mandelbrot fractal

The Misbehavior of Markets: A Fractal View of Financial Turbulence
by Benoit Mandelbrot and Richard L. Hudson
Published 7 Mar 2006

. • Reprint : Chapter N16 of Mandelbrot 1999a. Mandelbrot, Benoit B. 1975. Les objets fractals : forme, hasard et dimension. Paris : Flammarion. Mandelbrot, Benoit B. 1982. The Fractal Geometry of Nature. New York: W.H. Freeman & Co. Mandelbrot, Benoit B. 1985. Self-affine fractals and fractal dimension. Physica Scripta 32: 257-260. • Reprint: Dynamics of Fractal Surfaces. Edited by Fereydoon Family & Tamas Vicsek. Singapore: World Scientific, 1991, 11-20. • Reprint Chapter H21 of Mandelbrot 2002. Mandelbrot, Benoit B. 1986. Self-affine fractal sets, I: The basic fractal dimensions, II: Length and area measurements, III: Hausdorff dimension anomalies and their implications.

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Notes Bibliography Index Copyright Page ALSO BY BENOIT B. MANDELBROT Les objets fractals: forme, hasard et dimension (1975, 1984, 1989, 1995) Fractals: Form, Chance and Dimension (1977) The Fractal Geometry of Nature (1982) Fractals and Scaling in Finance: Discontinuity, Concentration, Risk (1997) Fractales, hasard et finance (1959–1997) (1997) Multifracals and 1/f Noise: Wild Self-Affinity in Physics (1999) Gaussian Self-Affinity and Fractals: Globality, the Earth, 1/f, and R/S (2002) Fractals, Graphics, and Mathematics Education (With M. L. Frame) (2002) Fractals and Chaos: The Mandelbrot Set and Beyond (2004) TO THE SCIENTIFIC READER: AN ABSTRACT Three states of matter—solid, liquid, and gas—have long been known.

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New York: Springer-Verlag. Mandelbrot, Benoit B. 1997b. Fractales, hasard et finance. Paris: Flammarion. Mandelbrot, Benoit B. 1997c. Three fractal models in finance: Discontinuity, concentration, risk. Economic Notes (Banca Monte dei Paschi di Siena SpA) 26 (2): 197-212. Mandelbrot, Benoit B. 1997d. Les fractales et la bourse. Pour la Science 242: 16-17. Mandelbrot, Benoit B. 1999a. Multifractals & 1/f Noise: Wild Self-Affinity in Physics. New York: Springer-Verlag. Mandelbrot, Benoit B. 1999b. Renormalization and fixed points in finance, since 1962. Physica A 263: 477-487. Mandelbrot, Benoit B. 1999c.

Chaos: Making a New Science
by James Gleick
Published 18 Oct 2011

Dewdney, “Computer Recreations,” Scientific American (August 1985), pp. 16–32. Peitgen and Richter in The Beauty of Fractals offer a detailed review of the mathematics, as well as some of the most spectacular pictures available. THE MOST COMPLEX OBJECT Hubbard, for example. “YOU OBTAIN AN INCREDIBLE VARIETY “Julia Sets and the Mandelbrot Set,” p. 161. IN 1979 MANDELBROT DISCOVERED Mandelbrot, Laff, Hubbard. A first-person account by Mandelbrot is “Fractals and the Rebirth of Iteration Theory,” in The Beauty of Fractals, pp. 151–60. AS HE TRIED CALCULATING Mandelbrot; The Beauty of Fractals. MANDELBROT STARTED WORRYING Mandelbrot. NO TWO PIECES ARE “TOGETHER” Hubbard.

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Review articles on applications of fractals have grown too common to list, but two useful examples are Leonard M. Sander, “Fractal Growth Processes,” Nature 322 (1986), pp. 789–93; Richard Voss, “Random Fractal Forgeries: From Mountains to Music,” in Science and Uncertainty, ed. Sara Nash (London: IBM United Kingdom, 1985). CHARTED ON THE OLDER MAN’S BLACKBOARD Houthakker, Mandelbrot. WASSILY LEONTIEF Quoted in Fractal Geometry, p. 423. INTRODUCED FOR A LECTURE Woods Hole Oceanographic Institute, August 1985. BORN IN WARSAW Mandelbrot. BOURBAKI Mandelbrot, Richter. Little has been written about Bourbaki even now; one playful introduction is Paul R.

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PIONEER-BY–NECESSITY “Second Stage,” p. 5. THIS HIGHLY ABSTRACT Mandelbrot; Fractal Geometry, p. 74; J. M. Berger and Benoit Mandelbrot, “A New Model for the Clustering of Errors on Telephone Circuits,” IBM Journal of Research and Development 7 (1963), pp. 224–36. THE JOSEPH EFFECT Fractal Geometry, p. 248. CLOUDS ARE NOT SPHERES Ibid., p. 1, for example. WONDERING ABOUT COASTLINES Ibid., p. 27. THE PROCESS OF ABSTRACTION Ibid., p. 17. “THE NOTION” Ibid., p. 18. ONE WINTRY AFTERNOON Mandelbrot. THE EIFFEL TOWER Fractal Geometry, p. 131, and “On Fractal Geometry,” p. 1663. 102 ORIGINATED BY MATHEMATICIANS F.

The Fractalist
by Benoit Mandelbrot
Published 30 Oct 2012

Copyright © 2012 by The Estate of Benoit Mandelbrot Afterword copyright © by Michael Frame All rights reserved. Published in the United States by Pantheon Books, a division of Random House, Inc., New York, and in Canada by Random House of Canada Limited, Toronto. Pantheon Books and colophon are registered trademarks of Random House, Inc. Library of Congress Cataloging-in-Publication Data Mandelbrot, Benoit B. The fractalist : memoir of a scientific maverick / Benoit Mandelbrot. p. cm. eISBN: 978-0-307-37860-6 1. Mandelbrot, Benoit B. 2. Mathematicians—France—Biography. 3. Fractals. I. Title. QA29.M34A3 2012 510.92—dc22 [B] 2012017896 www.pantheonbooks.com Cover image Benoit Mandelbrot.

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Imitation: the first step to understanding Surface dimension 2.15 (Illustration Credit bm1.7) Surface dimension 2.5 (Illustration Credit bm1.8) Surface dimension 2.8 (Illustration Credit bm1.9) Fractal forgeries showing the relationship between fractal dimensions and roughness “Cool Afternoon” (Illustration Credit bm1.10) “Lethe” (Illustration Credit bm1.11) Artistic renderings of fractal landscapes Fractal painting of flowers, Augusto Giacometti (Illustration Credit bm1.12) Cast of a human lung (Illustration Credit bm1.13) The Great Wave, Hokusai (Illustration Credit bm1.14) Rough deposit of gold (Illustration Credit bm1.15) Turbulence on Jupiter (Illustration Credit bm1.16) Science, Art, and Nature Zooming into the Mandelbrot set (Illustration Credit bm1.17) “Pharoah’s Breastplate,” limit set of circle inversions (Illustration Credit bm1.18) Variation of the Mandelbrot set (Illustration Credit bm1.19) Deep into the Mandelbrot set (Illustration Credit bm1.20) “Cave painting,” modified Mandelbrot set fragment (Illustration Credit bm1.21) Quarternion Julia sets (Illustration Credit bm1.22) Illustration Credits Reprinted from The Fractal Geometry of Nature: 29.1 Courtesy Michael Frame: aft.1, aft.3 Augusto Giacometti, 1912: bm1.12 Sigmund Handelman: itr.1, 21.6, 23.2, bm1.6 Eriko Hironaka: 25.7 Katsushika Hokusai, ca. 1829–33: bm1.14 Mark Laff: itr.1 Mark R.

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Based at IBM, Moving from Place to Place and Field to Field, 1964–79 25. Annus Mirabilis at Harvard: The Mandelbrot Set and Other Forays into Pure Mathematics, 1979–80 26. A Word and a Book: “Fractal” and The Fractal Geometry of Nature 27. At Yale: Rising to the University’s Highest Rank, Sterling Professorship, 1987–2004 28. Has My Work Founded the First-Ever Broad Theory of Roughness? 29. Beauty and Roughness: Full Circle Afterword by Michael Frame Inserts Illustration Credits About the Author Acknowledgments by Aliette Mandelbrot MY HUSBAND DIED shortly before The Fractalist went to the publisher. Benoit spent years writing this memoir.

The Physics of Wall Street: A Brief History of Predicting the Unpredictable
by James Owen Weatherall
Published 2 Jan 2013

“But then ‘a storm’ would come through . . .”: Mandelbrot describes this aspect of his wartime experience in Mandelbrot (1998). “This is a general property of fractals . . .”: There are many connections between fractals and fat-tailed distributions. That certain features of fractals exhibit fat tails is one such connection; another is that (some) fat-tailed distributions themselves exhibit self-similarity, in the form of power-law scaling in their tails. Mandelbrot was a central figure in identifying and exploring these relationships. See Mandelbrot (1997). “Known as the Butcher of Lyon . . .”: For more on Barbie, see Bower (1984) and McKale (2012)

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.”: Background material on World War II and the Holocaust in particular is from Dwork and van Pelt (2002), Fischel (1998), Rossel (1992), and Yahil (1987). “How long is Britain’s coastline?”: This question is taken up in Mandelbrot (1967). “. . . a coastline doesn’t have a length . . .”: The more precise version of this claim is that a coastline should be understood to have non-integer Hausdorff dimension, which means that the correct “measure” of a coastline does not behave like a length. “It was one of his first attempts . . .”: Mandelbrot coined the term fractal in Mandelbrot (1975), which was translated into English as Mandelbrot (1977). But Mandelbrot (1967) is one of the first places where he describes geometrical objects with non-integer Hausdorff dimension exhibiting self-similarity

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Whereas the vast majority of mathematicians focus on shapes that are “smooth,” the kinds of shapes you can make out of Play-Doh, Mandelbrot’s most famous discovery, which he named “fractal geometry,” arose out of the study of jagged and fractured shapes, like the surface of a mountain or a shard of broken glass. This work on fractal shapes made Mandelbrot realize that there are varieties of randomness in nature that are far more extreme than the kind of randomness you get by flipping a coin over and over again — with consequences for virtually all mathematical science, including finance. Mandelbrot was a revolutionary. Even today, decades after his most important papers, his ideas remain radical, with mainstream scientists in many fields still debating them.

Mapmatics: How We Navigate the World Through Numbers
by Paulina Rowinska
Published 5 Jun 2024

Robertson, ‘Benoit Mandelbrot’, MacTutor (Maths History), School of Mathematics and Statistics, University of St Andrews, July 1999, https://mathshistory.st-andrews.ac.uk/Biographies/Mandelbrot/. the École Polytechnique: Benoît Mandelbrot, ‘École Normale and Thought in Mathematics’, Web of Stories video, 24 January 2008, https://www.webofstories.com/play/benoit.mandelbrot/16. (and getting married in the meantime): Nigel Lesmoir-Gordon, ‘Benoît Mandelbrot Obituary’, The Guardian, 17 October 2010. very complicated and very simple at the same time: Benoit Mandelbrot, ‘Fractals and the Art of Roughness’, TED Talks video, February 2010, https://www.ted.com/talks/benoit_mandelbrot_fractals_and_the_art_of_roughness?language=en. no possible significance: Benoît Mandelbrot, ‘Errors of Transmission in Telephone Channels (50/144)’, Web of Stories video, n.d., https://www.youtube.com/watch?

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This might be the only case where the problematic ‘publish or perish’ approach, so common in academia, has resulted in something positive. Maybe Mandelbrot wasn’t the first to notice the need for fractal dimensions, but he was the first to understand its importance. Being an excellent science communicator, he managed not only to popularize fractals among fellow mathematicians but also to bring them to the wider world. Today, we find fractals everywhere, from medicine to meteorology, to art, to pop culture. Fractals, fractals everywhere I was too young to attend the premiere of Toy Story but old enough for Toy Story 2. I still remember the cinema trip, one of the first in my life.

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To visualize a mountain range, the poor computer would have to store information about all these shapes, which would have been impossible at a time when the most powerful machines had less memory than today’s smartphones. Here’s where Carpenter comes in. He stumbled upon the book The Fractal Geometry of Nature, in which Mandelbrot had described how fractals work and included pictures of fractally generated landscapes. This gave Carpenter a brilliant idea: instead of storing the information about all parts of a mountain range, the machine would need only the fractal pattern to visualize the whole landscape. By definition, a fractal is a repetition of itself, on different scales. The maths was there, but a computer algorithm – that is, a set of precise instructions to generate the landscape – was missing.

Programming HTML5 Applications
by Zachary Kessin
Published 9 May 2011

The model for worker communication is that the main task creates the worker, after which they pass messages back and forth as shown in Figure 8-2. Figure 8-2. Worker communication Web Worker Fractal Example Example 8-1 is the “Hello World” of Web Workers. A more complex example is called for. Figure 8-3 shows a visual representation of a Mandelbrot set computed in a Web Worker. Here the worker and the main thread split up the work to draw the fractal. The worker does the actual work of computing the Mandelbrot set, while the frontend script takes that raw data and displays it in the canvas. Figure 8-3. Mandelbrot example The frontend script (see Example 8-2) sets up the canvas element and scales it to fit in the page.

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To allow the inner function to have access to that object, which it will need to draw a pixel, it is necessary to alias it to a lexically scoped variable. By convention that variable is often called that. Example 8-2. Mandelbrot frontend var drawMandelSet = function drawMandelSet(){ var mandelPanel = $('body'); var width = mandelPanel.innerWidth(); var height = mandelPanel.innerHeight(); var range = [{ x: -2, y: -1.4 }, { x: 5, y: 1.4 }]; $('canvas#fractal').height(height + 100); $('canvas#fractal').width(width - 50); var left = 0; var top = 0; var canvas = $("canvas#fractal")[0]; var ctx = canvas.getContext("2d"); var params = { range: range, startx: 0.0, starty: 0.0, width: width, height: height }; var y_array = []; var worker = { params: params, draw: function draw(data){ data.forEach(function d(point){ if (this.axis.x[point.drawLoc.x] === undefined) { this.axis.x[point.drawLoc.x] = point.point.x; } if (this.axis.y[height - point.drawLoc.y] === undefined) { this.axis.y[height - point.drawLoc.y] = point.point.y; } ctx.fillStyle = pickColor(point.escapeValue); ctx.fillRect(point.drawLoc.x + 0.5, height - point.drawLoc.y + 0.5, 1, 1); }, this); }, axis: { x: [], y: [], find: function(x, y){ return new Complex(this.x[x], this.y[y]); }, reset: function(){ this.x = [], this.y = []; } }, myWorker: false, run: function startWorker(params){ this.myWorker = new Worker("js/worker.js"); var that = this; this.myWorker.postMessage(JSON.stringify(params)); this.myWorker.onmessage = function(event){ var data = JSON.parse(event.data); if (data.type === 'draw') { that.draw(JSON.parse(data.data)); } else if (event.data.type === 'log') { console.info(event); } }; } }; worker.run(params); return worker; }; $(document).ready(drawMandelSet); Function.prototype.createDelegate = function createDelegate(scope){ var fn = this; return function(){ fn.call(scope, arguments); }; }; function pickColor(escapeValue){ if (escapeValue === Complex.prototype.max_iteration) { return "black"; } var tone = 255 - escapeValue * 10; var colorCss = "rgb({r},{g},{b})".populate({ r: tone, g: tone, b: tone }); return colorCss; } String.prototype.populate = function populate(params) { var str = this.replace(/\{\w+\}/g, function stringFormatInner(word) { return params[word.substr(1, word.length - 2)]; }); return str; }; The actual worker (see Example 8-3) is very simple.

Scale: The Universal Laws of Growth, Innovation, Sustainability, and the Pace of Life in Organisms, Cities, Economies, and Companies
by Geoffrey West
Published 15 May 2017

I shall discuss this further in chapters 8 and 9 when I turn to cities and companies. In 1982 Mandelbrot published a highly influential and very readable semipopular book titled The Fractal Geometry of Nature.25 This inspired tremendous interest in fractals by showing their ubiquity across both science and the natural world. It stimulated a mini industry searching for fractals, finding them everywhere, measuring their dimensions, and showing how their magical properties result in wonderfully exotic geometric figures. Mandelbrot had shown how relatively simple algorithmic rules based on fractal mathematics can produce surprisingly complex patterns.

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Just as we need to know if it is in miles, centimeters, or angstroms, we also need to know the resolution that was used. Mandelbrot introduced the concept of a fractal dimension, defined by adding 1 to the exponent of the power law (the value of the slopes). Thus the fractal dimension of the South African coast is 1.02, Norway 1.52, and so on. The point of adding the 1 was to connect the idea of fractals to the conventional concept of ordinary dimensions discussed in chapter 2. Recall that a smooth line has dimension 1, a smooth surface dimension 2, and a volume dimension 3. Thus the South African coast is very close to being a smooth line because its fractal dimension is 1.02, which is very close to 1, whereas Norway is far from it because its fractal dimension of 1.52 is so much greater than 1.

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Richardson, in General Systems Yearbook 6 (1961): 139. 22. Benoit Mandelbrot, “How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension,” Science 156 (1967): 636–38. 23. See, for example, Rosario N. Mantegna and H. Eugene Stanley, An Introduction to Econophysics: Correlations and Complexity in Finance (Cambridge, UK: Cambridge University Press, 1999). 24. See, for example, J. B. Bassingthwaighte, L. S. Liebovitch, and B. J. West, Fractal Physiology (New York: Oxford University Press, 1994). 25. Mandelbrot, The Fractal Geometry of Nature. 26. See, for instance, Manfred Schroeder, Fractals, Chaos, Power Laws: Minutes from an Infinite Paradise (New York: W.

When Einstein Walked With Gödel: Excursions to the Edge of Thought
by Jim Holt
Published 14 May 2018

THE AVATARS OF HIGHER MATHEMATICS G. H. Hardy, A Mathematician’s Apology (Cambridge, 1940). Michael Harris, Mathematics Without Apologies: Portrait of a Problematic Vocation (Princeton, 2015). 8. BENOIT MANDELBROT AND THE DISCOVERY OF FRACTALS Benoit Mandelbrot, The Fractalist: Memoir of a Scientific Maverick (Pantheon, 2012). Benoit Mandelbrot and Richard L. Hudson, The (Mis)behavior of Markets: A Fractal View of Financial Turbulence (Basic, 2006). 9. GEOMETRICAL CREATURES Edwin A. Abbott, The Annotated Flatland: A Romance of Many Dimensions, with an introduction and notes by Ian Stewart (Perseus, 2002).

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In the late 1970s, he became famous for popularizing the idea of self-similarity and for coining the word “fractal” (from the Latin fractus, meaning “broken”) to designate self-similar forms. In 1980, he discovered the “Mandelbrot set,” whose shape—it looks a bit like a warty snowman or beetle—came to represent the newly fashionable science of chaos. What is perhaps less well known about Mandelbrot is the subversive work he did in economics. The financial models he created, based on his fractal ideas, implied that stock and currency markets were far riskier than the reigning consensus in business schools and investment banks supposed and that wild gyrations—like the 777-point plunge in the Dow on September 29, 2008—were inevitable.

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Once the confusion was cleared up, Mandelbrot was chosen by the camp’s commander to serve as a scientific liaison to academia. “I liaised with abandon,” he says, “and everyone was delighted.” At the same time, he began to indulge a passion for classical music, attending recitals in Paris by George Enescu and a “young and skinny (!) flutist named Jean-Pierre Rampal.” This passion, once Mandelbrot became famous, led to friendships with conductors like Solti and Abbado and with the composers Ligeti and Charles Wuorinen, whose music came to be influenced by Mandelbrot’s notion of fractal self-similarity. Released from the air force and still short of a doctorate, Mandelbrot, now twenty-six, became a “not-so-young” grad student at the University of Paris, “then at a low point in its long and often glorious history.”

The Golden Ratio: The Story of Phi, the World's Most Astonishing Number
by Mario Livio
Published 23 Sep 2003

You may have noticed that Elliott's wave interpretation has as one of its ingredients the concept that each part of the curve is a reduced-scale version of the whole, a concept central to fractal geometry. Indeed, in 1997, Benoit Mandelbrot published a book entitled Fractals and Scaling in Finance: Discontinuity, Concentration, Risk, which introduced well-defined fractal models into market economics. Mandelbrot built on the known fact that fluctuations in the stock market look the same when charts are enlarged or reduced to fit the same price and time scales. If you look at such a chart from a distance that does not allow you to read the scales, you will not be able to tell if it represents daily, weekly, or hourly variations. The main innovation in Mandelbrot's theory, as compared to standard portfolio theory, is in its ability to reproduce tumultuous trading as well as placid markets.

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Freeman and Company, 1989. Gleick, J. Chaos. New York: Penguin Books, 1987. Lesmoir-Gordon, N., Rood, W, andEdney, R. Introducing Fractal Geometry. Cambridge: Icon Books, 2000. Mandelbrot, B.B. Fractal Geometry of Nature. New York: W H. Freeman and Company, 1988. Mandelbrot, B.B. “A Multifractal Walk Down Wall Street,” Scientific American (February 1999): 70–73. Matthews, R. “The Power of One,” New Scientist, July 10, 1999, 27–30. Peitgen, H.-O., Jürgens, H., andSaupe, D. Chaos and Fractals. New York: Springer-Verlag, 1992. Peterson, I. “Fibonacci at Random,” Science News, 155 (1999): 376–377 Peterson, I.

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In other words, if we look at any pattern within the Golden Sequence, we discover that the same pattern is found in the sequence on another scale. Objects with this property, like the Russian Matrioshka dolls that fit one into the other, are known as, fractals. The name “fractal” (from the Latin fractus, meaning “broken, fragmented”) was coined by the famous Polish-French-American mathematician Benoit B. Mandelbrot, and it is a central concept in the geometry of nature and in the theory of highly irregular systems known as chaos. Fractal geometry represents a brilliant attempt to describe the shapes and objects of the real world. When we look around us, very few forms can be described in terms of the simple figures of Euclidean geometry, such as straight lines, circles, cubes, and spheres.

Complexity: A Guided Tour
by Melanie Mitchell
Published 31 Mar 2009

“the firing patterns of neurons”: Haslinger, R., Klinkner, K. L., and Shalizi, C. R., The computational structure of spike trains. Unpublished manuscript, 2007. “the universe is fractal-like”: Mandelbrot, B. B., The Fractal Geometry of Nature. New York: W. H. Freeman, 1977. “in general a fractal is a geometric shape”: Strogatz, S., Nonlinear Dynamics and Chaos. Reading, MA: Addison-Wesley, 1994. “fractal dimension”: A great introduction to fractals and the concept of fractal dimension is Mandelbrot’s book The Fractal Geometry of Nature. New York: W. H. Freeman, 1977. “I’ll do a calculation out of your sight”: For the Koch curve, 3 dimension = 4.

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The similarity of the shape of the coastline at different scales is called “self-similarity.” The term fractal was coined by the French mathematician Benoit Mandelbrot, who was one of the first people to point out that the world is full of fractals—that is, many real-world objects have a rugged self-similar structure. Coastlines, mountain ranges, snowflakes, and trees are often-cited examples. Mandelbrot even proposed that the universe is fractal-like in terms of the distribution of galaxies, clusters of galaxies, clusters of clusters, et cetera. Figure 7.3 illustrates some examples of self-similarity in nature. Although the term fractal is sometimes used to mean different things by different people, in general a fractal is a geometric shape that has “fine structure at every scale.”

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Although the term fractal is sometimes used to mean different things by different people, in general a fractal is a geometric shape that has “fine structure at every scale.” Many fractals of interest have the self-similarity property seen in the coastline example given above. The logistic-map bifurcation diagram from chapter 2 (figure 2.6) also has some degree of self-similarity; in fact the chaotic region of this (R greater than 3.57 or so) and many other systems are sometimes called fractal attractors. Mandelbrot and other mathematicians have designed many different mathematical models of fractals in nature. One famous model is the so-called Koch curve (Koch, pronounced “Coke,” is the name of the Swedish mathematician who proposed this fractal).

More Than You Know: Finding Financial Wisdom in Unconventional Places (Updated and Expanded)
by Michael J. Mauboussin
Published 1 Jan 2006

Lots of small events and a few very large events characterize a fractal system. Further, the average winnings per game is unstable with the St. Petersburg game, so no average accurately describes the game’s long-term outcome. Are stock market returns fractal? Benoit Mandelbrot shows that by lengthening or shortening the horizontal axis of a price series—effectively speeding up or slowing down time—price series are indeed fractal. Not only are rare large changes interspersed with lots of smaller ones, the price changes look similar at various scales (e.g., daily, weekly, and monthly returns). Mandelbrot calls financial time series multifractal, adding the prefix “multi” to capture the time adjustment.

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Petersburg Paradox,” http://plato.stanford.edu/entries/paradox-stpetersburg. 3 Much of this section relies on Larry S. Liebovitch and Daniela Scheurle, “Two Lessons from Fractals and Chaos,” Complexity, Vol. 5, 4, 2000, 34-43. See http://www.ccs.fau.edu/˜liebovitch/complexity-20.html. 4 See chapter 29. 5 Benoit B. Mandelbrot, “A Multifractal Walk down Wall Street,” Scientific American, February 1999, 70-73. Also see, Benoit B. Mandelbrot, Fractals and Scaling in Finance: Discontinuity, Concentration, Risk (New York: Springer Verlag, 1997). 6 If you assume that you flipped a coin nonstop sixteen hours a day (estimating eight hours of sleep), and if each coin flip takes three seconds, it would take 14.3 years to complete 100 million coin tosses. 7 Didier Sornette, Why Stock Markets Crash: Critical Events in Complex Financial Systems (Princeton, N.J.: Princeton University Press, 2003); also see Sornette’s Web site, http://www.ess.ucla.edu/faculty/sornette/. 8 See another classic article: Peter L.

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Proceedings of the Workshop on Simulation of Social Agents: Architectures and Institutions, Argonne National Laboratory and University of Chicago, October 2000, Argonne 2001, 33-51. Mandelbrot, Benoit, and Richard L. Hudson. The (Mis)Behavior of Markets: A Fractal View of Risk, Ruin, and Reward. New York: Basic Books, 2004. Rothschild, Michael. Bionomics. New York: Henry Holt and Company, 1990. Schroeder, Manfred. Fractals, Chaos, and Power Laws: Minutes from an Infinite Paradise. New York: W. H. Freeman, 1991. Seeley, Thomas A., P. Kirk Visscher, and Kevin M. Passino. “Group Decision Making in Honey Bee Swarms.”

Chaos Kings: How Wall Street Traders Make Billions in the New Age of Crisis
by Scott Patterson
Published 5 Jun 2023

Later that day, Taleb met a man he’d soon come to idolize: Benoit Mandelbrot. The maverick French mathematician, inventor of fractal geometry, and pioneer of chaos theory, was giving a lecture at NYU’s Courant Institute about two seemingly disconnected topics—fractals and finance. Taleb was intrigued. He had no idea how finance could have anything to do with fractals. Fractals, Mandelbrot had shown over decades of research, pop up everywhere. In science, engineering, in clouds, flowers, and snowflakes. A key idea behind fractal geometry is self-similarity (or self-affinity). By way of explanation Mandelbrot had asked, years before in 1967: How long is the coast of Britain?

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It measured phenomena that had smooth step-by-step transitions, with most samples falling within the safe confines of the middle of the bell curve. The bell curve didn’t capture the extreme volatility that can occur in a fractal world—the world of power laws, sudden jumps, wild leaps. Much of Mandelbrot’s work was based on power laws driving all sorts of phenomena, from cotton prices to income distributions to population densities in cities. Rather than adding up in linear fashion (1 + 2 + 3 etc.), which fit well within the bell curve, things governed by power laws can make dramatic, unexpected moves that live in the tails of the curve. Mandelbrot—his big-eared, balding basketball-size head glistening over an Apple laptop perched on the podium—told the NYU audience filled with quants, traders, and finance professors that if the bell curve truly captured the reality of the stock market, big crashes in the market like Black Monday would never happen.

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Mandelbrot was describing the exact experience he’d had as a trader in which only a few big days had mattered. After the talk, he introduced himself and asked Mandelbrot why he bothered himself with the mundane world of finance—a world Taleb viewed as a great place to make fuck-you money before moving on to higher, ethereal worlds of literature, theory, and philosophy. “Data,” Mandelbrot said, smiling, “A gold mine of data.” Taleb’s career had centered on the study of uncertainty, volatility, and its impact on option prices. He’d written a whole book about it. But he’d never realized there was a connection between fat tails and fractal geometry and all the fascinating math behind it. Here was a whole new way to think about randomness and Black Swans, he realized.

NumPy Cookbook
by Ivan Idris
Published 30 Sep 2012

For more information see the Wikipedia article already mentioned in this recipe: for n in range(ITERATIONS): print n mask = numpy.abs(z) <= 4 z[mask] = z[mask] ** 2 + c[mask] fractal[(fractal == MAX_COLOR) & (-mask)] = (MAX_COLOR - 1) * n / ITERATIONS Plot the fractal.Plot the fractal with Matplotlib: matplotlib.pyplot.subplot(211) matplotlib.pyplot.imshow(fractal) matplotlib.pyplot.title('Mandelbrot') matplotlib.pyplot.axis('off') Combine the fractal and Lena.Use the choose function to pick value from the fractal or Lena array: matplotlib.pyplot.subplot(212) matplotlib.pyplot.imshow(numpy.choose(fractal < lena, [fractal, lena])) matplotlib.pyplot.axis('off') matplotlib.pyplot.title('Mandelbrot + Lena') The following is the resulting image: The following is the complete code for this recipe: import numpy import matplotlib.pyplot import sys import scipy if(len(sys.argv) !

