are dominated by gravity but are almost oblivious to the delicate force of surface tension. A small insect would reverse that priority and would find surface tension anything but delicate. Steve Grand, in Creation: Life and How to Make It, is almost scathing about our preoccupation with matter itself. We have this tendency to think that only solid, material ‘things’ are ‘really’ things at all.

**
How I Became a Quant: Insights From 25 of Wall Street's Elite
** by
Richard R. Lindsey,
Barry Schachter

Albert Einstein, algorithmic trading, Andrew Wiles, Antoine Gombaud: Chevalier de Méré, asset allocation, asset-backed security, backtesting, bank run, banking crisis, Black-Scholes formula, Bonfire of the Vanities, Bretton Woods, Brownian motion, business cycle, business process, butter production in bangladesh, buy and hold, buy low sell high, capital asset pricing model, centre right, collateralized debt obligation, commoditize, computerized markets, corporate governance, correlation coefficient, creative destruction, Credit Default Swap, credit default swaps / collateralized debt obligations, currency manipulation / currency intervention, discounted cash flows, disintermediation, diversification, Donald Knuth, Edward Thorp, Emanuel Derman, en.wikipedia.org, Eugene Fama: efficient market hypothesis, financial innovation, fixed income, full employment, George Akerlof, Gordon Gekko, hiring and firing, implied volatility, index fund, interest rate derivative, interest rate swap, John von Neumann, linear programming, Loma Prieta earthquake, Long Term Capital Management, margin call, market friction, market microstructure, martingale, merger arbitrage, Myron Scholes, Nick Leeson, P = NP, pattern recognition, Paul Samuelson, pensions crisis, performance metric, prediction markets, profit maximization, purchasing power parity, quantitative trading / quantitative ﬁnance, QWERTY keyboard, RAND corporation, random walk, Ray Kurzweil, Richard Feynman, Richard Stallman, risk-adjusted returns, risk/return, shareholder value, Sharpe ratio, short selling, Silicon Valley, six sigma, sorting algorithm, statistical arbitrage, statistical model, stem cell, Steven Levy, stochastic process, systematic trading, technology bubble, The Great Moderation, the scientific method, too big to fail, trade route, transaction costs, transfer pricing, value at risk, volatility smile, Wiener process, yield curve, young professional

I, on the other hand, muddled along, testing model after model to little effect, all the while trying to make sense of my surroundings. I was to discover that graduate school had prepared me in a decidedly tangential manner for what I was to encounter. The foreign exchange markets, which I had studied extensively in the context of purchasing power parity, uncovered interest rate parity, and geometric JWPR007-Lindsey April 30, 2007 18:3 Andrew B. Weisman 189 Brownian motion, were almost unrecognizable to me. I frequently felt lost in a world of rapid-fire economic and political developments, blaring broker boxes, and arcane market nomenclature. It was as if I had embarked on a career as a professional pugilist armed with an extensive knowledge of anatomy and the basic instruction set that I must strike my opponent firmly about the head and abdomen while avoiding same.

pages: 692 words: 127,032

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Fool Me Twice: Fighting the Assault on Science in America
** by
Shawn Lawrence Otto

affirmative action, Albert Einstein, anthropic principle, Berlin Wall, Brownian motion, carbon footprint, Cepheid variable, clean water, Climategate, Climatic Research Unit, cognitive dissonance, Columbine, commoditize, cosmological constant, crowdsourcing, cuban missile crisis, Dean Kamen, desegregation, different worldview, double helix, energy security, Exxon Valdez, fudge factor, ghettoisation, global pandemic, Harlow Shapley and Heber Curtis, Harvard Computers: women astronomers, informal economy, Intergovernmental Panel on Climate Change (IPCC), invisible hand, Isaac Newton, Louis Pasteur, mutually assured destruction, Richard Feynman, Ronald Reagan, Saturday Night Live, shareholder value, sharing economy, smart grid, Solar eclipse in 1919, stem cell, the scientific method, The Wealth of Nations by Adam Smith, Thomas Kuhn: the structure of scientific revolutions, transaction costs, University of East Anglia, War on Poverty, white flight, Winter of Discontent, working poor, yellow journalism, zero-sum game

They do not extend in sudden and dramatic paradigm shifts, and they didn’t in Einstein’s day, either. In fact, many of the ideas Einstein developed were done collaboratively, with considerable debate, a prime example being the cosmological constant. His early papers were extensions of the work of Max Planck, the Austrian physicist Ludwig Boltzmann, and others, and his revolutionary findings on Brownian motion were independently discovered by Polish physicist Marian von Smoluchowski, who was also building on Boltzmann’s work. Hubble’s revolutionary discovery of the expansion of the universe also extended from ideas that were talked about for years. The redshift was first noted by American astronomer Vesto Slipher in 1912—nearly two decades before Hubble’s discovery. Galileo’s revolution was an extension of Copernicus’s writings of some seventy years before, which were widely discussed.

pages: 492 words: 141,544

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Red Moon
** by
Kim Stanley Robinson

artificial general intelligence, basic income, blockchain, Brownian motion, correlation does not imply causation, cryptocurrency, Deng Xiaoping, gig economy, Hyperloop, illegal immigration, income inequality, invisible hand, low earth orbit, Magellanic Cloud, megacity, precariat, Schrödinger's Cat, seigniorage, strong AI, Turing machine, universal basic income, zero-sum game

Valerie inquired. “Satyagraha.” “Isn’t that one kind of hard?” she asked. She had seen it performed once in New York, a modernist thing full of dancers with banners, weaving around a stage to a score like industrial music. Libretto in Sanskrit, she seemed to recall. No, they told her, it was easy. The crowd scenes were supposed to be chaotic, indeed in their version they aspired to a state of complete Brownian motion. The gravity made that easy, and often it created all kinds of accidental grace. John was shaking his head. Valerie said, “I love to dance,” which wasn’t quite true, but she was still working on wiping that amused look off John’s face. Time to finish that off for good. They rode up in a basket at the end of a counterweighted crane lift, and were taken to a cluster of midair platforms. There they joined one of the groups congregating on a big central platform, and after introductions, their hosts jumped up to a slightly higher platform, then crossed it and jumped again.

