combinatorial explosion

24 results back to index


pages: 398 words: 86,855

Bad Data Handbook by Q. Ethan McCallum

Amazon: amazon.comamazon.co.ukamazon.deamazon.fr

Amazon Mechanical Turk, asset allocation, barriers to entry, Benoit Mandelbrot, business intelligence, cellular automata, chief data officer, cloud computing, cognitive dissonance, combinatorial explosion, conceptual framework, database schema, en.wikipedia.org, Firefox, Flash crash, Gini coefficient, illegal immigration, iterative process, labor-force participation, loose coupling, natural language processing, Netflix Prize, quantitative trading / quantitative finance, recommendation engine, sentiment analysis, statistical model, supply-chain management, text mining, too big to fail, web application

–Guessing Text Encoding, Normalizing Text–Normalizing Text, Problem: Application-Specific Characters Leaking into Plain Text–Problem: Application-Specific Characters Leaking into Plain Text, Problem: Application-Specific Characters Leaking into Plain Text–Problem: Application-Specific Characters Leaking into Plain Text, Getting Reviews–Sentiment Classification, Sentiment Classification, Polarized Language–Polarized Language, Corpus Creation–Corpus Creation, Training a Classifier–Lessons Learned, Moving On to the Professional World, Government Data Is Very Real, Lessons Learned and Looking Ahead, File Formats–File Formats, File Formats, File Formats, File Formats, File Formats, File Formats, File Formats, File Formats, File Formats, File Formats, File Formats, File Formats, A Relational Cost Allocations Model–A Relational Cost Allocations Model, The Delicate Sound of a Combinatorial Explosion…–The Delicate Sound of a Combinatorial Explosion…, The Hidden Network Emerges–Finding Value in Network Properties Apache Thrift, File Formats columnar, Understand the Data Structure–Understand the Data Structure complexity of, increasing, The Delicate Sound of a Combinatorial Explosion…–The Delicate Sound of a Combinatorial Explosion… CSV, Is It Just Me, or Does This Data Smell Funny?, Understand the Data Structure–Understand the Data Structure, Keyword PPC Example–Keyword PPC Example, Problem: Application-Specific Characters Leaking into Plain Text–Problem: Application-Specific Characters Leaking into Plain Text, File Formats ER model, A Relational Cost Allocations Model–A Relational Cost Allocations Model Google Protocol Buffers, File Formats graph model, The Hidden Network Emerges–Finding Value in Network Properties human-readable format, Data Intended for Human Consumption, Not Machine Consumption–Data Spread Across Multiple Files, The Arrangement of Data–The Arrangement of Data, Reading Data from an Awkward Format–Reading Data Spread Across Several Files limiting analysis, The Arrangement of Data–The Arrangement of Data reading with software, Reading Data from an Awkward Format–Reading Data Spread Across Several Files JSON, Is It Just Me, or Does This Data Smell Funny?

We’ll also need queries for all the cases in between if we continue with this design to cover assets allocated to departments and products allocated to cost centers. Each new level of the query adds to a combinatorial explosion and begs many questions about the design. What happens if we change the allocation rules? What if a product can be allocated directly to a cost center instead of passing through a department? Are the queries efficient as the amount of data in the system increases? Is the system testable? To make matters worse, a real-world allocation model would also contain many more entities and associative entities. The Delicate Sound of a Combinatorial Explosion… We’ve introduced the problem and sketched out a rudimentary solution in just a few pages, but imagine how a real system like this might evolve over an extended period of months or even years with a team of people involved.

–Will This Be on the Test? JavaScript Object Notation, Is It Just Me, or Does This Data Smell Funny? (see JSON) jellyfish library, Python, Text Processing with Python JSON (JavaScript Object Notation), Is It Just Me, or Does This Data Smell Funny?, Understand the Data Structure–Understand the Data Structure, File Formats, File Formats, File Formats K Koch snowflake, The Delicate Sound of a Combinatorial Explosion… L Laiacano, Adam (author), (Re)Organizing the Web’s Data–Conclusion Levy, Josh (author), Bad Data Lurking in Plain Text–Exercises Logistic Regression classifier, Polarized Language longitudinal datasets, Imputation Bias: General Issues, Other Sources of Bias M machine-learning experts, outsourcing, How to Feed and Care for Your Machine-Learning Experts–Conclusion (see also data scientist) manufacturing data example, Example 1: Defect Reduction in Manufacturing–Example 1: Defect Reduction in Manufacturing Maximum Entropy classifier, Polarized Language McCallum, Q.


pages: 574 words: 164,509

Superintelligence: Paths, Dangers, Strategies by Nick Bostrom

Amazon: amazon.comamazon.co.ukamazon.deamazon.fr

agricultural Revolution, AI winter, Albert Einstein, algorithmic trading, anthropic principle, anti-communist, artificial general intelligence, autonomous vehicles, barriers to entry, bioinformatics, brain emulation, cloud computing, combinatorial explosion, computer vision, cosmological constant, dark matter, DARPA: Urban Challenge, data acquisition, delayed gratification, demographic transition, Douglas Hofstadter, Drosophila, Elon Musk, en.wikipedia.org, epigenetics, fear of failure, Flash crash, Flynn Effect, friendly AI, Gödel, Escher, Bach, income inequality, industrial robot, informal economy, information retrieval, interchangeable parts, iterative process, job automation, John von Neumann, knowledge worker, Menlo Park, meta analysis, meta-analysis, mutually assured destruction, Nash equilibrium, Netflix Prize, new economy, Norbert Wiener, NP-complete, nuclear winter, optical character recognition, pattern recognition, performance metric, phenotype, prediction markets, price stability, principal–agent problem, race to the bottom, random walk, Ray Kurzweil, recommendation engine, reversible computing, social graph, speech recognition, Stanislav Petrov, statistical model, stem cell, Stephen Hawking, strong AI, superintelligent machines, supervolcano, technological singularity, technoutopianism, The Coming Technological Singularity, The Nature of the Firm, Thomas Kuhn: the structure of scientific revolutions, transaction costs, Turing machine, Vernor Vinge, Watson beat the top human players on Jeopardy!, World Values Survey

One such early system, the Logic Theorist, was able to prove most of the theorems in the second chapter of Whitehead and Russell’s Principia Mathematica, and even came up with one proof that was much more elegant than the original, thereby debunking the notion that machines could “only think numerically” and showing that machines were also able to do deduction and to invent logical proofs.13 A follow-up program, the General Problem Solver, could in principle solve a wide range of formally specified problems.14 Programs that could solve calculus problems typical of first-year college courses, visual analogy problems of the type that appear in some IQ tests, and simple verbal algebra problems were also written.15 The Shakey robot (so named because of its tendency to tremble during operation) demonstrated how logical reasoning could be integrated with perception and used to plan and control physical activity.16 The ELIZA program showed how a computer could impersonate a Rogerian psychotherapist.17 In the mid-seventies, the program SHRDLU showed how a simulated robotic arm in a simulated world of geometric blocks could follow instructions and answer questions in English that were typed in by a user.18 In later decades, systems would be created that demonstrated that machines could compose music in the style of various classical composers, outperform junior doctors in certain clinical diagnostic tasks, drive cars autonomously, and make patentable inventions.19 There has even been an AI that cracked original jokes.20 (Not that its level of humor was high—“What do you get when you cross an optic with a mental object? An eye-dea”—but children reportedly found its puns consistently entertaining.) The methods that produced successes in the early demonstration systems often proved difficult to extend to a wider variety of problems or to harder problem instances. One reason for this is the “combinatorial explosion” of possibilities that must be explored by methods that rely on something like exhaustive search. Such methods work well for simple instances of a problem, but fail when things get a bit more complicated. For instance, to prove a theorem that has a 5-line long proof in a deduction system with one inference rule and 5 axioms, one could simply enumerate the 3,125 possible combinations and check each one to see if it delivers the intended conclusion.