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See also The Installing Matplotlib recipe in Chapter 1, Winding Along with IPython Combining images In this recipe, we will combine the famous Mandelbrot fractal (for more information on Madelbrot set visit http://en.wikipedia.org/wiki/Mandelbrot_set) and the image of Lena. These types of fractals are defined by a recursive formula, where you calculate the next complex number in a series by multiplying the current complex number you have, by itself and adding a constant to it. Getting ready Install SciPy, if necessary. The See Also section of this recipe, has a reference to the related recipe. How to do it... We will start by initializing the arrays, followed by generating and plotting the fractal, and finally, combining the fractal with the Lena image.

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We will start by initializing the arrays, followed by generating and plotting the fractal, and finally, combining the fractal with the Lena image. Initialize the arrays.We will initialize x, y, and z arrays corresponding to the pixels in the image area with the meshgrid, zeros, and linspace functions: x, y = numpy.meshgrid(numpy.linspace(x_min, x_max, SIZE), numpy.linspace(y_min, y_max, SIZE)) c = x + 1j * y z = c.copy() fractal = numpy.zeros(z.shape, dtype=numpy.uint8) + MAX_COLOR Generate the fractal.If z is a complex number, you have the following relation for a Mandelbrot fractal: In this equation, c is a constant complex number. This can be graphed in the complex plane with horizontal real values axis and vertical imaginary values axis.

Statistical Arbitrage: Algorithmic Trading Insights and Techniques
by Andrew Pole
Published 14 Sep 2007

The description of modeling the variation about the mean during periods of zero forecast activity is quite the same as the general description of the variation of the spread overall. Such self-similarity occurs throughout nature according to Benoit Mandelbrot, who invented a branch of mathematics called fractals for the study and analysis of such patterns. Mandelbrot, 2004, has argued that fractal analysis provides a better model for understanding the movements of prices of financial instruments than anything currently in the mathematical finance literature. It is unknown whether any successful trading strategies have been built using fractal analysis; Mandelbrot himself does not believe his tools are yet sufficiently developed for prediction of financial series to be feasible. 3.8 PRACTICAL MATTERS Forecasts of stock price movements are incredibly inaccurate.

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Johnson, N.L., S. Kotz, and N. Balakrishnan. Continuous Univariate Distributions, Volumes I and II. New York: John Wiley & Sons, 1994. Lehman Brothers. Algorithmic Trading. New York: Lehman Brothers, 2004. Mandelbrot, B.B. Fractals and Scaling in Finance: Discontinuity, Concentration, Risk. New York: Springer-Verlag, 1997. Mandelbrot B.B., and R.L. Hudson. The (Mis)Behavior of Markets: A Fractal View of Risk, Ruin, and Reward. New York: Basic Books, 2004. Orwell, George. 1984. New York: New American Library, 1950. Perold, A.F. (1988). ‘‘The Implementation Shortfall, Paper vs. Reality,’’ Journal of Portfolio Management, 14:3, 4–9.

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The maximum value this probability can assume is 12 when p = 12 (differentiate, equate to zero, solve). 4.2.5 Generalizations Financial time series are notorious for the tenacity with which they refuse to reveal underlying mathematical structure (though Mandelbrot, 2004, may demur from that statement). Features of such data, which often show up in statistical modeling, include: nonnormal distributions (returns are frequently characterized by leptokurtosis); nonconstant variance (market dynamics often produce bursts of high and low volatility, and modelers have tried many approaches from GARCH and its variants to Mandelbrot’s fractals, see Chapter 3); and serial dependence. The conditions of the theorem can be relaxed to accommodate all of these behaviors. 74 STATISTICAL ARBITRAGE The result extends to arbitrary continuous random variables directly: The constraint of support on the nonnegative real line is not required.

Antifragile: Things That Gain From Disorder
by Nassim Nicholas Taleb
Published 27 Nov 2012

Further, things that grow in a natural way, whether cities or individual houses, have a fractal quality to them. Like everything alive, all organisms, like lungs, or trees, grow in some form of self-guided but tame randomness. What is fractal? Recall Mandelbrot’s insight in Chapter 3: “fractal” entails both jaggedness and a form of self-similarity in things (Mandelbrot preferred “self-affinity”), such as trees spreading into branches that look like small trees, and smaller and smaller branches that look like a slightly modified, but recognizable, version of the whole. These fractals induce a certain wealth of detail based on a small number of rules of repetition of nested patterns.

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CEO Overconfidence and the Market’s Reaction.” Journal of Financial Economics 89(1): 20–43. Malmendier, U., and G. Tate, 2009, “Superstar CEOs.” Quarterly Journal of Economics 124(4): 1593–1638. Mandelbrot, Benoît B., 1983, The Fractal Geometry of Nature. W. H. Freeman. Mandelbrot, Benoît B., 1997, Fractals and Scaling in Finance: Discontinuity, Concentration, Risk. New York: Springer-Verlag. Mandelbrot, Benoît B., and N. N. Taleb, 2010, “Random Jump, Not Random Walk.” In Richard Herring, ed., The Known, the Unknown, and the Unknowable. Princeton, N.J.: Princeton University Press. Mansel, P., 2012, Levant.

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Just as with the unintrusive shoes that allow us to feel the terrain, modern technology allows some of us to reverse that trend, as expressed by Oswald Spengler, which makes civilization go from plants to stone, that is, from the fractal to the Euclidian. We are now moving back from the smooth stone to the rich fractal and natural. Benoît Mandelbrot wrote in front of a window overlooking trees: he craved fractal aesthetics so much that the alternative would have been inconceivable. Now modern technology allows us to merge with nature, and instead of a small window, an entire wall can be transparent and face lush and densely forested areas.

A Mathematician Plays the Stock Market
by John Allen Paulos
Published 1 Jan 2003

The branching of a tree appears the same to us as it does to birds, or even to worms or fungi in the idealized limiting case of infinite branching. As the mathematician Benoit Mandelbrot, the discoverer of fractals, has famously written, “Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.” These and many other shapes in nature are near fractals, having characteristic zigzags, push-pulls, bump-dents at almost every size scale, greater magnification yielding similar but ever more complicated convolutions. And the bottom line, or, in this case, the bottom fractal, for stocks? By starting with the basic up-down-up and down-up-down patterns of a stock’s possible movements, continually replacing each of these patterns’ three segments with smaller versions of one of the basic patterns chosen at random, and then altering the spikiness of the patterns to reflect changes in the stock’s volatility, Mandelbrot has constructed what he calls multifractal “forgeries.”

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Elliott believed as well that these patterns exist at many levels and that any given wave or cycle is part of a larger one and contains within it smaller waves and cycles. (To give Elliott his due, this idea of small waves within larger ones having the same structure does seem to presage mathematician Benoit Mandelbrot’s more sophisticated notion of a fractal, to which I’ll return later.) Using Fibonacci-inspired rules, the investor buys on rising waves and sells on falling ones. The problem arises when these investors try to identify where on a wave they find themselves. They must also decide whether the larger or smaller cycle of which the wave is inevitably a part may temporarily be overriding the signal to buy or sell.

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Yet another reason to suspect that parts of the market may be better modeled by nonlinear systems is that such systems’ “trajectories” often follow a fractal course. The trajectories of these systems, of which the stock price movements may be considered a proxy, turn out to be aperiodic and unpredictable and, when examined closely, evince even more intricacy. Still closer inspection of the system’s trajectories reveals yet smaller vortices and complications of the same general kind. In general, fractals are curves, surfaces, or higher dimensional objects that contain more, but similar, complexity the closer one looks. A shoreline, to cite a classic example, has a characteristic jagged shape at whatever scale we draw it; that is, whether we use satellite photos to sketch the whole coast, map it on a fine scale by walking along some small section of it, or examine a few inches of it through a magnifying glass.

The Simulation Hypothesis
by Rizwan Virk
Published 31 Mar 2019

It turns out you can do this infinitely because there are nooks and crannies all the way down (until, of course, you get to the point of atoms). Mandelbrot and others in this emerging science found that they could use computers to do a very large number of calculations. In fractal patterns, the input to the next iteration of an equation usually comes from the results of the previous run of the same equation. The Mandelbrot set, one of the best-known fractals, generated by rules that combined real and complex numbers repeatedly, wasn’t fully fleshed out until after the invention of the personal computer. According to the Fractal Foundation, this isn’t coincidental, since generating fractal patterns requires thousands or millions of iterations using the same algorithm again and again, which means that fractals are ideally suited for computer programs.

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They are created by repeating a simple process over and over in an ongoing feedback loop.”79 Fractals have been around since the 1980s. Benoit Mandelbrot, as a young mathematician and researcher, found patterns of self-similarity at different scales in many different kinds of problems, ranging from error codes in telephone lines, to the pattern of prices of commodities in the markets, to the structure of a coastline. The coastline example is perhaps the best way to understand fractals. The answer to the question “how long is a coastline?” depends very much on the scale you choose to measure it. You might measure it at the rate of miles from a satellite picture.

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According to the Fractal Foundation, this isn’t coincidental, since generating fractal patterns requires thousands or millions of iterations using the same algorithm again and again, which means that fractals are ideally suited for computer programs. Since the discovery of different types of fractal patterns, it’s been suggested that nature is a fractal-generating computer. Does the fact that fractal geometry exists in nature provide us with evidence that there is an element of computation in the natural world around us? The fact that computation is the only way to get natural shapes would seem to imply that something like a pixelated fractal pattern being computed is at work in the physical world around us. Even our current limited versions of fractals on computer screens, as pointed out earlier, aren’t full fractals because we are limited by pixels on a screen.

Why Stock Markets Crash: Critical Events in Complex Financial Systems
by Didier Sornette
Published 18 Nov 2002

In other words, the hierarchical diamond and tree networks have the property of reproducing themselves exactly on different magnifications. Such a property has been coined “fractal” by Mandelbrot [284], who recognized, based on the pioneering work of Richardson [343], that many natural and social phenomena are endowed, at least approximately, with the scale invariance symmetry. Many of us have met fractals through their beautiful, delicately complex pictures, which are usually computer generated. Modern Hollywood movies use landscapes, mountain ranges, cloud structures, and other artificial constructions that are computer generated according to recipes devised to obtain fractal geometries. It turns out that many of the natural structures of the world are approximately fractal [29, 126, 88, 31, 292, 394] and that our aesthetic sense resonates with fractal forms.

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Objects with fractional dimensions turn out to possess the property of scale invariance. To capture this novel concept, we already mentioned that the word “fractal” was coined by Mandelbrot [284], from the Latin root fractus to capture the rough, broken, and irregular characteristics of the objects presenting at least approximately the property of scale invariance. This roughness can be present at all scales, which distinguishes fractals from Euclidean shapes. Mandelbrot worked actively to demonstrate that this concept is not just a mathematical curiosity but has strong relevance to the real world. The remarkable fact is that this generalization, from integer dimensions to fractional dimensions, has a profound and intuitive interpretation: noninteger dimensions describe irregular sets consisting of parts similar to the whole.

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Forest fires: An example of self-organized critical behavior, Science 281, 1840–1842. 281. Malki, E. (1999). The Financial Crisis in Russia, ewp-mac/9901001. 282. Malkiel, B. G. (1999). A Random Walk Down Wall Street (Norton, New York). 283. Mandelbrot, B. B. (1967). How long is the coast of Britain? Statistical selfsimilarity and fractional dimension, Science 155, 636–638. 284. Mandelbrot, B. B. (1982). The Fractal Geometry of Nature (Freeman, San Francisco). 285. Mandelbrot, B. B. (1999). A multifractal walk down Wall Street, Scientific American 280, 70–73(February). 286. Mantegna, R. N., Buldyrev, S. V., Goldberger, A. L., Halvin, S., and Stanley, H. E. (1995).

The Myth of the Rational Market: A History of Risk, Reward, and Delusion on Wall Street
by Justin Fox
Published 29 May 2009

One starting point was the statistical framework assembled twenty-five years before by Benoit Mandelbrot. Mandelbrot hadn’t predicted black Monday. He hadn’t written anything about finance in years. But anyone who had studied his market writings from the 1960s was far less surprised by events on Wall Street than those who had restricted their reading to standard finance textbooks. Mandelbrot was by this time also becoming famous. His reputation-making Fractal Geometry of Nature came out in 1982. The year of the crash, journalist James Gleick’s bestselling book Chaos introduced him to a much wider readership. After 1987, Mandelbrot’s long-ignored ideas began to intrude upon the consciousness of Wall Street.

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It wasn’t just the ski jump line; the data was also “self-similar”—that is, charts of small snippets looked just like those of large swaths. Mandelbrot was later to find similar patterns in historical climate data along the Nile, the coast of Britain, and the ins and outs of tree bark. After he dubbed them “fractals” in 1982, he was hailed as a visionary, one of the progenitors of the new science of chaos and complexity that was transforming physics and other fields. By then, though, Mandelbrot had long abandoned finance. At the beginning he had been warmly welcomed into the small but growing fellowship of random walkers.

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I’m referring mainly to the account in Roger Lowenstein’s Buffett: The Making of an American Capitalist. 43. “A Conversation With Benjamin Graham,” Financial Analysts Journal (Sept./Oct. 1976): 20–23. CHAPTER 8: FISCHER BLACK CHOOSES TO FOCUS ON THE PROBABLE 1. Mandelbrot tells the story of encountering Zipf’s work in Benoit Mandelbrot and Richard L. Hudson, The (Mis)behavior of Markets: A Fractal View of Risk, Ruin, and Reward (New York: Basic Books, 2004), 150–59. The Zipf book mentioned is Human Behavior and the Principle of Least Effort: An Introduction to Human Ecology (Cambridge, Mass.: Addison-Wesley, 1949). 2. This field had been pioneered by Italian mathematical economist Vilfredo Pareto.

Think Complexity
by Allen B. Downey
Published 23 Feb 2012

How do these results bear on Bak’s claim that SOC explains the prevalence of critical phenomena in nature? Example 9-8. In The Fractal Geometry of Nature, Benoit Mandelbrot proposes what he calls a “heretical” explanation for the prevalence of long-tailed distributions in natural systems (page 344). It may not be, as Bak suggests, that many systems can generate this behavior in isolation. Instead there may be only a few, but there may be interactions between systems that cause the behavior to propagate. To support this argument, Mandelbrot points out the following: The distribution of observed data is often “the joint effect of a fixed underlying ‘true distribution’ and a highly variable ‘filter.’”

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, Explanatory Models exponent, Order of Growth exponential distribution, Continuous Distributions exponential growth, Order of Growth extend, Summing Lists F falsifiability, Falsifiability Fast Fourier Transform (FFT), Fast Fourier Transform FIFO queue, FIFO Implementation fireflies, Paradigm Shift? flock behavior, Boids for loop, Iterators forest, What’s a Graph? forest fire model, Fractal CAs, Percolation, Reductionism and Holism four-color theorem, The Axes of Scientific Models Fourier transform, Spectral Density fractal, Fractal CAs fractal cellular automaton, Fractal CAs fractal dimension, Fractals, Sand Piles fractal geometry, Sand Piles The Fractal Geometry of Nature, Reductionism and Holism fractals, Fractals free will, A New Kind of Thinking, Determinism frequency, Zipf’s Law, Spectral Density frequentist probability, A New Kind of Thinking Freud, Sigmund, Instrumentalism fringe science, Paradigm Shift?

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To estimate , I fit a line to this curve; its slope is 1.56. is a non-integer, which means that this set of points is a fractal. As t increases, the slope approaches , which is the fractal dimension of Sierpiński’s triangle. See http://en.wikipedia.org/wiki/Sierpinski_triangle. Example 8-1. Write a function that takes a CA object; plots versus , where ; and estimates . Can you find other CAs with non-integer fractal dimensions? Be careful, you might have to run the CA for a while before converges. Here are some functions from numpy you might find useful: cumsum, log, and polyfit. You can download my solution from http://thinkcomplex.com/fractal.py. Example 8-2. In 1990, Bak, Chen, and Tang proposed a cellular automaton that is an abstract model of a forest fire.

Currency Wars: The Making of the Next Gobal Crisis
by James Rickards
Published 10 Nov 2011

However, there is strong empirical evidence, first reported by Benoît Mandelbrot, that the magnitude and frequency of certain market prices plot out as a power-law degree distribution. Mandelbrot showed that a time series chart of these price moves exhibited what he called a “fractal dimension.” A fractal dimension is a dimension greater than one and less than two, expressed as a fraction such as 1½; the word “fractal” is just short for “fractional.” A line has one dimension (length) and a square has two dimensions (length and width). A fractal dimension of 1½ is something in between. A familiar example is the ubiquitous stock market chart of the kind shown in daily papers and financial websites.

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The extended analysis that follows, including elements of diversity, connectedness, interdependence and adaptability, draws on a series of lectures under the title “Understanding Complexity,” delivered in 2009 by Professor Scott E. Page of the University of Michigan. 207 However, there is strong empirical evidence, first reported by Benoît Mandelbrot . . . This discussion of fractal dimensions in market prices draws on Benoît Mandelbrot and Richard L. Hudson, The (Mis)Behavior of Markets: A Fractal View of Risk, Ruin, and Reward, New York: Basic Books, 2004. 218 Chaisson posits that the universe is best understood . . . The discussion of Chaisson’s theory of free energy rate densities is from Eric J. Chaisson, Cosmic Evolution: The Rise of Complexity in Nature, Cambridge: Harvard University Press, 2001.

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MacMillan, Margaret. Paris 1919: Six Months That Changed the World. New York: Random House, 2001. Makin, John H. The Global Debt Crisis: America’s Growing Involvement. New York: Basic Books, 1984. Mallaby, Sebastian. More Money Than God. New York: Penguin, 2010. Mandelbrot, Benoît, and Richard L. Hudson. The (Mis)Behavior of Markets: A Fractal View of Risk, Ruin, and Reward. New York: Basic Books, 2004. Mead, Walter Russell. God and Gold: Britain, America, and the Making of the Modern World. New York: Random House, 2007. Meltzer, Allan H. A History of the Federal Reserve, Volume 1: 1913–1951. Chicago: University of Chicago Press, 2003.

Overcomplicated: Technology at the Limits of Comprehension
by Samuel Arbesman
Published 18 Jul 2016

Corky Ramirez: Note that in the episode “The Van Buren Boys,” someone is referred to as “Ramirez” in a bar (though I believe his name is stressed differently than Kramer’s pronunciation of Corky Ramirez). Perhaps he is visible in the room, but it is unclear. Seinfeld superfans: please send me mail. delightfully evocative term: “greeblies”: : Or, alternatively, “greebles.” Kelly, What Technology Wants, 318. the mathematician Benoit Mandelbrot: Benoit B. Mandelbrot, The Fractal Geometry of Nature (New York: W. H. Freeman and Company, 1982), 1. Recall “Funes the Memorious”: Borges, “Funes, His Memory,” in Collected Fictions, 131–37. “The patterns of a river network”: Philip Ball, Branches, vol. 3 of Nature’s Patterns: A Tapestry in Three Parts (Oxford, UK: Oxford University Press, 2009), 181.

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You can’t have a futuristic starship that is all angles and smooth sides; you need to add ports and vents and sundry other impenetrable doodads and whatsits, pipes and bumps, indentations and grooves. Think of the ships in Battlestar Galactica or Star Wars. They are more visually intriguing thanks to their complications of unknown purpose. This process of greebling is closely related to a well-known quote from the mathematician Benoit Mandelbrot, who coined the term “fractal”: “Why is geometry often described as ‘cold’ and ‘dry’? One reason lies in its inability to describe the shape of a cloud, a mountain, a coastline, or a tree. Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.”

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The law professor David Post and the biologist Michael Eisen teamed up to examine this as well, and while they admit they can’t prove that a legal statement can always branch further, and that it’s “turtles all the way down,” they do note that “we have never met a legal question that could not be decomposed into subquestions.” Post and Eisen even show through simulations that certain types of branching structures that mimic legal systems actually can have a fractal structure. Testing this, they find features indicative of fractals when looking at actual legal citations of court case opinions. The fractal complexity of the law might be more than an evocative metaphor. As the scholars Mark Flood and Oliver Goodenough recognize, “Much of the value of good contracts and good lawyering derives from the seemingly tedious planning for all the ways that a relationship might run off the rails.”

Growth: From Microorganisms to Megacities
by Vaclav Smil
Published 23 Sep 2019

Richardson (1948) used power law to explain the variation of the frequency of fatal conflicts with their magnitude. And Benoit Mandelbrot’s pioneering studies of self-similarity and fractal structures further expanded the applications of power laws: after all, the “probability distribution of a self-similar random variable X must be of the form Pr(X>x) = x-D, which is commonly called hyperbolic or Pareto distribution” (Mandelbrot 1977, 320). Mandelbrot’s D, fractal dimension, has many properties of a “dimension” but it is fractional (Mandelbrot 1967). Mandelbrot (1977) had introduced a more general power law—nearly the most general, as Gell-Mann put it—by modifying the inverse sequence, by adding a constant to the rank, and by allowing squares, cubes, square roots or any other powers of fractions (Gell-Mann 1994).

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Protein quality and growth in malnourished children. Food and Nutrition Bulletin 37:S29–S36. Mandelbrot, B. 1967. How long is the coast of Britain? Statistical self-similarity and fractional dimension. Science 156:636–638. Mandelbrot, B. 1975. Stochastic models for the Earth’s relief, the shape and the fractal dimension of the coastlines, and the number-area rule for islands. Proceedings of the National Academy of Sciences of the USA 72:3825–3828. Mandelbrot, B. 1977. Fractals: Form, Chance and Dimension. San Francisco: Freeman. Mandelbrot, B. B. 1982. The Fractal Geometry of Nature. New York: Freeman. MAN Diesel. 2007. MAN Diesel Sets New World Standard. https://pdfs.semanticscholar.org/b85a/f0ad9b92e1ff3797672805dadce123e2a6cf.pdf.

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Jaromír Korčák called attention to the duality of statistical distribution, with the outcome of organic growth organized in normal fashion, while the distribution of the planet’s physical characteristics—area and depth of lakes, size of islands, area of watersheds, length of rivers—follows inverse power law with distributions highly skewed leftward (Korčák 1938 and 1941). Korčák’s law was later made better known, via Fréchet (1941), by Benoit Mandelbrot in his pioneering work on fractals (Mandelbrot 1967, 1975, 1977, 1982). But a recent reexamination of Korčák’s law concluded that his ranked properties cannot be described with a single power-law exponent and hence the law is not strictly valid even for sets consisting of strictly similar fractal objects presented in his original publications (Imre and Novotný 2016). The Gutenberg-Richter law—the second author’s name is well known due to his classification system of earthquake magnitudes (Richter 1935)—relates the total number of earthquakes, N, to their magnitude, M (Gutenberg and Richter 1942).

On the Future: Prospects for Humanity
by Martin J. Rees
Published 14 Oct 2018

Conway indulged in a lot of ‘trial and error’ before he came up with a simple ‘virtual world’ that allowed for interesting emergent variety. He used pencil and paper, before the days of personal computers, but the implications of the Game of Life only emerged when the greater speed of computers could be harnessed. Likewise, early PCs enabled Benoit Mandelbrot and others to plot out the marvellous patterns of fractals—showing how simple mathematical formulas can encode intricate apparent complexity. Most scientists resonate with the perplexity expressed in a classic essay by the physicist Eugene Wigner, titled ‘The Unreasonable Effectiveness of Mathematics in the Natural Sciences’.2 And also with Einstein’s dictum that ‘the most incomprehensible thing about the universe is that it is comprehensible’.

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There’s an important difference, however, between ‘Kolmogorov complexity’ and whether something actually looks complicated. For instance, Conway’s Game of Life leads to complicated-looking structures. But these can all be described by a short programme: take a particular starting position, and then iterate, over and over again, according to the simple rules of the game. The intricate fractal pattern of Mandelbrot’s set is likewise the result of a simple algorithm. But these are exceptions. Most things in our everyday environment are too complicated to be predicted, or even fully described in detail. But much of their essence can nonetheless be captured by a few key insights. Our perspective has been transformed by great unifying ideas.

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Consider an example from geometry, where points in the plane are designated by two numbers, the distance along the x-axis and along the y-axis. Anyone who has studied geometry at school would recognise the equation x2 + y2 = 1 as describing a circle. The famous Mandelbrot set is described by an algorithm that can be written down in a few lines. And its shape can be plotted by even a modestly powered computer—its ‘Kolmogorov complexity’ isn’t high. But no human who is just given the algorithm can grasp and visualise this immensely complicated ‘fractal’ pattern in the same sense that they can visualise a circle. We can expect further dramatic advances in the sciences during this century. Many questions that now perplex us will be answered, and new questions will be posed that we can’t even conceive today.

Gnuplot in Action: Understanding Data With Graphs
by Philipp Janert
Published 2 Jan 2010

In contrast, the long interval between 1,500 and 10,000 iteration steps is colored in a uniform white, because there are only few pixels in the image falling into this region (mostly the thin white boundaries that you can see around the solid black regions, which belong to the interior or the Mandelbrot set). There’s no reason to waste visual gradients on parameter ranges that occupy only a small and not very relevant area of the plot. Grayscale is of course only the first step. In color figure 5, I show the same data set, plotted with two different palettes, which are also listed in listing 9.3. One is huebased; the other is luminance-based. According to our guidelines, a luminance-based 6 This isn’t the place to give a detailed introduction to fractals and the Mandelbrot set. Plenty of information is readily available on the Internet—the Wikipedia entry for the Mandelbrot set is a good place to start. 172 CHAPTER 9 Color Figure 9.3 A black-and-white rendition of a section of the Mandelbrot set.

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See exploratory data analysis edge effects 282 enabling interlacing 207 multiplot mode 176 polar mode 184 encoding option 322 enhanced text mode 202 control characters 203 examples 204 options 339 enhancing quantitative perception 289 enum type indicator xxviii environment variables 194, 234 EPS file 211 epslatex terminals 212 error integral functions 317 errorbars 78 Euclidean distance 150 European Union 262 every directive 31 example data sets airplane 301 allometric scaling 254 armor 301 car data 246, 251, 275 Chebyshev polynomial 178 curb weight 246 diesel fuel 251 diffusion limited aggregation (DLA) 6 draft lottery 248 European Union 262 flow balance 287 fractal 6, 171 fuel consumption 275 glass data 265 ice cream 111 lottery 248 353 example data sets (continued) mammals 254 Mandelbrot set 171 marathon 4, 280 miles per gallon (mpg) 275 price 246 spectrum 104 sunspots 284 web traffic 252 examples axes 123 enhanced text mode 204 fit command 195 scatter plots 246, 248 executing commands in subshells 225 exit command 309 exp kernel 150 explanations 102 data files 102 plot command 102 explicit mode 158 exploratory data analysis (EDA) 11 exponential functions 316 export script 27 exporting 25, 201 expressions (math) 38 F false-color plot 161 features abbreviations 23 autoscale 94 multiplot 175 sensible defaults 23 smooth cumulative 260 field separators 52 fig terminal 220 file formats EPS 210 GIF 207 JPG 208 PDF 217 PNG 207 PostScript 210 SVG 208 file system (commands) 310 files data 51 data sets 30 examples of data 20 exporting graphs to 201 initialization 235 input data 296 loading 25 output 298 plotting data from 20 plotting unsorted data 32 reading palettes from 156 reading tic labels from 122 saving 25 filled plot styles 81 financebars style 80 fit command 191, 314 control variables 193 environmental variables 194 example 195 options 194 output variables 193 tips 194 fit option 322 flow balance 287 flt type indicator xxviii flushing output channels 205 font default 202 directive 206 PostScript 202, 210–211, 216 specifying 210 terminals 202 TrueType 202, 206–207, 211 font tables 232, 341 fontpath option 207, 322 forcing interactive sessions 229 format cb option 159 format option 331 formats data files 51 grid 146 matrix 148 formatting tic labels 118 fractal 6, 171 freefont project 207 frequency directive 33, 35, 257 fsteps style 72 fuel consumption 275 functions Bessel 317 built-in 38 column 42 column manipulation 319 complex arguments 318 creating palettes with 155 cumulative distribution 259 error integral 317 exponential 316 gamma 317 gprint() 122 hyperbolic 316 imag() 41 keyword 155 logarithmic 316 miscellaneous 318 plotting 43 rand() 38, 256 real() 41 scanf() 128 smooth frequency 256 smooth kdensity 258 strftime() 127 strings 56, 318 system() 225 time column handling 319 trigonometric 316 user-defined 39 valid() 43 xticlabels() 122 yticlabels() 122, 263 G gamma functions 317 Gaussian kernel 150, 258 generating logarithmic plots 44 textual output 59 GIF terminal 207 glass data 265 global plot styles 68, 70 GNU software, compared with gnuplot 13 gnuplot 3, 13 benefits 14 building 303 calling 228 as CGI script 239 command history 61 compared with GNU software 13 configuring 307 examples 4, 6 help 61 hot keys 62 installing 303 invoking 17, 229 limitations 15 mailing list 14, 345 mousing 62–63 new features 14 obtaining 303 tricks and warnings 44 web pages 239 web sites 305 354 gpic terminal 220 gprint() function 122 Grace graphing tool 349 graphical analysis 3, 9–10 benefits 12 limitations 12 resources 345 graphical analysis techniques 273 banking 284 changing appearance 284 changing compositions problems 292 comparing data 278 core principle 274 enhancing quantitative perception 289 housekeeping 296 iteration 275 judging lengths/ distances 287 plot ranges 291 presentation graphics 298 responsiveness 280 transformation 275 truncation 280 zero in plot range 291 graphical methods 245 counting statistics 256 multivariate data 264 ranked data 262 relationships 246 graphics file formats 206 presentation 11, 298 graphicx package (LaTeX) 212 graphing tools 348 graphs 92 aligned on common axis 181 arrays with layout 177 arrows 94 components 92 coordinates 93 creating with palettes 157 decorations 94 exporting 25 exporting to file 201 key 100 legend 100 lifecycle 296 objects 99 pm3d mode 157 polar mode 185 presentation 10 scatter plot 23 stacked 293 text labels 97 understanding data with 10, 301 within graphs 179 grid axes 123 grid cbtics option 159 grid format 146 grid mcbtics option 159 grid option 332 H half-tone shading example 87 hann kernel 150 hardware requirements xxix head option 95 header option 216 heat scale palette 165 help command 61, 309 hidden3d option 136, 335 histeps style 72 histograms 74, 256 history command 61, 309 history feature 17 historysize option 322 hot key bindings, creating custom 236 hot keys 62 housekeeping 296 graph lifecycle 296 input data files 296 output files 298 hue-based palette 166 hue-saturation-value (HSV) scheme 153, 165 hyperbolic functions 316 I ice cream 111 idx type indicator xxviii if command 315 imag() function 41 image analysis 11 implicit mode 158 impulses style 73 including EPS files in LaTeX documents 211 index directive 31 indexing strings 56 initialization file 235 inline plot styles 68 input axes 128 data files 296 redirection 226 insets 176 INSTALL file 306 INSTALL.gnu file 306 installing 308 gnuplot 303 on Linux 304 on Mac OS X 304 on Windows 304 int type indicator xxviii interactive terminals 218 options 343 interlacing 207 interpolate keyword 158 interpolating between colors 154 interpolation curves 37 invoking gnuplot 17, 229 isosamples option 136, 335 iteration 273, 275 case study 275 defined 10 J jitter plots 256 JPG terminal 208 judging lengths/distances 287 K kdensity directive 258 Kelley, Colin (software developer) 13 kernel 258 density estimates 258 Gaussian 258 smoothing 150 key 22, 100 appearance 104 default settings 104 explanation 102 layout 101 option 327 placement 101 turning on/off 101 keyboard event 238 keywords butt 205 columnsfirst 177 corners2color 158 dashed 205 default 159 downwards 177 dynamic 209 functions 155 355 keywords (continued) interpolate 158 offset 138, 178 rounded 205 rowsfirst 177 scale 178 solid 205 title 22 trianglepattern 138 upwards 177 knots, splines 249 kst graphing tool 348 L _label option 332 label option 327 labels (scatter plots) 251 landscape option 209 LaTeX EPS file 211 PostScript plots 211 tricks 217 layout directive 177 key 101 source tree 306 least squares fitting 191 legend.