pages: 508 words: 137,199

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Stamping Butterflies
** by
Jon Courtenay Grimwood

affirmative action, Brownian motion, Burning Man, carbon-based life, Chuck Templeton: OpenTable:, dark matter, phenotype

It merely put them into the hands of our dangerous lunatics as opposed to their dangerous lunatics... She sighed. "We'd need your agreement," Professor Mayer said. "And you needn't feel guilty about the man who takes your place. He's going to die anyway... Why would we do this?" she asked, watching smoke trickle towards the ceiling. A whole world of rigid rules covering temperature, convection and Brownian motion all busily pretending to be truly chaotic. No wonder she loved smoking so much. "Because we've got a situation. And mostly it's that we now know who you really are..." Not a flicker from Prisoner Zero. "...and according to your family you're already dead." Professor Mayer glanced round the prisoner's new room with its neat bed, built-in shower and view of the Mediterranean. Dr. Petrov could be forgiven her verdict of emotional autism, naïve though it was, because the man seemed totally oblivious to anything going on around him.

pages: 505 words: 142,118

**
A Man for All Markets
** by
Edward O. Thorp

3Com Palm IPO, Albert Einstein, asset allocation, beat the dealer, Bernie Madoff, Black Swan, Black-Scholes formula, Brownian motion, buy and hold, buy low sell high, carried interest, Chuck Templeton: OpenTable:, Claude Shannon: information theory, cognitive dissonance, collateralized debt obligation, Credit Default Swap, credit default swaps / collateralized debt obligations, diversification, Edward Thorp, Erdős number, Eugene Fama: efficient market hypothesis, financial innovation, George Santayana, German hyperinflation, Henri Poincaré, high net worth, High speed trading, index arbitrage, index fund, interest rate swap, invisible hand, Jarndyce and Jarndyce, Jeff Bezos, John Meriwether, John Nash: game theory, Kenneth Arrow, Livingstone, I presume, Long Term Capital Management, Louis Bachelier, margin call, Mason jar, merger arbitrage, Murray Gell-Mann, Myron Scholes, NetJets, Norbert Wiener, passive investing, Paul Erdős, Paul Samuelson, Pluto: dwarf planet, Ponzi scheme, price anchoring, publish or perish, quantitative trading / quantitative ﬁnance, race to the bottom, random walk, Renaissance Technologies, RFID, Richard Feynman, risk-adjusted returns, Robert Shiller, Robert Shiller, rolodex, Sharpe ratio, short selling, Silicon Valley, Stanford marshmallow experiment, statistical arbitrage, stem cell, stocks for the long run, survivorship bias, The Myth of the Rational Market, The Predators' Ball, the rule of 72, The Wisdom of Crowds, too big to fail, Upton Sinclair, value at risk, Vanguard fund, Vilfredo Pareto, Works Progress Administration

He wrote down equations that correctly predicted the statistical properties of the random motion of the particles. Until that time no one had ever seen a molecule or an atom (molecules are groups of atoms of various types bound together by electrical forces), and their existence had been disputed. Here was the final proof that atoms and molecules were real. This article became one of the most widely cited in all of physics. Unknown to Einstein, his equations describing the Brownian motion of pollen particles were essentially the same as the equations that Bachelier had used for his thesis five years earlier to describe a very different phenomenon, the ceaseless, irregular motion of stock prices. Bachelier employed the equations to deduce the “fair” prices for options on the underlying stocks. Unlike Einstein’s work, Bachelier’s remained generally unknown until future Nobel laureate (1970) Paul Samuelson came across it in a Paris library in the 1950s and had it translated into English.

**
The Science of Language
** by
Noam Chomsky

Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Alfred Russel Wallace, British Empire, Brownian motion, dark matter, Drosophila, epigenetics, finite state, Howard Zinn, phenotype, statistical model, stem cell, Steven Pinker, theory of mind

Even great scientists, such as, say, Poincaré – one of the twentieth century's greatest scientists – just laughed at it. [Those who laughed] were very much under Machian [Ernst Mach's] influence: if you can't see it, touch it . . . [you can't take it seriously]; so you just have a way of calculating. Boltzmann actually committed suicide – in part, apparently, because of his inability to get anyone to take him seriously. By a horrible irony, he did it in 1905, the year that Einstein's Brownian motion paper came out, and everyone began to take it seriously. And it goes on. I've been interested in the history of chemistry. Into the 1920s, when I was born – so it isn't that far back – leading scientists would have just ridiculed the idea of taking any of this seriously, including Nobel prizewinning chemists. They thought of [atoms and other such ‘devices’] as ways of calculating the results of experiments.

pages: 509 words: 132,327

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Rise of the Machines: A Cybernetic History
** by
Thomas Rid

1960s counterculture, A Declaration of the Independence of Cyberspace, agricultural Revolution, Albert Einstein, Alistair Cooke, Apple II, Apple's 1984 Super Bowl advert, back-to-the-land, Berlin Wall, British Empire, Brownian motion, Buckminster Fuller, business intelligence, Charles Lindbergh, Claude Shannon: information theory, conceptual framework, connected car, domain-specific language, Douglas Engelbart, Douglas Engelbart, dumpster diving, Extropian, full employment, game design, global village, Haight Ashbury, Howard Rheingold, Jaron Lanier, job automation, John Markoff, John von Neumann, Kevin Kelly, Kubernetes, Marshall McLuhan, Menlo Park, Mitch Kapor, Mother of all demos, new economy, New Journalism, Norbert Wiener, offshore financial centre, oil shale / tar sands, pattern recognition, RAND corporation, Silicon Valley, Simon Singh, speech recognition, Steve Jobs, Steve Wozniak, Steven Levy, Stewart Brand, technoutopianism, Telecommunications Act of 1996, telepresence, The Hackers Conference, Vernor Vinge, Whole Earth Catalog, Whole Earth Review, Y2K, Yom Kippur War, Zimmermann PGP