But as the task becomes more difficult, the method of exhaustive search soon runs into trouble. Proving a theorem with a 50-line proof does not take ten times longer than proving a theorem that has a 5-line proof: rather, if one uses exhaustive search, it requires combing through 550 ≈ 8.9 × 1034 possible sequences—which is computationally infeasible even with the fastest supercomputers. To overcome the combinatorial explosion, one needs algorithms that exploit structure in the target domain and take advantage of prior knowledge by using heuristic search, planning, and flexible abstract representations—capabilities that were poorly developed in the early AI systems. The performance of these early systems also suffered because of poor methods for handling uncertainty, reliance on brittle and ungrounded symbolic representations, data scarcity, and severe hardware limitations on memory capacity and processor speed.

In practice, however, getting evolutionary methods to work well requires skill and ingenuity, particularly in devising a good representational format. Without an efficient way to encode candidate solutions (a genetic language that matches latent structure in the target domain), evolutionary search tends to meander endlessly in a vast search space or get stuck at a local optimum. Even if a good representational format is found, evolution is computationally demanding and is often defeated by the combinatorial explosion. Neural networks and genetic algorithms are examples of methods that stimulated excitement in the 1990s by appearing to offer alternatives to the stagnating GOFAI paradigm. But the intention here is not to sing the praises of these two methods or to elevate them above the many other techniques in machine learning. In fact, one of the major theoretical developments of the past twenty years has been a clearer realization of how superficially disparate techniques can be understood as special cases within a common mathematical framework.


pages: 396 words: 117,149

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

Amazon: amazon.comamazon.co.ukamazon.deamazon.fr

3D printing, Albert Einstein, Amazon Mechanical Turk, Arthur Eddington, Benoit Mandelbrot, bioinformatics, Black Swan, Brownian motion, cellular automata, Claude Shannon: information theory, combinatorial explosion, computer vision, constrained optimization, correlation does not imply causation, 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 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, P = NP, PageRank, pattern recognition, phenotype, planetary scale, pre–internet, random walk, Ray Kurzweil, recommendation engine, Richard Feynman, Richard Feynman, Second Machine Age, self-driving car, Silicon Valley, speech recognition, statistical model, Stephen Hawking, Steven Levy, Steven Pinker, superintelligent machines, the scientific method, The Signal and the Noise by Nate Silver, theory of mind, transaction costs, Turing machine, Turing test, Vernor Vinge, Watson beat the top human players on Jeopardy!, white flight

When the number of things an algorithm needs to do grows exponentially with the size of its input, computer scientists call it a combinatorial explosion and run for cover. In machine learning, the number of possible instances of a concept is an exponential function of the number of attributes: if the attributes are Boolean, each new attribute doubles the number of possible instances by taking each previous instance and extending it with a yes or no for that attribute. In turn, the number of possible concepts is an exponential function of the number of possible instances: since a concept labels each instance as positive or negative, adding an instance doubles the number of possible concepts. As a result, the number of concepts is an exponential function of an exponential function of the number of attributes! In other words, machine learning is a combinatorial explosion of combinatorial explosions. Perhaps we should just give up and not waste our time on such a hopeless problem?

It helps that, if the goal is to cure cancer, we don’t necessarily need to understand all the details of how tumor cells work, only enough to disable them without harming normal cells. In Chapter 6, we’ll also see how to orient learning toward the goal while steering clear of the things we don’t know and don’t need to know. More immediately, we know we can use inverse deduction to infer the structure of the cell’s networks from data and previous knowledge, but there’s a combinatorial explosion of ways to apply it, and we need a strategy. Since metabolic networks were designed by evolution, perhaps simulating it in our learning algorithms is the way to go. In the next chapter, we’ll see how to do just that. Deeper into the brain When backprop first hit the streets, connectionists had visions of quickly learning larger and larger networks until, hardware permitting, they amounted to artificial brains.

In the days before computers, a police artist could quickly put together a portrait of a suspect from eyewitness interviews by selecting a mouth from a set of paper strips depicting typical mouth shapes and doing the same for the eyes, nose, chin, and so on. With only ten building blocks and ten options for each, this system would allow for ten billion different faces, more than there are people on Earth. In machine learning, as elsewhere in computer science, there’s nothing better than getting such a combinatorial explosion to work for you instead of against you. What’s clever about genetic algorithms is that each string implicitly contains an exponential number of building blocks, known as schemas, and so the search is a lot more efficient than it seems. This is because every subset of the string’s bits is a schema, representing some potentially fit combination of properties, and a string has an exponential number of subsets.


pages: 696 words: 143,736

The Age of Spiritual Machines: When Computers Exceed Human Intelligence by Ray Kurzweil

Amazon: amazon.comamazon.co.ukamazon.deamazon.fr

Ada Lovelace, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Albert Einstein, Any sufficiently advanced technology is indistinguishable from magic, Buckminster Fuller, call centre, cellular automata, combinatorial explosion, complexity theory, computer age, computer vision, cosmological constant, cosmological principle, Danny Hillis, double helix, Douglas Hofstadter, first square of the chessboard / second half of the chessboard, fudge factor, George Gilder, Gödel, Escher, Bach, I think there is a world market for maybe five computers, information retrieval, invention of movable type, Isaac Newton, iterative process, Jacquard loom, Jacquard loom, John von Neumann, Lao Tzu, Law of Accelerating Returns, mandelbrot fractal, Marshall McLuhan, Menlo Park, natural language processing, Norbert Wiener, optical character recognition, pattern recognition, phenotype, Ralph Waldo Emerson, Ray Kurzweil, Richard Feynman, Richard Feynman, Schrödinger's Cat, Search for Extraterrestrial Intelligence, self-driving car, Silicon Valley, speech recognition, Steven Pinker, Stewart Brand, stochastic process, technological singularity, Ted Kaczynski, telepresence, the medium is the message, traveling salesman, Turing machine, Turing test, Whole Earth Review, Y2K

He was probably playing ball with one of his sons. He saw the ball rolling on a curved surface ... AND CONCLUDED—EUREKA—SPACE IS CURVED! CHAPTER FIVE CONTEXT AND KNOWLEDGE PUTTING IT ALL TOGETHER So how well have we done? Many apparently difficult problems do yield to the application of a few simple formulas. The recursive formula is a master at analyzing problems that display inherent combinatorial explosion, ranging from the playing of board games to proving mathematical theorems. Neural nets and related self-organizing paradigms emulate our pattern-recognition faculties, and do a fine job of discerning such diverse phenomena as human speech, letter shapes, visual objects, faces, fingerprints, and land terrain images. Evolutionary algorithms are effective at analyzing complex problems, ranging from making financial investment decisions to optimizing industrial processes, in which the number of variables is too great for precise analytic solutions.