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In general, the colors are distributed rather uniformly over the entire spectrum, because this matches up with the regularly varying function in this plot. 9.4.2 A complex figure As an example of a graph that includes a lot of fine detail, I’ve chosen a section from the edge of the Mandelbrot set. The Mandelbrot set is the set of all points in the complex plane for which a certain simple iteration process stays bounded. What’s noteworthy here is that the border between points inside the set and outside of it isn’t smooth—in fact the border is “infinitely” complicated, showing details at all levels of magnification.6 For points far from the Mandelbrot set, the iteration will diverge quickly (after just a few steps). But as we approach the border, the iteration will take many more steps before finally diverging.

How Big Things Get Done: The Surprising Factors Behind Every Successful Project, From Home Renovations to Space Exploration
by Bent Flyvbjerg and Dan Gardner
Published 16 Feb 2023

Manchester Evening News, February 15. Mandelbrot, Benoit B. 1960. “The Pareto-Lévy Law and the Distribution of Income.” International Economic Review 1 (2): 79–106. Mandelbrot, Benoit B. 1963. “New Methods in Statistical Economics.” Journal of Political Economy 71 (5): 421–40. Mandelbrot, Benoit B. 1963. “The Variation of Certain Speculative Prices.” The Journal of Business 36 (4): 394–419; correction printed in Mandelbrot, Benoit B. 1972. The Journal of Business 45 (4): 542–43; revised version reprinted in Mandelbrot, Benoit B. 1997. Fractals and Scaling in Finance. New York: Springer, 371–418. Mandelbrot, Benoit B. 1997.

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Mandelbrot, Benoit B. 1997. Fractals and Scaling in Finance. New York: Springer. Mandelbrot, Benoit B., and Richard L. Hudson. 2008. The (Mis)behavior of Markets. London: Profile Books. Mandelbrot, Benoit B., and James R. Wallis. 1968. “Noah, Joseph, and Operational Hydrology.” Water Resources Research 4 (5): 909–18. Mann, Michael E. 2021. The New Climate War: The Fight to Take the Planet Back. London: Scribe. Marewski, Julian N., Wolfgang Gaissmaier, and Gerd Gigerenzer. 2010. “Good Judgments Do Not Require Complex Cognition.” Cognitive Processing 11 (2): 103–21. Marković, Dimitrije, and Claudius Gros. 2014. “Power Laws and Self-Organized Criticality in Theory and Nature.”

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This gives you the magic of what I call “scale-free scalability,” meaning you can scale up or down following the same principles independently of where you are scalewise, which is exactly what you want in order to build something huge with ease. The mathematician Benoit Mandelbrot, who first laid out the science of scale-free scalability, called this attribute “fractal”—like one of those popular Internet memes in which you see a pattern, then zoom into a detail within the pattern and discover that it looks the same as the pattern as a whole, and you keep zooming in and keep discovering the same pattern.11 Modularity can do astonishing things.

Debunking Economics - Revised, Expanded and Integrated Edition: The Naked Emperor Dethroned?
by Steve Keen
Published 21 Sep 2011

Mackay, C. (1841) Extraordinary Popular Delusions and the Madness of Crowds, New York: Crown Trade Paperbacks, www.litrix.com/madraven/madne001.htm. Mandel, E. (1971) The Formation of the Economic Thought of Karl Marx, London: NLB. Mandelbrot, B. (1971) ‘Linear regression with non-normal error terms: a comment,’ Review of Economics and Statistics, 53(2): 205–6. Mandelbrot, B. (2005) ‘The inescapable need for fractal tools in finance,’ Annals of Finance, 1(2): 193–5. Mandelbrot, B. B. and R. L. Hudson (2004) The (Mis)behaviour of Markets: A fractal view of risk, ruin and reward, London: Profile. Mankiw, N. G. (2008) Principles of Microeconomics, 5E, Boston, MA: South-Western College Publishers.

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Given that it is a relatively new field, there are numerous explanations of the volatility of financial markets within Econophysics – including Power Law models of stock market movements (Gabaix, Gopikrishnan et al. 2006), Didier Sornette’s earthquake-based analysis (Sornette 2003), Joe McCauley’s empirically derived Fokker-Planck model (McCauley 2004), and Mandelbrot’s fractal geometry (Mandelbrot and Hudson 2004) – and it would require another book to detail them all. A unifying theme is that the behavior of financial markets is driven by the interactions of numerous market participants with each other, and these generate a highly unstable and therefore relatively unpredictable time series in financial data themselves.

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An analogous distinction between three states of randomness – mild, slow and wild – arises from the mathematics of fractal geometry. Conventional finance theory assumes that variation of prices can be modeled by random processes that, in effect, follow the simplest ‘mild’ pattern, as if each uptick or downtick were determined by the toss of a coin. What fractals show […] is that by that standard, real prices ‘misbehave’ very badly. A more accurate, multifractal model of wild price variation paves the way for a new, more reliable type of financial theory. (Mandelbrot and Hudson 2004: v) Economists teach that markets can be described by equilibrium.

The Doomsday Calculation: How an Equation That Predicts the Future Is Transforming Everything We Know About Life and the Universe
by William Poundstone
Published 3 Jun 2019

We need to be dealing with a process that has no characteristic time scale or lifespan, or at any rate, none that we know about. Fractals and Scale Invariance “Scale invariance” may be an unfamiliar term. Here’s one more likely to ring a bell: “fractal.” That word was coined by Benoit Mandelbrot to describe the fascinating unruliness of nature. Coastlines, snowflakes, clouds, and landscapes resist the straitjackets of Euclidean geometry. A coastline is not a “line.” A snowflake is not a hexagon. The defining quality of a fractal is scale invariance, or self-similarity. When a picture or diagram or chart of a fractal is zoomed in or out, its crinkly detail looks pretty much the same.

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To the right of Mitchell, though easily missed, is the familiar face of Albert Einstein, shown in profile. The speeding rocket and slow-growing hemlock allude to Einstein’s thought experiments of racing trains and light beams, used to develop his theory of relativity. Standing in front of Einstein is Benoit Mandelbrot, the IBM mathematician who described the concept of fractals. The hemlock tree and rocket blast are fractals, complex shapes in which each part resembles the whole. Zeno of Elea, a Greek philosopher whose features are known from ancient busts, dangles a cigarette. Zeno propounded the paradox of Achilles and the Tortoise. Swift Achilles challenges the Tortoise to a footrace.

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Craters come in all sizes, so it is hard to get a sense of scale. Even on Earth, where gentle rains and greenery erase the scars of planetary trauma, scientific photographs of rock formations often include a measuring stick for scale; otherwise it might be hard to judge the size. Mandelbrot said that fractals are all around us. They are the rule, not the exception. Gott’s Copernican method works when our knowledge of a duration has this fractal-like uncertainty. That is, we don’t have a sense of the overall time scale; we don’t know whether a measured past duration is a large or small part of the whole. This does not apply to a seventeen-year cicada, whose time scale is conveniently disclosed up front.

The Creativity Code: How AI Is Learning to Write, Paint and Think
by Marcus Du Sautoy
Published 7 Mar 2019

The computer is making no choices that are not programmed in before it starts calculating. Why do computer fractal images, although new and surprising, still feel so anaemic and lifeless? Perhaps the answer lies in the fact that they do not form a bridge between two conscious worlds. Computer-generated fractals have nonetheless made their creators big money, as fractals have proven to be a highly effective way to simulate the natural world. In his seminal book The Fractal Geometry of Nature, Benoit Mandelbrot explained how Nature uses fractal algorithms to make ferns, clouds, waves, mountains. It was reading this book that inspired Loren Carpenter, an engineer working at Boeing, to experiment with code to simulate natural worlds on the computer.

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It is a shape that is in some sense scale-less because you cannot discern from a section at what scale of magnification you are. The most iconic of these fractals is named after the mathematician who sparked the explosion of computer-generated images: the Mandelbrot set. Anyone who went clubbing in the 1980s would recognise this shape as the one that would be projected onto walls as DJs spun their psychedelic music. By infinitely zooming in on the image, the graphics created a sense of falling into some dreamlike world without ever touching the ground. These shapes could never have been discovered without the power of the computer. But is that art? In his ‘Fractal Art Manifesto’, published in 1999, Kerry Mitchell tried to distinguish fractal art from something a machine was doing.

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E., 154 local maximum 41–2, 42, 97 Loebner, Hugh 257–8 logos 166 London Zoo 107 Lord of the Rings, The 242, 246, 270 Lovelace, Ada 1–2, 7–8, 44, 65, 75, 91, 102–3, 109, 196, 219, 229, 235, 272, 300 Lovelace Test 7–8, 102–3, 219–20 Lubat, Bernard 219–20 Lucasfilm 114–15 machine learning 9, 13, 96, 299, 305; art and 126, 127, 132, 137, 140, 143, 144; biases and blind spots 91–5; birth of 29–43, 65, 66–7; computer vision and 70–80, 76, 92–4, 143; creativity and 2, 5, 299; data creation and 67–8, 69–70, 83, 88–9; language and 260, 284; mathematics 168, 233, 235, 238, 253; music and 207, 209, 212, 228, 229–30; neural networks and see neural networks; reinforcement learning and 96–7; supervised learning 95–6, 97, 137; tabula rasa learning 73, 97, 98; transformational impact of 66–7 see also artificial intelligence (AI) Macintosh computer 117 Malevich, Kasimir 11 Mandelbrot, Benoit: The Fractal Geometry of Nature 114 Mandelbrot set 113 Mankoff, Bob 284 Markov, Andrey 214–18 Markov chain 214–18, 216, 217, 221, 222, 223 Maros caves, Sulawesi 103–4 Martin, George R. R.: A Song of Ice and Fire/Game of Thrones 56, 120 Martinez, David 123 Maslon LLP 109 Massive Attack 226–8, 229 Mathematical Society of France 279 mathematics: AI and proving mathematical theorems 233–53; AI as threat to job of mathematician 5–7, 17, 43, 151–5, 233; algorithms, development of and 44–65, 45, 50, 51, 52, 58, 59, 60, 63; art and see art; art of 150–68; birth of 44–5; chess and see chess; complexity of, increasing 176–85; computers as partners in proving deep theorems 169–85; creativity and 3–4, 5, 7, 10, 12, 14, 15–16, 17, 18, 98, 150–2, 181–2; drugs and 181–2; Go and see Go; language and 269, 276, 278, 279–80, 284, 289, 291–3, 297; limits of human 176–80; music and see musical composition; narrative art of 241–53, 250; origins of 155–68; pattern recognition and 20–1, 155–6; proof, mathematical game of 152–5; proof, narrative quality of 245–50; proof, origins of 161–8; proof, social context of 182–3; pure and applied, separation of 182; recommender algorithms and 84–6, 85, 86, 89–90; surprise, element of and 248–50, 250; tales, generating new mathematical 291–3 Mayans 157 McCarthy, John 24 McEwan, Ian 306 McHugh, Tommy 133, 134 medieval polyphony 187, 189 MENACE (algorithm) 24 Messiaen, Olivier 90; Quartet for the End of Time 205 Métamatics 119 metric spaces 240–1 Metropolitan Police, British 77 Michie, Donald 2, 24 Microsoft 72, 73, 127, 131; Kinect/Xbox 72–6, 79, 81–2; Microsoft Research Cambridge 174–6; Rembrandt project 127–32 Millennium Prize Problems 152, 172 Minsky, Marvin 2 Mitchell, Kerry: ‘Fractal Art Manifesto’ 114 Mitsuku (chatbot) 258–9, 260 Mizar Mathematical Library 236–41, 244, 246, 253 Modus Ponens 162 Modus Tollens 162–3 Monbiot, George: Out of the Wreckage 296 Monet, Claude 10, 138 Monster Symmetry Group 10, 177 Morris, Desmond 107 Mozart, Wolfgang Amadeus 2, 3, 5, 10, 13, 194, 197, 198, 200, 227, 230, 231, 280; Musikalisches Würfelspiel 194–5 Muggleton, Stephen 291 Murray, Sean 116 muses 13–14 musical composition 185, 186–233; algorithms and composition, correlation between 186–9; Bach as first musical coder 189–94, 195, 197, 198, 200, 201, 205 see also Bach, Johann Sebastian; DeepBach and 207–12; Emmy and 195–207, 197, 199; MduS and 186–8; mathematics and 186–212, 214–18, 216, 217, 221, 222, 223, 230; Mozart’s Musikalisches Würfelspiel and 194–5; songwriting 213–32 see also songwriting; Turing Test and 200–2, 220–1 Musil, Robert 276 Musk, Elon 25 Namagiri 14 Nam June Paik 119 NaNoGenMo (National Novel Generation Month) 282–3 Narrative Science 293, 295 Naruto (macaque) 108–9 National Novel Writing Month 282 Nature 28, 152 Neanderthals 104, 231 Nees, Georg 110, 111–12, 113, 114, 117, 126 Nekrasov, Pavel 215, 217 Netflix 44, 83, 91, 135, 286; prize challenge 83–9, 85, 86, 91 neural networks 24, 27, 33, 68–70, 68, 70, 93–4, 272–3 new/novelty, creativity and 3, 4, 7–8, 12, 13, 16, 17, 40–3, 102–3, 109, 138–41, 140, 167–8, 238–9, 291–3, 299, 301 Newton, Isaac 92, 171, 239 New York Times, The 29, 139 Nielsen, Frank 210 Nietzsche, Friedrich 169 Nobel Prize 16, 57, 179 No-Free Lunch Theorem 95 No Man’s Sky (game) 116 Norton, Simon 18 number theory 4, 11, 14 Oates, Joyce Carol 15 Obrist, Hans-Ulrich 102, 106, 146, 147, 148 Odd Order Theorem 175 OKCupid 57 On-Line Encyclopaedia of Integer Sequences 291–2 Orwell, George 303 Osborn, Alex 301 Oulipo (Ouvroir de littérature potentielle) 278–80 over-fitting 74–6, 75 Oxford University 19, 53–4, 110, 155, 171, 181, 234, 235 Pachet, François 210, 214, 218–24, 225 Pacific Journal of Math 175 Page, Larry 48–9, 51–2, 57 ‘Painting Fool, The’ 119–22, 200, 291 Paleolithic flutes 231 Parker, Charlie 218, 222–3 Pask, Gordon 119 pattern recognition 6, 20–1, 99–101, 155–6, 186–7 Peña, Javier López 55 pendulum, chaotic 123–5 People for the Ethical Treatment of Animals (PETA) 108–9 perceptron 68–70, 68, 70 Perelman, Grigori 11, 152 Philips Company 119 Picasso, Pablo 5, 9, 11, 13, 111, 135, 136–7, 138–9, 142, 222; Les Demoiselles d’Avignon 138–9 Pissarro, Camille 10, 138 Pixar 115, 116, 124 place value system 157–8 Plato 13–14, 105 PlayStation 4 116 Pleiades 156 Poincaré Conjecture 11, 152 Poincaré, Henri 11, 150, 152, 244–5, 250 polis 166 ‘Pollockizer, The’ 124 Pollock, Jackson 117–19, 148, 302; MduS attempts to fake work 123–5; No. 5, 1948 123 prime numbers 11, 44, 53, 154, 164, 165, 166–7, 175, 178, 205, 239, 245–6, 247–8, 249, 251, 277, 285, 292 proairetic code 251–2 probability 27, 37, 71, 82, 91–2, 96, 101, 182, 214–18, 219, 229, 252, 270, 284 Proceedings of the Natural Academy of Sciences 57 profnath 62–5 prolation canon 187, 206 Propp, Vladimir 290 PropperWryter 290 Pushkin, Alexander 265; Eugene Onegin 214, 217–18 quadratic equations 75, 159–60, 161 quantum physics 53, 92, 112–13, 227–8, 235 Queneau, Raymond 278, 279; 100,000,000,000,000 Poems 279–80 Quill 293 Ramanujan 14 Raskin, Jef 117 Rayner, Alex 145 recommender algorithms 44, 79–80, 81–90, 85, 86, 91 Reddit 54 Redmond, Michael 38 refactorable numbers 292–3 Reflection (app) 229 reinforcement learning 27, 96–7 Rembrandt van Rijn 3, 106, 126–31, 132, 143, 151, 301; AI attempts to recreate works of 127–32; Tobit and Anna 130–1 Renoir, Pierre-Auguste 10, 122 Rescue on Fractals (game) 115–16 Richter, Gerhard: 4900 Farben 99–103, 106, 146, 155 Riedl, Mark 286, 287, 306 Riemann Hypothesis 178 robots 32, 71, 94, 119, 129, 262, 271–3 Rogers, Carl 255; ‘Towards a Theory of Creativity’ 301–2 Roman Empire 157 Romantic movement, musical 12, 13 Rosenblatt, Frank 24 Roth, Alvin 57 Royal Society 9, 233; Computing Laboratory 277 Rutgers University 132–3, 138, 139 Rutter, Brad 261, 262 Saleh, Babek 134 Samuel, Arthur 24 Scape (app) 229 scenius 15 Scheherazade-IF 286–8, 306 Schoenberg, Arnold 11, 190, 205, 223 Schöffer, Nicholas: CYSP 1 118–19 Schwartz, Oscar 282 Scriabin, Alexander 199, 199 Scrubs (TV series) 284 Searle, John 164, 273–5 Sedol, Lee 22, 30, 32, 33–40, 97, 131, 219–20 Seeker, The (algorithmic novel) 282–3, 305 Seinfeld (TV series) 284 Serpentine Gallery, London 99–102, 105, 106, 146, 147, 155 Shakespeare, William 5, 16, 127; As You Like It 303; Othello 3, 23 Shalosh B.

The Singularity Is Near: When Humans Transcend Biology
by Ray Kurzweil
Published 14 Jul 2005

The primary problem with Bell's perspective is that he fails to account for the self-organizing, chaotic, and fractal nature of the brain's design. It's certainly true that the brain is complex, but a lot of the complication is more apparent than real. In other words, the principles of the design of the brain are simpler than they appear. To understand this, let's first consider the fractal nature of the brain's organization, which I discussed in chapter 2. A fractal is a rule that is iteratively applied to create a pattern or design. The rule is often quite simple, but because of the iteration the resulting design can be remarkably complex. A famous example of this is the Mandelbrot set devised by mathematician Benoit Mandelbrot.20 Visual images of the Mandelbrot set are remarkably complex, with endlessly complicated designs within designs.

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I would agree that the roughly thirty to one hundred million bytes of information in the genome do not represent a simple design (certainly far more complex than the six characters in the definition of the Mandelbrot set), but it is a level of complexity that we can already manage with our technology. Many observers are confused by the apparent complexity in the brain's physical instantiation, failing to recognize that the fractal nature of the design means that the actual design information is far simpler than what we see in the brain. I also mentioned in chapter 2 that the design information in the genome is a probabilistic fractal, meaning that the rules are applied with a certain amount of randomness each time a rule is iterated.

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A famous example of this is the Mandelbrot set devised by mathematician Benoit Mandelbrot.20 Visual images of the Mandelbrot set are remarkably complex, with endlessly complicated designs within designs. As we look at finer and finer detail in an image of the Mandelbrot set, the complexity never goes away, and we continue to see ever finer complication. Yet the formula underlying all of this complexity is amazingly simple: the Mandelbrot set is characterized by a single formula Z = Z2 + C, in which Z is a "complex" (meaning two-dimensional) number and C is a constant. The formula is iteratively applied, and the resulting two-dimensional points are graphed to create the pattern.

The Biology of Belief: Unleashing the Power of Consciousness, Matter & Miracles
by Bruce H. Lipton
Published 1 Jan 2005

These natural images can only be created by using the recently discovered mathematics called fractal geometry. French mathematician Benoit Mandelbrot launched the field of fractal mathematics and geometry in 1975. Like quantum physics, fractal (fractional) geometry forces us to consider those irregular patterns, a quirkier world of curvy shapes and objects with more than three dimensions. The mathematics of fractals is amazingly simple because you need only one equation, using only simple multiplication and addition. The same equation is then repeated ad infinitum. For example, the “Mandelbrot set” is based on the simple formula of taking a number, multiplying it by itself and then adding the original number.

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The result of that equation is then used as the input of the subsequent equation; the result of that equation is then used as the input for the next equation and so on. The challenge is that even though each equation follows the same formula, these equations must be repeated millions of times to actually visualize a fractal pattern. The manual labor and time needed to complete millions of equations prevented early mathematicians from recognizing the value of fractal geometry. With the advent of powerful computers Mandelbrot was able to define this new math. Inherent in the geometry of fractals is the creation of ever-repeating, “self-similar” patterns nested within one another. You can get a rough idea of the repeating shapes by picturing the eternally popular toy, hand-painted Russian nesting dolls.

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Evolution, the expansion of awareness, can then be physically defined by the increase of membrane surface area. Mathematical studies have found that fractal geometry is the best way to get the most surface area (membrane) within a three-dimensional space (cell). Therefore, evolution becomes a fractal affair. Repeating patterns in nature are a necessity, not a coincidence, of “fractal” evolution. My point is not to get caught up in the mathematical details of the modeling. There are repetitive fractal patterns in nature and in evolution as well. The strikingly beautiful, computer-generated pictures that illustrate fractal patterns should remind us that, despite our modern angst and the seeming chaos of our world, there is order in nature, and there is nothing truly new under the sun.

Capitalism 4.0: The Birth of a New Economy in the Aftermath of Crisis
by Anatole Kaletsky
Published 22 Jun 2010

Mandelbrot, in his book The Misbehaviour of Markets, described how forty years of effort to interest economists in fractal geometry were ridiculed or ignored, despite the fact that they seemed to provide a much better analysis of extreme market behavior than standard methods. Consider, for example, this paragraph written by Mandelbrot some five years before the Lehman crisis: The odds of financial ruin in a free global-market economy have been grossly underestimated. There is no limit to how bad a bank’s losses can get. Its own bankruptcy is the least of the worries; it will default on its obligations to other banks—and so the losses will spread from one inter-linked financial house to another.

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Bit by bit, from a bad seed a big but sickly tree is built with glue, nails, screws and scaffolding. Conventional economics assumes the financial system is a linear, continuous, rational machine and these false assumptions are built into the risk models used by many of the world’s banks.1 Despite the success achieved by fractal geometry and nonlinear modeling in the study of earthquakes, weather, evolution, ecology, and other complex systems, Mandelbrot always faced the same objection from economists when he proposed applying similar techniques to markets. These non-Gaussian mathematical methods could only provide approximations, as opposed to the precise answers offered by the Efficient Market Hypothesis and Gaussian statistics.2 The fact that the exact answers of EMH bore no relation to reality did not seem to deter “scientific” economists.

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For more details, see Chapter 11. 4 This accelerator-multiplier concept, first proposed by Sir Roy Harrod, was later refined by Paul Samuelson and Sir John Hicks and became the standard Keynesian business cycle model. 5 Justin Lahart, “In Time of Tumult, Obscure Economist Gains Currency,” Wall Street Journal, August 18, 2007. 6 George Soros, The Soros Lectures: At the Central European University. 7 Alan Greenspan, “The Challenge of Central Banking,” remarks at the Annual Dinner and Francis Boyer Lecture of the American Enterprise Institute for Public Policy Research, Washington, DC, December 5, 1996. Available from http://www.federalreserve.gov/boarddocs/speeches/1996/19961205.htm. 8 Robert Shiller, Irrational Exuberance. 9 Benoit Mandelbrot and Richard Hudson, The (Mis)behavior of Markets: A Fractal View of Risk, Ruin and Reward, 4. 10 Nassim Nicholas Taleb, Fooled by Randomness: The Hidden Role of Chance in the Markets and in Life and the Black Swan: The Impact of the Highly Probable. 11 The term normal distribution describes prices or any other form of data that cluster predictably and reliably around a mean value in a bell curve pattern. 12 Malcolm C.

The Simpsons and Their Mathematical Secrets
by Simon Singh
Published 29 Oct 2013

(And he solved them by hand, without determinants.) When I asked him how he knew the formula would be a cubic polynomial, he said: “What else would it be?” APPENDIX 4 Fractals and Fractional Dimensions We normally think of fractals as patterns that consist of self-similar patterns at every scale. In other words, the overall pattern associated with an object persists as we zoom in and out. As the father of fractals Benoit Mandelbrot pointed out, these self-similar patterns are found in nature: “A cauliflower shows how an object can be made of many parts, each of which is like a whole, but smaller.

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We actually have this amazing sequence, because they fly through this huge fractal landscape that represents the area between two dimensions and three dimensions. The scene contains some pretty amazing computer graphics.” The fractal landscape is particularly appropriate, because fractals actually exhibit a fractional dimensionality. The fractal landscape appears on the journey between the two-dimensional and three-dimensional worlds, which is exactly where one might expect to find a fractional dimension. If you want to know more about fractals, please refer to appendix 4, where there is a very brief overview of this topic, focusing particularly on how an object can possibly be fractionally dimensional.

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Joke 6 Q: What’s big, grey, and proves the uncountability of the decimal numbers? 2 points A: Cantor’s diagonal elephant. Joke 7 Q: What’s the world’s longest song? 2 points A: “0 Bottles of Beer on the Wall.” Joke 8 Q: What does the “B.” in Benoit B. Mandelbrot stand for? 4 points A: Benoit B. Mandelbrot. Joke 9 Q: What do you call a young eigensheep? 1 point A: A lamb, duh! Joke 10 One day, ye director of ye royal chain mail factory was asked to submit a sample in order to try to win a very large order for chain mail tunics and leggings. Though the tunic sample was accepted, he was told that the leggings were too long.

This Will Make You Smarter: 150 New Scientific Concepts to Improve Your Thinking
by John Brockman
Published 14 Feb 2012

Lately, one of many projects has been to revisit the aesthetic space of scientific visualizations, and another the epitome of mathematics made tangible: fractals, which I had done almost twenty years ago with virtuoso coder Ben Weiss, now enjoying them via realtime flythroughs on a handheld little smartphone. Here was the most extreme example: A tiny formula, barely one line on paper, used recursively, yields worlds of complex images of amazing beauty. (Ben had the distinct pleasure of showing Benoit Mandelbrot an alpha version at a TED conference just months before Mandelbrot’s death.) My hesitation about overuse of parsimony was expressed perfectly in a quote from Albert Einstein, arguably the counterpart blade to Ockham’s razor: “Things should be made as simple as possible—but not simpler.”

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You’ll observe a frequent desire to move beyond deductive reasoning and come up with more rigorous modes of holistic or emergent thinking. You’ll also get a sense of the emotional temper of the group. People in this culture love neat puzzles and cool questions. Benoit Mandelbrot asked his famous question “How long is the coast of Britain?” long before this symposium was written, but it perfectly captures the sort of puzzle people in this crowd love. The question seems simple. Just look it up in the encyclopedia. But as Mandelbrot observed, the length of the coast of Britain depends on what you use to measure it. If you draw lines on a map to approximate the coastline, you get one length, but if you try to measure the real bumps in every inlet and bay, the curves of each pebble and grain of sand, you get a much different length.

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Remarkably, once the dust began to settle, it became apparent that the statistical properties of the resulting Internet were quite special: The time delays for packet transmission, the network topology, and even the information transmitted exhibit fractal properties. However you look at the Internet—locally or globally, on short time scales or long—it looks exactly the same. Although the discovery of this fractal structure, around 1995, was an unwelcome surprise because standard traffic-control algorithms, as used by routers, were designed assuming that all properties of the network dynamics would be random, the fractality is also broadly characteristic of biological networks. Without a master blueprint, the evolution of an Internet is subject to the same underlying statistical laws that govern biological evolution, and structure emerges spontaneously, without the need for a controlling entity.