It didn’t mention the unsuccessful experiments in the little MIT lab or any mechanical implementation of his theory. The paper mentioned the antiaircraft problem only two times, buried in a forest of mathematical formulas on page 76. Neither the title nor the introduction or index contained a single reference to the problem that had motivated the project’s funding. Instead, Wiener offered a mind-numbing alphabet soup of abstruse mathematics: Brownian motion, Cesàro partial sum, Fourier integral, Hermitian form, Lebesgue measure, Parseval’s theorem, Poisson distribution, Schwarz inequality, Stieltjes integral, Weyl’s lemma, and many more. When Weaver received the paper, he had it classified and bound in an orange cover. Engineers nicknamed the document “yellow peril,” a joking reference to the paper’s impenetrable theory and lack of practical relevance.

pages: 504 words: 139,137

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Efficiently Inefficient: How Smart Money Invests and Market Prices Are Determined
** by
Lasse Heje Pedersen

activist fund / activist shareholder / activist investor, algorithmic trading, Andrei Shleifer, asset allocation, backtesting, bank run, banking crisis, barriers to entry, Black-Scholes formula, Brownian motion, business cycle, buy and hold, buy low sell high, capital asset pricing model, commodity trading advisor, conceptual framework, corporate governance, credit crunch, Credit Default Swap, currency peg, David Ricardo: comparative advantage, declining real wages, discounted cash flows, diversification, diversified portfolio, Emanuel Derman, equity premium, Eugene Fama: efficient market hypothesis, fixed income, Flash crash, floating exchange rates, frictionless, frictionless market, Gordon Gekko, implied volatility, index arbitrage, index fund, interest rate swap, late capitalism, law of one price, Long Term Capital Management, margin call, market clearing, market design, market friction, merger arbitrage, money market fund, mortgage debt, Myron Scholes, New Journalism, paper trading, passive investing, price discovery process, price stability, purchasing power parity, quantitative easing, quantitative trading / quantitative ﬁnance, random walk, Renaissance Technologies, Richard Thaler, risk-adjusted returns, risk/return, Robert Shiller, Robert Shiller, selection bias, shareholder value, Sharpe ratio, short selling, sovereign wealth fund, statistical arbitrage, statistical model, stocks for the long run, stocks for the long term, survivorship bias, systematic trading, technology bubble, time value of money, total factor productivity, transaction costs, value at risk, Vanguard fund, yield curve, zero-coupon bond

In its most extreme form, it says not only that markets discount the future, but they accurately reflect all fundamentals of economies and everything that’s known about companies and so on and so forth, and they synthesize this information into completely perfect prices. This theory would be laughable if it wasn’t so widely believed in. It’s come out of valuing options and modeling diffusion processes: price movement as a diffusion using the Brownian motion and the heat equation. That is a good approximation for modeling short-term options, but to extend that to the idea that there is this perfect matrix of prices that reflects everything perfectly is putting too much weight on a small base of evidence, as they say in science. LHP: So how do your models exploit that markets are not perfectly efficient? DWH: Markets are social institutions and reflect all sorts of phenomena that you’d expect such social institutions to reflect.

pages: 515 words: 143,055

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The Attention Merchants: The Epic Scramble to Get Inside Our Heads
** by
Tim Wu

1960s counterculture, Affordable Care Act / Obamacare, AltaVista, Andrew Keen, anti-communist, Apple II, Apple's 1984 Super Bowl advert, barriers to entry, Bob Geldof, borderless world, Brownian motion, Burning Man, Cass Sunstein, citizen journalism, colonial rule, East Village, future of journalism, George Gilder, Golden Gate Park, Googley, Gordon Gekko, housing crisis, informal economy, Internet Archive, Jaron Lanier, Jeff Bezos, jimmy wales, Live Aid, Mark Zuckerberg, Marshall McLuhan, McMansion, Nate Silver, Network effects, Nicholas Carr, placebo effect, post scarcity, race to the bottom, road to serfdom, Saturday Night Live, science of happiness, self-driving car, side project, Silicon Valley, slashdot, Snapchat, Steve Jobs, Steve Wozniak, Steven Levy, Ted Nelson, telemarketer, the built environment, The Chicago School, the scientific method, The Structural Transformation of the Public Sphere, Tim Cook: Apple, Torches of Freedom, Upton Sinclair, upwardly mobile, white flight, zero-sum game

There can be no doubt that Facebook gained in its early days owing to potential for erotic encounter, particularly at a moment when volume was prized over quality of connection by many users. No student newspaper failed to mention dates arranged on the site; yet Facebook was always coy on this point, maintaining a plausible deniability, and never marketed itself as a dating site. Rather, it replicated the ambiguity of college life itself, with its collisions more like Brownian motion than traditional romantic pursuit. Everyone knew that joining a certain club or even attending college would eventually lead to opportunities; making it too explicit would only ruin the effect. In the long run Facebook’s indeterminacy would prove strategically shrewd, as other sites demonstrated the limitations of being defined by sex or romance. With its paying customers looking for love, Match.com would make some money but never approach Facebook financially, despite a head start.

