Zeno's paradox

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pages: 315 words: 89,861

The Simulation Hypothesis by Rizwan Virk

3D printing, Albert Einstein, Apple II, artificial general intelligence, augmented reality, Benoit Mandelbrot, bioinformatics, butterfly effect, discovery of DNA, Dmitri Mendeleev, Elon Musk, en.wikipedia.org, Ernest Rutherford, game design, Google Glasses, Isaac Newton, John von Neumann, Kickstarter, mandelbrot fractal, Marc Andreessen, Minecraft, natural language processing, Pierre-Simon Laplace, Ralph Waldo Emerson, Ray Kurzweil, Richard Feynman, Schrödinger's Cat, Search for Extraterrestrial Intelligence, Silicon Valley, Stephen Hawking, Steve Jobs, Steve Wozniak, technological singularity, Turing test, Vernor Vinge, Zeno's paradox

., you can always find an infinite number of numbers in between any two numbers), how is it possible to touch an object such as a wall? You would always have to cover half the distance and never actually get there. Zeno (or Xeno, whichever spelling you prefer) of Elea was a Greek philosopher who described many different paradoxes. One paradox involved Achilles and a tortoise. If the tortoise was ahead of Achilles, how could he possibly ever catch it if he always had to make up half the distance? Figure 25: Zeno's paradox with Achilles and the tortoise. When I first heard about this paradox, my initial reaction was that space must be quantized — there must be some minimum distance that we traverse, otherwise, per the paradox, we would never be able to get two objects in the physical world to meet. We’d always be stuck trying to make up half the distance. Later, I discovered that I wasn’t alone in this reaction, and it got me thinking about the analogy of pixels in video games and whether pixels existed in the physical world around us.

pages: 476 words: 120,892

Life on the Edge: The Coming of Age of Quantum Biology by Johnjoe McFadden, Jim Al-Khalili

agricultural Revolution, Albert Einstein, Alfred Russel Wallace, bioinformatics, complexity theory, dematerialisation, double helix, Douglas Hofstadter, Drosophila, Ernest Rutherford, Gödel, Escher, Bach, invention of the printing press, Isaac Newton, James Watt: steam engine, Louis Pasteur, New Journalism, phenotype, Richard Feynman, Schrödinger's Cat, theory of mind, traveling salesman, uranium enrichment, Zeno's paradox

Plenio, “Highly efficient energy excitation transfer in light-harvesting complexes: the fundamental role of noise-assisted transport,” Journal of Chemical Physics, vol. 131 (2009), 105106–21. 2 M. Mohseni, P. Rebentrost, S. Lloyd and A. Aspuru-Guzik, “Environment-assisted quantum walks in photosynthetic energy transfer,” Journal of Chemical Physics, vol. 129: 17 (2008), 174106. 3 B. Misra and G. Sudarshan, “The Zeno paradox in quantum theory,” Journal of Mathematical Physics, vol. 18 (1977), p. 746: http://dx.doi.org/10.1063/1.523304. 4 S. Lloyd, M. Mohseni, A. Shabani and H. Rabitz, “The quantum Goldilocks effect: on the convergence of timescales in quantum transport,” arXiv preprint, arXiv:1111.4982, 2011. 5 A. W. Chin, S. F. Huelga and M. B. Plenio, “Coherence and decoherence in biological systems: principles of noise-assisted transport and the origin of long-lived coherences,” Philosophical Transactions of the Royal Society A, vol. 370 (2012), pp. 3658–71; A.

pages: 443 words: 131,268

Martians by Kim Stanley Robinson

A Pattern Language, Colonization of Mars, double helix, epigenetics, Live Aid, scientific worldview, Zeno's paradox

Breakfast a succession of Cassatts as painted by Bonnard, or Hogarth. “Hey I'm going to finish my book today.” “Good.” “David, hurry up and get dressed, it's almost time for school.” David looks up from a book. “What?” “Get dressed it's almost time. Tim, do you want cereal?” “No.” “Okay.” He puts Tim back on a chair in front of cereal. “This okay?” “No.” Shoveling it in. School time approaches and David begins his daily reenactment of Zeno's paradox, a false conundrum first proposed by Zeno, concerning Achilles and how the closer it came time to go to school the slower Achilles moved and the less he heard from the surrounding world, until he entered an entirely different space-time continuum interacting very weakly with this one. Wondering how Neutrino Boy can ever have become so absentminded, his father reads the coffee cups while grinding the beans for his little morning pitcher of Greek coffee.

pages: 863 words: 159,091

A Manual for Writers of Research Papers, Theses, and Dissertations, Eighth Edition: Chicago Style for Students and Researchers by Kate L. Turabian

Bretton Woods, conceptual framework, correlation does not imply causation, illegal immigration, Menlo Park, meta analysis, meta-analysis, Steven Pinker, Telecommunications Act of 1996, yellow journalism, Zeno's paradox

Glasgow: HarperCollins, 2002. 1. James, Robert Clarke, and Glenn James. Mathematics Dictionary. 5th ed. New York: Van Nostrand Reinhold, 1992. 1. Schwartzman, Steven. The Words of Mathematics: An Etymological Dictionary of Mathematical Terms Used in English. Washington, DC: Mathematical Association of America, 1994. 2. Darling, David J. The Universal Book of Mathematics: From Abracadabra to Zeno's Paradoxes. Hoboken, NJ: Wiley, 2004. 2. Ito, Kiyosi, ed. Encyclopedic Dictionary of Mathematics. 2nd ed. 2 vols. Cambridge: MIT Press, 1993. 2. Weisstein, Eric W. CRC Concise Encyclopedia of Mathematics. 2nd ed. Boca Raton, FL: Chapman & Hall/CRC, 2003. 3. Pemberton, John E. How to Find Out in Mathematics: A Guide to Sources of Information. 2nd rev. ed. Oxford: Pergamon, 1969. 4. East European Scientific Abstracts.

pages: 607 words: 185,228

Antarctica by Kim Stanley Robinson

Exxon Valdez, Fermat's Last Theorem, gravity well, hiring and firing, late capitalism, lateral thinking, Occam's razor, Turing test, Zeno's paradox

As it was, however, the objective dangers underfoot were great enough to put her in a high state of apprehension for her clients' sake. A guide was only as happy as her least happy client, and right now she was surrounded by a bunch of frost-flocked insect-eyed mute people, Ta Shu and Jack enjoying themselves, the rest really eager for this part to be over. And yet as it got higher it got steeper, and they had to go slower. It was as if they were trapped in Zeno's paradox, and halving the distance to the top in increments of time that remained the same. Burning and freezing; waiting for Val to screw in ice screws, or screw them out; looking or not looking at the blue gaping fissures in the ice underfoot, each one a potential deathtrap. Thus it was nearly three in the afternoon when they finally came under the Hansen Shoulder, where a narrow ramp of ice led them right under its exposed rock, up toward the polar plateau.