Power, Sex, Suicide: Mitochondria and the Meaning of Life
by Nick Lane
Published 14 Oct 2005

If a fractal is broken into its constituent parts, each part still looks more or less the same, because, as the pioneer of fractal geometry Benoit Mandelbrot put it, ‘the shapes are made of parts similar to the whole in some way’. Fractals can be formed randomly by natural forces such as wind, rain, ice, erosion, and gravity, to generate natural fractals, like mountains, clouds, rivers, and coastlines. Indeed, Mandelbrot described fractals as ‘the geometry of nature’, and in his landmark paper, published in Science, in 1967, he applied this approach to the question advanced in its title: How Long is the Coast of Britain? Fractals can also be generated mathematically, often by using a reiterative geometric formula to specify the angle and density of branches (the ‘fractal dimension’).

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On Being the Right Size, ed. John Maynard-Smith. Oxford University Press, Oxford, UK, 1985. Mandelbrot, Benoit. The Fractal Geometry of Nature. W. H. Freeman, New York, 1977. Ridley, Mark. Mendel’s Demon. Weidenfeld & Nicolson, London, UK, 2000. The power laws of biology Bennett, A. F. Structural and functional determinates of metabolic rate. American Zoologist 28: 699–708; 1988. 336 Further Reading Heusner, A. Size and power in mammals. Journal of Experimental Biology 160: 25–54; 1991. Kleiber, M. The Fire of Life. Wiley, New York, USA, 1961. Fractal geometry and scaling Banavar, J., Damuth, J., Maritan, A., and Rinaldo, A.

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They came up with a radical explanation based on the fractal geometry of branching supply networks, such as the circulatory system of mammals, the respiratory tubes of insects (the trachea), and the plant vascular system. Their densely mathematical model was published in Science in 1997, and the ramifications (if not the maths) swiftly captured the imagination of many. The fractal tree of life Fractals (from the Latin fractus, broken) are geometric shapes that look similar at any scale. If a fractal is broken into its constituent parts, each part still looks more or less the same, because, as the pioneer of fractal geometry Benoit Mandelbrot put it, ‘the shapes are made of parts similar to the whole in some way’.

Programming Rust: Fast, Safe Systems Development
by Jim Blandy and Jason Orendorff
Published 21 Nov 2017

This section’s program plots the Mandelbrot set, a fractal produced by iterating a simple function on complex numbers. Plotting the Mandelbrot set is often called an embarrassingly parallel algorithm, because the pattern of communication between the threads is so simple; we’ll cover more complex patterns in Chapter 19, but this task demonstrates some of the essentials. To get started, we’ll create a fresh Rust project: $ cargo new --bin mandelbrot Created binary (application) `mandelbrot` project All the code will go in mandelbrot/src/main.rs, and we’ll add some dependencies to mandelbrot/Cargo.toml. Before we get into the concurrent Mandelbrot implementation, we need to describe the computation we’re going to perform.

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, Macro Basicsabout, Macro Basics fragment types supported by, Fragment Types main(), Handling Errors in main() Mandelbrot setbasics of calculation, What the Mandelbrot Set Actually Is concurrent implementation, Concurrency concurrent program for, A Concurrent Mandelbrot Program mapping from pixels to complex numbers, Mapping from Pixels to Complex Numbers parsing pair command-line arguments, Parsing Pair Command-Line Arguments plotting, Plotting the Set rendering with fork-join parallelism, Revisiting the Mandelbrot Set running the plotter, Running the Mandelbrot Plotter writing image files, Writing Image Files map adapter, map and filter map typesBTreeMap<K, V>, HashMap<K, V> and BTreeMap<K, V> HashMap<K, V>, HashMap<K, V> and BTreeMap<K, V> map, defined, HashMap<K, V> and BTreeMap<K, V> map.entry(key), Entries mapping, Mapping from Pixels to Complex Numbers match expressions, A Simple Web Server, if and match Matsakis, Niko, Rayon max method, max, min max_by method, max_by, min_by max_by_key method, max_by_key, min_by_key memoryenums in, Enums in Memory raw pointers and, Moving into and out of Memory strings in, Strings in Memory types for representing sequence of values in, Arrays, Vectors, and Slices memory ordering, Atomics method calls, fully qualified, Fully Qualified Method Calls methodscalling, Function and Method Calls defining with impl, Defining Methods with impl fully qualified method calls, Fully Qualified Method Calls integers and, Integer Types min method, max, min min_by method, max_by, min_by min_by_key method, max_by_key, min_by_key Model-View-Controller (MVC), Using Closures Effectively modules, Modulesin separate files, Modules in Separate Files items, Items, the Building Blocks of Rust libraries and, Turning a Program into a Library paths and imports, Paths and Imports standard prelude, The Standard Prelude Morris worm, Why Rust?

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/src/lib.rs --crate-name image --crate-type lib --extern png=.../libpng-16c24f58491a5853.rlib ...` Compiling mandelbrot v0.1.0 (file://.../mandelbrot) Running `rustc src/main.rs --crate-name mandelbrot --crate-type bin --extern crossbeam=.../libcrossbeam-ba292320058da7df.rlib --extern image=.../libimage-254ec48c8f0684f2.rlib ...` $ We reformatted the rustc command lines for readability, and we deleted a lot of compiler options that aren’t relevant to our discussion, replacing them with an ellipsis (...). You might recall that by the time we were done, the Mandelbrot program’s main.rs contained three extern crate declarations: extern crate num; extern crate image; extern crate crossbeam; These lines simply tell Rust that num, image, and crossbeam are external libraries, not part of the Mandelbrot program itself.

The Quants
by Scott Patterson
Published 2 Feb 2010

Leland and Mark Rubinstein, published in Portfolio Insurance: A Guide to Dynamic Hedging, edited by Donald Luskin (John Wiley & Sons, 1988). “Even if one were to have lived”: The age of the universe is 13.5 billion years, not 20 billion. When German tanks rumbled into France: Some details of Mandelbrot’s life come from a series of interviews with Mandelbrot in the summer of 2008. Many also come from the book The (Mis)Behavior of Markets: A Fractal View of Financial Turbulence, by Benoit Mandelbrot and Richard L. Hudson (Basic Books, 2006). “I realized that the existence of the smile”: My Life as a Quant, by Emanuel Derman (John Wiley & Sons, 2004), 226. A squad of fifty armed federal marshals: Certain details come from Den of Thieves, by James Stewart (Simon & Schuster, 1991).

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Out at the no-man’s-land on the wings of the bell curve lurked a dark side of markets that haunted the quants like a bad dream, one many had seemingly banished into subconsciousness. Mandelbrot’s message had been picked up years later by Nassim Taleb, who repeatedly warned quants that their models were doomed to fail because unforeseen black swans (which reputedly didn’t exist) would swoop in from nowhere and scramble the system. Such notions threatened to devastate the elegant mathematical world of quants such as Cootner and Fama. Mandelbrot had been swiftly attacked, and—though he remained a mathematical legend and created an entire new field known as fractal geometry and pioneering discoveries in the science of chaos—was soon forgotten in the world of quants as little more than a footnote in their long march to victory.

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The flaw had already been identified decades earlier by one of the most brilliant mathematicians in the world: Benoit Mandelbrot. When German tanks rumbled into France in 1940, Benoit Mandelbrot was sixteen years old. His family, Lithuanian Jews, had lived in Warsaw before moving to Paris in 1936 amid a spreading economic depression. Mandelbrot’s uncle, Szolem Mandelbrojt, had moved to Paris in 1929 and quickly rose to prominence among the city’s mathematical elite. Young Mandelbrot studied under his uncle and entered a French secondary school. But his life was upended when the Nazis invaded. As the Germans closed in, the Mandelbrot family fled to the small hill town of Tulle in southwest France, where they had friends.

The Patterning Instinct: A Cultural History of Humanity's Search for Meaning
by Jeremy Lent
Published 22 May 2017

While this might sound rather mystical, recent breakthroughs in mathematics have demonstrated Cheng's statements to be a perceptive insight into the nature of reality. Fractal geometry, pioneered by mathematician Benoit Mandelbrot, shows how nature forms intricate patterns that replicate themselves at different scales, each pattern nested inside another. Examples of these fractal patterns are observable in clouds, coastlines, ferns, and sand dunes.41 Since Mandelbrot's discovery, biologists have come to recognize that the design of life itself is fractal, with cells self-organizing to form organisms, which then self-organize into communities of organisms and ecosystems. In the human body, fractal designs have been discovered in systems as diverse as blood vessels, lungs, heart rate, the digestive system, and brain networks, so much so that fractal behavior in a system is coming to be seen as a sign of good health.

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Now, in systems thinking, a new set of methods was emerging to investigate the unequal world of those other things.20 A brilliant mathematician, Benoit Mandelbrot, developed a new branch of mathematics, called fractal geometry, to describe this non-Newtonian world. His 1983 book The Fractal Geometry of Nature had a profound effect on the field of mathematics. Mandelbrot explained in clear terms the limitations of classical theory: Most of nature is very, very complicated. How could one describe a cloud? A cloud is not a sphere…. It is like a ball but very irregular. A mountain? A mountain is not a cone…. If you want to speak of clouds, of mountains, of rivers, of lightning, the geometric language of school is inadequate. The fractal forms that Mandelbrot's mathematical formulas create have a delicate grace that mirrors the beauty of nature itself (figure 19.1).

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The fractal forms that Mandelbrot's mathematical formulas create have a delicate grace that mirrors the beauty of nature itself (figure 19.1). Fractal geometry helped instigate a deeper understanding of patterns in nature. One profound insight was that the same design tends to repeat itself at larger or smaller scales. Coastlines, cloudscapes, sand dunes, and rivers all demonstrate what is known as scale independency, creating similar patterns both close up and from a distance. Biologists began to recognize these fractal patterns in all kinds of living systems: leaf veins, tree branches, blood vessels, lung brachia, and neurons.

Skin in the Game: Hidden Asymmetries in Daily Life
by Nassim Nicholas Taleb
Published 20 Feb 2018

“Genetic Origins of the Minoans and Mycenaeans.” Nature 548, no. 7666: 214–218. MacLean, Leonard C., Edward O. Thorp, and William T. Ziemba, 2011. The Kelly Capital Growth Investment Criterion: Theory and Practice, vol. 3. World Scientific. Mandelbrot, Benoit, 1982. The Fractal Geometry of Nature. Freeman and Co. ———, 1997. Fractals and Scaling in Finance: Discontinuity, Concentration, Risk. New York: Springer-Verlag. Mandelbrot, Benoit B., and N. N. Taleb, 2010. “Random Jump, Not Random Walk.” In Richard Herring, ed., The Known, the Unknown, and the Unknowable. Princeton, N.J.: Princeton University Press. Margalit, Avishai, 2002.

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Chapter 13 The Merchandising of Virtue Sontag is about Sontag—Virtue is what you do when nobody is looking—Have the guts to be unpopular—Meetings breed meetings—Call someone lonely on Saturdays after tennis Lycurgus, the Spartan lawmaker, responded to a suggestion to allow democracy there, saying “begin with your own family.” I will always remember my encounter with the writer and cultural icon Susan Sontag, largely because I met the great Benoit Mandelbrot on the same day. It took place in 2001, two months after the terrorist event of September, in a radio station in New York. Sontag, who was being interviewed, was piqued by the idea of a fellow who “studies randomness” and came to engage me. When she discovered that I was a trader, she blurted out that she was “against the market system” and turned her back to me as I was in mid-sentence, just to humiliate me (note here that courtesy is an application of the Silver Rule), while her assistant gave me a look as if I had been convicted of child killing.

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Or not explicitly “maximize” anything, just do things because that is what makes us human. Violence: Pinker (2011), Cirillo and Taleb (2016, 2018). Renormalization: Galam (2008, 2012). Renormalization group in Binney et al. (1992). Thick Blood: Margalit (2002). Bounded Rationality: Gigerenzer and Brighton (2009), Gigerenzer (2010). Lindy Effect: Eliazar (2017), Mandelbrot (1982, 1997); also Antifragile. Periander of Corinth: in Early Greek Philosophy: Beginning and Early Ionian Thinkers, Part 1. Genes and Minority Rule: Lazaridis (2017), Zalloua, private discussions. Languages move much faster than genes. Northern Europeans are surprised to hear that (1) ancient and modern Greeks can be actually the same people, (2) “Semitic people” such as the Phoenicians are closer genetically to the “Indo-European” Ancient than to “Semites,” though linguistically far apart.

Licence to be Bad
by Jonathan Aldred
Published 5 Jun 2019

Snowflakes are called ‘scale-invariant’ by physicists because their crystal structure looks the same no matter how much we magnify them. Snowflakes are an example of what the mathematician Benoît Mandelbrot calls fractals – structures with no natural or normal size and which recur at different scales. (Another example is trees: the pattern of branches looks like the pattern of leaves on a branch, and also the pattern of veins in a leaf). Mandelbrot noticed that prices in financial markets have this property: a graph showing the price over time of some stock or market index will look much the same, whether the time period covered is several decades, a few seconds, or anything in between.

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The late Tony Atkinson was a world authority on inequality and this is the best recent book for a careful and thorough discussion of the facts of inequality. 2 Mishel, L., and Sabadish, N., CEO Pay in 2012 was Extraordinarily High Relative to Typical Workers and Other High Earners (Economic Policy Institute, 2013). 3 Speech at the Royal Geographical Society Presidential Dinner, London, 1991. 4 On histories of the effect of Reagan’s and Thatcher’s ideas, one inspiration for this book was Daniel Rodgers’s superb Age of Fracture (Harvard: Harvard University Press, 2011). See especially chapter 2. 5 Strathern, P. (2001), Dr Strangelove’s Game (London: Hamish Hamilton), 227. 6 Atkinson, 19–20. 7 See Economist, 13 October 2012, ‘The Rich and the Rest’, and research cited there. 8 Quoted in Benoit Mandelbrot; Hudson, Richard L. (2004), The (Mis) behavior of Markets: A Fractal View of Risk, Ruin, and Reward (New York: Basic Books), 155. 9 Hacker, J., and Pierson, P. (2010), ‘Winner-Take-All Politics’, Politics and Society, 38 (2010), 152–204. 10 See for instance Atkinson, 80–81 and J. Stiglitz (2012), The Price of Inequality (London: Allen Lane), 27–8. 11 Norton, M., and Ariely, Dan, ‘Building a Better America – One Wealth Quintile at a Time’, Perspectives in Psychological Science, 6 (2011), 9–12; Davidai, S., and Gilovich, T. (2015), ‘Building a More Mobile America – One Income Quintile at a Time’, in ibid., 10, 60–71; survey conducted by Fondation-Jean-Jaurès at https://jean-jaures.org/nos-productions/la-perception-des-inegalites-dans-le-monde. 12 See for instance M.

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objection, 107, 119–20 Friedman, Milton, 4–5, 56, 69, 84, 88, 126, 189 awarded Nobel Prize, 132 and business responsibility, 2, 152 debate with Coase at Director’s house, 50, 132 as dominant Chicago thinker, 50, 132 on fairness and justice, 60 flawed arguments of, 132–3 influence on modern economics, 131–2 and monetarism, 87, 132, 232 at Mont Pèlerin, 5, 132 rejects need for realistic assumptions, 132–3 Sheraton Hall address (December 1967), 132 ‘The Methodology of Positive Economics’ (essay, 1953), 132–3 ‘The Social Responsibility of Business is to Increase Its Profits’ (article, 1970), 2, 152 Frost, Gerald, Antony Fisher: Champion of Liberty (2002), 7* Galbraith, John Kenneth, 242–3 game theory assumptions of ‘rational behaviour’, 18, 28, 29–32, 35–8, 41–3, 70, 124 Axelrod’s law of the instrument, 41 backward induction procedure, 36–7, 38 and Cold War nuclear strategy, 18, 20, 21–2, 24, 27, 33–4, 35, 70, 73, 198 focus on consequences alone, 43 as form of zombie science, 41 and human awareness, 21–3, 24–32 and interdependence, 23 limitations of, 32, 33–4, 37–40, 41–3 minimax solution, 22 multiplicity problem, 33–4, 35–7, 38 Nash equilibrium, 22–3, 24, 25, 27–8, 33–4, 41–2 the Nash program, 25 and nature of trust, 28–31, 41 the Prisoner’s Dilemma, 26–8, 29–32, 42–3 real world as problem for, 21–2, 24–5, 29, 31–2, 37–8, 39–40, 41–3 rise of in economics, 40–41 and Russell’s Chicken, 33–4 and Schelling, 138–9 and spectrum auctions, 39–40 theory of repeated games, 29–30, 35 tit-for-tat, 30–31 and trust, 29, 30–31, 32, 41 uses of, 23–4, 34, 38–9 view of humanity as non-cooperative/distrustful, 18, 21–2, 25–32, 36–8, 41–3 Von Neumann as father of, 18, 19, 20–22, 25, 26, 28, 30, 34, 41 zero-sum games, 21–2 Gates, Bill, 221–2 Geithner, Tim, 105 gender, 127–8, 130–31, 133, 156 General Electric, 159 General Motors (GM), 215–16 George, Prince of Cambridge, 98 Glass–Steagall Act, repeal of, 194 globalization, 215, 220 Goldman Sachs, 182, 184, 192 Google, 105 Gore, Al, 39 Great Reform Act (1832), 120 greed, 1–2, 196, 197, 204, 229, 238 Greenspan, Alan, 57, 203 Gruber, Jonathan, 245 Haifa, Israel, 158, 161 Harper, ‘Baldy’, 7 Harsanyi, John, 34–5, 40 Harvard Business Review, 153 Hayek, Friedrich and Arrow’s framework, 78–9 economics as all of life, 8 and Antony Fisher, 6–7 influence on Thatcher, 6, 7 and Keynesian economics, 5–6 and legal frameworks, 7* at LSE, 4 at Mont Pèlerin, 4, 5, 6, 15 and Olson’s analysis, 104 and public choice theory, 89 rejection of incentive schemes, 156 ‘spontaneous order’ idea, 30 The Road to Serfdom (1944), 4, 5, 6, 78–9, 94 healthcare, 91–2, 93, 178, 230, 236 hedge funds, 201, 219, 243–4 Heilbroner, Robert, The Worldly Philosophers, 252 Heller, Joseph, Catch-22, 98, 107, 243–4 Helmsley, Leona, 105 hero myths, 221–3, 224 Hewlett-Packard, 159 hippie countercultural, 100 Hoffman, Abbie, Steal This Book, 100 Holmström, Bengt, 229–30 homo economicus, 9, 10, 12, 140, 156–7 and Gary Becker, 126, 129, 133, 136 and behaviour of real people, 15, 136, 144–5, 171, 172, 173, 250–51 and behavioural economics, 170, 171, 172, 255 long shadow cast by, 248 and Nudge economists, 13, 172, 173, 174–5, 177 Hooke, Robert, 223 housing market, 128–9, 196, 240–41 separate doors for poor people, 243 Hume, David, 111 Huxley, Thomas, 114 IBM, 181, 222 identity, 32, 165–6, 168, 180 Illinois, state of, 46–7 immigration, 125, 146 Impossibility Theorem, 72, 73–4, 75, 89, 97 Arrow’s assumptions, 80, 81, 82 and Duncan Black, 77–8 and free marketeers, 78–9, 82 as misunderstood and misrepresented, 76–7, 79–82 ‘paradox of voting’, 75–7 as readily solved, 76–7, 79–80 Sen’s mathematical framework, 80–81 incentives adverse effect on autonomy, 164, 165–6, 168, 169–70, 180 authority figure–autonomy contradiction, 180 and behavioural economics, 171, 175, 176–7 cash and non-cash gifts, 161–2 context and culture, 175–6 contrast with rewards and punishments, 176–7 ‘crowding in’, 176 crowding out of prior motives, 160–61, 162–3, 164, 165–6, 171, 176 impact of economists’ ideas, 156–7, 178–80 and intrinsic motivations, 158–60, 161–3, 164, 165–6, 176 and moral disengagement, 162, 163, 164, 166 morally wrong/corrupting, 168–9 origins in behaviourism, 154 and orthodox theory of motivation, 157–8, 164, 166–7, 168–70, 178–9 payments to blood donors, 162–3, 164, 169, 176 as pervasive in modern era, 155–6 respectful use of, 175, 177–8 successful, 159–60 as tools of control/power, 155–7, 158–60, 161, 164, 167, 178 Indecent Proposal (film, 1993), 168 India, 123, 175 individualism, 82, 117 and Becker, 134, 135–8 see also freedom, individual Industrial Revolution, 223 inequality and access to lifeboats, 150–51 and climate change, 207–9 correlation with low social mobility, 227–8, 243 and demand for positional goods, 239–41 and economic imperialism, 145–7, 148, 151, 207 and efficiency wages, 237–8 entrenched self-deluding justifications for, 242–3 and executive pay, 215–16, 219, 224, 228–30, 234, 238 as falling in 1940–80 period, 215, 216 Great Gatsby Curve, 227–8, 243 hero myths, 221–3, 224 increases in as self-perpetuating, 227–8, 230–31, 243 as increasing since 1970s, 2–3, 215–16, 220–21 and lower growth levels, 239 mainstream political consensus on, 216, 217, 218, 219–21 marginal productivity theory, 223–4, 228 new doctrine on taxation since 1970s, 232–5 and Pareto, 217, 218–19, 220 poverty as waste of productive capacity, 238–9 public attitudes to, 221, 226–8 rises in as not inevitable, 220, 221, 242 role of luck downplayed, 222, 224–6, 243 scale-invariant nature of, 219, 220 ‘socialism for the rich’, 230 Thatcher’s praise of, 216 and top-rate tax cuts, 231, 233–5, 239 trickle-down economics, 232–3 US and European attitudes to, 226–7 ‘you deserve what you get’ belief, 223–6, 227–8, 236, 243 innovation, 222–3, 242 Inside Job (documentary, 2010), 88 Institute of Economic Affairs, 7–8, 15, 162–3 intellectual property law, 57, 68, 236 Ishiguro, Kazuo, Never Let Me Go, 148 Jensen, Michael, 229 Journal of Law and Economics, 49 justice, 1, 55, 57–62, 125, 137 Kahn, Herman, 18, 33 Kahneman, Daniel, 170–72, 173, 179, 202–3, 212, 226 Kennedy, President John, 139–40 Keynes, John Maynard, 11, 21, 162, 186, 204 and Buchanan’s ideology, 87 dentistry comparison, 258–9, 261 on economics as moral science, 252–3 Friedman’s challenge to orthodoxy of, 132 Hayek’s view of, 5–6 massive influence of, 3–4, 5–6 on power of economic ideas, 15 and probability, 185, 186–7, 188–9, 190, 210 vision of the ideal economist, 20 General Theory (1936), 15, 188–9 Khomeini, Ayatollah, 128 Khrushchev, Nikita, 139–40, 181 Kilburn Grammar School, 48 Kildall, Gary, 222 Kissinger, Henry, 184 Knight, Frank, 185–6, 212 Krugman, Paul, 248 Kubrick, Stanley, 35*, 139 labour child labour, 124, 146 and efficiency wages, 237–8 labour-intensive services, 90, 92–3 lumpenproletariat, 237 Olson’s hostility to unions, 104 Adam Smith’s ‘division of labour’ concept, 128 Laffer, Arthur, 232–3, 234 Lancet (medical journal), 257 Larkin, Philip, 67 law and economics movement, 40, 55, 56–63, 64–7 Lazear, Edward, ‘Economic Imperialism’, 246 legal system, 7* and blame for accidents, 55, 60–61 and Chicago School, 49, 50–52, 55 and Coase Theorem, 47, 49, 50–55, 63–6 criminal responsibility, 111, 137, 152 economic imperialist view of, 137 law and economics movement, 40, 55, 56–63, 64–7 ‘mimic the market’ approach, 61–3, 65 Posner’s wealth-maximization principle, 57–63, 64–7, 137 precautionary principle, 211–12, 214 transaction costs, 51–3, 54–5, 61, 62, 63–4, 68 Lehmann Brothers, 194 Lexecon, 58, 68 Linda Problem, 202–3 LineStanding.com, 123 Little Zheng, 123, 124 Lloyd Webber, Andrew, 234–5, 236 lobbying, 7, 8, 88, 115, 123, 125, 146, 230, 231, 238 loft-insulation schemes, 172–3 logic, mathematical, 74–5 The Logic of Life (Tim Harford, 2008), 130 London School of Economics (LSE), 4, 48 Long-Term Capital Management (LTCM), 201, 257 Machiavelli, Niccoló, 89, 94 Mafia, 30 malaria treatments, 125, 149 management science, 153–4, 155 Mandelbrot, Benoît, 195, 196, 201 Mankiw, Greg, 11 marginal productivity theory, 223–4 Markowitz, Harry, 196–7, 201, 213 Marx, Karl, 11, 101, 102, 104, 111, 223 lumpenproletariat, 237 mathematics, 9–10, 17–18, 19, 21–4, 26, 247, 248, 255, 259 of 2007 financial crash, 194, 195–6 and Ken Arrow, 71, 72, 73–5, 76–7, 82–3, 97 axioms (abstract assumptions), 198 fractals (scale-invariance), 194, 195–6, 201, 219 and orthodox decision theory, 190–91, 214 Ramsey Rule on discounting, 208–9, 212 and Savage, 189–90, 193, 197, 198, 199, 205 and Schelling, 139 Sen’s framework on voting systems, 80–81 standard deviation, 182, 192, 194 and stock market statistics, 190–91, 195–6 use of for military ends, 71–2 maximizing behaviour and Becker, 129–31, 133–4, 147 and catastrophe, 211 and Coase, 47, 55, 59, 61, 63–9 economic imperialism, 124–5, 129–31, 133–4, 147, 148–9 Posner’s wealth-maximization principle, 57–63, 64–7, 137 profit-maximizing firms, 228 see also wealth-maximization principle; welfare maximization McCluskey, Kirsty, 194 McNamara, Robert, 138 median voter theorem, 77, 95–6 Merton, Robert, 201 Meucci, Antonio, 222 microeconomics, 9, 232, 259 Microsoft, 222 Miles, David, 258 Mill, John Stuart, 102, 111, 243 minimum wage, national, 96 mobility, economic and social correlation with inequality, 226–8, 243 as low in UK, 227 as low in USA, 226–7 US–Europe comparisons, 226–7 Modern Times (Chaplin film, 1936), 154 modernism, 67 Moivre, Abraham de, 193 monetarism, 87, 89, 132, 232 monopolies and cartels, 101, 102, 103–4 public sector, 48–9, 50–51, 93–4 Mont Pèlerin Society, 3–9, 13, 15, 132 Morgenstern, Oskar, 20–22, 24–5, 28, 35, 124, 129, 189, 190 Mozart, Wolfgang Amadeus, 91, 92–3 Murphy, Kevin, 229 Mussolini, Benito, 216, 219 Nash equilibrium, 22–3, 24, 25, 27–8, 33–4, 41–2 Nash, John, 17–18, 22–3, 24, 25–6, 27–8, 33–4, 41–2 awarded Nobel Prize, 34–5, 38, 39, 40 mental health problems, 25, 26, 34 National Health Service, 106, 162 ‘neoliberalism’, avoidance of term, 3* Neumann, John von ambition to make economics a science, 20–21, 24–5, 26, 35, 125, 151, 189 as Cold War warrior, 20, 26, 138 and expansion of scope of economics, 124–5 as father of game theory, 18, 19, 20–22, 25, 26, 28, 30, 34, 41 final illness and death of, 19, 34, 35, 43–4 genius of, 19–20 as inspiration for Dr Strangelove, 19 and Nash’s equilibrium, 22–3, 25, 38* simplistic view of humanity, 28 theory of decision-making, 189, 190, 203 neuroscience, 14 New Deal, US, 4, 194, 231 Newton, Isaac, 223 Newtonian mechanics, 21, 24–5 Nixon, Richard, 56, 184, 200 NORAD, Colorado Springs, 181 nuclear weapons, 18–19, 20, 22, 27, 181 and Ellsberg, 200 and game theory, 18, 20, 21–2, 24, 27, 33–4, 35, 70, 73, 198 MAD (Mutually Assured Destruction), 35, 138 and Russell’s Chicken, 33–4 and Schelling, 138, 139 Nudge economists, 13, 171–5, 177–8, 179, 180, 251 Oaten, Mark, 121 Obama, Barack, 110, 121, 157, 172, 180 Olson, Mancur, 103, 108, 109, 119–20, 122 The Logic of Collective Action (1965), 103–4 On the Waterfront (Kazan film, 1954), 165 online invisibility, 100* organs, human, trade in, 65, 123, 124, 145, 147–8 Orwell, George, Nineteen Eighty-Four, 42–3 Osborne, George, 233–4 Packard, David, 159 Paine, Tom, 243 Pareto, Vilfredo 80/20 rule’ 218 and inequality, 217, 218–19, 220 life and background of, 216–17 Pareto efficiency, 217–18, 256* Paul the octopus (World Cup predictor, 2010), 133 pensions, workplace, 172, 174 physics envy, 9, 20–21, 41, 116, 175–6, 212, 247 Piketty, Thomas, 234, 235 plastic shopping bag tax, 159–60 Plato’s Republic, 100–101, 122 political scientists and Duncan Black, 78, 95–6 Black’s median voter theorem, 95–6 Buchanan’s ideology, 84–5 crises of the 1970s, 85–6 influence of Arrow, 72, 81–2, 83 see also public choice theory; social choice theory Posner, Richard, 54, 56–63, 137 ‘mimic the market’ approach, 61–3, 65 ‘The Economics of the Baby Shortage’ (1978), 61 precautionary principle, 211–12, 214 price-fixing, 101, 102, 103–4 Princeton University, 17, 19–20 Prisoner’s Dilemma, 26–8, 29–32, 42–3 prisons, cell upgrades in, 123 privatization, 50, 54, 88, 93–4 probability, 182–4 and Keynes, 185, 186–7, 188–9, 210 Linda Problem, 202–3 modern ideas of, 184–5 Ramsey’s personal probabilities (beliefs as probabilities), 187–8, 190, 197, 198, 199, 204–5 and Savage, 190, 193, 197, 198, 199, 203, 205 ‘Truth and Probability’ (Ramsey paper), 186–8, 189, 190 see also risk and uncertainty Proceedings of the National Academy of Sciences, 22 productivity Baumol’s cost disease, 90–92, 93, 94 and efficiency wages, 237–8 improvement in labour-intensive services, 92–3 labour input, 92 protectionism, 246, 255 psychology availability heuristic, 226 behaviourism, 154–8, 237 and behavioural economics, 12, 170–71 cognitive dissonance, 113–14 and financial incentives, 156–7, 158–60, 163–4, 171 framing effects, 170–71, 259 of free-riding, 113–14, 115 intrinsic motivations, 158–60, 161–3, 164, 165–6, 176 irrational behaviour, 12, 15, 171 learning of social behaviour, 163–4 moral disengagement, 162, 163, 164, 166 motivated beliefs, 227 ‘self-command’ strategies, 140 view of in game theory, 26–31 view of in public choice theory, 85–6 and welfare maximization, 149 ‘you deserve what you get’ belief, 223–6, 227–8, 236, 243 public choice theory as consensus view, 84–5 and crises of the 1970s, 85–6 foolish voter assumption, 86–8 ‘paradox of voter turnout’, 88–9, 95–6, 115–16 partial/self-contradictory application of, 86, 87–9 ‘political overload’ argument, 85, 86–7 ‘public bad, private good’ mantra, 93–4, 97 and resistance to tax rises, 94, 241 self-fulfilling prophecies, 95–7 and selfishness, 85–6, 87–8, 89, 94, 95–7 as time-bomb waiting to explode, 85 public expenditure in 1970s and ’80s, 89 Baumol’s cost disease, 90–92, 93, 94 and Keynesian economics, 4 and public choice theory, 85–8, 89, 241 and tax rises, 241–2 public-sector monopolies, 48–9, 50–51, 93–4 Puzzle of the Harmless Torturers, 118–19 queue-jumping, 123, 124 QWERTY layout, 42 racial discrimination, 126–7, 133, 136, 140 Ramsey, Frank, 186–8, 189, 190, 205, 208 Ramsey Rule, 208–9, 212 RAND Corporation, 17, 41, 103, 138, 139 and Ken Arrow, 70–71, 72–3, 74, 75–6, 77, 78 and behaviourism, 154 and Cold War military strategy, 18, 20, 21–2, 24, 27, 33–4, 70, 73, 75–6, 141, 200, 213 and Ellsberg, 182–4, 187, 197–8, 200 and Russell’s Chicken, 33 Santa Monica offices of, 18 self-image as defender of freedom, 78 rational behaviour assumptions in game theory, 18, 28, 29–32, 35–8, 41–3, 70, 124 axioms (abstract mathematical assumptions), 198 Becker’s version of, 128–9, 135, 140, 151 behavioural economics/Nudge view of, 173, 174–5 distinction between values and tastes, 136–8 economic imperialist view of, 135, 136–8, 140, 151 and free-riding theory, 100–101, 102, 103–4, 107–8, 109–10, 115–16 and orthodox decision theory, 198, 199 public choice theory relates selfishness to, 86 term as scientific-sounding cover, 12 see also homo economicus Reader’s Digest, 5, 6 Reagan, Ronald, 2, 87–8, 89, 104, 132 election of as turning point, 6, 216, 220–21 and top-rate tax cuts, 231, 233 regulators, 1–2 Chicago view of, 40 Reinhart, Carmen, 258 religion, decline of in modern societies, 15, 185 renewable energy, 116 rent-seeking, 230, 238 ‘right to recline’, 63–4 risk and uncertainty bell curve distribution, 191–4, 195, 196–7, 201, 203–4, 257 catastrophes, 181–2, 191, 192, 201, 203–4, 211–12 delusions of quantitative ‘risk management’, 196, 213 Ellsberg’s experiment (1961), 182–4, 187, 197, 198–200 errors in conventional thinking about, 191–2, 193–4, 195–7, 204–5, 213 financial orthodoxy on risk, 196–7, 201–2 and First World War, 185 and fractals (scale-invariance), 194, 195–6, 201 hasard and fortuit, 185* ‘making sense’ of through stories, 202–3 ‘measurable’ and ‘unmeasurable’ distinction, 185–6, 187–9, 190, 210–11, 212–13 measurement in numerical terms, 181–4, 187, 189, 190–94, 196–7, 201–2, 203–5, 212–13 orthodox decision theory, 183–4, 185–6, 189–91, 193–4, 201–2, 203–5, 211, 212–14 our contemporary orthodoxy, 189–91 personal probabilities (beliefs as probabilities), 187–8, 190, 197, 198, 199, 204–5 precautionary principle, 211–12, 214 pure uncertainty, 182–3, 185–6, 187–9, 190, 197, 198–9, 210, 211, 212, 214, 251 redefined as ‘volatility’, 197, 213 the Savage orthodoxy, 190–91, 197, 198–200, 203, 205 scenario planning as crucial, 251 Taleb’s black swans, 192, 194, 201, 203–4 ‘Truth and Probability’ (Ramsey paper), 186–8, 189, 190 urge to actuarial alchemy, 190–91, 197, 201 value of human life (‘statistical lives’), 141–5, 207 see also probability Robertson, Dennis, 13–14 Robinson, Joan, 260 Rodrik, Dani, 255, 260–61 Rogoff, Ken, 258 Rothko, Mark, 4–5 Rumsfeld, Donald, 232–3 Russell, Bertrand, 33–4, 74, 97, 186, 188 Ryanair, 106 Sachs, Jeffrey, 257 Santa Monica, California, 18 Sargent, Tom, 257–8 Savage, Leonard ‘Jimmie’, 189–90, 193, 203, 205scale-invariance, 194, 195–6, 201, 219 Scandinavian countries, 103, 149 Schelling, Thomas, 35* on access to lifeboats, 150–51 awarded Nobel Prize, 138–9 and Cold War nuclear strategy, 138, 139–40 and economic imperialism, 141–5 and game theory, 138–9 and Washington–Moscow hotline, 139–40 work on value of human life, 141–5, 207 ‘The Intimate Contest for Self-command’ (essay, 1980), 140, 145 ‘The Life You Save May be Your Own’ (essay, 1968), 142–5, 207 Schiphol Airport, Amsterdam, 172 Schmidt, Eric, 105 Scholes, Myron, 201 Schwarzman, Stephen, 235 Second World War, 3, 189, 210 selfishness, 41–3, 178–9 and Becker, 129–30 and defence of inequality, 242–3 as free marketeers’ starting point, 10–12, 13–14, 41, 86, 178–9 and game theory, 18 and public choice theory, 85–6, 87–8, 89, 94, 95–7 Selten, Reinhard, 34–5, 36, 38, 40 Sen, Amartya, 29, 80–81 service sector, 90–93, 94 Shakespeare, William, Measure for Measure, 169 Shaw, George Bernard, 101 Shiller, Robert, 247 Simon, Herbert, 223 Skinner, Burrhus, 154–5, 158 Smith, Adam, 101, 111, 122 The Wealth of Nations (1776), 10–11, 188–9 snowflakes, 195 social choice theory, 72 and Ken Arrow, 71–83, 89, 95, 97, 124–5, 129 and Duncan Black, 78, 95 and free marketeers, 79, 82 Sen’s mathematical framework, 80–81 social media, 100* solar panels, 116 Solow, Bob, 163, 223 Sorites paradox, 117–18, 119 sovereign fantasy, 116–17 Soviet Union, 20, 22, 70, 73, 82, 101, 104, 167, 237 spectrum auctions, 39–40, 47, 49 Stalin, Joseph, 70, 73, 101 the state anti-government attitudes in USA, 83–5 antitrust regulation, 56–8 dismissal of almost any role for, 94, 135, 235–6, 241 duty over full employment, 5 economic imperialist arguments for ‘small government’, 135 increased economic role from 1940s, 3–4, 5 interventions over ‘inefficient’ outcomes, 53 and monetarism, 87, 89 and Mont Pèlerin Society, 3, 4, 5 and privatization, 50, 54, 88, 93–4 public-sector monopolies, 48–50, 93–4 replacing of with markets, 79 vital role of, 236 statistical lives, 141–5, 207 Stern, Nick, 206, 209–10 Stigler, George, 50, 51, 56, 69, 88 De Gustibus Non Est Disputandum (with Becker, 1977), 135–6 Stiglitz, Joseph, 237 stock markets ‘Black Monday’ (1987), 192 and fractals (scale-invariance), 194, 195–6, 201 orthodox decision theory, 190–91, 193–4, 201 Strittmatter, Father, 43–4 Summers, Larry, 10, 14 Sunstein, Cass, 173 Nudge (with Richard Thaler, 2008), 171–2, 175 Taleb, Nassim, 192 Tarski, Alfred, 74–5 taxation and Baumol’s cost disease, 94 and demand for positional goods, 239–41 as good thing, 231, 241–2, 243 Laffer curve, 232–3, 234 new doctrine of since 1970s, 232–4 property rights as interdependent with, 235–6 public resistance to tax rises, 94, 239, 241–2 and public spending, 241–2 revenue-maximizing top tax rate, 233–4, 235 tax avoidance and evasion, 99, 105–6, 112–13, 175, 215 ‘tax revolt’ campaigns (1970s USA), 87 ‘tax as theft’ culture, 235–6 top-rate cuts and inequality, 231, 233–5, 239 whines from the super-rich, 234–5, 243 Taylor, Frederick Winslow, 153–4, 155, 167, 178, 237 Thaler, Richard, 13 Nudge (with Cass Sunstein, 2008), 171–2, 175 Thatcher, Margaret, 2, 88, 89, 104, 132 election of as turning point, 6, 216, 220–21 and Hayek, 6, 7 and inequality, 216, 227 privatization programme, 93–4 and top-rate tax cuts, 231 Theory of Games and Economic Behavior (Von Neumann and Morgenstern, 1944), 20, 21, 25, 189 Titanic, sinking of (1912), 150 Titmuss, Richard, The Gift Relationship, 162–3 tobacco-industry lobbyists, 8 totalitarian regimes, 4, 82, 167–8, 216, 219 see also Soviet Union trade union movement, 104 Tragedy of the Commons, 27 Truman, Harry, 20, 237 Trump, Donald, 233 Tucker, Albert, 26–7 Tversky, Amos, 170–72, 173, 202–3, 212, 226 Twitter, 100* Uber, 257 uncertainty see risk and uncertainty The Undercover Economist (Tim Harford, 2005), 130 unemployment and Coase Theorem, 45–7, 64 during Great Depression, 3–4 and Keynesian economics, 4, 5 United Nations, 96 universities auctioning of places, 124, 149–50 incentivization as pervasive, 156 Vietnam War, 56, 198, 200, 249 Villari, Pasquale, 30 Vinci, Leonardo da, 186 Viniar, David, 182, 192 Volkswagen scandal (2016), 2, 151–2 Vonnegut, Kurt, 243–4 voting systems, 72–4, 77, 80, 97 Arrow’s ‘Independence of Irrelevant Alternatives’, 81, 82 Arrow’s ‘Universal Domain’, 81, 82 and free marketeers, 79 ‘hanging chads’ in Florida (2000), 121 recount process in UK, 121 Sen’s mathematical framework, 80–81 Waldfogel, Joel, 161* Wanniski, Jude, 232 Watertown Arsenal, Massachusetts, 153–4 Watson Jr, Thomas J., 181 wealth-maximization principle, 57–63 and Coase, 47, 55, 59, 63–9 as core principle of current economics, 253 created markets, 65–7 extension of scope of, 124–5 and justice, 55, 57–62, 137 and knee space on planes, 63–4 practical problems with negotiations, 62–3 and values more important than efficiency, 64–5, 66–7 welfare maximization, 124–5, 129–31, 133–4, 148–9, 176 behavioural economics/Nudge view of, 173 and vulnerable/powerless people, 146–7, 150 welfare state, 4, 162 Wilson, Charlie, 215 Wittgenstein, Ludwig, 186, 188 Wolfenschiessen (Swiss village), 158, 166–7 Woolf, Virginia, 67 World Bank, 96 World Cup football tournament (2010), 133 World Health Organization, 207 Yale Saturday Evening Pest, 4–5 Yellen, Janet, 237 THE BEGINNING Let the conversation begin … Follow the Penguin twitter.com/penguinukbooks Keep up-to-date with all our stories youtube.com/penguinbooks Pin ‘Penguin Books’ to your pinterest.com/penguinukbooks Like ‘Penguin Books’ on facebook.com/penguinbooks Listen to Penguin at soundcloud.com/penguin-books Find out more about the author and discover more stories like this at penguin.co.uk ALLEN LANE UK | USA | Canada | Ireland | Australia India | New Zealand | South Africa Allen Lane is part of the Penguin Random House group of companies whose addresses can be found at global.penguinrandomhouse.com First published 2019 Copyright © Jonathan Aldred, 2019 The moral right of the author has been asserted Jacket photograph © Getty Images ISBN: 978-0-241-32544-5 This ebook is copyright material and must not be copied, reproduced, transferred, distributed, leased, licensed or publicly performed or used in any way except as specifically permitted in writing by the publishers, as allowed under the terms and conditions under which it was purchased or as strictly permitted by applicable copyright law.