pages: 523 words: 148,929

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Physics of the Future: How Science Will Shape Human Destiny and Our Daily Lives by the Year 2100
** by
Michio Kaku

agricultural Revolution, AI winter, Albert Einstein, Asilomar, augmented reality, Bill Joy: nanobots, bioinformatics, blue-collar work, British Empire, Brownian motion, cloud computing, Colonization of Mars, DARPA: Urban Challenge, delayed gratification, double helix, Douglas Hofstadter, en.wikipedia.org, friendly AI, Gödel, Escher, Bach, hydrogen economy, I think there is a world market for maybe five computers, industrial robot, Intergovernmental Panel on Climate Change (IPCC), invention of movable type, invention of the telescope, Isaac Newton, John Markoff, John von Neumann, life extension, Louis Pasteur, Mahatma Gandhi, Mars Rover, mass immigration, megacity, Mitch Kapor, Murray Gell-Mann, new economy, oil shale / tar sands, optical character recognition, pattern recognition, planetary scale, postindustrial economy, Ray Kurzweil, refrigerator car, Richard Feynman, Rodney Brooks, Ronald Reagan, Search for Extraterrestrial Intelligence, Silicon Valley, Simon Singh, social intelligence, speech recognition, stem cell, Stephen Hawking, Steve Jobs, telepresence, The Wealth of Nations by Adam Smith, Thomas L Friedman, Thomas Malthus, trade route, Turing machine, uranium enrichment, Vernor Vinge, Wall-E, Walter Mischel, Whole Earth Review, X Prize

Effects that we can ignore, such as van der Waals forces, surface tension, the uncertainty principle, the Pauli exclusion principle, etc., become dominant in the nanoworld. To appreciate this problem, imagine that the atom is the size of a marble and that you have a swimming pool full of these atoms. If you fell into the swimming pool, it would be quite different from falling into a swimming pool of water. These “marbles” would be constantly vibrating and hitting you from all directions, because of Brownian motion. Trying to swim in this pool would be almost impossible, since it would be like trying to swim in molasses. Every time you tried to grab one of the marbles, it would either move away from you or stick to your fingers, due to a complex combination of forces. In the end, both scientists agreed to disagree. Although Smalley was unable to throw a knockout punch against the molecular replicator, several things became clear after the dust settled.

pages: 286 words: 94,017

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Future Shock
** by
Alvin Toffler

Albert Einstein, Brownian motion, Buckminster Fuller, Charles Lindbergh, cognitive dissonance, Colonization of Mars, corporate governance, East Village, global village, Haight Ashbury, information retrieval, invention of agriculture, invention of movable type, invention of writing, longitudinal study, Marshall McLuhan, mass immigration, Menlo Park, New Urbanism, Norman Mailer, post-industrial society, RAND corporation, social intelligence, the market place, Thomas Kuhn: the structure of scientific revolutions, urban renewal, Whole Earth Catalog, zero-sum game

And by attracting community and parental participation—businessmen, trade unionists, scientists, and others—the movement could build broad political support for the super-industrial revolution in education. It would be a mistake to assume that the present-day educational system is unchanging. On the contrary, it is undergoing rapid change. But much of this change is no more than an attempt to refine the existent machinery, making it ever more efficient in pursuit of obsolete goals. The rest is a kind of Brownian motion, self-canceling, incoherent, directionless. What has been lacking is a consistent direction and a logical starting point. The council movement could supply both. The direction is super-industrialism. The starting point: the future. THE ORGANIZATIONAL ATTACK Such a movement will have to pursue three objectives—to transform the organizational structure of our educational system, to revolutionize its curriculum, and to encourage a more future-focused orientation.

pages: 442 words: 39,064

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Why Stock Markets Crash: Critical Events in Complex Financial Systems
** by
Didier Sornette

Asian financial crisis, asset allocation, Berlin Wall, Bretton Woods, Brownian motion, business cycle, buy and hold, capital asset pricing model, capital controls, continuous double auction, currency peg, Deng Xiaoping, discrete time, diversified portfolio, Elliott wave, Erdős number, experimental economics, financial innovation, floating exchange rates, frictionless, frictionless market, full employment, global village, implied volatility, index fund, information asymmetry, intangible asset, invisible hand, John von Neumann, joint-stock company, law of one price, Louis Bachelier, mandelbrot fractal, margin call, market bubble, market clearing, market design, market fundamentalism, mental accounting, moral hazard, Network effects, new economy, oil shock, open economy, pattern recognition, Paul Erdős, Paul Samuelson, quantitative trading / quantitative ﬁnance, random walk, risk/return, Ronald Reagan, Schrödinger's Cat, selection bias, short selling, Silicon Valley, South Sea Bubble, statistical model, stochastic process, stocks for the long run, Tacoma Narrows Bridge, technological singularity, The Coming Technological Singularity, The Wealth of Nations by Adam Smith, Tobin tax, total factor productivity, transaction costs, tulip mania, VA Linux, Y2K, yield curve

In other words, we have in mind the process of the emergence of intelligent behaviors at a macroscopic scale that individuals at the microscopic scale cannot perceive. This process has been discussed in biology, for instance in animal populations such as ant colonies or in connection with the emergence of conciousness [8, 198] Let us mention another realization of this concept, which is found in the information contained in options prices on the ﬂuctuations of their underlying assets. Despite the fact that the prices do not follow geometrical Brownian motion, whose existence is a prerequisite for most options pricing models, traders have apparently adapted to empirically incorporating subtle information in the correlation of price distributions with fat tails [337]. In this case and in contrast to the crashes, the traders 280 chapter 7 have had time to adapt. The reason is probably that traders have been exposed for decades to options trading in which the characteristic time scale for option lifetime is in the range of month to years at most.