With little fingers and computation, nanomachines would have in their Lilliputian world what people have in the big world: intelligence and the ability to manipulate their environment. Then these little machines could build replicas of themselves, achieving the field’s key objective. The reason that self-replication is important is that it is too expensive to build these tiny machines one at a time. To be effective, nanometer-sized machines need to come in the trillions. The only way to achieve this economically is through combinatorial explosion: let the machines build themselves. Drexler, Merkle (a coinventor of public key encryption, the primary method of encrypting messages), and others have convincingly described how such a self-replicating nanorobot—nanobot—could be constructed. The trick is to provide the nanobot with sufficiently flexible manipulators—arms and hands—so that it is capable of building a copy of itself. It needs some means for mobility so that it can find the requisite raw materials.

I do this not to belabor the issue of chess playing, but rather because it illustrates a clear contrast. Raj Reddy, Carnegie Mellon University’s AI guru, cites studies of chess as playing the same role in artificial intelligence that studies of E. coli play in biology: an ideal laboratory for studying fundamental questions.5 Computers use their extreme speed to analyze the vast combinations created by the combinatorial explosion of moves and countermoves. While chess programs may use a few other tricks (such as storing the openings of all master chess games in this century and precomputing endgames), they essentially rely on their combination of speed and precision. In comparison, humans, even chess masters, are extremely slow and imprecise. So we precompute all of our chess moves. That’s why it takes so long to become a chess master, or the master of any pursuit.


pages: 509 words: 92,141

The Pragmatic Programmer by Andrew Hunt, Dave Thomas

Amazon: amazon.comamazon.co.ukamazon.deamazon.fr

A Pattern Language, Broken windows theory, business process, buy low sell high, c2.com, combinatorial explosion, continuous integration, database schema, domain-specific language, general-purpose programming language, Grace Hopper, if you see hoof prints, think horses—not zebras, index card, loose coupling, Menlo Park, MVC pattern, premature optimization, Ralph Waldo Emerson, revision control, Schrödinger's Cat, slashdot, sorting algorithm, speech recognition, traveling salesman, urban decay, Y2K

Rather than digging though a hierarchy yourself, just ask for what you need directly: We added a method to Selection to get the time zone on our behalf: the plotting routine doesn't care whether the time zone comes from the Recorder directly, from some contained object within Recorder, or whether Selection makes up a different time zone entirely. The selection routine, in turn, should probably just ask the recorder for its time zone, leaving it up to the recorder to get it from its contained Location object. Traversing relationships between objects directly can quickly lead to a combinatorial explosion[1] of dependency relationships. You can see symptoms of this phenomenon in a number of ways: [1] If n objects all know about each other, then a change to just one object can result in the other n – 1 objects needing changes. Large C or C++ projects where the command to link a unit test is longer than the test program itself "Simple" changes to one module that propagate through unrelated modules in the system Developers who are afraid to change code because they aren't sure what might be affected Systems with many unnecessary dependencies are very hard (and expensive) to maintain, and tend to be highly unstable.

Anyone can ask a witness questions in the pursuit of the case, post the transcript, and move that witness to another area of the blackboard, where he might respond differently (if you allow the witness to read the blackboard too). A big advantage of systems such as these is that you have a single, consistent interface to the blackboard. When building a conventional distributed application, you can spend a great deal of time crafting unique API calls for every distributed transaction and interaction in the system. With the combinatorial explosion of interfaces and interactions, the project can quickly become a nightmare. Organizing Your Blackboard When the detectives work on large cases, the blackboard may become cluttered, and it may become difficult to locate data on the board. The solution is to partition the blackboard and start to organize the data on the blackboard somehow. Different software systems handle this partitioning in different ways; some use fairly flat zones or interest groups, while others adopt a more hierarchical treelike structure.