How to Create a Mind: The Secret of Human Thought Revealed
by Ray Kurzweil
Published 13 Nov 2012

For a more complete description of this argument, see the section “[The Impact…] on the Intelligent Destiny of the Cosmos: Why We Are Probably Alone in the Universe” in chapter 6 of The Singularity Is Near by Ray Kurzweil (New York: Viking, 2005). 5. James D. Watson, Discovering the Brain (Washington, DC: National Academies Press, 1992). 6. Sebastian Seung, Connectome: How the Brain’s Wiring Makes Us Who We Are (New York: Houghton Mifflin Harcourt, 2012). 7. “Mandelbrot Zoom,” http://www.youtube.com/watch?v=gEw8xpb1aRA; “Fractal Zoom Mandelbrot Corner,” http://www.youtube.com/watch?v=G_GBwuYuOOs. Chapter 1: Thought Experiments on the World 1. Charles Darwin, The Origin of Species (P. F. Collier & Son, 1909), 185/95–96. 2. Darwin, On the Origin of Species, 751 (206.1.1-6), Peckham’s Variorum edition, edited by Morse Peckham, The Origin of Species by Charles Darwin: A Variorum Text (Philadelphia: University of Pennsylvania Press, 1959). 3.

…

As MIT neuroscientist Sebastian Seung says, “Identity lies not in our genes, but in the connections between our brain cells.”6 We need to distinguish between true complexity of design and apparent complexity. Consider the famous Mandelbrot set, the image of which has long been a symbol of complexity. To appreciate its apparent complication, it is useful to zoom in on its image (which you can access via the links in this endnote).7 There is endless intricacy within intricacy, and they are always different. Yet the design—the formula—for the Mandelbrot set couldn’t be simpler. It is six characters long: Z = Z2 + C, in which Z is a “complex” number (meaning a pair of numbers) and C is a constant. It is not necessary to fully understand the Mandelbrot function to see that it is simple. This formula is applied iteratively and at every level of a hierarchy.

…

Its repeating structure is not as simple as that of the six-character formula of the Mandelbrot set, but it is not nearly as complex as the millions of quotations on the brain’s complexity would suggest. This neocortical design is repeated over and over at every level of the conceptual hierarchy represented by the neocortex. Einstein articulated my goals in this book well when he said that “any intelligent fool can make things bigger and more complex…but it takes…a lot of courage to move in the opposite direction.” One view of the display of the Mandelbrot set, a simple formula that is iteratively applied. As one zooms in on the display, the images constantly change in apparently complex ways.

Money Changes Everything: How Finance Made Civilization Possible
by William N. Goetzmann
Published 11 Apr 2016

It was a nice refinement of Regnault’s hypothesis articulated almost precisely a century prior. Although Mandelbrot ultimately developed a fractal-based option-pricing model with two of his students that allowed for extreme events and a more general stochastic process, for various reasons Mandelbrot never saw it adopted in practice to any great extent. I suspect that this is because the solution, while potentially useful, is complicated and contradicts most other tools that quantitative financiers use. With Mandelbrot’s models, it is all or nothing. You have to take a leap beyond the world of Brownian motion and throw out old friends like Bernoulli’s law of large numbers.

…

In fact, the non-normality of security prices had been well known for decades prior to the crash of 2008—and for that matter the crash of 1987, as was the potential for extreme events. The “high priest” of non-normality before Nassim Taleb ever started to trade or write about extreme events was Benoit Mandelbrot, the creator of fractal geometry, a mathematician who both carried the mantle of French mathematical finance and who also believed he had discovered its fatal flaw. Mandelbrot was a student of Paul Lévy’s—the son of the man who gave Bachelier bad marks at his examination at the École Polytechnique in 1900. Lévy’s research focused on “stochastic processes”: mathematical models that describe the behavior of some variable through time.

…

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. The crash of 1987 was not a surprise to him—he took it as a vindication of his theory.

How Not to Network a Nation: The Uneasy History of the Soviet Internet (Information Policy)
by Benjamin Peters
Published 2 Jun 2016

These postwar happenings are described briefly below. In 1947, the year before he published Cybernetics with the MIT Press, Wiener attended Szolem Mandelbrot’s congress on harmonic analysis in Nancy, France, which resulted in a French book contract for the book that, while initially resisted by the MIT Press, sold a sensational 21,000 copies over three reprints in six months after its release in 1948. Three years later, in 1951, at the invitation of Benoit Mandelbrot, the founder of fractals and Szolem’s nephew, Wiener returned to lecture at Collège de France. Between 1947 and 1952, a flurry of press coverage and public controversy sprung up between two camps of anticybernetic communists and anticommunist cyberneticists.32 (Jacques Lacan, who served in the French army, may very well have been among the anticommunists and early cyberneticists at the time.)

…

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.

…

R., 19, 27, 91, 97 Liebniz, Gottlob, 67 Linear modeling, 68–69, 205 Linear programming, 68 Llull, Ramon, 42 “A Logical Calculus of the Ideas Immanent in Nervous Activity,” 18 Losev, V., 119 L’viv System, 154 Lyapunov, Aleksei, 34–36, 40, 43–44, 46, 82, 85, 89, 169, 183, 216 Lysenko, Trofim, 32, 40 MacKay, Donald, 27 Macropiping, 118 Macy Conferences on Cybernetics, 18–19 “The Main Features of Cybernetics,” 35–39 Malinovksy, Boris, 117, 154, 166–167 “Man-Computer Symbiosis,” 91 Mandelbrot, Benoit, 25, 28 Mandelbrot, Szolem, 25, 28 Mansfield amendments, 93 Market economy, 22 “Mark III, a Calculator,” 30 Markov, Andrei, Jr., 34, 42, 46 Marx, Karl, 58, 65, 74, 199, 204 Marxism-Leninism, 33, 139, 194–195 Mar’yanovich, T. P., 118 Materialism, 39–40 “A Mathematical Theory of Communication,” 98 Matiukhin, Nikolai, 84–85, 91 “The Matter of the Whole Country,” 167 Maturana, Humberto, 27, 96 McCarthy, John, 178 McCulloch, Warren, 18–19, 22–23, 27, 54, 95–96, 100, 119–120, 193, 202 Mead, Margaret, 19 Media technologies, 205–206 Mendeleev, Dmitri, 32 Merton, Robert, 97 MESM (malaya electronicheskaya schetnaya mashina), 126, 128 Messages, theory of, 17–18, 20 Microcomputers, 127.

The Man From the Future: The Visionary Life of John Von Neumann
by Ananyo Bhattacharya
Published 6 Oct 2021

When a Hungarian-speaking factory worker in Tennessee wrote to him in 1939 asking how he could learn secondary school mathematics, von Neumann asked his friend Ortvay to send school books.4 Benoît Mandelbrot, whose stay at the IAS had been sponsored by von Neumann, unexpectedly found himself in his debt again many years later. Sometime after von Neumann’s death, prompted by a clash of personalities with his manager at IBM, Mandelbrot went looking for a new job – and found that the way had been made easier for him. Von Neumann had spread the word widely that his research could be of great significance – but was very risky. ‘He may really sink,’ von Neumann warned them, says Mandelbrot. ‘If he’s in trouble, please help him.’5 Which of these was the real von Neumann?

…

The truth was that von Neumann had been unhappy at the IAS for several years before his death. ‘Von Neumann, when I was there at Princeton, was under extreme pressure,’ says Benoît Mandelbrot, who had come to the IAS in 1953 at von Neumann’s invitation, ‘from mathematicians, who were despising him for no longer being a mathematician; by the physicists, who were despising him for never having been a real physicist; and by everybody for having brought to Princeton this collection of low-class individuals called “programmers”’. ‘Von Neumann,’ Mandelbrot continues, ‘was simply being shunned. And he was not a man to take it.’102 Von Neumann had explored several offers before settling on a free-ranging ‘professor at large’ position at UCLA, where he had been promised state-of-the-art computing facilities would be established.

…

Stan isław Ulam,’John von Neumann 1903–1957’, Bulletin of the American Mathematical Society, 64(3) (1958), pp. 1–49. 100. John von Neumann, Documentary Mathematical Association of America, 1966. Many thanks to David Hoffman, the film’s producer, for sending me the DVD in 2019. Now available to watch here: https://archive.org/details/JohnVonNeumannY2jiQXI6nrE. 101. Macrae, John von Neumann. 102. ‘Benoît Mandelbrot – Post-doctoral Studies: Weiner and Von Neumann (36/144)’, Web of Stories – Life Stories of Remarkable People, https://www.youtube.com/watch?v=U9kw6Reml6s. 103. https://rjlipton.wpcomstaging.com/the-gdel-letter/. Also see Richard J. Lipton, 2010, The P=NP Question and Gödel’s Lost Letter, Springer, New York. 104.

Wireless
by Charles Stross
Published 7 Jul 2009

The terror is fading, replaced by a sense of disappointment. I trail after him. “The staff have names for you all. Turing, Cantor, Mandelbrot, and Godel. You’re not Cantor or Turing. That makes you one of Mandelbrot or Godel.” “So you’re undecided?” There’s a coffee table with a pile of newspapers on it in the middle of the dayroom, a couple of elderly chesterfields, and three armchairs that could have been looted from an old-age home sometime before the First World War. “And in any case, we haven’t been formerly introduced. So you might as well call me Alice.” Alice—or Mandelbrot or Godel or whoever he is—sits down. The armchair nearly swallows him. He beams at my bafflement, delighted to have found a new victim for his doubtless-ancient puns.

…

He’s wearing tinted round spectacles that look like they fell off the back of a used century. “What? What?” he demands querulously. “He doesn’t know anything,” Alice confides in—this must be Godel, I realize, which means Alice is Mandelbrot—Godel, then with a wink at me, “He doesn’t know anything, either.” Godel shuffles into the restroom. “Is it teatime already?” “No!” Mandelbrot puts his mug down. “Get a watch!” “I was only asking because Alan and Georg are still playing—” This has gone far enough. Apprehension dissolves into indignation. “It’s not chess!” I point out. “And none of you are insane.”

…

It landed on my boss’s desk, and he sent me to find out why.” THUD. Godel bounces off the wall again, showing remarkable resilience for such old bones. “Do shut up, old fellow,” chides Mandelbrot. “You’ll attract Her attention.” “I’ve met someone with K. Syndrome, and I shared a house with some real lunatics once,” I hint. “Save it for someone who cares.” “Oh bother,” says Godel, and falls silent. “We’re not mad,” Mandelbrot admits. “We’re just differently sane.” “Then why are you here?” “Public health.” He takes a sip of tea and pulls a face. “Everyone else’s health. Tell me, do they still keep an IBM 1602 in the back of the steam-ironing room?”

Places of the Heart: The Psychogeography of Everyday Life
by Colin Ellard
Published 14 May 2015

Fractal dimensions for scenes lie between the numbers one and two, suggesting that they are neither quite one- nor two-dimensional geometric objects. In fact, the very name “fractal” is meant to convey this property of having a fractional dimensionality lying somewhere between whole numbers. Though this might seem a bit puzzling to picture, what it really means is that fractal objects defy some of the rules of conventional nonfractal geometry. In his original formulation of fractal dimension, the Polish mathematician Benoit Mandelbrot considered how one might go about measuring the length of a jagged coastline using a measuring stick. Because it contains a vast number of detailed curves and angles, the measured length of the coastline will depend on the length of the stick.

…

Indeed, Jackson Pollock’s paintings, though they may seem to be nothing more than a random collection of lines and splashes of color, when subjected to mathematical routines, reveal strong underlying fractal properties.14 The degree to which a visual scene is fractal in nature can be measured with any one of a number of mathematical routines that yield a number known as the scene’s fractal dimension. Understanding exactly how to interpret a given fractal dimension would take us too far into some complicated mathematics, but one way to think about this number is to think first of the dimensionality of simple geometric objects. A line has one dimension. A plane has two dimensions. A sphere has three dimensions. Fractal dimensions for scenes lie between the numbers one and two, suggesting that they are neither quite one- nor two-dimensional geometric objects.

…

As the stick becomes shorter and shorter, the length of the coastline will seem to become longer and longer. Fractal dimension describes the relationship between the length of the measuring stick and the measured length of the coastline. If the coastline happened to be a perfect straight line, its fractal dimension would be 1, so not really a fractal at all. Using mathematical tools that aren’t much different from unleashing a range of measuring sticks of different sizes on an image, it’s possible to arrive at a number that characterizes the fractal dimension of the image. When these tools are applied to scenes of nature, the measured fractal dimension often lands at a value somewhere between 1.3 and 1.5.

Think Twice: Harnessing the Power of Counterintuition
by Michael J. Mauboussin
Published 6 Nov 2012

A number of high-profile financial blowups, including Long-Term Capital Management, show the danger of this bias.15 Benoit Mandelbrot, a French mathematician and the father of fractal geometry, was one of the earliest and most vocal critics of using normal distributions to explain how asset prices move.16 His chapter in The Random Character of Stock Market Prices, published in 1964, created a stir because it demonstrated that asset price changes were much more extreme than previous models had assumed. Paul Cootner, an economist at MIT and the editor of the volume, was unconvinced of Mandelbrot’s case. “If [Mandelbrot] is right,” he wrote, “almost all of our statistical tools are obsolete.

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Almost without exception, past econometric work is meaningless.”17 But Cootner could rest easy, because Mandelbrot’s ideas never penetrated mainstream economics. Philip Mirowski, a historian and philosopher of economic thought at Notre Dame, notes, “The simple historical fact is that [Mandelbrot’s economic ideas] have been by and large ignored, with some few exceptions… which seem to have been subsequently abandoned by their authors.”18 A few years ago, I went to a dinner in New York City that included Mandelbrot. I showed up late and saw just two seats free. Mandelbrot arrived shortly after me and explained that his tardiness was due to an incompetent driver, whom he fired. Mandelbrot then leaned over and asked, “Would you mind giving me a ride home?”

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Taleb, The Black Swan, discusses a similar concept he calls the “ludic fallacy.” 15. Donald MacKenzie, An Engine, Not a Camera: How Financial Models Shape Markets (Cambridge: MIT Press, 2006). 16. Benoit Mandelbrot, “The Variation of Certain Speculative Prices,” in The Random Character of Stock Market Prices, ed. Paul H. Cootner, (Cambridge: MIT Press, 1964), 369–412. This is also a core theme of Taleb, The Black Swan. See also Benoit Mandelbrot and Richard L. Hudson, The (Mis)Behavior of Markets (New York: Basic Books, 2004). 17. Paul H. Cootner, “Comments on The Variation of Certain Speculative Prices,” in Cootner, The Random Character of Stock Market Prices, 413–418. 18.

What We Cannot Know: Explorations at the Edge of Knowledge
by Marcus Du Sautoy
Published 18 May 2016

The strip has the surprising property that if you cut it down the middle, it doesn’t come apart into two loops, as you might expect, but remains intact. It’s still a single loop but with two twists in it. The cracker I ended up with wasn’t too bad, even if I say so myself. Even the joke was quite funny. What does the B in Benoit B. Mandelbrot stand for? Benoit B. Mandelbrot. (If you still aren’t laughing, the thing you’re missing is that Mandelbrot discovered the fractals that featured in my First Edge, those geometric shapes that never get simpler, however much you zoom in on them.) The paradox was one of my all-time favourites. It consisted of the two statements that opened this chapter, one on either side of a card.

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Our problem as humans, when it comes to appreciating the chance of a miracle such as life occurring, is that we have not evolved minds able to navigate very large numbers. Probability is therefore something we have little intuition for. THE FRACTAL TREE OF LIFE But it’s not only the mathematics of probability that is at work in evolution. The evolutionary tree itself has an interesting quality that is similar to the shapes that appear in chaos theory, a quality known as fractal. The fractal evolutionary tree. The evolutionary tree is a picture of the evolution of life on Earth. Making your way through the tree corresponds to a movement through time. Each time the tree branches, this represents the evolution of a new species.

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The nature of the tree is such that the overall shape seems to be repeated on smaller and smaller scales. This is the characteristic feature of a shape mathematicians call a fractal. If you zoom in on a small part of the tree it looks remarkably like the large-scale structure of the tree. This self-similarity means that it is very difficult to tell at what scale we are looking at the tree. This is the classic characteristic of a fractal. Fractals are generally the geometric signature of a chaotic system, so it is suggestive of chaotic dynamics at work in evolution: the small changes in the genetic code that can result in huge changes in the outcome of evolution.