pages: 645 words: 184,311

**
American Gods
** by
Neil Gaiman

airport security, book scanning, Brownian motion, Golden Gate Park, Lao Tzu

Shadow had never seen the Nile, but there was a blinding afternoon sun burning on the wide brown river that made him think of the muddy expanse of the Nile: not the Nile as it is now, but as it was long ago, flowing like an artery through the papyrus marshes, home to cobra and jackal and wild cow... A road sign pointed to Thebes. The road was built up about twelve feet, so he was driving above the marshes. Clumps and clusters of birds in flight were questing back and forth, black dots against the blue sky, moving in some desperate Brownian motion. In the late afternoon the sun began to lower, gilding the world in elf-light, a thick warm custardy light that made the world feel unearthly and more than real, and it was in this light that Shadow passed the sign telling him he was Now Entering Historical Cairo. He drove under a bridge and found himself in a small port town. The imposing structures of the Cairo courthouse and the even more imposing customs house looked like enormous freshly baked cookies in the syrupy gold of the light at the end of the day.

pages: 611 words: 188,732

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Valley of Genius: The Uncensored History of Silicon Valley (As Told by the Hackers, Founders, and Freaks Who Made It Boom)
** by
Adam Fisher

Airbnb, Albert Einstein, AltaVista, Apple II, Apple's 1984 Super Bowl advert, augmented reality, autonomous vehicles, Bob Noyce, Brownian motion, Buckminster Fuller, Burning Man, Byte Shop, cognitive dissonance, disintermediation, don't be evil, Donald Trump, Douglas Engelbart, Dynabook, Elon Musk, frictionless, glass ceiling, Hacker Ethic, Howard Rheingold, HyperCard, hypertext link, index card, informal economy, information retrieval, Jaron Lanier, Jeff Bezos, Jeff Rulifson, John Markoff, Jony Ive, Kevin Kelly, Kickstarter, knowledge worker, life extension, Marc Andreessen, Mark Zuckerberg, Marshall McLuhan, Maui Hawaii, Menlo Park, Metcalfe’s law, Mother of all demos, move fast and break things, move fast and break things, Network effects, new economy, nuclear winter, PageRank, Paul Buchheit, paypal mafia, peer-to-peer, Peter Thiel, pets.com, pez dispenser, popular electronics, random walk, risk tolerance, Robert Metcalfe, rolodex, self-driving car, side project, Silicon Valley, Silicon Valley startup, skunkworks, Skype, social graph, social web, South of Market, San Francisco, Startup school, Steve Jobs, Steve Wozniak, Steven Levy, Stewart Brand, Ted Nelson, telerobotics, The Hackers Conference, the new new thing, Tim Cook: Apple, tulip mania, V2 rocket, Whole Earth Catalog, Whole Earth Review, Y Combinator

They were already imagining virtual reality right around the corner and stuff like that. Brian Behlendorf: At Wired in the summer of ’93 I was setting up a website, but I was also fixing bugs, I was adding features, and sending them upstream over this e-mail list to the kids at the University of Illinois building, this along with everyone else, the other users, and we were trading these fixes like baseball cards. This was kind of like the Brownian motion of how technology improvement took place in the early days of the web. Louis Rossetto: It was only in the second issue that we had a small news item in the front talking about Tim Berners-Lee in Geneva. That was the first mention of the web in our magazine. But not the last. Then it became something we were paying attention to. Howard Rheingold: And so Louis thought, Okay—let’s create a web-based cultural publication that we’ll make money on.

pages: 662 words: 180,546

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Never Let a Serious Crisis Go to Waste: How Neoliberalism Survived the Financial Meltdown
** by
Philip Mirowski

"Robert Solow", Alvin Roth, Andrei Shleifer, asset-backed security, bank run, barriers to entry, Basel III, Berlin Wall, Bernie Madoff, Bernie Sanders, Black Swan, blue-collar work, Bretton Woods, Brownian motion, business cycle, capital controls, Carmen Reinhart, Cass Sunstein, central bank independence, cognitive dissonance, collapse of Lehman Brothers, collateralized debt obligation, complexity theory, constrained optimization, creative destruction, credit crunch, Credit Default Swap, credit default swaps / collateralized debt obligations, crony capitalism, dark matter, David Brooks, David Graeber, debt deflation, deindustrialization, do-ocracy, Edward Glaeser, Eugene Fama: efficient market hypothesis, experimental economics, facts on the ground, Fall of the Berlin Wall, financial deregulation, financial innovation, Flash crash, full employment, George Akerlof, Goldman Sachs: Vampire Squid, Hernando de Soto, housing crisis, Hyman Minsky, illegal immigration, income inequality, incomplete markets, information asymmetry, invisible hand, Jean Tirole, joint-stock company, Kenneth Arrow, Kenneth Rogoff, Kickstarter, knowledge economy, l'esprit de l'escalier, labor-force participation, liberal capitalism, liquidity trap, loose coupling, manufacturing employment, market clearing, market design, market fundamentalism, Martin Wolf, money market fund, Mont Pelerin Society, moral hazard, mortgage debt, Naomi Klein, Nash equilibrium, night-watchman state, Northern Rock, Occupy movement, offshore financial centre, oil shock, Pareto efficiency, Paul Samuelson, payday loans, Philip Mirowski, Ponzi scheme, precariat, prediction markets, price mechanism, profit motive, quantitative easing, race to the bottom, random walk, rent-seeking, Richard Thaler, road to serfdom, Robert Shiller, Robert Shiller, Ronald Coase, Ronald Reagan, savings glut, school choice, sealed-bid auction, Silicon Valley, South Sea Bubble, Steven Levy, technoutopianism, The Chicago School, The Great Moderation, the map is not the territory, The Myth of the Rational Market, the scientific method, The Wisdom of Crowds, theory of mind, Thomas Kuhn: the structure of scientific revolutions, Thorstein Veblen, Tobin tax, too big to fail, transaction costs, Vilfredo Pareto, War on Poverty, Washington Consensus, We are the 99%, working poor