Index A Accessor function, 31 ACM, see Association for Computing Machinery Active code generator, 104 Activity diagram, 150 Advanced C++ Programming Styles and Idioms, 265 Advanced Programming in the Unix Environment, 264 Aegis transaction-based configuration management, 246, 271 Agent, 76, 117, 297 Algorithm binary chop, 180 choosing, 182 combinatoric, 180 divide-and-conquer, 180 estimating, 177, 178 linear, 177 O() notation, 178, 181 quicksort, 180 runtime, 181 sublinear, 177 Allocations, nesting, 131 Analysis Patterns, 264 Anonymity, 258 AOP, see Aspect-Oriented Programming Architecture deployment, 156 flexibility, 46 prototyping, 55 temporal decoupling, 152 Art of Computer Programming, 183 Artificial intelligence, marauding, 26 Aspect-Oriented Programming (AOP), 39, 273 Assertion, 113, 122, 175 side effects, 124 turning off, 123 Association for Computing Machinery (ACM), 262 Communications of the ACM, 263 SIGPLAN, 263 Assumptions, testing, 175 “at” command, 231 Audience, 21 needs, 19 auto_ptr, 134 Automation, 230 approval procedures, 235 build, 88, 233 compiling, 232 cron, 231 documentation, 251 scripts, 234 team, 229 testing, 29, 238 Web site generation, 235 awk, 99 B Backus-Naur Form (BNF), 59n Base class, 112 bash shell, 80, 82n Bean, see Enterprise Java Beans (EJB) Beck, Kent, 194, 258 Beowulf project, 268 “Big O” notation, 177 “Big picture”, 8 Binary chop, 97, 180 Binary format, 73 problems parsing, 75 bison, 59, 269 BIST, see Built-In Self Test Blackboard system, 165 partitioning, 168 workflow, 169 Blender example contract for, 119, 289 regression test jig, 305 workflow, 151 BNF, see Backus-Naur Form (BNF) Boiled frog, 8, 175, 225 Boundary condition, 173, 243 Brain, Marshall, 265 Branding, 226 Brant, John, 268 “Broken Window Theory”, 5 vs. stone soup, 9 Brooks, Fred, 264 Browser, class, 187 Browser, refactoring, 187, 268 Bug, 90 failed contract as, 111 see also Debugging; Error Build automation, 88, 233 dependencies, 233 final, 234 nightly, 231 refactoring, 187 Built-In Self Test (BIST), 189 Business logic, 146 Business policy, 203 C C language assertions, 122 DBC, 114 duplication, 29 error handling, 121 error messages, 115 macros, 121 Object Pascal interface, 101 C++ language, 46 assertions, 122 auto_ptr, 134 books, 265 DBC, 114 decoupling, 142 DOC++, 251, 269 duplication, 29 error messages, 115 exceptions, 132 unit tests, 193 Caching, 31 Call, routine, 115, 173 Cascading Style Sheets (CSS), 253 Cat blaming, 3 herding, 224 Schrödinger’s, 47 Catalyzing change, 8 Cathedrals, xx Cetus links, 265 Change, catalyzing, 8 Christiansen, Tom, 81 Class assertions, 113 base, 112 coupling, 139, 142 coupling ratios, 242 encapsulating resource, 132 invariant, 110, 113 number of states, 245 resource allocation, 132 subclass, 112 wrapper, 132, 133, 135, 141 Class browser, 187 ClearCase, 271 Cockburn, Alistair, xxiii, 205, 264, 272 Code generator, 28, 102 active, 104 makefiles, 232 parsers, 105 passive, 103 Code profiler, 182 Code reviews, 33, 236 Coding algorithm speed, 177 comments, 29, 249 coupled, 130 coverage analysis, 245 database schema, 104 defensive, 107 and documentation, 29, 248 estimating, 68 exceptions, 125 implementation, 173 iterative, 69 “lazy”, 111 metrics, 242 modules, 138 multiple representations, 28 orthogonality, 34, 36, 40 ownership, 258 prototypes, 55 server code, 196 “shy”, 40, 138 specifications, 219 tracer bullets, 49–51 unit testing, 190, 192 see also Coupled code; Decoupled code; Metadata; Source code control system (SCCS) Cohesion, 35 COM, see Component Object Model Combinatorial explosion, 140, 167 Combinatoric algorithm, 180 Command shell, 77 bash, 80 Cygwin, 80 vs. GUI, 78 UWIN, 81 Windows, 80 Comment, 29, 249 avoiding duplication, 29 DBC, 113 parameters, 250 types of, 249 unnecessary, 250 see also Documentation Common Object Request Broker (CORBA), 29, 39, 46 Event Service, 160 Communicating, 18 audience, 19, 21 duplication, 32 e-mail, 22 and formal methods, 221 presentation, 20 style, 20 teams, 225 users, 256 writing, 18 Communications of the ACM, 263 Comp.object FAQ, 272 Compiling, 232 compilers, 267 DBC, 113 warnings and debugging, 92 Component Object Model (COM), 55 Component-based systems, see Modular system Concurrency, 150 design, 154 interfaces, 155 and Programming by Coincidence, 154 requirements analysis of, 150 workflow, 150 Concurrent Version System (CVS), 271 Configuration cooperative, 148 dynamic, 144 metadata, 147 Configuration management, 86, 271 Constantine, Larry L., 35 Constraint management, 213 Constructor, 132 initialization, 155 Contact, authors’ e-mail, xxiii Context, use instead of globals, 40 Contract, 109, 174 see also Design by contract (DBC) Controller (MVC), 162 Coplien, Jim, 265 CORBA, see Common Object Request Broker Coupled code, 130 coupling ratios, 242 minimizing, 138, 158 performance, 142 temporal coupling, 150 see also Decoupled code Coverage analysis, 245 Cox, Brad J., 189n Crash, 120 Critical thinking, 16 cron, 231 CSS, see Cascading Style Sheets CVS, see Concurrent Version System Cygwin, 80, 270 D Data blackboard system, 169 caching, 31 dictionary, 144 dynamic data structures, 135 global, 40 language, 60 normalizing, 30 readable vs. understandable, 75 test, 100, 243 views, 160 visualizing, 93 see also Metadata Data Display Debugger (DDD), 93, 268 Database active code generator, 104 schema, 105f, 141, 144 schema maintenance, 100 DBC, see Design by contract DDD, see Data Display Debugger Deadline, 6, 246 Deadlock, 131 Debugging, 90 assertions, 123 binary search, 97 bug location, 96 bug reproduction, 93 checklist, 98 compiler warnings and, 92 corrupt variables, 95 “Heisenbug”, 124 rubber ducking, 95 and source code branching, 87 surprise bug, 97 and testing, 92, 195 time bomb, 192 tracing, 94 view, 164 visualizing data, 93 Decision making, 46 Decoupled code, 38, 40 architecture, 152 blackboard system, 166 Law of Demeter, 140 metadata, 145 minimizing coupling, 138 modular testing, 244 physical decoupling, 142 temporal coupling, 150 workflow, 150 see also Coupled code Defensive coding, 107 Delegation, 304 Delphi, 55 see also Object Pascal Demeter project, 274 Demeter, Law of, 140 Dependency, reducing, see Modular system; Orthogonality Deployment, 156 Deployment descriptor, 148 Design accessor functions, 31 concurrency, 154 context, 174 deployment, 156 design/methodology testing, 242 metadata, 145 orthogonality, 34, 37 physical, 142 refactoring, 186 using services, 154 Design by contract (DBC), 109, 155 and agents, 117 assertions, 113 class invariant, 110 as comments, 113 dynamic contracts, 117 iContract, 268 language support, 114 list insertion example, 110 pre- and postcondition, 110, 113, 114 predicates, 110 unit testing, 190 Design Patterns, 264 observer, 158 singleton, 41 strategy, 41 Destructor, 132 Detectives, 165 Development tree, 87 Development, iterative, 69 Divide-and-conquer algorithm, 180 DOC++ documentation generator, 251, 269 DocBook, 254 Documentation automatic updating, 251 and code, 29, 248 comments, 29, 113, 249, 251 executable, 251 formats, 253 HTML, 101 hypertext, 210 internal/external, 248 invariant, 117 mark-up languages, 254 orthogonality, 42 outline, 18 requirements, 204 technical writers, 252 word processors, 252, 254 writing specifications, 218 see also Comment; Web documentation Dodo, 148 Domain, problem, 58, 66 Don’t repeat yourself, see DRY principle Downloading source code, see Example code Dr.


pages: 72 words: 21,361

Race Against the Machine: How the Digital Revolution Is Accelerating Innovation, Driving Productivity, and Irreversibly Transforming Employment and the Economy by Erik Brynjolfsson

Amazon: amazon.comamazon.co.ukamazon.deamazon.fr

Amazon Mechanical Turk, Any sufficiently advanced technology is indistinguishable from magic, autonomous vehicles, business process, call centre, combinatorial explosion, corporate governance, crowdsourcing, David Ricardo: comparative advantage, easy for humans, difficult for computers, Erik Brynjolfsson, factory automation, first square of the chessboard, first square of the chessboard / second half of the chessboard, Frank Levy and Richard Murnane: The New Division of Labor, hiring and firing, income inequality, job automation, John Maynard Keynes: technological unemployment, Joseph Schumpeter, Khan Academy, Kickstarter, knowledge worker, labour mobility, Loebner Prize, low skilled workers, minimum wage unemployment, patent troll, pattern recognition, Ray Kurzweil, rising living standards, Robert Gordon, self-driving car, shareholder value, Skype, too big to fail, Turing test, Tyler Cowen: Great Stagnation, Watson beat the top human players on Jeopardy!, winner-take-all economy

Here’s a simple proof: suppose the people in a small company write down their work tasks— one task per card. If there were only 52 tasks in the company, as many as in a standard deck of cards, then there would be 52! different ways to arrange these tasks.8 This is far more than the number of grains of rice on the second 32 squares of a chessboard or even a second or third full chessboard. Combinatorial explosion is one of the few mathematical functions that outgrows an exponential trend. And that means that combinatorial innovation is the best way for human ingenuity to stay in the race with Moore’s Law. Most of the combinations may be no better than what we already have, but some surely will be, and a few will be “home runs” that are vast improvements. The trick is finding the ones that make a positive difference.


pages: 405 words: 117,219

In Our Own Image: Savior or Destroyer? The History and Future of Artificial Intelligence by George Zarkadakis