The Joys of Compounding: The Passionate Pursuit of Lifelong Learning, Revised and Updated
by Gautam Baid
Published 1 Jun 2020

Instead, they cropped up about once every three to four years [emphasis added].9 Benoit Mandelbrot was a Polish-born mathematician and polymath who developed a new branch of mathematics known as fractal geometry, which recognizes the hidden order in the seemingly disordered, the plan in the unplanned, the regular pattern in the irregularity of nature. Mandelbrot found that the underlying power law that was evident in random patterns in nature also applies to the positive and negative price movements of many financial instruments. The movement of stock prices followed a power law rather than a Gaussian or normal distribution. In his book The (Mis)Behavior of Markets, written with Richard Hudson, Mandelbrot invoked the important concept of “clustering”: Market turbulence tends to cluster.

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(Hoboken, NJ: Wiley, 2005). 7. Quoted in Foulke, “Warren Buffett on LTCM.” 8. Buffett FAQ, 2006 Berkshire Hathaway Annual Meeting, http://buffettfaq.com. 9. Sebastian Mallaby, More Money Than God: Hedge Funds and the Making of a New Elite (London: Penguin, 2011). 10. Benoit Mandelbrot and Richard L. Hudson, The (Mis)Behavior of Markets: A Fractal View of Financial Turbulence (New York: Basic Books, 2006), 20, 217, 248. 11. Benjamin Graham and David Dodd, Security Analysis: The Classic 1934 Edition (New York: McGraw-Hill Education, 1996). 12. Howard Marks, The Most Important Thing Illuminated: Uncommon Sense for the Thoughtful Investor (New York: Columbia University Press, 2013). 13.

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Maloney, Michael, and H. Harold Mulherin. “The Complexity of Price Discovery in an Efficient Market: The Stock Market Reaction to the Challenger Crash.” Journal of Corporate Finance 9, no. 4 (2003): 453–479. https://www.sciencedirect.com/science/article/pii/S092911990200055X. Mandelbrot, Benoit, and Richard L. Hudson. The (Mis)Behavior of Markets: A Fractal View of Financial Turbulence. New York: Basic Books, 2006. Marks, Howard. “Dare to Be Great.” Memo to Oaktree clients. Oaktree, September 7, 2006. https://www.oaktreecapital.com/docs/default-source/memos/2006-09-07-dare-to-be-great.pdf. ——. “Howard Marks: Investing in an Unknowable Future.”

Memory Machines: The Evolution of Hypertext
by Belinda Barnet
Published 14 Jul 2013

Machine-Enhanced (Re)minding: The Development of Storyspace  115 Conclusion 137 Notes 143 Bibliography 149 Index 157 Foreword TO MANDELBROT IN HEAVEN Stuart Moulthrop A certain confusion may befall us when we praise pioneers, especially while they are still with us. This hazard was apparent to the troubadour and know-hit wonder Jonathan Coulton, when he wrote one of the great tunes of popular science, ‘Mandelbrot Set’: Mandelbrot’s in heaven At least he will be when he’s dead Right now he’s still alive and teaching math at Yale The song was released in October 2004, giving it a nice run of six years before its lyrics were compromised by Benoît Mandelbrot’s passing in 2010. Even thus betrayed to history, ‘Mandelbrot Set’ still marks the contrast between extraordinary and ordinary lives, dividing those who change the world, in ways tiny or otherwise, from those who sing about them or merely ruminate.

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For Mum and Dad, because you believed in me; For Ollie, Isabel and Laura, because I believe in you There is a vision offered in these pages, simple unified and sweeping: it is a unified concept of interconnected ideas and data, and of how these ideas and data may be stored and published […] this new way of handling information is to represent its true interconnections. —Ted Nelson, Literary Machines CONTENTS Foreword To Mandelbrot in Heaven Stuart Moulthrop Preface Chapter 1. Technical Evolution  ix xix 1 Chapter 2. Memex as an Image of Potentiality  11 Chapter 3. Augmenting the Intellect: NLS 37 Chapter 4. The Magical Place of Literary Memory: Xanadu 65 Chapter 5. Seeing and Making Connections: HES and FRESS 91 Chapter 6. Machine-Enhanced (Re)minding: The Development of Storyspace  115 Conclusion 137 Notes 143 Bibliography 149 Index 157 Foreword TO MANDELBROT IN HEAVEN Stuart Moulthrop A certain confusion may befall us when we praise pioneers, especially while they are still with us.

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Genius finds ‘infinite complexity […] defined by simple rules’, as Coulton also sings, though any such simplicity depends crucially on the beholder. Cosmic rules may have gorgeous clarity to a mind like Mandelbrot’s. For the rest of us, the complexities of the universe are more often bewildering. Nothing is more bewildering, of course, than genius. As simple minds see it, those who light the world go to heaven before their time, and the pathos of this fate stamps the work of any chronicler with embarrassment. The singer, enraptured, invents a rapture: Mandelbrot’s in heaven – well, actually not (originally not, though he is now) – you get the idea. Time is not on our side when we try to give genius its due; we get no help, likewise, from metaphysics.

Radical Uncertainty: Decision-Making for an Unknowable Future
by Mervyn King and John Kay
Published 5 Mar 2020

The application of power laws to economics was pioneered in the early 1960s by the Polish-French-American mathematician Benoit Mandelbrot. He established that movements in cotton prices could be described by a power law. 9 Power laws have a property of ‘scale invariance’. If you look at a snowflake under a powerful microscope, the shape of every small part you see is the same as the shape you see with the naked eye. The property which creates this beautiful structure is called fractal geometry. The graph of securities price movements in every minute looks very similar to the graph of securities price movements on every day.

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Kung Bushmen, 216 , 217 , 325 Lampert, Eddie, 287–9 , 292 Lampson, Butler, 28 Landon, Alf, 240 , 390 Laplace, Pierre-Simon, 70 , 199 Lascaux cave paintings, 216 law: civil law and common law jurisdictions, 205–6 , 213–14 ; ‘eat what you kill’ policies, 409 ; legal reasoning, 194–5 , 196–8 , 205–7 , 210–14 , 410 , 415 , 416 ; presumption of innocence, 210 ; and probabilistic reasoning, 196 , 197 , 198–203 , 206–7 , 210–12 , 214 ; ‘the prosecutor’s fallacy’, 201–2 , 203 ; ‘reasonable doubt’ concept, 198 , 201 , 205–6 , 211–12 ; and ‘rodeo problem’, 206–7 ; search for ‘best explanation’, 211–14 ; and statistical discrimination, 207–8 Lawson, Nigel, 291 Leamer, Edward, 100 Leamon, Nathan, The Test , 268 Lee, General Robert E., 188 Leeson, Nick, 411 Lehman Brothers, failure of (2008), 5 , 36 , 158–9 , 267 , 410–11 , 412 Leonardo da Vinci, 219 , 421 , 428 LeRoy, Stephen, 74 , 78 Let’s Make a Deal (US quiz show), 62–3 , 65 , 69 Lewis, Michael, 135 , 215 ; The Undoing Project , 121 , 393–4 Libet, Benjamin, 171 LIBOR scandal, 192 Libratus (poker-playing computer), 263 life expectancy, 43 , 56 , 57 , 161 , 232–3 Lincoln, Abraham, 266 , 269 , 290 Literary Digest , 240 , 390 Livy (Roman historian), 54 , 186 , 187 Lloyds Bank, 325 Lloyd’s of London, 55–6 , 322–4 , 325 , 326 Loch Ness monster, 325 , 326 Loewenstein, George, 128–9 , 135 , 310 London School of Economics, 339 , 382–3 Long Term Capital Management, 153 , 309 Louis XIV, King of France, 411 Lucas, Robert, 36 , 92 , 93 , 338–9 , 341 , 345 , 346 , 348 , 354 Maa-speaking people of East Africa, 160–1 , 189 MacArthur, Douglas, 292–3 , 420 Macartney, Lord, 419 Mackay, Charles, Extraordinary Popular Delusions and the Madness of Crowds , 315 Malthus, Thomas, 253 , 358–61 , 362–3 Mandelbrot, Benoit, 238 Manhattan grid plan, 424–5 Manville, Brook, 374 Mao Tse-tung, 4–5 , 292 Markowitz, Harry, 307 , 308 , 309–10 , 318 , 320 , 332 , 333 , 366 Márquez, Gabriel García, 226 Marshall, Alfred, 276 , 381 , 382 Marshall, Barry, 284 , 306 Marshall, George, 292 Marxism, 220 Mary Celeste mystery (1872), 33–4 , 44 Mary Poppins (film, 1964), 306 mathematical reasoning, xiv , 12 , 19 , 42–3 , 47 , 53–4 , 93 , 343 , 401 , 404–5 ; appropriate use of, 383 ; fixed point theorems, 254 ; fractal geometry, 238–9 ; ‘grand auction’ of Arrow and Debreu, 343–5 ; and historical narratives, 188 ; small world applications of, 175–6 Matsushita, Konosuke, 410 Mauss, Marcel, The Gift (1925), 190–1 Max Planck Institute, Berlin, 152 maximising behaviour, xiv , 258 , 381–2 ; ‘ambiguity aversion’ concept, 135 ; and evolutionary rationality, 157 , 158 , 166–7 ; and greed, 127–8 , 409 ; limits to, xiv–xv , 41–4 , 152 , 171–2 , 310 , 345 , 382 , 400–1 , 435–44 ; maximising expected utility, 108 , 111–14 , 115–18 , 129–30 , 400 ; and utilitarian theory, 110–11 Maxwell, Robert, 312 , 313 May, Robert, 375 Maynard, John, 156 McHugh, Dodd, 425 McLaren racing team, 391 McNamara, Robert, 281–2 , 298–300 McRaven, Admiral William, 298 Meadow, Professor Sir Roy, 197–8 , 200 , 201 medicine, 22 , 32 , 39–40 , 88–9 , 383 , 384 , 387 ; computer technologies, 185–6 ; doctors’ decision-making, 184–6 , 194 , 398–9 ; HIV infections, 375–6 ; infectious diseases, 282–3 , 285 ; puerperal fever, 282–3 , 306 ; ‘randomised controlled trials’ (RCTs), 243–5 ; screening for cancer, 66–7 , 206 ; stomach ulcers, 284 , 306 ; twentieth century improvements, 57 ; and uncertainty, 44–5 mercantilism, 249 Mercier, Hugo, 162 , 272 , 415 Méré, Chevalier de, 53 , 59 , 60 , 61 Merton, Robert C., 309 Merton, Robert K., 35–6 , 309 MESSENGER (NASA probe), 18–19 , 26 , 35 , 218 , 394 meteorology, 23 , 43 , 101–2 , 406 Michelangelo, 421 , 428 Michelson, Albert, 430 Microsoft, 29 , 30–1 migration, 369–70 , 372 ; European to USA, 427 military campaigns and strategy, 3–4 , 24–6 , 292–3 , 294–5 , 298–300 , 412–13 , 433 military-industrial complex, 294 Mill, John Stuart, 110 , 429–30 ; System of Logic (1843), 70 Miller, Arthur, Death of a Salesman , 220 Ming emperors, 419 Mintzberg, Henry, 296 , 410 Mirowski, Philip, 388 MMR triple vaccine, 394 mobile phones, 30–1 , 38–9 , 257 , 344 models: appropriate use of, 376–7 ; of Canadian fisheries, 368–9 , 370 , 371–2 , 423 ; consulting firms, 180 , 182–3 , 275–6 , 365 , 370–1 , 405 ; EU migration models, 370 , 372 ; invented numbers in, 320 , 363–4 , 365 , 371 , 373 , 404 , 405 , 423 ; maps as not the territory, 391–4 ; microeconomic research, 382 , 392 ; misuse/abuse of, 312–13 , 320 , 368–76 , 405 ; at NASA, 373–4 , 391–2 ; policy-based evidence, 370–1 , 373–4 , 405 , 412–13 ; and public consultation, 372 ; reproduction of large/real-world, 390–2 ; role of incentives/targets, 409 ; stationarity as assumed, 333 , 339 , 340–1 , 349 , 350 , 366–7 , 371–2 ; as tools, 384–6 ; transport modelling, 363–5 , 370 , 371 , 372 , 396 , 404 , 407 ; WebTAG, 363–4 , 365 , 371 , 404 , 407 ; WHO HIV model, 375–6 ; see also economic models; small world models Moivre, Abraham de, 57–8 , 233 money supply, 96 Moneyball (film, 2011), 273 MONIAC (Monetary National Income Analogue Computer) machine, 339 ‘Monte Carlo simulations’, 365 Montgomery, Bernard Law, 293 Moore, Dudley, 97 Morgenstern, Oskar, 111 , 133 , 435–7 Moses, Robert, 425 Mourinho, José, 265 Mrs White’s Chocolate House (St James’s), 55 Murray, Bill, 419 Musk, Elon, 128 , 130 , 307 Mussabini, Sam, 273 mutualisation: in insurance markets, 325–6 ; and !

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If the variable is the product of many such independent factors, the resulting frequency distribution will be lognormal . 5 Table 205, Statistical Abstract of the United States: 2011 , p. 135. 6 The distribution was first published by Poisson, together with his probability theory, in 1837 in his work Recherches sur la Probabilité des Jugements en Matière Criminelle et en Matière Civile . 7 Zipf (1935 and 1949). 8 Technically, the expectation will be infinite if the exponent is less than 2 (and the second and higher moments are always infinite). 9 Mandelbrot (1963). 10 An exception is the excellent survey of power laws by Gabaix (2009). 11 Midanik (1982). 12 For further analysis, see Nate Silver’s discussion of how polls performed in the 2016 presidential election (2016). 13 Lowe et al. (2017). 14 Barns (2015). 15 Bohannon (2015). 16 Cartwright and Hardie (2012) emphasises the importance of differentiating between efficacy – ‘it worked there’ – and effectiveness – ‘it will work here’. 17 Ioannidis (2005). 18 Chang and Li (2015). 19 Camerer et al. (2016). 20 Nelson, Simmons and Simonsohn (2011). 14.

The Man Who Solved the Market: How Jim Simons Launched the Quant Revolution
by Gregory Zuckerman
Published 5 Nov 2019

Or, to be fair to the computers, by computers programmed by fallible people and trusted by people who did not understand the computer programs’ limitations. As computers came in, human judgment went out.” During the 1980s, Professor Benoit Mandelbrot—who had demonstrated that certain jagged mathematical shapes called fractals mimic irregularities found in nature—argued that financial markets also have fractal patterns. This theory suggested that markets will deliver more unexpected events than widely assumed, another reason to doubt the elaborate models produced by high-powered computers. Mandelbrot’s work would reinforce the views of trader-turned-author Nassim Nicholas Taleb and others that popular math tools and risk models are incapable of sufficiently preparing investors for large and highly unpredictable deviations from historic patterns—deviations that occur more frequently than most models suggest.

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(Kelly formula), 91–92, 96, 127 Kempe, Julia, 272 Kennedy, John F., 31, 78 Kepler Financial Management, 133–34, 157, 166–67 kernel methods, 84–86, 96 Kirtland Air Force Base, 170–71 Klein, Naomi, 321 Koch, Charles, 278 Koch, David, 278 Kochen, Simon, 69–70, 71, 103 Kononenko, Alexey, 236–37, 241–43, 262–63, 270–71 Kostant, Bertram, 18, 20 Kovner, Bruce, 140 Kurz, Christopher, 121–22 Kushner, Jared, 281, 292 Lackman, Abe, 286 Laufer, Henry, xi, 101 background of, 140–41 Long Island Sound estate of, 227–28 at Renaissance, 109, 141–44, 149–50, 201, 229–31, 233 at Stony Brook, 77, 78, 84–85, 141–42 trading models, 77, 107–18, 142–43, 149–50, 156, 168, 189, 197, 229–30, 253, 258 Laufer, Marsha Zlatin, 141–42 Law of Vibration, 123 Lawrence School, 13 Leave.EU, 280–81 L’eggs, 162 Lehman Brothers, 173, 264, 309 Leibler, Dick, 26, 30–31, 32 Leinweber, David, 204 Leo, Leonard, 290 Let’s Make a Deal (TV show), 211 leverage, 188 Lewinsky, Monica, 208 Lieberman, Louis, 46 Limroy, 50–51, 53, 54, 55, 58, 98, 346 linear regression, 83–84 liquidity, 229 Lo, Andrew, 123, 124 locals, 110 Loma Prieta earthquake of 1989, 107 Long-Term Capital Management (LTCM), 209–11, 212–13, 226, 256 Lord Jim, The (yacht), 60 loss aversion, 152 Lott, John R., Jr., 207 Lourie, Robert, 11, 228, 257 Lux, Hal, 218 Lynch, Carolyn, 162 Lynch, Peter, xvi, 3, 161–63 McCain, John, 304 McCarthy, David, 154 McCarthy, Eugene, 74 McGrayne, Sharon, 202 machine learning, 4–5, 47–48, 144, 205, 215, 315 McNulty, Bill, 295 Macrae, Kenny, 267 macro investors, 164 “macroscopic variables,” 29 Madoff, Bernard, 146n, 198 Magellan Fund, 161–63, 333 Magerman, David, xi background of, 182–84 computer hacking of, 191–93, 213 confrontational behavior of, 235, 270 education of, 183–85 at IBM, 177, 181, 185, 191–92 Mercers and, 195, 213–14, 232, 277, 291–99, 318 at Penn, 270 philanthropic activity of, 270, 318 presidential election of 2016 and Trump, 290–94 Magerman, David, at Renaissance Brown and, 181–82, 191–95, 241, 294, 296, 297, 299, 318 computer bug, 194–95, 213 departures, 262–63, 269–70 firing, 317–18 Kononenko and, 237, 241–43, 262–63, 270–71 lawsuit and financial settlement, 318–19 misgivings of, 269–70 recruitment of, 181–82, 186–87 return to, 270–71 Simons and, 181–82, 186–87, 234–35, 237, 296–99 tech bubble, 215–17 trading system, 186–87, 191–95, 213–17, 234–36 Magerman, Debra, 291, 292 Magerman, Melvin, 182–83, 184 Mahlmann, Karsten, 114 Malloy, Martin, 259 management fees, 115n, 248 Man AHL, 313 Mandelbrot, Benoit, 127 Man for All Markets, A (Thorp), 128 Manhattan Fund, 123 market neutral, 166–67, 211, 255 Markov chains, 46–48, 81 Markov model, xx, 29, 174 Markowitz, Harry, 30 Massachusetts Institute of Technology (MIT), 9, 14–16, 17, 20–21, 89–91, 325–26 Mathematical Sciences Research Institute, 236–37 Math for America, 269, 296–99, 321 Matrix, The (movie), 307 Mattone, Vinny, 210–11 Mayer, Jane, 280 Mayer, Jimmy, 15, 16–17, 21, 38–39, 50 Mazur, Barry, 15 Medallion Fund basket options, 225–27 fees, 145–46, 235–36, 271, 315–16 financial crisis and, 257–61, 263–64 GAM Investments, 153–54 launch of, 98 move into stock investing, 157–58 returns, xvi, 140, 145–46, 151, 153, 156, 157, 215, 217–18, 223–24, 225, 247–48, 255, 271, 315–16, 319, 331–32 returns comparison, 333 Sharpe ratio, 218, 223–24, 245 size limit, 246–47 trading models, 107–9, 113, 138–40, 142–43, 156–57, 168, 197–205, 271–74 Media Research Center, 304 Mercer, Diana, 179, 186, 214, 228, 288 Mercer, Heather Sue, 207, 214, 228 Mercer, Jennifer “Jenji,” 179, 186, 228 Mercer, Rebekah, xi, 228 Bannon and Breitbart News, 278–83, 288–90, 294–95, 301–2 emergence as right-wing donor, 277–79, 301–2 Magerman and, 214, 291, 293, 298, 299 political blowback and, 301–2, 303–5 presidential election of 2016 and Trump, xviii, 279–86, 288–90, 294–95 at Renaissance, 214 Mercer, Robert, xi background of, 169–70 education of, 169–70 emergence as right-wing donor, xviii, 276–86, 325–26 at IBM, 4–5, 169, 171–81, 187–88, 202 interest in computers, 170–71 at Kirtland Air Force Base, 170–71 libertarian views of, 171, 207–8, 232, 235, 275–77 presidential election of 2016 and Trump, xviii, 279–87, 291–95, 299–300, 302 Stony Brook Harbor estate (Owl’s Nest), 228, 275, 288–89, 295 Mercer, Robert, at Renaissance client presentations, 251 as co-CEO, xviiin, 231, 290, 301 equity stake, 201 financial crisis and, 257–61 Magerman and, 195, 213–14, 232, 277, 291–99, 318 management, 230–31, 232–33, 237, 241–43, 254–55, 289–90 political blowback and, 291–305 recruitment of, 169, 179–80 resignation of, 301–2, 319 statistical-arbitrage trading system, 4–5, 187–91, 193–95, 197–99, 205–8, 213–14, 221–22, 223, 229–32, 255, 272 tech bubble, 215–17 Mercer, Thomas, 169, 179 Mercer, Virginia, 169 Mercer Family Foundation, 276 Meriwether, John, 209–11, 212 Merrill Lynch, 19–20, 54, 96 Merton, Robert C., 209 Mexico–United States border wall, 290–91 Microsoft, 38, 59 Milken, Michael, 105–6, 129 Millennium Management, 238, 252–54 minimal varieties, 26–28, 38 “Minimal Varieties in Riemannian Manifolds” (Simons), 28 Mirochnikoff, Sylvain, 278 Mississippi, 13–14 Mnuchin, Steve, 282 Monemetrics Ax at, 34, 51–52, 72–73 Baum at, 45, 49–60, 63–65 founding and naming of, 44–45 Hullender at, 54–59, 74 name change to Renaissance, 61.

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Hutton, 64 efficient market hypothesis, 111, 152, 179 Einhorn, David, 264, 309 Einstein, Albert, 27, 128 Elias, Peter, 90–91 email spam, 174 embeddings, 141 endowment effect, 152 Englander, Israel, 238, 252–54, 310 English, Chris, 298, 299 Enron, 226 Esquenazi, Edmundo, 17, 21, 38–39, 50 Euclidean Capital, 308 European Exchange Rate Mechanism, 165 European Union, 280–81 Evans, Robert, 128 Everything Must Go (movie), 270 Exxon, 132, 173 Facebook, 303–4, 318 facial dysplasia, 147 factor investing, 30, 132–33, 315 Farage, Nigel, 280–81 Farkas, Hershel, 34–35 Federalist Society, 290 Federal Reserve, 56–57, 59, 65, 151, 211 Fermat conjecture, 69–70 Ferrell, Will, 270 Fidelity Investments, 161–63 Fields Medal, 28 financial crisis of 2007–2008, 255–62, 263–64 financial engineering, 126 Financial Times, 229 First Amendment, 277 Fischbach, Gerald, 268 flash crash of 2010, 314 Food and Drug Administration, 206, 311 Fortran, 170 Fort Thomas Highlands High School, 88–89 fractals, 127 Franklin Electronic Publishers, 61 freediving, 239 Freedom Partners Action Fund, 278 Freifeld, Charlie, 38–39, 44, 67 Frey, Robert, 200, 240 at Kepler, 133, 157, 166–67, 180 Mercer and election of 2016, 302–3 at Morgan Stanley, 131, 132–33 statistical-arbitrage trading system, 131, 132–33, 157, 166–67, 186–90 Fried, Michael, 72 fundamental investing, 127–28, 161–63, 247, 310 game theory, 2, 88, 93 GAM Investments, 153–54 Gann, William D., 122–23 Gasthalter, Jonathan, 263 gender discrimination, 168, 168n, 176–77, 207 German deutsche marks, 52, 57–58, 110–11, 164–65 Geron Corporation, 310 ghosts, 111 gold, 3, 40, 57, 63–64, 116, 207 Goldman Sachs, 126, 133–34, 256 Goldsmith, Meredith, 176–77 Gone With the Wind (Mitchell), 88 Goodman, George, 124–25 Google, 48, 272–73 Gore, Al, 212 Graham, Benjamin, 127 Granade, Matthew, 312 Greenspan, Alan, 59 Griffin, Ken, 256, 310–11 Gross, Bill, 3, 163–64, 309 Grumman Aerospace Corporation, 56, 78 Gulfstream G450, 257, 267, 325 Hamburg, Margaret, 206 Hanes, 162 Harpel, Jim, 13–14, 283 Harrington, Dan, 297 Harvard University, 15, 17, 21–22, 23, 46–48, 173, 176, 185, 272 head and shoulders pattern, 123–24 Heritage at Trump Place, 278 Heritage Foundation, 278 Hewitt, Jennifer Love, 270 high-frequency trading, 107, 222–23, 271 Hitler, Adolph, 165, 282 holonomy, 20 Homma, Munehisa, 122 housing market, 224–25, 255, 261, 309 Hullender, Greg, 53–59, 74 human longevity, 276 IBM, 33, 37, 169, 171–79, 311 Icahn, Carl, 282 illegal immigrants, 290–91 information advantage, 105–6 information theory, 90–91 insider trading, 310 Institute for Defense Analyses (IDA), 23–26, 28–29, 30–32, 35, 46–49, 93–94 Institutional Investor, 218, 223 interest rates, 163–64, 224–25, 272–73 Internal Revenue Service (IRS), 227 Iraq, invasion of Kuwait, 116, 117 Israel, 184–85, 262 iStar, 26 Japanese yen, 49–50, 52–53, 54–55, 65 Jean-Jacques, J.

The Master Algorithm: How the Quest for the Ultimate Learning Machine Will Remake Our World
by Pedro Domingos
Published 21 Sep 2015

Gary Marcus, Adam Marblestone, and Tom Dean make the case against in “The atoms of neural computation” (Science, 2014). “The unreasonable effectiveness of data,” by Alon Halevy, Peter Norvig, and Fernando Pereira (IEEE Intelligent Systems, 2009), argues for machine learning as the new discovery paradigm. Benoît Mandelbrot explores the fractal geometry of nature in the eponymous book* (Freeman, 1982). James Gleick’s Chaos (Viking, 1987) discusses and depicts the Mandelbrot set. The Langlands program, a research effort that seeks to unify different subfields of mathematics, is described in Love and Math, by Edward Frenkel (Basic Books, 2014). The Golden Ticket, by Lance Fortnow (Princeton University Press, 2013), is an introduction to NP-completeness and the P = NP problem.

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How much of the character of physical law percolates up to higher domains like biology and sociology remains to be seen, but the study of chaos provides many tantalizing examples of very different systems with similar behavior, and the theory of universality explains them. The Mandelbrot set is a beautiful example of how a very simple iterative procedure can give rise to an inexhaustible variety of forms. If the mountains, rivers, clouds, and trees of the world are all the result of such procedures—and fractal geometry shows they are—perhaps those procedures are just different parametrizations of a single one that we can induce from them. In physics, the same equations applied to different quantities often describe phenomena in completely different fields, like quantum mechanics, electromagnetism, and fluid dynamics.

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See S curves Long-tail phenomenon, 12, 299 Long-term potentiation, 27 Loopy belief propagation, 163–164, 231 Lorenz, Konrad, 138 Low-pass filter, 133 Machine learners, knowledge engineers vs., 34–38 Machine learning, 6–10 analogy and, 178–179 bias and variance and, 78–79 big data and, 15–16 business and, 10–13 chunking, 223–227 clustering, 205–210 dimensionality reduction, 211–217 effect on employment, 276–279 exponential function and, 73–74 fitness function and, 123 further readings, 297–298 future of, 21–22 impact on daily life, 298 effect on employment, 276–279 meta-learning, 237–239 nature vs. nurture debate and, 29, 137–139 Newton’s principle and, 65–66 planetary-scale, 256–259 politics and, 16–19 principal-component analysis, 211–217 problem of unpredictability and, 38–40 reinforcement learning, 218–223, 226–227 relational learning, 227–233 relationship to artificial intelligence, 8 science and, 13–16, 235–236 significance tests and, 76–77 as technology, 236–237 Turing point and, 286, 288 war and, 19–21, 279–282 See also Algorithms Machine-learning problem, 61–62, 109–110 Machine-translation systems, 154 MacKay, David, 170 Madrigal, Alexis, 273–274 Malthus, Thomas, 178, 235 Manchester Institute of Biotechnology, 16 Mandelbrot set, 30, 300 Margins, 192–194, 196, 241, 242, 243, 307 Markov, Andrei, 153 Markov chain Monte Carlo (MCMC), 164–165, 167, 170, 231, 241, 242, 253, 256 Markov chains, 153–155, 159, 304–305 Markov logic. See Markov logic networks (MLNs) Markov logic networks (MLNs), 246–259, 309–310 classes and, 257 complexity and, 258–259 parts and, 256–257 with hierarchical structure, 256–257 See also Alchemy Markov networks, 171–172, 229, 240, 245, 253, 306 Marr, David, 89 Marr’s three levels, 89 Master Algorithm, 239–246 Alchemy and, 250–259 Bayes’ theorem and, 148 brain as, 26–28 CanceRx, 259–261 candidates that fail as, 48–50 chunking and, 226 complexity of, 40–41 as composite picture of current and future learners, 263–264 computer science and, 32–34 equation, 50 evolution and, 28–29 five tribes and, 51–55 future and, 292 goal of, 39 Google and, 282 invention of, 25–26 Markov logic networks and, 236–250 meta-learning and, 237–239 physics and, 29–31 practical applications of, 41–45 statistics and, 31–32 symbolism and, 90–91 theory of everything and, 46–48 Turing point and, 286, 288 as unifier of machine learning, 237 unity of knowledge and, 31 Match.com, 12, 265 Matrix factorization for recommendation systems, 215 Maximum likelihood principle, 166–167, 168 Maxwell, James Clerk, 235 McCulloch, Warren, 96 McKinsey Global Institute, 9 MCMC.