Let us look more closely at the practical mechanics of orthodox contemporary “economics imperialism.” While gleefully encroaching upon the spheres of interest of other disciplines, orthodox economics has also freely appropriated formalisms and methods from those other disciplines: think of the advent of “experimental economics” or the embrace of magnetic resonance imaging, or attempts to absorb chaos theory or nonstandard analysis or Brownian motion through the Ito calculus. Indeed, if there has been any conceptual constant throughout the history of neoclassical theory since the 1870s, it has been slavish attempts to slake its physics envy through gorging on half-digested imitations of physical models. A social science so promiscuous in its avidity to mimic the tools and techniques of other disciplines has no principled discrimination about what constitutes just and proper argumentation within its own sphere; and this has only become aggravated in the decades since 1980.

pages: 579 words: 183,063

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Tribe of Mentors: Short Life Advice From the Best in the World
** by
Timothy Ferriss

23andMe, A Pattern Language, agricultural Revolution, Airbnb, Albert Einstein, Bayesian statistics, bitcoin, Black Swan, blockchain, Brownian motion, Buckminster Fuller, Clayton Christensen, cloud computing, cognitive dissonance, Colonization of Mars, corporate social responsibility, cryptocurrency, David Heinemeier Hansson, dematerialisation, don't be evil, double helix, effective altruism, Elon Musk, Ethereum, ethereum blockchain, family office, fear of failure, Gary Taubes, Geoffrey West, Santa Fe Institute, Google Hangouts, Gödel, Escher, Bach, haute couture, helicopter parent, high net worth, In Cold Blood by Truman Capote, income inequality, index fund, Jeff Bezos, job satisfaction, Johann Wolfgang von Goethe, Kevin Kelly, Lao Tzu, Law of Accelerating Returns, Lyft, Mahatma Gandhi, Marc Andreessen, Marshall McLuhan, Mikhail Gorbachev, minimum viable product, move fast and break things, move fast and break things, Naomi Klein, non-fiction novel, Peter Thiel, profit motive, Ralph Waldo Emerson, Ray Kurzweil, Saturday Night Live, side project, Silicon Valley, Skype, smart cities, smart contracts, Snapchat, Steve Jobs, Steven Pinker, Stewart Brand, TaskRabbit, Tesla Model S, too big to fail, Turing machine, uber lyft, web application, Whole Earth Catalog, Y Combinator

And by “unreasonably effective,” I mean something quite specific: Something is unreasonably effective if it seems to be useful outside the scope of its assumptions, outside the scope of the context in/for which it was developed. Mathematics is unreasonably effective because it applies to lots of fields that have nothing to do with mathematics or the context in which that math is developed. Economics is unreasonably effective because it is useful even though the assumptions made are often obviously false: assumptions like rationality, quadratic utility, efficiency, and prices following Brownian motion. Statistics is unreasonably effective because it seems to be useful even when we make obviously false assumptions, like when we assume that things are normally distributed even when they aren’t. But also because it seems it works well even when we blatantly disrespect best practices (like by changing our methods or hypothesis after observing data, then doing hypothesis tests). Using unreasonably effective theories is very defensible (in my opinion) when we don’t have better strategies.

pages: 678 words: 216,204

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The Wealth of Networks: How Social Production Transforms Markets and Freedom
** by
Yochai Benkler

affirmative action, barriers to entry, bioinformatics, Brownian motion, call centre, Cass Sunstein, centre right, clean water, commoditize, dark matter, desegregation, East Village, fear of failure, Firefox, game design, George Gilder, hiring and firing, Howard Rheingold, informal economy, information asymmetry, invention of radio, Isaac Newton, iterative process, Jean Tirole, jimmy wales, John Markoff, Kenneth Arrow, longitudinal study, market bubble, market clearing, Marshall McLuhan, Mitch Kapor, New Journalism, optical character recognition, pattern recognition, peer-to-peer, pre–internet, price discrimination, profit maximization, profit motive, random walk, recommendation engine, regulatory arbitrage, rent-seeking, RFID, Richard Stallman, Ronald Coase, Search for Extraterrestrial Intelligence, SETI@home, shareholder value, Silicon Valley, Skype, slashdot, social software, software patent, spectrum auction, technoutopianism, The Fortune at the Bottom of the Pyramid, The Nature of the Firm, transaction costs, Vilfredo Pareto

This stickiness could be the efficacy of a cluster of connections in pursuit of a goal one cares about, as in the case of the newly emerging peer-production enterprises. It could be the ways in which the internal social interaction has combined social norms with platform design to offer relatively stable relations with others who share common interests. Users do not amble around in a social equivalent of Brownian motion. They tend to cluster in new social relations, albeit looser and for more limited purposes than the traditional pillars of community. 667 The conceptual answer has been that the image of "community" that seeks a facsimile of a distant pastoral village is simply the wrong image of how we interact as social beings. We are a networked society now--networked individuals connected with each other in a mesh of loosely knit, overlapping, flat connections.

pages: 695 words: 219,110

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The Fabric of the Cosmos
** by
Brian Greene

airport security, Albert Einstein, Albert Michelson, Arthur Eddington, Brownian motion, clockwork universe, conceptual framework, cosmic microwave background, cosmological constant, dark matter, dematerialisation, Hans Lippershey, Henri Poincaré, invisible hand, Isaac Newton, Murray Gell-Mann, Richard Feynman, Stephen Hawking, urban renewal

As we will see in Chapter 13, recent work in string theory has suggested that strings may be much larger than the Planck length, and this has a number of potentially critical implications—including the possibility of making the theory experimentally testable. 13. The existence of atoms was initially argued through indirect means (as an explanation of the particular ratios in which various chemical substances would combine, and later, through Brownian motion); the existence of the first black holes was confirmed (to many physicists’ satisfaction) by seeing their effect on gas that falls toward them from nearby stars, instead of “seeing” them directly. 14. Since even a placidly vibrating string has some amount of energy, you might wonder how it’s possible for a string vibrational pattern to yield a massless particle. The answer, once again, has to do with quantum uncertainty.