Amazon: amazon.comamazon.co.ukamazon.deamazon.fr

3D printing, Ada Lovelace, agricultural Revolution, Airbnb, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, anthropic principle, Asperger Syndrome, autonomous vehicles, barriers to entry, battle of ideas, Berlin Wall, bioinformatics, British Empire, business process, carbon-based life, cellular automata, Claude Shannon: information theory, combinatorial explosion, complexity theory, continuous integration, Conway's Game of Life, cosmological principle, dark matter, dematerialisation, double helix, Douglas Hofstadter, Edward Snowden, epigenetics, Flash crash, Google Glasses, Gödel, Escher, Bach, income inequality, index card, industrial robot, Internet of things, invention of agriculture, invention of the steam engine, invisible hand, Isaac Newton, Jacquard loom, Jacquard loom, Jacques de Vaucanson, James Watt: steam engine, job automation, John von Neumann, Joseph-Marie Jacquard, millennium bug, natural language processing, Norbert Wiener, On the Economy of Machinery and Manufactures, packet switching, pattern recognition, Paul Erdős, post-industrial society, prediction markets, Ray Kurzweil, Rodney Brooks, Second Machine Age, self-driving car, Silicon Valley, speech recognition, stem cell, Stephen Hawking, Steven Pinker, strong AI, technological singularity, The Coming Technological Singularity, the scientific method, theory of mind, Turing complete, Turing machine, Turing test, Tyler Cowen: Great Stagnation, Vernor Vinge, Von Neumann architecture, Watson beat the top human players on Jeopardy!, Y2K

This meant that the machine ought to be able to solve any problem using first principles and experience derived from learning. Early models of general-solving were built, but could not scale up. Systems could solve one general problem but not any general problem.6 Algorithms that searched data in order to make general inferences failed quickly because of something called ‘combinatorial explosion’: there were simply too many interrelated parameters and variables to calculate after a number of steps. An approach called ‘heuristics’ tried to solve the combinatorial explosion problem by ‘pruning’ branches off the tree of the search executed by any given algorithm; but even this was shown to be of limited value. In the end, AI researchers came to realise that problems such as the recognition of faces or objects required ‘common sense’ reasoning, which was fiendishly difficult to code.


pages: 196 words: 58,122

AngularJS by Brad Green, Shyam Seshadri

Amazon: amazon.comamazon.co.ukamazon.deamazon.fr

combinatorial explosion, continuous integration, Firefox, Google Chrome, MVC pattern, node package manager, single page application, web application, WebSocket

End-to-End/Integration Tests As applications grow (and they tend to, really fast, before you even realize it), testing whether they work as intended manually just doesn’t cut it anymore. After all, every time you add a new feature, you have to not only verify that the new feature works, but also that your old features still work, and that there are no bugs or regressions. If you start adding multiple browsers, you can easily see how this can become a combinatorial explosion! AngularJS tries to ease that by providing a Scenario Runner that simulates user interactions with your application. The Scenario Runner allows you to describe your application in a Jasmine-like syntax. Just as with the unit tests before, we will have a series of describes (for the feature), and individual its (to describe each individual functionality of the feature). As always, you can have some common actions, to be performed before and after each spec (as we call a test).


pages: 222 words: 53,317

Overcomplicated: Technology at the Limits of Comprehension by Samuel Arbesman

Amazon: amazon.comamazon.co.ukamazon.deamazon.fr

3D printing, algorithmic trading, Anton Chekhov, Apple II, Benoit Mandelbrot, citation needed, combinatorial explosion, Danny Hillis, David Brooks, discovery of the americas, en.wikipedia.org, Erik Brynjolfsson, Flash crash, friendly AI, game design, Google X / Alphabet X, Googley, HyperCard, Inbox Zero, Isaac Newton, iterative process, Kevin Kelly, Machine translation of "The spirit is willing, but the flesh is weak." to Russian and back, mandelbrot fractal, Minecraft, Netflix Prize, Nicholas Carr, Parkinson's law, Ray Kurzweil, recommendation engine, Richard Feynman, Richard Feynman, Richard Feynman: Challenger O-ring, Second Machine Age, self-driving car, software studies, statistical model, Steve Jobs, Steve Wozniak, Steven Pinker, Stewart Brand, superintelligent machines, Therac-25, Tyler Cowen: Great Stagnation, urban planning, Watson beat the top human players on Jeopardy!, Whole Earth Catalog, Y2K

Modularity embodies the principle of abstraction, allowing a certain amount of managed complexity through compartmentalization. Unfortunately, understanding individual modules—or building them to begin with—doesn’t always yield the kinds of expected behaviors we might hope for. If each module has multiple inputs and multiple outputs, when they are connected the resulting behavior can still be difficult to comprehend or to predict. We often end up getting a combinatorial explosion of interactions: so many different potential interactions that the number of combinations balloons beyond our ability to handle them all. For example, if each module in a system has a total of six distinct inputs and outputs, and we have only ten modules, there are more ways of connecting all these modules together than there are stars in the universe. In some realms that can be heavily regulated, such as finance or corporate structures, our dreams of increasing modularity or finding the ideal level of interoperability might work.


pages: 237 words: 64,411

Humans Need Not Apply: A Guide to Wealth and Work in the Age of Artificial Intelligence by Jerry Kaplan

Amazon: amazon.comamazon.co.ukamazon.deamazon.fr

Affordable Care Act / Obamacare, Amazon Web Services, asset allocation, autonomous vehicles, bank run, bitcoin, Brian Krebs, buy low sell high, Capital in the Twenty-First Century by Thomas Piketty, combinatorial explosion, computer vision, corporate governance, crowdsourcing, en.wikipedia.org, Erik Brynjolfsson, estate planning, Flash crash, Gini coefficient, Goldman Sachs: Vampire Squid, haute couture, hiring and firing, income inequality, index card, industrial robot, invention of agriculture, Jaron Lanier, Jeff Bezos, job automation, John Maynard Keynes: Economic Possibilities for our Grandchildren, Loebner Prize, Mark Zuckerberg, mortgage debt, natural language processing, Own Your Own Home, pattern recognition, Satoshi Nakamoto, school choice, Schrödinger's Cat, Second Machine Age, self-driving car, sentiment analysis, Silicon Valley, Silicon Valley startup, Skype, software as a service, The Chicago School, Turing test, Watson beat the top human players on Jeopardy!, winner-take-all economy, women in the workforce, working poor, Works Progress Administration

Ultimately, this style of AI came to be called the symbolic systems approach. But the early AI researchers quickly ran into a problem: the computers didn’t seem to be powerful enough to do very many interesting tasks. Formalists who studied the arcane field of theory of computation understood that building faster computers could not address this problem. No matter how speedy the computer, it could never tame what was called the “combinatorial explosion.” Solving real-world problems through step-wise analysis had this nasty habit of running out of steam the same way pressure in a city’s water supply drops when vast new tracts of land are filled with housing developments. Imagine finding the quickest driving route from San Francisco to New York by measuring each and every way you could possibly go; your trip would never get started. And even today, that’s not how contemporary mapping applications give you driving instructions, which is why you may notice that they don’t always take the most efficient route.


pages: 390 words: 113,737

Someone comes to town, someone leaves town by Cory Doctorow

Amazon: amazon.comamazon.co.ukamazon.deamazon.fr

Burning Man, clean water, combinatorial explosion, dumpster diving

It was easy enough to understand why the arbiters of the system subdivided Motorized Land Vehicles (629.2) into several categories, but here in the 629.22s, where the books on automobiles were, you could see the planners' deficiencies. Automobiles divided into dozens of major subcategories (taxis and limousines, buses, light trucks, cans, lorries, tractor trailers, campers, motorcycles, racing cars, and so on), then ramified into a combinatorial explosion of sub-sub-sub categories. There were Dewey numbers on some of the automotive book spines that had twenty digits or more after the decimal, an entire Dewey Decimal system hidden between 629.2 and 629.3. To the librarian, this shelf-reading looked like your garden-variety screwing around, but what really made her nervous were Alan's excursions through the card catalogue, which required constant tending to replace the cards that errant patrons made unauthorized reorderings of.