Atrocity Archives
by Stross, Charles
Published 13 Jan 2004

And in a vanishingly small number of the other universes there are things that listen, and talk back--see Al-Hazred, Nietzsche, Lovecraft, Poe, et cetera. The many-angled ones, as they say, live at the bottom of the Mandelbrot set, except when a suitable incantation in the platonic realm of mathematics--computerised or otherwise--draws them forth. (And you thought running that fractal screen-saver was good for your computer?) Oh, and did I mention that the inhabitants of those other universes don't play by our rule book? Just solving certain theorems makes waves in the Platonic over-space.

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Only God and Bridget--and possibly Boris, though he won't say anything--know why I'm booked into an O&O course three days after getting off the plane, but something dire will probably happen if I don't turn up. The Dustbin isn't part of the Laundry, it's regular civil service, so I try to dig up a shirt that isn't too crumpled, and a tie. I own two ties--a Wile E. Coyote tie, and a Mandelbrot set tie that's particularly effective at inducing migraines--and a sports jacket that's going a bit threadbare at the cuffs. Don't want to look too out of place, do I? Someone might ask questions, and after the auto-da-fé I've just been through I do not want anyone mentioning my name in Bridget's vicinity for the next year.

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I've been spending all my time reading, getting indigestion along the way. It's just such a waste--all that stuff, locked up behind the Official Secrets Act!" "Yeah, well." It's my turn to pull a face now. "In principle, I kind of agree with you. In practice . . . how to put it? This stuff has repercussions. The many-angled ones live at the bottom of the Mandelbrot set; play around with it for too long and horrible things can happen to you." I shrug. "And you know what students are like." "Yes, well." She stands up, straightening her skirt with one hand and holding the book with the other. "I suppose you've got more experience of that than I have. But, well."

When Computers Can Think: The Artificial Intelligence Singularity
by Anthony Berglas , William Black , Samantha Thalind , Max Scratchmann and Michelle Estes
Published 28 Feb 2015

There are mathematical systems that can produce complex artefacts from simple definitions. One well-known example is the Mandelbrot fractal set shown below. One can zoom into this diagram indefinitely and similar, complex, but nonrepeating patterns will be seen. Mandelbrot Set Public Wikipedia Amazingly, all this stunning complexity is produced by the following simple equation appropriately interpreted:z’ = z2 + c So if something vaguely analogous to this type of fractal formula could be stored in our DNA, a small amount of DNA could result in very complex structures. However, while the Mandelbrot formula can produce this stunningly complex pattern, it cannot produce arbitrary patterns.

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Motivation to build an AGI 24. Premature destruction of humanity 25. Outcome against a superior chess player 6. Silicon versus Meat Based Intelligence 1. Silicon vs. neurons 2. Speech understanding 3. Other hardware estimates 4. Small size of genome 5. Chimpanzee intelligence 6. Packing density, fractals, and evolution 7. Repeated patterns 8. Small DNA, small program 7. Related Work 1. Many very recent new books 2. Kurzweil 2000, 2006, 2013 3. Storrs Hall 2007 4. Yudkowsky 2008 5. Sotala, Yampolskiy 2013 6. Nilsson 2009 7. Barrat 2013 8. Muehlhauser 2013 9. Del Monte 2014 10. Armstrong 2014 11. Bostrom 2014 12.

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Most new genes are slight variations on old genes, but this gene sprung out of nowhere about 6 to 1 million years ago, after the chimpanzee split and it seems to be heavily involved with brain activity. So it may turn out that just a few very special differences in our genotype have resulted in our relatively high intelligence. Packing density, fractals, and evolution The information in genes is tightly packed, with many complex transcription processes. These include using different parts of the same gene to produce different proteins, and many complex mechanisms to control whether genes are actually expressed. Still, there is no way that any sort of explicit wiring diagram for our 86 billion neurons could possibly be represented in a few megabytes of data.

Them And Us: Politics, Greed And Inequality - Why We Need A Fair Society
by Will Hutton
Published 30 Sep 2010

Only an earthquake can persuade them to put up their hands and acknowledge they were wrong. When the mathematician Benoit Mandelbrot began developing his so-called fractal mathematics and power laws in the early 1960s, arguing that the big events outside the normal distribution are the ones that need explaining and assaulting the whole edifice of mathematical theory and the random walk, MIT’s Professor Paul Cootner (the great random walk theorist) exclaimed: ‘surely, before consigning centuries of work to the ash pile, we should like some assurance that all our work is truly useless’. Mandelbrot withdrew from economics to ask the same questions in the natural sciences.38 Forty-five years later, we have the assurance that Cootner demanded.

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See Brad DeLong, Andrei Shleifer, Larry Summers and Michael Waldman (1990) ‘Noise Trader Risk in Financial Markets’, Journal of Political Economy 98: 703–38. 35 Anil Kashyap, Raghuram Rajan and Jeremy Stein (2008) ‘Rethinking Capital: Regulation’, paper for the Federal Reserve Bank of Kansas City. 36 Andrew Haldane (2009) ‘Why Banks Failed the Stress Test’, presentation to the Marcus-Evans Conference on Stress-Testing, 9–10 February. 37 James G. Rickards, ‘The Risks of Financial Modeling: VaR and the Economic Meltdown’, testimony before the Subcommittee on Investigations and Oversight Committee on Science and Technology, US House of Representatives, 10 September 2009. 38 Benoit Mandelbrot (2008) The (Mis)Behavior of Markets: A Fractal View of Risk, Ruin and Reward, Profile Books. For another interesting example of cross-fertilisation, see Didier Sornette (2003) Why Stockmarkets Crash: Critical Events in Complex Financial Systems, Princeton University Press. 39 See Justin Fox (2009) The Myth of the Rational Market: A History of Risk, Reward, and Delusion on Wall Street, HarperBusiness. 40 The following example is paraphrased from Baseline Scenario: http://baselinescenario.com/2009/10/01/the-economics-of-models/. 41 Gillian Tett (2009) Fool’s Gold: How Unrestrained Greed Corrupted a Dream, Shattered Global Markets and Unleashed a Catastrophe, Little, Brown. 42 Lucien Bebchuk and Jesse Fried (2004) Pay without Performance: The Unfulfilled Promise of Executive Compensation, Harvard University Press. 43 Lucian Bebchuk and Holger Spamann (2009) ‘Regulating Bankers’ Pay’, Harvard Law and Economics Discussion Paper No. 641. 44 Jesse Eisinger, ‘London Banks, Falling Down’, Portfolio, 13 August 2008, at http://www.portfolio.com/views/columns/wall-street/2008/08/13/Problemsin-British-Banking-System/. 45 Philip Augar (2009) Chasing Alpha: How Reckless Growth and Unchecked Ambition Ruined the City’s Golden Decade, The Bodley Head. 46 Albert-Laszlo Baraasi (2002) Linked: The New Science of Networks, Basic Books.

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See also Matthew Jackson (2008) Social and Economic Networks, Princeton University Press. 47 Nicholas Christakis and James Fowler (2010) Connected: The Amazing Power of Social Lives and How They Shape Our Lives, Harper Press. 48 Robert M. May, Simon A. Levin and George Sugihara (2008) ‘Ecology for Bankers’, Nature 451 (21): 893–5. 49 Richard Bookstaber (2007) A Demon of Our Own Design: Markets, Hedge Funds, and the Perils of Financial Innovation, John Wiley & Sons. 50 Cited by Benoit Mandelbrot (2008) The (Mis)Behavior of Markets: A Fractal View of Risk, Ruin and Reward, Profile Books, p. 154. 51 Ibid. 52 Andrew Haldane (2009) ‘Rethinking the Financial Network’, presentation to the Financial Students Association, Amsterdam. 53 Bobbi Low, Elinor Ostrom, Carl Simon and James Wilson, ‘Redundancy and Diversity’, in Wilson Fikret Berkes, Johan Colding and Carl Folke (eds) (2003) Navigating Social-Ecological Systems: Building Resilience for Complexity and Change, Cambridge University Press. 54 Scott Page (2007) The Difference: How the Power of Diversity Creates Better Groups, Firms, Schools, and Societies, Princeton University Press.

How Markets Fail: The Logic of Economic Calamities
by John Cassidy
Published 10 Nov 2009

THE COIN-TOSSING VIEW OF FINANCE 88 Bachelier’s theory of speculation: See Peter L. Bernstein, Capital Ideas: The Improbable Origins of Modern Wall Street (New York: Free Press, 1993), 17–18. 88 “[t]he mathematical expectation . . .”: Quoted in ibid., 21. 88 “Suppose you see . . .”: Benoit Mandelbrot and Richard Hudson, The (Mis)behavior of Markets: A Fractal View of Risk, Ruin, and Reward (New York: Basic Books, 2006), 52. 89 “even if his powers . . .”: Quoted in Bernstein, Capital Ideas, 134. 90 Fama’s follow-up paper: Eugene Fama, “Efficient Capital Markets: A Review of Theory and Empirical Work,” Journal of Finance 25, no. 2 (1970): 383–417; summarized in Bernstein, Capital Ideas, 137–38. 90 “The past history of stock prices . . .”: Burton Gordon Malkiel, A Random Walk Down Wall Street: The Best and Latest Investment Advice Money Can Buy, 6th ed.

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And firms and investors that rely on these models to manage risk may well be exposing themselves to danger. The economics profession didn’t exactly embrace Mandelbrot’s criticisms. As the 1970s proceeded, the use of quantitative techniques became increasingly common on Wall Street. The coin-tossing view of finance made its way into the textbooks and, with the help of Burton Malkiel, onto the bestsellers list. By the 1980s, many M.B.A. students were being taught that the efficient market hypothesis was a description of reality, and Mandelbrot’s strictures had been largely forgotten. “Modern finance was the official religion,” Mandelbrot later recalled. “My hypothesis contradicted it; and I was about as welcome in the established church of economics as a heretical Arian at the Council of Nicene.” 8.

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Grossman and Stiglitz entitled their paper “On the Impossibility of Informationally Efficient Markets.” Other economic theorists admired its terse logic, but it didn’t have much immediate impact on Wall Street. The aforementioned Benoit Mandelbrot, who is perhaps best known as one of the founders of chaos theory, was another skeptic of the efficient market hypothesis. In the early 1960s, when he was working in the research department at IBM, Mandelbrot got interested in some of the new theories that were being developed to explain how financial markets worked, and he started to gather evidence on how they performed. The Harvard economist Hendrik Houthakker, whom he met while giving a talk in Cambridge, gave him the records of daily movements in the prices of cotton and cotton futures going back more than a century, which he had obtained from the New York Cotton Exchange.

Capital Ideas: The Improbable Origins of Modern Wall Street
by Peter L. Bernstein
Published 19 Jun 2005

Twenty years after writing his dissertation, he remarked that his analysis had embodied “images taken from natural phenomena . . . a strange and unexpected linkage and a starting point for great progress.” His superiors did not agree. Although Poincarè, his teacher, wrote that “M. Bachelier has evidenced an original and precise mind,” he also observed that “The topic is somewhat remote from those our candidates are in the habit of treating.”5 Benoit Mandelbrot, the pioneer of fractal geometry and one of Bachelier’s great admirers, recently suggested that no one knew where to pigeonhole Bachelier’s findings. There was no ready means to retrieve them, assuming that someone wanted to. Sixty years were to pass before anyone took the slightest notice of his work. ••• The key to Bachelier’s insight is his observation, expressed in a notably modern manner, that “contradictory opinions concerning [market] changes diverge so much that at the same instant buyers believe in a price increase and sellers believe in a price decrease.”6 Convinced that there is no basis for believing that—on the average—either sellers or buyers consistently know any more about the future than the other, he arrived at an astonishing conjecture: “It seems that the market, the aggregate of speculators, at a given instant can believe in neither a market rise nor a market fall, since, for each quoted price, there are as many buyers as sellers.”7 (emphasis added) The fond hopes of home buyers in California during the 1980s provide a vivid example of Bachelier’s perception.

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Mandelbrot’s research implied that stocks are riskier than had been assumed, that diversification might not work as well as Markowitz had indicated, that measures like variance could be highly unstable, and that major price movements would cluster more closely than anticipated. Mandelbrot’s view of the stock market was the genesis of what is known today as Chaos Theory, of which Mandelbrot himself is an articulate proponent. The events of October 1987 and less dramatic but qualitatively similar episodes lend some credence to Mandelbrot’s warnings. Despite those events, however, Mandelbrot remains on the periphery of financial theory, both because of the inconvenience to analysts of accepting his arguments and because of the natural human desire to hope that fluctuations will remain within familiar bounds. ••• Soon after his foray into the feverish world described by Mandelbrot, Fama turned to full analysis of the random behavior of stock prices.

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Cootner’s book also contained a short article by Fama, reprinted from the Journal of Business for October 1963, in which Fama expanded on an analysis of market behavior conducted by Benoit Mandelbrot, a French mathematician living in the United States whose work was published in the same issue of the journal. Mandelbrot proposed that stock prices fluctuate so irregularly because they are not sufficiently well behaved to submit to the kind of rigorous statistical analysis recommended by Bachelier and Samuelson. Mandelbrot’s research implied that stocks are riskier than had been assumed, that diversification might not work as well as Markowitz had indicated, that measures like variance could be highly unstable, and that major price movements would cluster more closely than anticipated.

New Dark Age: Technology and the End of the Future
by James Bridle
Published 18 Jun 2018

The reason, as he came to understand, was that the length of the border depended upon the tools used to measure it: as these became more accurate, the length actually increased, as smaller and smaller variations in the line were taken into account.41 Coastlines were even worse, leading to the realisation that it is in fact impossible to give a completely accurate account of the length of a nation’s borders. This ‘coastline paradox’ came to be known as the Richardson effect, and formed the basis for Benoît Mandelbrot’s work on fractals. It demonstrates, with radical clarity, the counterintuitive premise of the new dark age: the more obsessively we attempt to compute the world, the more unknowably complex it appears. 3 Climate There was a video on YouTube that I watched over and over again, until it got taken down.

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When Google first released an untrained classifier network on 10 million random YouTube videos in 2012, the first thing it learned to see, without prompting, was a cat’s face: the spirit animal of the internet.32 Mordvintsev’s network thus dreamed of what it knew, which was more cats and dogs. Further iterations produced Boschian hellscapes of infinite architecture, including arches, pagodas, bridges, and towers in infinite, fractal progressions, according to the neurons activated. But the one constant that recurs throughout DeepDream’s creations is the image of the eye – dogs’ eyes, cats’ eyes, human eyes; the omnipresent, surveillant eye of the network itself. The eye that floats in DeepDream’s skies recalls the all-seeing eye of dystopian propaganda: Google’s own unconscious, composed of our memories and actions, processed by constant analysis and tracked for corporate profit and private intelligence.

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Questions were asked in parliaments; national scientific organisations were flooded with enquiries; atmospheric scientists were barracked at conferences. Online, shaky videos of blue skies besmirched with smog, and planes trailing black smoke, proliferate. Groups of individuals gather in forums and Facebook groups to swap anecdotes and images. The chemtrails theory is multifaceted and hydra-like; its adherents believe in fractal versions of the same idea. For some, the chemicals sprayed by commercial, military, and mystery aircraft are part of a widespread programme of solar radiation management: the creation of cloud cover to reduce sunlight and slow – or accelerate – global warming. The chemicals used cause cancer, Alzheimer’s, skin diseases and deformities.

Clojure Programming
by Chas Emerick , Brian Carper and Christophe Grand
Published 15 Aug 2011

Visualizing the Mandelbrot Set in Clojure Let’s take a look at a somewhat more interesting example than the overused Fibonacci and prime number generators that are often used for microbenchmarking numeric performance. Visualizing the Mandelbrot Set[349] (or really, any fractal shape visualization) has long been a common practicum, and it will serve well here as a demonstration of how to optimize numeric algorithms in Clojure. The Mandelbrot Set is defined by a complex polynomial that is applied iteratively: zk+1 = zk2 + c where c (a complex number) is a member of the Mandelbrot Set if zk+1 is bounded as k increases when z0 is initialized to 0. c’s that produce unbounded results from this calculation are said to escape to infinity.

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[mandelbrot-grid] (doseq [row mandelbrot-grid] (doseq [escape-iter row] (print (if (neg? escape-iter) \* \space))) (println))) (defn render-image "Given a mandelbrot set membership grid as returned by a call to `mandelbrot`, returns a BufferedImage with the same resolution as the grid that uses a discrete grayscale color palette." [mandelbrot-grid] (let [palette (vec (for [c (range 500)] (Color/getHSBColor 0.0 0.0 (/ (Math/log c) (Math/log 500))))) height (count mandelbrot-grid) width (count (first mandelbrot-grid)) img (BufferedImage. width height BufferedImage/TYPE_INT_RGB) ^java.awt.Graphics2D g (.getGraphics img)] (doseq [[y row] (map-indexed vector mandelbrot-grid) [x escape-iter] (map-indexed vector row)] (.setColor g (if (neg?

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, Reference Equality (=), Numeric Equivalence (==), Optimizing Numeric Performance, Automating type hinting of multidimensional array operations, Declare Functions to Take and Return Primitives, Type errors and warnings, Use Primitive Arrays Judiciously, Automating type hinting of multidimensional array operations, Visualizing the Mandelbrot Set in Clojure, Visualizing the Mandelbrot Set in Clojure equality and equivalence, Equality and Equivalence, Equivalence can preserve your sanity, Object Identity (identical?), Reference Equality (=), Numeric Equivalence (==) numeric equivalence, Numeric Equivalence (==) object identity, Object Identity (identical?) reference equality, Reference Equality (=) Mandelbrot Set, Visualizing the Mandelbrot Set in Clojure, Visualizing the Mandelbrot Set in Clojure mathematics, Clojure Mathematics, Scale and Rounding Modes for Arbitrary-Precision Decimals Ops, Bounded Versus Arbitrary Precision, Bounded Versus Arbitrary Precision, Unchecked Ops, Scale and Rounding Modes for Arbitrary-Precision Decimals Ops bounded versus arbitrary precision, Bounded Versus Arbitrary Precision, Bounded Versus Arbitrary Precision scale and rounding modes, Scale and Rounding Modes for Arbitrary-Precision Decimals Ops unchecked ops, Unchecked Ops numerics, Clojure Numerics, The Rules of Numeric Contagion, Clojure Prefers 64-bit (or Larger) Representations, Clojure Has a Mixed Numerics Model, Rationals, The Rules of Numeric Contagion mixed numerics model, Clojure Has a Mixed Numerics Model numeric contagion, The Rules of Numeric Contagion rationals, Rationals representations, Clojure Prefers 64-bit (or Larger) Representations optimizing numeric performance, Optimizing Numeric Performance, Automating type hinting of multidimensional array operations, Declare Functions to Take and Return Primitives, Type errors and warnings, Use Primitive Arrays Judiciously, Automating type hinting of multidimensional array operations declare functions, Declare Functions to Take and Return Primitives, Type errors and warnings primitive arrays, Use Primitive Arrays Judiciously, Automating type hinting of multidimensional array operations O objects, Java Interop: . and new, Comparing Values to Mutable Objects, Comparing Values to Mutable Objects, A Critical Choice, A Critical Choice, Using Java Classes, Methods, and Fields, Clojure Has a Mixed Numerics Model, Object Identity (identical?)

Irrational Exuberance: With a New Preface by the Author
by Robert J. Shiller
Published 15 Feb 2000

The literature on applications of chaos theory to economics usually does not stress the kind of price feedback model discussed here, but it may nonetheless offer some insights into the sources of complexity in financial markets. See Michael Boldrin and Michael Woodford, “Equilibrium Models Displaying Endogenous Fluctuations and Chaos: A Survey,” Journal of Monetary Economics, 25(2) (1990): 189–222, for a survey of this literature. See also Benoit Mandelbrot, Fractals and Scaling in Finance: Discontinuity, Concentration, Risk (New York: Springer-Verlag, 1997); and Brian Arthur, John H. Holland, Blake LeBaron, Richard Palmer, and Paul Tayler, “Asset Pricing under Endogenous Expectations in an Artificial Stock Market,” in W. B. Arthur, S. Durlauf, and D. Lane (eds.), The Economy as an Evolving Complex System II (Reading, Mass.: Addison-Wesley, 1997).

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RE F E RE N CE S 277 Mackay, Charles. Memoirs of Extraordinary Popular Delusions and the Madness of Crowds. London: Bentley, 1841. Maier, N. R. F. “Reasoning in Humans. II. The Solution of a Problem and Its Appearance in Consciousness.” Journal of Comparative Psychology, 12 (1931): 181–94. Mandelbrot, Benoit. Fractals and Scaling in Finance: Discontinuity, Concentration, Risk. New York: Springer-Verlag, 1997. Marsh, Terry A., and Robert C. Merton. “Dividend Variability and Variance Bounds Tests for the Rationality of Stock Market Prices.” American Economic Review, 76(3) (1986): 483–98. Mehra, Raj, and Edward C.

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Nellie, 238n7, 262n31 Levine, Ross, 237n1 Lichtenstein, Sarah, 142 Lin, Hsiou-Wei, 239n17 Lo, Andrew, 237n11 290 Logistic curve, 158, 257n13 London stock exchange, 3, 81 Long Term Capital Management, 189 Long-term investing, 176–77, 197–200 Long-term returns, 10–14, 194–95 Loomis, Graham, 243n12 Lopez-de-Silanes, Florencio, 237n1 Loser stocks, 130 Lotteries, 40–41 Lotus Development Corporation, 154 Loughran, Tim, 259n21 Lucas, Deborah, 263n14 Lynch, Peter, 181, 259n17 Maas, Anne, 255n16 McDonald’s, 177 Mackay, Charles, 177 Mackinlay, Craig, 237n11 McKinley, William, 102 MacNeil/Lehrer NewsHour, 73 McNichols, Maureen, 239n17 Macro markets, 229–31 Macro Markets (Shiller), 230 Macro securities, 230, 267n30 Magical thinking, 143 Maier, N. R. F., 166, 257n19 Malaysia, 5 Managed capitalism, 112 Managerial revolutions, 113 Mandel, Michael, 112 Mandelbrot, Benoit, 244n22 Marcos, Ferdinand, 123 Marsh, Terry, 189, 261n26 Martin, William McChesney, 224 Massachusetts Investors Trust, 35 Master-charting, 106 Mean reversion, 129, 252n13 Media, 71–95, 118, 163, 203, 206, 208–9, 241n40, 245–48n1–24; attention cascades and, 79–82, 88; big price changes and absence of news, 78–79; bull market of 1990s INDEX and, 113; crash of 1929 and, 82–88; crash of 1987 and, 88–95; cultivation of debate by, 72–74; effect of significant world events on prices, 75–77; epidemics and, 160–62; expansion of business reporting, 19, 28–29; face-to-face communications versus, 154–57; market moves and, 72; market outlook and, 74–75; new era thinking and, 98; origins of, 245n1; peak of 1901 and, 100–101; psychological anchors and, 147; record overload and, 75; speculative bubbles and, 95; tag-along news and, 77–78 Mehra, Raj, 263n1 Mehta, Harshad (“Big Bull”), 127 Mehta Peak, 127 Meksi, Aleksander, 65 Meltzer, Allan, 84 Mergers, 106 Merrill Lynch, xv, 22 Merton, Robert, 189, 261n26 Mexican peso crisis, 128–29 Mexico, 5 Microsoft, 211, 212 Milestones for Dow, 137 Milgram, Stanley, 150–51, 256n4 Milgrom, Paul, 255n20 Millennium.

Present Shock: When Everything Happens Now
by Douglas Rushkoff
Published 21 Mar 2013

Many of the “quant” teams at hedge funds and the risk-management groups within brokerage houses use fractals to find technical patterns in stock market movements. They believe that, unlike traditional measurement and prediction, these nonlinear, systems approaches transcend the human inability to imagine the unthinkable. Even Black Swan author Nassim Taleb, who made a career of warning economists and investors against trying to see the future, believes in the power of fractals to predict the sudden shifts and wild outcomes of real markets. He dedicated the book to Benoit Mandelbrot. While fractal geometry can certainly help us find strong, repeating patterns within the market activity of the 1930s Depression, it did not predict the crash of 2007.

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Since they were successfully applied by IBM’s Benoit Mandlebrot to the problem of seemingly random, intermittent interference on phone lines, fractals have been used to identify underlying patterns in weather systems, computer files, and bacteria cultures. Sometimes fractal enthusiasts go a bit too far, however, using these nonlinear equations to mine for patterns in systems where none exist. Applied to the stock market or to consumer behavior, fractals may tell less about those systems than about the people searching for patterns within them. There is a dual nature to fractals: They orient us while at the same time challenging our sense of scale and appropriateness.

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It’s a sensibility we find reinforced by systems theory and chaos math. Fractals (those computer-rendered topologies that were to early cyberculture what paisley was to the 1960s) help us make sense of rough, natural phenomena, everything from clouds and waves to rocks and forests. Unlike traditional, Euclidean mathematics, which has tended to smooth out complexity, reducing it down to oversimplified lines and curves, fractal geometry celebrates the way real objects aren’t really one, two, or three dimensions, but ambiguously in between. Fractals are really just recursive equations—iterations upon iterations of numbers.

Polaroids From the Dead
by Douglas Coupland
Published 1 Jan 1996

“Kwakiutl and Haida chants,” says Tamara, burrowing into her fanny pack full of pine cones and polished moonstones for a sugar cube, which she finds, then swallows. “Isn’t it great?” She offers a cube to Daniel, who awkwardly declines. The Econoline van next to the fire hosts a 24-inch Hitachi monitor displaying a never-ending spiral of vibrant Mandelbrot fractal patterns. Daniel hears a helium-charged squeaking voice shopping for Ecstasy. Nearby dogs (so many dogs!) gobble discarded grilled-cheese sandwiches and sniff one another’s bums, remembering each other from Dead shows in Meadowlands, Nassau and Shoreline. Emerson and Dale—friends of Ross—discuss the evening’s possible lineup of songs with a curatorial facility Daniel had considered to be held only by his mother’s wine-bore boyfriends.

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This is the Arboretum Restoration Project to preserve marsh and restore oaks. The grass isn’t mown here—it is an experiment in anti-landscaping: to restore what once was. Wear thick pants if you visit—the oatlike grass is dense with last year’s dead brown thistles, brambles, fan palms, orange California poppies and skinny fractal-shaped skeletons of some sort of plant that is, for the moment, out of season but seems to grow quickly enough when in season. There are adolescent oaks, swampy patches, ant holes and chatting birds. A myriad of plants, many of them rare, are tiny but lush in April, and will soon render the landscape almost impenetrable.

The New Trading for a Living: Psychology, Discipline, Trading Tools and Systems, Risk Control, Trade Management
by Alexander Elder
Published 28 Sep 2014

Earlier we spoke about the one great advantage of a private trader over professionals—he may wait for a good trade instead of having to be active each day. The chaos theory confirms that message. The chaos theory also teaches us that orderly structures that emerge from chaos are fractal. The sea coast appears equally jagged whether you look down on it from space or an airplane, from a standing position or on your knees through a magnifying glass. Market patterns are fractal as well. If I show you a set of charts of the same market, having removed time markings, you will not be able to tell whether it is monthly, weekly, daily, or a 5-minute chart. Later in this book (Chapter 39), we'll return to this theme, and you'll see why it is so important to analyze markets in more than one timeframe.

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Channels show where to expect support and resistance in the future. Channels help identify buying and selling opportunities and avoid bad trades. The original research into trading channels was conducted by J. M. Hurst and described in his 1970 book, The Profit Magic of Stock Transaction Timing. The late great mathematician Benoit Mandelbrot was hired by the Egyptian government to create a mathematical model of cotton prices—the main agricultural export of that country. After extensive study, the scientist made this finding: “prices oscillate above and below value.” It may sound simple, but in fact it's profound. If we accept this mathematical finding and if we have the means to define value and measure an average oscillation, we'll have a trading system.

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on CFDs cutting of former institutional traders inability to manage on options per share, limiting psychological effect of 6% Rule to limit 2% Rule to limit Loss aversion Lovvorn, Kerry Low-priced stocks, indictors based on volume of “Low” volume M MAs, see Moving averages MACD, see Moving Average Convergence-Divergence MACD-Histogram combined with channels divergences in Impulse system and market psychology peaks and valleys seasons of semiautomatic divergence scanner slope of time windows of trading rules in Triple Screen system MACD Lines crossover of Signal lines and MACD line in divergences and market psychology trading rules Mackay, Charles MacMillan, Lawrence Magic method gurus Managing trades forecasting vs. and poll-taking by reading markets and managing yourself Mandelbrot, Benoit Margins Margin calls Market(s): attempts to manipulate and automatic trading systems comparing volumes of contango as crowds. See also Mass psychology crowd mentality experts on independent thinking vs. of individuals leaders of crowds reasons for joining crowds wisdom of crowds ETFs groups vs. individuals in harshness of inability to control inside information in overbought and oversold randomness in reading seasons of size of source of money in spikes in as sport theories of timeframes of analysis using multiple timeframes conflicting trading ranges vs. trends in worldwide crowds Market cycle gurus Market data: in computerized technical analysis in moving averages Market indexes, in technical analysis Market makers Market noise: perceived cycles as and placement of stops setting stops outside zone of Market orders bid-ask spreads for slippage on Market panics Market participants, groups of Market tide screen (Triple Screen system) Market time Market Vane Market wave screen (Triple Screen trading system) MAS (Most Active Stocks) indicator Mass manias Mass psychology and emergence of gurus managing trades forecasting vs.