pages: 795 words: 215,529

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Genius: The Life and Science of Richard Feynman
** by
James Gleick

Albert Einstein, American ideology, Arthur Eddington, Brownian motion, double helix, Douglas Hofstadter, Ernest Rutherford, gravity well, Gödel, Escher, Bach, Isaac Newton, John von Neumann, Menlo Park, Murray Gell-Mann, mutually assured destruction, Norbert Wiener, Norman Mailer, pattern recognition, Pepto Bismol, Richard Feynman, Richard Feynman: Challenger O-ring, Ronald Reagan, Rubik’s Cube, Sand Hill Road, Schrödinger's Cat, sexual politics, Stephen Hawking, Steven Levy, the scientific method, Thomas Kuhn: the structure of scientific revolutions, uranium enrichment

His readers—and at first they were few—found no fancy mathematics, just this shift of vision, a bit of physical intuition laid atop a foundation of clean, classical mechanics. Few immediately recognized the power of Feynman’s vision. One who did was the Polish mathematician Mark Kac, who heard Feynman describe his path integrals at Cornell and immediately recognized a kinship with a problem in probability theory. He had been trying to extend the work of Norbert Wiener on Brownian motion, the herky-jerky random motion in the diffusion processes that so dominated Feynman’s theoretical work at Los Alamos. Wiener, too, had created integrals that summed many possible paths a particle could take, but with a crucial difference in the handling of time. Within days of Feynman’s talk, Kac had created a new formula, the Feynman-Kac Formula, that became one of the most ubiquitous of mathematical tools, linking the applications of probability and quantum mechanics.

pages: 1,261 words: 294,715

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Behave: The Biology of Humans at Our Best and Worst
** by
Robert M. Sapolsky

autonomous vehicles, Bernie Madoff, biofilm, blood diamonds, British Empire, Broken windows theory, Brownian motion, car-free, clean water, cognitive dissonance, corporate personhood, corporate social responsibility, Daniel Kahneman / Amos Tversky, delayed gratification, desegregation, different worldview, double helix, Drosophila, Edward Snowden, en.wikipedia.org, epigenetics, Flynn Effect, framing effect, fudge factor, George Santayana, global pandemic, hiring and firing, illegal immigration, impulse control, income inequality, John von Neumann, Loma Prieta earthquake, long peace, longitudinal study, loss aversion, Mahatma Gandhi, meta analysis, meta-analysis, Mohammed Bouazizi, Monkeys Reject Unequal Pay, mouse model, mutually assured destruction, Nelson Mandela, Network effects, out of africa, Peter Singer: altruism, phenotype, placebo effect, publication bias, RAND corporation, risk tolerance, Rosa Parks, selective serotonin reuptake inhibitor (SSRI), self-driving car, Silicon Valley, social intelligence, Stanford marshmallow experiment, Stanford prison experiment, stem cell, Steven Pinker, strikebreaker, theory of mind, transatlantic slave trade, traveling salesman, trickle-down economics, twin studies, ultimatum game, Walter Mischel, wikimedia commons, zero-sum game

.* The main point here is that transposons occur in the brain.11 In humans transpositional events occur in stem cells in the brain when they are becoming neurons, making the brain a mosaic of neurons with different DNA sequences. In other words, when you make neurons, that boring DNA sequence you inherited isn’t good enough. Remarkably, transpositional events occur in neurons that form memories in fruit flies. Even flies evolved such that their neurons are freed from the strict genetic marching orders they inherit. Chance Finally, chance lessens genes as the Code of Codes. Chance, driven by Brownian motion—the random movement of particles in a fluid—has big effects on tiny things like molecules floating in cells, including molecules regulating gene transcription.12 This influences how quickly an activated TF reaches the DNA, splicing enzymes bump into target stretches of RNA, and an enzyme synthesizing something grabs the two precursor molecules needed for the synthesis. I’ll stop here; otherwise, I’ll go on for hours.

pages: 1,202 words: 424,886

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Stigum's Money Market, 4E
** by
Marcia Stigum,
Anthony Crescenzi

accounting loophole / creative accounting, Asian financial crisis, asset allocation, asset-backed security, bank run, banking crisis, banks create money, Black-Scholes formula, Brownian motion, business climate, buy and hold, capital controls, central bank independence, centralized clearinghouse, corporate governance, credit crunch, Credit Default Swap, currency manipulation / currency intervention, David Ricardo: comparative advantage, disintermediation, distributed generation, diversification, diversified portfolio, financial innovation, financial intermediation, fixed income, full employment, high net worth, implied volatility, income per capita, intangible asset, interest rate derivative, interest rate swap, large denomination, locking in a profit, London Interbank Offered Rate, margin call, market bubble, market clearing, market fundamentalism, money market fund, mortgage debt, Myron Scholes, offshore financial centre, paper trading, pension reform, Ponzi scheme, price mechanism, price stability, profit motive, Real Time Gross Settlement, reserve currency, risk tolerance, risk/return, seigniorage, shareholder value, short selling, technology bubble, the payments system, too big to fail, transaction costs, two-sided market, value at risk, volatility smile, yield curve, zero-coupon bond, zero-sum game

The Cox-Ross-Rubinstein binomial tree and Monte Carlo simulation can be used in these cases. APPENDIX TO CHAPTER 17 The Black-Scholes Formula The Black-Scholes formula assumes: 1. Frictionless, competitive, continuous markets, and no constraints on short sales. 2. A constant risk-free rate of interest. 3. No dividends or coupons paid by the underlying asset, although this assumption can be relaxed. 4. The underlying asset follows a geometric Brownian motion. This means that percentage returns are normally distributed. Let C = the price of a call option St = the price of the underlying asset today t = current date T = expiration date K = the strike price r = the risk-free rate σ = the volatility of the underlying asset Where and and N(.) is the cumulative distribution function for the standard normal distribution. The Greek letters for a call option are: SUGGESTED READINGS Cox, John C., and Mark Rubinstein, Options Markets (Upper Saddle River, N.J.: Prentice Hall, 1985).