pages: 339 words: 88,732

The Second Machine Age: Work, Progress, and Prosperity in a Time of Brilliant Technologies by Erik Brynjolfsson, Andrew McAfee

Amazon: amazon.comamazon.co.ukamazon.deamazon.fr

2013 Report for America's Infrastructure - American Society of Civil Engineers - 19 March 2013, 3D printing, access to a mobile phone, additive manufacturing, Airbnb, Albert Einstein, Amazon Mechanical Turk, Amazon Web Services, American Society of Civil Engineers: Report Card, Any sufficiently advanced technology is indistinguishable from magic, autonomous vehicles, barriers to entry, Baxter: Rethink Robotics, British Empire, business intelligence, business process, call centre, clean water, combinatorial explosion, computer age, computer vision, congestion charging, corporate governance, crowdsourcing, David Ricardo: comparative advantage, employer provided health coverage, en.wikipedia.org, Erik Brynjolfsson, factory automation, falling living standards, Filter Bubble, first square of the chessboard / second half of the chessboard, Frank Levy and Richard Murnane: The New Division of Labor, Freestyle chess, full employment, game design, global village, happiness index / gross national happiness, illegal immigration, immigration reform, income inequality, income per capita, indoor plumbing, industrial robot, informal economy, inventory management, James Watt: steam engine, Jeff Bezos, jimmy wales, job automation, John Maynard Keynes: Economic Possibilities for our Grandchildren, John Maynard Keynes: technological unemployment, Joseph Schumpeter, Kevin Kelly, Khan Academy, knowledge worker, Kodak vs Instagram, law of one price, low skilled workers, Lyft, Mahatma Gandhi, manufacturing employment, Mark Zuckerberg, Mars Rover, means of production, Narrative Science, Nate Silver, natural language processing, Network effects, new economy, New Urbanism, Nicholas Carr, Occupy movement, oil shale / tar sands, oil shock, pattern recognition, payday loans, price stability, Productivity paradox, profit maximization, Ralph Nader, Ray Kurzweil, recommendation engine, Report Card for America’s Infrastructure, Robert Gordon, Rodney Brooks, Ronald Reagan, Second Machine Age, self-driving car, sharing economy, Silicon Valley, Simon Kuznets, six sigma, Skype, software patent, sovereign wealth fund, speech recognition, statistical model, Steve Jobs, Steven Pinker, Stuxnet, supply-chain management, TaskRabbit, technological singularity, telepresence, The Bell Curve by Richard Herrnstein and Charles Murray, The Signal and the Noise by Nate Silver, The Wealth of Nations by Adam Smith, total factor productivity, transaction costs, Tyler Cowen: Great Stagnation, Vernor Vinge, Watson beat the top human players on Jeopardy!, winner-take-all economy, Y2K

In the early 1950s, machines were taught how to play checkers and could soon beat respectable amateurs.28 In January 1956, Herbert Simon returned to teaching his class and told his students, “Over Christmas, Al Newell and I invented a thinking machine.” Three years later, they created a computer program modestly called the “General Problem Solver,” which was designed to solve, in principle, any logic problem that could be described by a set of formal rules. It worked well on simple problems like Tic-Tac-Toe or the slightly harder Tower of Hanoi puzzle, although it didn’t scale up to most real-world problems because of the combinatorial explosion of possible options to consider. Cheered by their early successes and those of other artificial intelligence pioneers like Marvin Minsky, John McCarthy and Claude Shannon, and Simon and Newell were quite optimistic about how rapidly machines would master human skills, predicting in 1958 that a digital computer would be the world chess champion by 1968.29 In 1965, Simon went so far as to predict, “machines will be capable, within twenty years, of doing any work a man can do.”30 Simon won the Nobel Prize in Economics in 1978, but he was wrong about chess, not to mention all the other tasks that humans can do.


pages: 311 words: 94,732

The Rapture of the Nerds by Cory Doctorow, Charles Stross

Amazon: amazon.comamazon.co.ukamazon.deamazon.fr

3D printing, Ayatollah Khomeini, butterfly effect, cognitive dissonance, combinatorial explosion, complexity theory, Credit Default Swap, dematerialisation, Drosophila, epigenetics, Extropian, gravity well, greed is good, haute couture, hive mind, margin call, phenotype, Plutocrats, plutocrats, rent-seeking, Richard Feynman, Richard Feynman, telepresence, Turing machine, Turing test, union organizing

* * * When the limit is reached, it jars Huw’s self-sense like a long fall to a hard floor, every virtual bone and joint buckling and bending, spine compressing, jaws clacking together. It has been going so well, the end in sight, the time running fast but Huw and father-thing and ambassador running faster, and now— “I’m stuck,” Huw says. “Not a problem. We could play this game forever—the number of variables gives rise to such a huge combinatorial explosion that there isn’t enough mass in this universe to explore all the possible states. The objective of the exercise was to procure a representative sample of moves, played by a proficient emissary, and we’ve now delivered that.” “Hey, wait a minute! ...” Huw’s stomach does a backflip, followed by a triple somersault, and is preparing to unicycle across a tightrope across the Niagara Falls while carrying a drunken hippo on his back: “You mean that was it?”


pages: 303 words: 67,891

Advances in Artificial General Intelligence: Concepts, Architectures and Algorithms: Proceedings of the Agi Workshop 2006 by Ben Goertzel, Pei Wang

Amazon: amazon.comamazon.co.ukamazon.deamazon.fr

AI winter, artificial general intelligence, bioinformatics, brain emulation, combinatorial explosion, complexity theory, computer vision, conceptual framework, correlation coefficient, epigenetics, friendly AI, information retrieval, Isaac Newton, John Conway, Loebner Prize, Menlo Park, natural language processing, Occam's razor, p-value, pattern recognition, performance metric, Ray Kurzweil, Rodney Brooks, semantic web, statistical model, strong AI, theory of mind, traveling salesman, Turing machine, Turing test, Von Neumann architecture, Y2K

But we could move toward AGI a lot faster if there were a nicer programming language with anywhere near the same scalability as C++. Moving on: This is not quite a bottleneck, but I would say that if the Novamente system is going to fail to achieve AGI, which I think is quite unlikely, then it would be because of a failure in the aspect of the design wherein the different parts of the system all interact with each other dynamically, to stop each other from coming to horrible combinatorial explosions. A difficult thing is that AI is all about emergence and synergy, so that in order to really test your system, you have test all the parts, put them together in combination, and look at the emergence effects. And that’s actually hard. The most basic bottleneck is that you are building an emergent system that has to be understood and tested as a whole, rather than a system that can be implemented and tested piece by piece.


pages: 528 words: 146,459

Computer: A History of the Information Machine by Martin Campbell-Kelly, William Aspray, Nathan L. Ensmenger, Jeffrey R. Yost

Amazon: amazon.comamazon.co.ukamazon.deamazon.fr

Ada Lovelace, air freight, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Apple's 1984 Super Bowl advert, barriers to entry, Bill Gates: Altair 8800, borderless world, Buckminster Fuller, Build a better mousetrap, Byte Shop, card file, cashless society, cloud computing, combinatorial explosion, computer age, deskilling, don't be evil, Douglas Engelbart, Dynabook, fault tolerance, Fellow of the Royal Society, financial independence, Frederick Winslow Taylor, game design, garden city movement, Grace Hopper, informal economy, interchangeable parts, invention of the wheel, Jacquard loom, Jacquard loom, Jeff Bezos, jimmy wales, John von Neumann, linked data, Mark Zuckerberg, Marshall McLuhan, Menlo Park, natural language processing, Network effects, New Journalism, Norbert Wiener, Occupy movement, optical character recognition, packet switching, PageRank, pattern recognition, pirate software, popular electronics, prediction markets, pre–internet, QWERTY keyboard, RAND corporation, Robert X Cringely, Silicon Valley, Silicon Valley startup, Steve Jobs, Steven Levy, Stewart Brand, Ted Nelson, the market place, Turing machine, Vannevar Bush, Von Neumann architecture, Whole Earth Catalog, William Shockley: the traitorous eight, women in the workforce, young professional

The resulting rationalization of production processes and standardization of components had reduced manufacturing costs to such an extent that IBM had no effective competition in punched-card machines at all. The biggest problem, however, was not in hardware but in software. Because the number of software packages IBM offered to its customers was constantly increasing, the proliferation of computer models created a nasty gearing effect: given m different computer models, each requiring n different software packages, a total of m × n programs had to be developed and supported. This was a combinatorial explosion that threatened to overwhelm IBM at some point in the not-too-distant future. Just as great a problem was that of the software written by IBM’s customers. Because computers were so narrowly targeted at a specific market niche, it was not possible for a company to expand its computer system in size by more than a factor of about two without changing to a different computer model. If this was done, then all the user’s applications had to be reprogrammed.


pages: 463 words: 118,936

Darwin Among the Machines by George Dyson

Amazon: amazon.comamazon.co.ukamazon.deamazon.fr

Ada Lovelace, Alan Turing: On Computable Numbers, with an Application to the Entscheidungsproblem, Albert Einstein, anti-communist, British Empire, carbon-based life, cellular automata, Claude Shannon: information theory, combinatorial explosion, computer age, Danny Hillis, fault tolerance, Fellow of the Royal Society, finite state, IFF: identification friend or foe, invention of the telescope, invisible hand, Isaac Newton, Jacquard loom, Jacquard loom, James Watt: steam engine, John Nash: game theory, John von Neumann, Menlo Park, Nash equilibrium, Norbert Wiener, On the Economy of Machinery and Manufactures, packet switching, pattern recognition, phenotype, RAND corporation, Richard Feynman, Richard Feynman, spectrum auction, strong AI, the scientific method, The Wealth of Nations by Adam Smith, Turing machine, Von Neumann architecture

The success of such a network may be evaluated by examining the number of congressmen surviving an attack and comparing such number to the number of congressmen able to communicate with one another and vote via the communications network. Such an example is, of course, farfetched but not completely without utility.”51 The more alternative connection paths there are between the nodes of a communications net, the more resistant it is to damage from within or without. But there is a combinatorial explosion working the other way: the more you increase the connectivity, the more intelligence and memory is required to route messages efficiently through the net. In a conventional circuit-switched communications network, such as the telephone system, a central switching authority establishes an unbroken connection for every communication, mediating possible conflicts with other connections being made at the same time.


pages: 746 words: 221,583

The Children of the Sky by Vernor Vinge

Amazon: amazon.comamazon.co.ukamazon.deamazon.fr

combinatorial explosion, epigenetics, indoor plumbing, megacity, random walk, risk tolerance, technological singularity, the scientific method, Vernor Vinge

Similarly, Amdi had probably said that “someone” had betrayed “something”—but the software had generated the particular nouns from a long list of suspects. It was amazing that Jefri had even made it onto that list, much less coming out at the top. So what logic had put him there? She drilled down through the program’s reasoning, into depths she had never visited. As suspected, the “why I chose ‘this’ over ‘that’” led to a combinatorial explosion. She could spend centuries studying this—and get nowhere. Ravna leaned back in her chair, turning her head this way and that, trying to get the stress out her neck. What am I missing? Of course, the program could simply be broken. Oobii’s emergency automation was specially designed to run in the Slow Zone, but the surveillance program was a bit of purely Beyonder software, not on the ship’s Usables manifest.


pages: 933 words: 205,691

Hadoop: The Definitive Guide by Tom White

Amazon: amazon.comamazon.co.ukamazon.deamazon.fr

Amazon Web Services, bioinformatics, business intelligence, combinatorial explosion, database schema, Debian, domain-specific language, en.wikipedia.org, fault tolerance, full text search, Grace Hopper, information retrieval, Internet Archive, linked data, loose coupling, openstreetmap, recommendation engine, RFID, SETI@home, social graph, web application

It also specifies many of the other features of Avro that implementations should support. One area that the specification does not rule on, however, is APIs: implementations have complete latitude in the API they expose for working with Avro data, since each one is necessarily language-specific. The fact that there is only one binary format is significant, since it means the barrier for implementing a new language binding is lower, and avoids the problem of a combinatorial explosion of languages and formats, which would harm interoperability. Avro has rich schema resolution capabilities. Within certain carefully defined constraints, the schema used to read data need not be identical to the schema that was used to write the data. This is the mechanism by which Avro supports schema evolution. For example, a new, optional field may be added to a record by declaring it in the schema used to read the old data.


pages: 556 words: 46,885

The World's First Railway System: Enterprise, Competition, and Regulation on the Railway Network in Victorian Britain by Mark Casson

Amazon: amazon.comamazon.co.ukamazon.deamazon.fr

banking crisis, barriers to entry, Beeching cuts, British Empire, combinatorial explosion, Corn Laws, corporate social responsibility, David Ricardo: comparative advantage, intermodal, iterative process, joint-stock company, joint-stock limited liability company, knowledge economy, linear programming, Network effects, New Urbanism, performance metric, railway mania, rent-seeking, strikebreaker, the market place, transaction costs

The method by which his counterfactual canal system was derived is not fully explained in the Appendix, and his estimate of its performance is based on guesswork (p. 38). Network optimization cannot be eVected by linear programming, as Fogel mistakenly suggests. Making a connection between two locations involves a binary decision: the two locations are either connected or they are not. Network optimization is therefore an integer programming problem, and problems of this kind encounter combinatorial explosion: the number of possible network structures increases at an accelerating rate as the number of locations to be served rises. An additional complexity arises from the fact that the optimal location for a railway junction may be in the middle of the countryside rather than at a town. Constraining all junctions to be at towns may reduce the performance of a network quite considerably. As indicated above, the actual network made extensive use of rural junctions, at places such as Crewe, Swindon, and Eastleigh, and lesser-known centres such as Evercreech, Broom, and Melton Constable.