pages: 1,336 words: 415,037

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The Snowball: Warren Buffett and the Business of Life
** by
Alice Schroeder

affirmative action, Albert Einstein, anti-communist, Ayatollah Khomeini, barriers to entry, Bob Noyce, Bonfire of the Vanities, Brownian motion, capital asset pricing model, card file, centralized clearinghouse, Charles Lindbergh, collateralized debt obligation, computerized trading, corporate governance, corporate raider, Credit Default Swap, credit default swaps / collateralized debt obligations, desegregation, Donald Trump, Eugene Fama: efficient market hypothesis, Everybody Ought to Be Rich, global village, Golden Gate Park, Haight Ashbury, haute cuisine, Honoré de Balzac, If something cannot go on forever, it will stop - Herbert Stein's Law, In Cold Blood by Truman Capote, index fund, indoor plumbing, intangible asset, interest rate swap, invisible hand, Isaac Newton, Jeff Bezos, John Meriwether, joint-stock company, joint-stock limited liability company, Long Term Capital Management, Louis Bachelier, margin call, market bubble, Marshall McLuhan, medical malpractice, merger arbitrage, Mikhail Gorbachev, money market fund, moral hazard, NetJets, new economy, New Journalism, North Sea oil, paper trading, passive investing, Paul Samuelson, pets.com, plutocrats, Plutocrats, Ponzi scheme, Ralph Nader, random walk, Ronald Reagan, Scientific racism, shareholder value, short selling, side project, Silicon Valley, Steve Ballmer, Steve Jobs, supply-chain management, telemarketer, The Predators' Ball, The Wealth of Nations by Adam Smith, Thomas Malthus, too big to fail, transcontinental railway, Upton Sinclair, War on Poverty, Works Progress Administration, Y2K, yellow journalism, zero-coupon bond

“Billy Rogers Died of Drug Overdose,” Omaha World-Herald, April 2, 1987; “Cause Is Sought in Death of Jazz Guitarist Rogers,” Omaha World-Herald, February 21, 1987. 35. Interview with Arjay Miller. 36. Interviews with Verne McKenzie, Malcolm “Kim” Chace III, Don Wurster, Dick and Mary Holland. 37. Interview with George Brumley. 38. Louis Jean-Baptiste Alphonse Bachelier, Theory of Speculation, 1900. Bachelier applied the scientific theory of “Brownian motion” to the market, probably the first of many attempts to bring the rigor and prestige of hard science to the soft science of economics. 39. Charles Ellis, Investment Policy: How to Win the Loser’s Game. Illinois: Dow-Jones-Irwin, 1985, which is based on his article “Winning the Loser’s Game” in the July/August 1975 issue of the Financial Analysts Journal. 40. The modern-day equivalents of Tweedy Browne’s Jamaica Water warrants still exist, for example. 41.

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Principles of Corporate Finance
** by
Richard A. Brealey,
Stewart C. Myers,
Franklin Allen

3Com Palm IPO, accounting loophole / creative accounting, Airbus A320, Asian financial crisis, asset allocation, asset-backed security, banking crisis, Bernie Madoff, big-box store, Black-Scholes formula, break the buck, Brownian motion, business cycle, buy and hold, buy low sell high, capital asset pricing model, capital controls, Carmen Reinhart, carried interest, collateralized debt obligation, compound rate of return, computerized trading, conceptual framework, corporate governance, correlation coefficient, credit crunch, Credit Default Swap, credit default swaps / collateralized debt obligations, cross-subsidies, discounted cash flows, disintermediation, diversified portfolio, equity premium, eurozone crisis, financial innovation, financial intermediation, fixed income, frictionless, fudge factor, German hyperinflation, implied volatility, index fund, information asymmetry, intangible asset, interest rate swap, inventory management, Iridium satellite, Kenneth Rogoff, law of one price, linear programming, Livingstone, I presume, London Interbank Offered Rate, Long Term Capital Management, loss aversion, Louis Bachelier, market bubble, market friction, money market fund, moral hazard, Myron Scholes, new economy, Nick Leeson, Northern Rock, offshore financial centre, Ponzi scheme, prediction markets, price discrimination, principal–agent problem, profit maximization, purchasing power parity, QR code, quantitative trading / quantitative ﬁnance, random walk, Real Time Gross Settlement, risk tolerance, risk/return, Robert Shiller, Robert Shiller, shareholder value, Sharpe ratio, short selling, Silicon Valley, Skype, Steve Jobs, The Nature of the Firm, the payments system, the rule of 72, time value of money, too big to fail, transaction costs, University of East Anglia, urban renewal, VA Linux, value at risk, Vanguard fund, yield curve, zero-coupon bond, zero-sum game, Zipcar

Kendall, “The Analysis of Economic Time Series, Part I. Prices,” Journal of the Royal Statistical Society 96 (1953), pp. 11–25. Kendall’s idea was not wholly new. It had been proposed in an almost forgotten thesis written 53 years earlier by a French doctoral student, Louis Bachelier. Bachelier’s accompanying development of the mathematical theory of random processes anticipated by five years Einstein’s famous work on the random Brownian motion of colliding gas molecules. See L. Bachelier, Théorie de la Speculation (Paris: Gauthiers-Villars, 1900). Reprinted in English (A. J. Boness, trans.) in P. H. Cootner (ed.), The Random Character of Stock Market Prices (Cambridge, MA: MIT Press, 1964), pp. 17–78. 3The drift is equal to the expected outcome: (1/2)(3) + (1/2)(–2.5) = .25%. 4The green line in Figure 13.1 shows the actual Standard and Poor’s Index for February 2002 to February 2007; the red is a series of cumulated random numbers.