pages: 798 words: 240,182

The Transhumanist Reader by Max More, Natasha Vita-More

Amazon: amazon.comamazon.co.ukamazon.deamazon.fr

23andMe, Any sufficiently advanced technology is indistinguishable from magic, artificial general intelligence, augmented reality, Bill Joy: nanobots, bioinformatics, brain emulation, Buckminster Fuller, cellular automata, clean water, cloud computing, cognitive bias, cognitive dissonance, combinatorial explosion, conceptual framework, Conway's Game of Life, cosmological principle, data acquisition, discovery of DNA, Drosophila, en.wikipedia.org, experimental subject, Extropian, fault tolerance, Flynn Effect, Francis Fukuyama: the end of history, Frank Gehry, friendly AI, game design, germ theory of disease, hypertext link, impulse control, index fund, John von Neumann, joint-stock company, Kevin Kelly, Law of Accelerating Returns, life extension, Louis Pasteur, Menlo Park, meta analysis, meta-analysis, moral hazard, Network effects, Norbert Wiener, P = NP, pattern recognition, phenotype, positional goods, prediction markets, presumed consent, Ray Kurzweil, reversible computing, RFID, Richard Feynman, Ronald Reagan, silicon-based life, Singularitarianism, stem cell, stochastic process, superintelligent machines, supply-chain management, supply-chain management software, technological singularity, Ted Nelson, telepresence, telepresence robot, telerobotics, the built environment, The Coming Technological Singularity, the scientific method, The Wisdom of Crowds, transaction costs, Turing machine, Turing test, Upton Sinclair, Vernor Vinge, Von Neumann architecture, Whole Earth Review, women in the workforce

Finally, there are limiting factors to fast growth, such as economic returns (if very few can afford a new technology it will be very expensive and not as profitable as a mass market technology), constraints on development speed (even advanced manufacturing processes need time for reconfiguration, development, and testing), human adaptability, and especially the need for knowledge. As the amount of knowledge grows, it becomes harder and harder to keep up and to get an overview, necessitating specialization. Even if information technologies can help somewhat, the basic problem remains, with the combinatorial explosion of possible combinations of different fields. This means that a development project might need specialists in many areas, which in turns means that there is a smaller size of group able to do the development. In turn, this means that it is very hard for a small group to get far ahead of everybody else in all areas, simply because it will not have the necessary know-how in all necessary areas.


pages: 647 words: 43,757

Types and Programming Languages by Benjamin C. Pierce

Amazon: amazon.comamazon.co.ukamazon.deamazon.fr

Albert Einstein, combinatorial explosion, experimental subject, finite state, Henri Poincaré, recommendation engine, sorting algorithm, Turing complete, Turing machine, type inference, Y Combinator

Our goal is to develop algorithms for checking membership in the least and greatest fixed points of a generating function F. The basic steps in these algorithms will involve “running F backwards”: to check membership for an element x, we need to ask how x could have been generated by F. The advantage of an invertible F is that there is at most one way to generate a given x. For a non-invertible F, elements can be generated in multiple ways, leading to a combinatorial explosion in the number of paths that the algorithm must explore. From now on, we restrict our attention to invertible generating functions. 21.5.3 Definition: An element x is F-supported if support F (x)↓; otherwise, x is Funsupported. An F-supported element is called F-ground if support F (x) = ∅. Note that an unsupported element x does not appear in F(X) for any X, while a ground x is in F(X) for every X.


pages: 834 words: 180,700

The Architecture of Open Source Applications by Amy Brown, Greg Wilson

Amazon: amazon.comamazon.co.ukamazon.deamazon.fr

8-hour work day, anti-pattern, bioinformatics, c2.com, cloud computing, collaborative editing, combinatorial explosion, computer vision, continuous integration, create, read, update, delete, Debian, domain-specific language, en.wikipedia.org, fault tolerance, finite state, Firefox, friendly fire, linked data, load shedding, locality of reference, loose coupling, Mars Rover, MVC pattern, premature optimization, recommendation engine, revision control, side project, Skype, slashdot, social web, speech recognition, the scientific method, The Wisdom of Crowds, web application, WebSocket

For example, there is a JavascriptExecutor interface that provides the ability to execute arbitrary chunks of Javascript in the context of the current page. A successful cast of a WebDriver instance to that interface indicates that you can expect the methods on it to work. Figure 16.1: Accountant and Stockist Depend on Shop Figure 16.2: Shop Implements HasBalance and Stockable 16.4.2. Dealing with the Combinatorial Explosion One of the first things that is apparent from a moment's thought about the wide range of browsers and languages that WebDriver supports is that unless care is taken it would quickly face an escalating cost of maintenance. With X browsers and Y languages, it would be very easy to fall into the trap of maintaining X×Y implementations. Reducing the number of languages that WebDriver supports would be one way to reduce this cost, but we don't want to go down this route for two reasons.


pages: 846 words: 232,630

Darwin's Dangerous Idea: Evolution and the Meanings of Life by Daniel C. Dennett

Amazon: amazon.comamazon.co.ukamazon.deamazon.fr

Albert Einstein, Alfred Russel Wallace, anthropic principle, buy low sell high, cellular automata, combinatorial explosion, complexity theory, computer age, conceptual framework, Conway's Game of Life, Danny Hillis, double helix, Douglas Hofstadter, Drosophila, finite state, Gödel, Escher, Bach, In Cold Blood by Truman Capote, invention of writing, Isaac Newton, Johann Wolfgang von Goethe, John von Neumann, Murray Gell-Mann, New Journalism, non-fiction novel, Peter Singer: altruism, phenotype, price mechanism, prisoner's dilemma, QWERTY keyboard, random walk, Richard Feynman, Richard Feynman, Rodney Brooks, Schrödinger's Cat, Stephen Hawking, Steven Pinker, strong AI, the scientific method, theory of mind, Thomas Malthus, Turing machine, Turing test

I do not at all intend this to be a shocking indictment, just a reminder of something quite obvious: no remotely compelling system of ethics has ever been made computationally tractable, even indirectly, for real-world moral problems. So, even though there has been no dearth of utilitarian (and Kantian, and contractarian, etc.) arguments in favor of particular policies, institutions, practices, and acts, these have all been heavily hedged with ceteris paribus clauses and plausibility claims about their idealizing assumptions. These hedges are designed to overcome the combinatorial explosion of calculation that threatens if one actually attempts — as theory says one must — to consider all things. And as arguments — not derivations — they have all been controversial (which is not to say that none of them could be sound in the last analysis). To get a better sense of the difficulties that contribute to actual moral reasoning, let us give ourselves a smallish moral problem and see what we do with it.


pages: 923 words: 516,602

The C++ Programming Language by Bjarne Stroustrup

Amazon: amazon.comamazon.co.ukamazon.deamazon.fr

combinatorial explosion, conceptual framework, database schema, distributed generation, fault tolerance, general-purpose programming language, index card, iterative process, job-hopping, locality of reference, Menlo Park, Parkinson's law, premature optimization, sorting algorithm

Consequently, we could simply declare only one version of the equality operator for ccoom mpplleexx: bbooooll ooppeerraattoorr==(ccoom mpplleexx,ccoom mpplleexx); vvooiidd ff(ccoom mpplleexx { xx==yy; xx==33; 33==yy; } xx, ccoom mpplleexx yy) // means operator==(x,y) // means operator==(x,complex(3)) // means operator==(complex(3),y) There can be reasons for preferring to define separate functions. For example, in some cases the conversion can impose overheads, and in other cases, a simpler algorithm can be used for specific argument types. Where such issues are not significant, relying on conversions and providing only the most general variant of a function – plus possibly a few critical variants – contains the combinatorial explosion of variants that can arise from mixed-mode arithmetic. Where several variants of a function or an operator exist, the compiler must pick ‘‘the right’’ variant based on the argument types and the available (standard and user-defined) conversions. Unless a best match exists, an expression is ambiguous and is an error (see §7.4). An object constructed by explicit or implicit use of a constructor is automatic and will be destroyed at the first opportunity (see §10.4.10).