Trend Following: How Great Traders Make Millions in Up or Down Markets
by Michael W. Covel
Published 19 Mar 2007

Institutional Investor, Vol. 34, No. 11 (November 1, 2000), 38. 17. Jerry Parker, The State of the Industry. Managed Account Reports, Inc. (June 2000). 18. Daniel P. Collins, Chenier: Systematizing What Works (Trader Profile). Futures, Vol. 32, No. 9 (July 1, 2003), 86. 19. Roger Lowenstein, Wall Street Journal, June 13, 2003. 20. Benoit B. Mandelbrot, A Multifractal Walk Down Wall Street. Scientific American, Vol. 280, No. 2 (February 1999), 70–73. 21. Larry Swedroe, Buckingham Asset Management. See http://www. bamstl.com/. 22. Larry Swedroe, Buckingham Asset Management. See http://www. bamstl.com/. 23. Mark Rzepczynski, Ph.D., Return Distribution Properties of JWH Investment Programs, Stock and Bond Indices, and Hedge Funds.

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See also drawdowns handling, 22-23, 195-196 Long-Term Capital Management (LTCM) collapse, 156 zero-sum trading, 114-120 lottery example (risk and reward), 250-251 Lowenstein, Roger, 259 Lueck, Martin, 29 lumber trading, 134 Lynch, Peter, 110 Madoff, Bernard, 22, 223 The Man Group, 15, 29, 148, 157-158, 287 Managed Account Reports, 376 Mandelbrot, Benoit B., 228 manias, prospect theory, 194-199 Marcus, Michael, 19, 60, 62, 285 Marino, Dan, 261 market defined, 3-4 inefficiency of, 288-290 role of speculation in, 6 market price. See price market theories fundamental analysis, 7-9 technical analysis, 9-11 Market Wizards (Schwager), xvi, 58 Markowitz, Harry, xx, 86 Martin, Michael, 64 435 Index Martinez, Pedro, 186, 188 Mauboussin, Michael, 124, 181, 218, 226, 286 McCann, Timothy, 285 McCarver, Tim, 214 Meaden, Nicola, 102 Mechanica software, 385-393 mechanical trading systems, 11-12 Melamed, Leo, 123, 273-274 Memos from the Chairman (Greenberg), 205 Mencken, H.

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Donald Rumsfeld, Secretary of Defense 200310 Chaos theory dictates that the world is not linear. The unexpected happens. Spending your time looking for “perfect” is an exercise in futility. The future is unknown no matter how educated a fundamental forecast. Manus J. Donahue III, author of An Introduction to Chaos Theory and Fractal Geometry, addressed a chaotic, nonlinear world: “The world of mathematics has been confined to the linear world for centuries. That is to say, mathematicians and physicists have overlooked dynamical systems as random and unpredictable. The only systems that could be understood in the past were those that were believed to be linear, that is to say, systems that follow predictable patterns and arrangements.

Corporate Finance: Theory and Practice
by Pierre Vernimmen , Pascal Quiry , Maurizio Dallocchio , Yann le Fur and Antonio Salvi
Published 16 Oct 2017

The term is used for perfectly predictable series of data that appear to be illogical. These models are used in a number of sciences, including economics. Mandelbrot has put forward that fractals (or to be more precise, multi-fractals) could provide accurate representations of market price movements. This assumption does not fit with the efficient market theory, not only because the statistical rule for modelling prices is different, but more importantly because Mandelbrot’s assumptions imply that prices have memory, i.e. that they are not independent from past prices. Section 19.6 Term structure of interest rates Because it is a single-period model, the CAPM draws no distinction between short-term and long-term interest rates.

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The first issue with efficient market theory seems very intuitive: how can markets be so volatile? Information on Sanofi is not published every second. Nevertheless, the share price does move at each instant. There seems to be some kind of noise around fundamental value. As described by Benoit Mandelbrot, who first used fractals in economics, prices evolve in a discrete way rather than in a continuous manner. Dual listing and closed-end funds. Dual listings are shares of twin companies listed on two different markets. Their stream of dividends is, by definition, identical but we can observe that their price can differ over a long period of time.

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labour risk large shareholder, company without last in, first out (LIFO) method LBO see leveraged buyout LBU see leveraged build-up lead manager, banks lease rights leases legal action legal framework, shareholders legal merger legal protection, corporate structure legal risks legal structure listed companies mergers and acquisitions lenders to companies internal financing LBO funds restructuring plans letter of intent (LOI) level of control, consolidation leverage effects calculation capital structure cost of capital cost of debt enterprise value equation formulation financing and futures/options margin analysis practical problems presentation principle of risk management usefulness uses/limitations of leveraged build-up (LBU) leveraged buyout (LBO) company managers employee-shareholders financial theory funds larger context market negotiating strategy players principle private equity funds structures transactions types warrants (leveraged) management buyout ((L)MBO) leveraged recapitalisation liabilities balance sheet bankruptcy consolidated accounts deferred financing sources cost illiquidity risk legal merger maturity structure negotiation and off-balance-sheet option theory pensions as shareholders licensing offers, real options lifecycle of company lifecycle of financing sources lifecycle theory, company value LIFO see last in, first out method limited companies limited liability limited share partnerships (LSPs) liquid funds, foregoing liquidation of assets liquidation value, SOTP method liquidity analysing balance sheet cash investment centralisation of consideration of financing choice effects of investments lack of listed companies market data markets secondary market shares standardisation of contracts working capital liquidity crisis liquidity discount assessment liquidity flows estimation liquidity preference theory liquidity premium liquidity ratios liquidity risk listed companies capital increases capital markets consolidated accounts control change corporate governance IPOs minority interests preference shares ROCE for ROE for shareholder structure taking over working capital listed contracts listing bonds shares subsidiaries (L)MBO see (leveraged) management buyout loan documentation loans amortisation asset-backed banks bonds and to companies convertible bonds and corporate risk principal amount of real estate backing see also business loan types; syndicated loans lock up commitment locked-box system locking in future prices/rates logistics LOI (letter of intent) long form report (vendor due diligence) long positions long-term bonds long-term financial resources long-term marketable securities long-term rates liquidity premium maturities long-term ratings lookback options loss-making companies loss probability risk losses capital carried forward deferred tax assets/liabilities see also impairment losses; profit and loss love money loyalty, shareholders LSPs see limited share partnerships M&A see mergers and acquisitions MAC see material adverse change macroeconomic factors majority shareholders, listed companies management accounting approach management buy-in (MBI) management companies, LBO funds management compensation transparency management control combination debt financial control separation management incentive package management-incentivisation tools management reputation management strategy, definition management team motivation managerial entrenchment managers character importance internal financing LBO company minority shareholder as role in value creation share issue trade receivables warrant benefits working capital management see also corporate managers; entrepreneurs; financial manager mandated lead arrangers (MLAs) mandatory convertibles mandatory offers Mandelbrot’s assumptions, fractals MAR see market abuse regulations margin analysis risks structure margin calls marginal return, retained earnings margins profitability distinction ROCE calculation working capital market bonds corporate control definition efficient markets key data leveraged buyout strategic position in see also financial markets market abuse regulations (MAR) market authority role market-based economies market-based relationship, supplier/company market capitalisation market changes bankruptcy risk linked to market choice, IPOs market criteria, value creation market data, cost of capital market economies see market-based economies market in equilibrium theory market growth market independence, SOTP method market indicators market leverage see also leverage effects market logic market multiples market portfolio market positions, risk market rates, bonds and market risk hedging position/measurement of value and market scope, company control market segmentation market share market supervisory authorities market theory, perfect capital market value book value and capital employed company management effect cost of financing equity capital equity/debt fair value financial securities financing sources goodwill intangible fixed assets intrinsic value and investments solvency SOTP method underlying asset market value added (MVA) marketable debt securities marketable securities marketing campaigns mass production master credit agreement matching hypothesis material adverse change (MAC) mathematical approach, risk assessment mathematical hope concept maturities/maturity cash flow value choosing debt futures interest rate relationship yield to maturity of bonds maturity of company payout ratio real-estate financing maturity mismatch, illiquidity risk maturity of options maturity structure illiquidity risk liabilities maximum rise assessment MBI see management buy-in mean value multiples measures of stock market value creation Meckling, W.

In Pursuit of the Perfect Portfolio: The Stories, Voices, and Key Insights of the Pioneers Who Shaped the Way We Invest
by Andrew W. Lo and Stephen R. Foerster
Published 16 Aug 2021

An occasional presenter was Benoit Mandelbrot, a highly regarded mathematician on staff as a researcher at the IBM Thomas J. Watson Research Center and a visiting professor at Harvard University, today best known for his work on fractals and their irregular geometry. Fama enjoyed strolling the campus with Mandelbrot and learned much about probability distributions from him, including Mandelbrot’s research on cotton prices. As noted earlier, most people are familiar with the normal distribution or bell curve, in which a population clusters around an average much like the shape of a bell. However, Mandelbrot studied other distributions that had “fatter” tails than the normal distribution, meaning a greater likelihood of extreme events.

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Fama also showed that successive price changes conformed to a probability distribution—not the heads/tails of the coin flip but instead something closer to the classic bell curve or normal distribution. Fama concluded that “chart reading, though perhaps an interesting pastime, is of no real value to the stock market investor.”20 Furthermore, he found statistical evidence, consistent with Mandelbrot’s research into cotton prices, that stock price changes or returns were distributed with fatter tails than one would expect with a normal distribution. In other words, on numerous occasions there were more extreme daily gains and losses of the sort that would only occur once in several decades if stock returns were truly following a normal distribution.

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K., 259 KMV, Merton Model and, 185 Kogelman, Stanley, 212, 214 Koopmans, Tjalling, 20–21; association with Marschak, 20–21; linear programming and, 26–27, 40; as Nobel Prize winner, 22 Kritzman, Mark, 45 Kurosawa, Akira, 308 Langetieg, Terry, 214 Law, John, 10–11 Law, William, 10 law of the average covariance, 40–41 LeBaron, Dean, 348n46 Leibowitz, Martin, 199–225; alpha and, 218–20; asset allocation and, 216–18, 223–24; asset-liability management and, 213–15; awards and recognition received by, 199–200; bond price volatility and, 211; bonds and, 202, 203–13; bond swaps and, 211–12; collaboration with Homer, 206, 208, 209–12; connections to other pioneers, xiv; early life of, 200; education of, 201, 202; endowment model and, 220–21; impact of bond return assessment and, 210–11; at Morgan Stanley, 216; operations research work of, 201–2; Perfect Portfolio of, 221–25, 316–17; publications of, 199, 201, 209, 212, 213–14, 217, 218–19, 220–21; relationship with Homer, 202–3; on risk, 216–18, 220–21, 224, 316–17; at Salomon Brothers, 204–13; at TIAA-CREF, 215–16 Lekdijk Bovendams bonds, 7–8 Leontief, Wassily, 179 LeRoy, Stephen, 234–35 Leuthold Group, 125 Levite, Gertrude, 281 Lewis, Michael, 354n56 liability-driven investing, Leibowitz’s work in, 213–15 Liar’s Poker (Lewis), 354n56 Liber de Ludo Aleae (The Book on Games of Chance) (Cardano), 15 Lieberman, Gerald, 201 Liew, John, 110 Lincoln, Robert, 256 linear programming, 26–27, 40 Lintner, John, 70–71 Litzenberger, Robert, tribute to Sharpe, 75 Lo, Andrew, 320 Locke, John, 333 Long-Term Capital Management (LTCM), 158, 188–89 Lorie, James, 90, 147, 158, 201 Los Angeles Dodgers, 176 “The Loser’s Game” (Ellis), 255, 264 Lucas, Robert E., Jr., 344n28 Lufkin, Dan, 260 MacAvoy, Paul, 183 MacBeth, James, 99–100, 143 Mackay, Charles, 9 Maclachlan, Fiona, 38 MacroShares, 250–51 Mahovlich, Frank, 350n4 Mahovlich, Pete, 350n4 Malkiel, Burton, 277; on Bogle’s influence, 113; praise for Bogle’s foresight, 125; publications of, 276; on savings, 276 Mandelbrot, Benoit, 86 Manias, Panics, and Crashes: A History of Financial Crises (Kindleberger), 240–41 Manuel I Komnenos, 7 Marcus, Jim, 202, 356n9 market efficiency: Markowitz on, 47, 310; Thaler on, 245. See also efficient market hypothesis (EMH) “Market Efficiency, Long-Term Returns, and Behavioral Finance” (Thaler), 245 “Market Efficiency: A Theoretical Distinction and So What?”

Fooled by Randomness: The Hidden Role of Chance in Life and in the Markets
by Nassim Nicholas Taleb
Published 1 Jan 2001

In Eatwell, J., Milgate, M., and Newman P., eds., 1987, The New Palgrave: A Dictionary of Economics. London: Macmillan. MacKay, Charles, 2002, Extraordinary Popular Delusions and the Madness of Crowds. New York: Metro Books. Magee, Bryan, 1997, Confessions of a Philosopher. London: Weidenfeld & Nicholson. Mandelbrot, Benoit B., 1997, Fractals and Scaling in Finance. New York: Springder-Verlag. Markowitz, Harry, 1959, Portfolio Selection: Efficient Diversification of Investments, 2nd ed. New York: Wiley. Meehl, Paul E., 1954, Clinical Versus Statistical Predictions: A Theoretical Analysis and Revision of the Literature.

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While it is clear that the world produces clusters it is also sad that these may be too difficult to predict (outside of physics) for us to take their models seriously. Once again the important fact is knowing the existence of these nonlinearities, not trying to model them. The value of the great Benoit Mandelbrot’s work lies more in telling us that there is a “wild” type of randomness of which we will never know much (owing to their unstable properties). Our Brain Our brain is not cut out for nonlinearities. People think that if, say, two variables are causally linked, then a steady input in one variable should always yield a result in the other one.

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The reasons economists never liked to use it is that it does not offer tractable properties—economists like to write papers in which they offer the illusion of solutions, particularly in the form of mathematical answers. A Pareto-Levy distribution does not provide them with such luxury. For economic discussions on the ideas of Pareto, see Zajdenweber (2000), Bouvier (1999). For a presentation of the mathematics of Pareto-Levy distributions, see Voit (2001), and Mandelbrot (1997). There is a recent rediscovery of power law dynamics. Intuitively a power law distribution has the following property: If the power exponent were 2, then there would be 4 times more people with an income higher than $1 million than people with $2 million. The effect is that there is a very small probability of having an event of an extremely large deviation.

Turing's Cathedral
by George Dyson
Published 6 Mar 2012

Veblen, adds Montgomery, “said he and Einstein and Weyl didn’t feel up to that.”49 The other Institute was the annually changing group of mostly young visitors at the beginning of their careers, interspersed with occasional established scholars taking a year off. Benoît Mandelbrot, who arrived at von Neumann’s invitation in the fall of 1953 to begin a study of word frequency distributions (sampling the occurrence of probably, sex, and Africa) that would lead to the field known as fractals, notes that the Institute “had a clear purpose and a rather strange structure in which to assemble people: heavenly bodies in residence, and then nobody, nobody, nobody, and then mostly young people. Now it has a much more balanced distribution in terms of age and fame.” Mandelbrot got along wonderfully with von Neumann, admiring how he “had accumulated a number of people who were not part of the Princeton pigeon holes,” while observing that among the visiting scholars, “everybody else had the dreadful feeling that this may be the best year of their life, so why wasn’t it more enjoyable?”

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Nothing about computers, the subject that we knew was dearest to von Neumann’s heart. Somebody said in a voice loud enough to be heard all over the hall, ‘Aufgewärmte Suppe,’ which is German for ‘warmed-up soup.’ ”53 Afterward, says Benoît Mandelbrot, “I saw von Neumann leaving the hall. He was all by himself, lost in thought. Nobody was following him, and he was rushing somewhere, by himself.” Over the next several days, Mandelbrot noticed an “old man, hanging around with us, and I asked him what he was doing.” This was Michael Fekete, with whom von Neumann had published his first paper, at age eighteen, in 1922. Fekete, who had gone on to become the first professor of mathematics at the Hebrew University of Jerusalem, answered that “von Neumann wrote his first paper in collaboration with me.

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Archivists Christine Di Bella, Erica Mosner, and all the staff at the Institute, especially Linda Cooper, helped in every capacity, and the current trustees, especially Jeffrey Bezos, have lent continuing encouragement and support. Many of the surviving eyewitnesses—including Alice Bigelow, Julian Bigelow, Andrew and Kathleen Booth, Raoul Bott, Martin and Virginia Davis, Akrevoe Kondopria Emmanouilides, Gerald and Thelma Estrin, Benoît Mandelbrot, Harris Mayer, Jack Rosenberg, Atle Selberg, Joseph and Margaret Smagorinsky, Françoise Ulam, Nicholas Vonneumann, Willis Ware, and Marina von Neumann Whitman—took time to speak with me. “You’re within about five years of not having a testifiable witness,” Joseph Smagorinsky warned me in 2004. In 2003 the Bigelow family allowed me to go through the boxes of papers that Julian had saved.

Handbook of Modeling High-Frequency Data in Finance
by Frederi G. Viens , Maria C. Mariani and Ionut Florescu
Published 20 Dec 2011

Scale-invariant truncated Levy process. Europhys Lett 2000;52:491–497. 26. Shiryaev AN. Essentials of the stochastic finance. World Scientific, Hackensack, New Jersey; 2008. 27. Hurst HE. Long term storage of reservoirs. Trans Am Soc Civ Eng 1950;116:770–808. 28. Mandelbrot BB, Van Ness JW. Fractional Brownian motions, fractional noises and applications. SIAM Rev 1968;10(4): 422–437. 29. Mandelbrot BB. The fractal geometry of nature. New York: Freeman and Co.; 1982. 30. Ivanova K, Ausloos M. Application of the Detrended Fluctuation Analysis (DFA) method for describing cloud breaking. Physica A 1999;274:349–354. 162 CHAPTER 6 Long Correlations Applied to the Study of Memory 31.

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This model assumes that the increment of the logarithm of prices follows a diffusive process with Gaussian distribution [12]. However, the empirical study of temporal series of some of the most important indices shows that in short time intervals, the associated pdfs have greater kurtosis than a Gaussian distribution [5]. The first step to explain this behavior was done in 1963 by Mandelbrot [13]. He developed a model for the evolution of cotton prices by a stable stochastic non-Gaussian Levy process; these types of non-Gaussian processes were first introduced and studied by Levy [14]. The other major problem encountered in the analysis of the behavior of different time-series data is the existence of long-term or short-term correlations in the behavior of financial markets (established versus emerging markets [15], developed countries’ market indices [1–5], Bombay stock exchange index [16], Latin American indices [17], and the references therein).

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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.

The Loop: How Technology Is Creating a World Without Choices and How to Fight Back
by Jacob Ward
Published 25 Jan 2022

Goldman titled his article “Lindy’s Law,” and successive generations of writers seized on his theme as a way of predicting the longevity of certain ideas and works of art. This wasn’t just wannabe Late Night writers ruminating over bad coffee. Goldman’s concept launched a whole world of statistical thinking. The mathematician Benoit Mandelbrot updated the model in a 1982 book about fractals to posit that comedians who have made appearances in the past are more likely to make them in the future. Nicholas Taleb carried Mandelbrot’s concept into his book Black Swan, and in his book Antifragile put a specific math to the notion that as an idea survives, its longevity increases. “Every year that passes without extinction doubles the additional life expectancy,” Taleb writes.

The Road to Ruin: The Global Elites' Secret Plan for the Next Financial Crisis
by James Rickards
Published 15 Nov 2016

Good Money Part I: The New World. Indianapolis: Liberty Fund, 1999. ———. Good Money Part II: The Standard. Indianapolis: Liberty Fund, 1999. Hudson, Michael. Killing the Host: How Financial Parasites and Debt Destroy the Global Economy. Bergenfield, NJ: ISLET, 2015. Hudson, Richard L., and Benoit Mandelbrot. The (Mis)behavior of Markets: A Fractal View of Risk, Ruin, and Reward. New York: Basic Books, 2004. Hui, Pak Ming, Paul Jefferies, and Neil F. Johnson. Financial Market Complexity: What Physics Can Tell Us About Market Behavior. Oxford: Oxford University Press, 2003. Jensen, Henrik Jeldtoft. Self-Organized Criticality: Emergent Complex Behavior in Physical and Biological Systems.

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Conspiracies of the Ruling Class: How to Break Their Grip Forever. New York: Simon & Schuster, 2016. Lowenstein, Roger. When Genius Failed: The Rise and Fall of Long-Term Capital Management. New York: Random House, 2000. Makin, John H. The Global Debt Crisis: America’s Growing Involvement. New York: Basic Books, 1984. Mandelbrot, Benoit B. The Fractal Geometry of Nature. New York: W. H. Freeman and Company, 1983. Martin, Felix. Money: The Unauthorized Biography. New York: Alfred A. Knopf, 2014. Marx, Karl. Selected Writings. Edited by David McLellan. New York: Oxford University Press, 1977. McGrayne, Sharon Bertsch. The Theory That Would Not Die: How Bayes’ Rule Cracked the Enigma Code, Hunted Down Russian Submarines, and Emerged Triumphant from Two Centuries of Controversy.

To Sleep in a Sea of Stars
by Christopher Paolini
Published 14 Sep 2020

A sigil lay there, set within the surface of the material, and the sight of it froze her in place. The emblem was a line of fractal shapes, coiled close, one upon another. Kira couldn’t decipher any meaning, but she recognized the language as belonging to the same, all-important pattern that guided the Soft Blade’s existence. Unable to take her eyes off the sigil, she backed away. “What is it?” Falconi asked. “I think the Vanished made the Great Beacon,” she said. Koyich readjusted the sling on his gun. “What makes you think that?” She pointed. “Fractals. They were obsessed with fractals.” “That doesn’t help us now,” said Koyich. “Not unless you can read them.”

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To that end, Kira was willing to fight, and she was willing to kill and destroy in order to stop the graspers. Then her vision sharpened and telescoped, and she felt as if she were falling into the fractal. It expanded before her in endless layers of detail, flowering into an entire universe of theme and variation.… Pain roused Kira. Shocking, searing pain. The pressure around her torso vanished, and she filled her lungs with a desperate gasp before loosing a scream. Her vision cleared, and she saw the tentacle still encircling her. Only now a belt of thorns—black and shiny and tangled in a familiar fractal shape—extended from her torso, piercing the twitching limb. She could feel the thorns, same as her arms or legs, new additions but familiar.

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“Therefore, we wished to thank you for sharing the information about your suit with us, and—” “—for giving us the opportunity to explore the Jelly ship—” “—and we wish to give you this,” said Jorrus. He handed her a small, gem-like token. It was a disk of what looked like sapphire with a fractal pattern embedded within. The sight of the fractal gave Kira a shiver of familiarity. The pattern wasn’t the one from her dreams, but it was similar. “What is it?” Veera spread her hands in a gesture of benediction. “Safe passage to the Motherhouse of our order, the Nova Energium, in orbit around Shin-Zar. We know—” “—you feel compelled to assist the League, and we would not dissuade you.

Descartes' Error: Emotion, Reason and the Human Brain
by António R. Damásio
Published 1 Jan 1994

If those symbols were not imageable, we would not know them and would not be able to manipulate them consciously. In this regard, it is interesting to observe that some insightful mathematicians and physicists describe their thinking as dominated by images. Often the images are visual, and they even can be somatosensory. Not surprisingly, Benoit Mandelbrot, whose life work is fractal geometry, says he always thinks in images.14 He relates that the physicist Richard Feynman was not fond of looking at an equation without looking at the illustration that went with it (and note that both equation and illustration were images, in fact). As for Albert Einstein, he had no doubts about the process: The words or the language, as they are written or spoken, do not seem to play any role in my mechanism of thought.

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N. Shepard and L. A. Cooper (1982). Mental Images and Their Transformations. Cambridge, MA: MIT Press. S. M. Kosslyn (1980). Image and Mind. Cambridge, MA: Harvard University Press. For a historical review, see also Howard Gardner (1985). The Mind’s New Science. New York: Basic Books. 14. B. Mandelbrot, personal communication. 15. A. Einstein, cited in J. Hadamard (1945). The Psychology of Invention in the Mathematical Field. Princeton, NJ: Princeton University Press. 16. The following are key references on this subject: D. H. Hubel and T. N. Wiesel (1965). Binocular interaction in striate cortex of kittens reared with artificial squint, Journal of Neurophysiology, 28:1041–59.

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C., 281, 291, 296 Lezak, M., 272 “Liberte” (Eluard), 253 Lima, Almeida, 58, 265–66 Limbic cortex, 27 Limbic system, 28, 118 Livingstone, M. S., 279 Llinas, Rodolfo, 236, 277 Lowel, S., 277 Luria, A. R., 294 MacMillan, M. B., 16, 270 McCulloch, Warren, 12–13 McEwan, B. S., 281 McGinness, E., 277 McKinley, J. C., 272 McLaughlin, T., 282 McNeil, B. J., 272 Magnusson, D., 295 Maljkovic, V., 279 Mandelbrot, Benoit, 107, 280 Mandler, George, 129, 283, 294 Manktelow, K. I., 288 Marcel, A., 64, 273 Marder, E., 282 Marshall, J., 270 Martin, J. H., 271 Means-End Problem-Solving Procedure, 47 Medawar, J. S., 296 Medawar, P. B., 296 Medicine, neurobiology and, 254–58 Meningiomas, 35–36 Merzenich, Michael, 103, 144, 278, 280 Mesulam, M.

The Great Mental Models: General Thinking Concepts
by Shane Parrish
Published 22 Nov 2019

My First Summer in the Sierra. Boston: Houghton Mifflin, 1911. 5 Schiff, Stacy. Cleopatra: A Life. New York: Back Bay Books, 2010. 6 Wollstonecraft, Mary. A Vindication of the Rights of Woman. London: 1792. 7 Hardin, Garrett. Filters Against Folly. New York: Penguin, 1985. Probabilistic Thinking 1 Mandelbrot, Benoit. The Fractal Geometry of Nature. New York: W.H. Freeman and Company, 1977. 2 Kahneman, Daniel and Tversky, Amos. Judgment under Uncertainty: Heuristics and Biases. Science. Volume 185, 1974. 3 Bernstein, Peter L. Against the Gods: The Remarkable Story of Risk. New York: John Wiley and Sons, 1996.

Tools for Computational Finance
by Rüdiger Seydel
Published 2 Jan 2002

Cambridge University Press, Cambridge (2002). L.W. MacMillan: Analytic approximation for the American put option. Advances in Futures and Options Research 1 (1986) 119-139. R. Mainardi, M. Roberto, R. Gorenflo, E. Scalas: Fractional calculus and continuous-time finance II: the waiting-time distribution. Physica A 287 (2000) 468-481. B.B. Mandelbrot: A multifractal walk down Wall Street. Scientific American, Febr. 1999, 50–53. M. Marchesi, S. Cinotti, S. Focardi, M. Raberto: Development and testing of an artificial stock market. Proceedings Urbino 2000, Ed. I.-G. Bischi (2000). References [Mar78] [Ma68] [MaB64] [Mas99] [MaPS02] [MaN98] [Mayo00] [McW01] [MeVN02] [Mer73] [Mer76] [Me90] [Mik98] [Mi74] [Moe76] [Moro95] [MC94] [Mo98] [Mo96] [MR97] [Ne96] [New97] [Ni78] [Ni92] 289 W.

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T T T The first two terms represent a straight-line connection between y0 and yT . This straight line stands for the trend. The term Wt − Tt WT describes the stochastic fluctuation. For its realization an appropriate volatility can be prescribed (−→ Exercise 3.7). Another alternative to fill large gaps is to apply fractal interpolation [Man99]. 3.5 Monte Carlo Simulation As pointed out in Section 2.4 in the context of calculating integrals, Monte Carlo is attractive in high-dimensional spaces. The same characterization holds when Monte Carlo is applied to the valuation of options. For sake of clarity we describe the approach in the one-dimensional context.

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John Wiley, New York (1979). 284 References [BV00] [BS73] [Blo86] [BP00] [Bo98] [BoM58] [BBG97] [BTT00] [Br91] [BrS77] [BrS02] [Br94] [BrD97] [BrG97] [BrG04] [BH98] [BuJ92] [CaMO97] [CaF95] [CaM99] [Cash84] [CDG00] G.I. Bischi, V. Valori: Nonlinear effects in a discrete-time dynamic model of a stock market. Chaos, Solitons and Fractals 11 (2000) 21032121. F. Black, M. Scholes: The pricing of options and corporate liabilities. J. Political Economy 81 (1973) 637–659. E.C. Blomeyer: An analytic approximation for the American put price for options with dividends. J. Financial Quantitative Analysis 21 (1986) 229-233. J.-P. Bouchaud, M.

Frequently Asked Questions in Quantitative Finance
by Paul Wilmott
Published 3 Jan 2007

This is more like an actuarial approach to model risk. • If neither of the above is possible then he could widen his bid-ask spreads. He will then only trade with those people who have significantly different market views from him. References and Further Reading Mandelbrot, B & Hudson, R 2004 The (Mis)Behaviour of Markets: A Fractal View of Risk, Ruin and Reward. Profile Books How Robust is the Black-Scholes Model? Short Answer Very robust. You can drop quite a few of the assumptions underpinning Black-Scholes and it won’t fall over. Example Transaction costs? Simply adjust volatility.

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If Wt is the BM at time t then for every t, τ ≥ 0, Wt+τ − Wt is independent of {Wu : 0 ≤ u ≤ t}, and has a normal distribution with zero mean and variance τ. The important properties of BM are as follows. • Finiteness: the scaling of the variance with the time step is crucial to BM remaining finite. • Continuity: the paths are continuous, there are no discontinuities. However, the path is fractal, and not differentiable anywhere. • Markov: the conditional distribution of Wt given information up until τ < t depends only on Wτ . • Martingale: given information up until τ < t the conditional expectation of Wt is Wτ. • Quadratic variation: if we divide up the time 0 to t in a partition with n + 1 partition points ti = it/n then • Normality: Over finite time increments ti−1 to ti, is normally distributed with mean zero and variance ti − ti−1.

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After the second iteration you add an area that is number of sides multiplied by area of a single small triangle which is one ninth of the previously added triangle. If we use An to be the area after n iterations (when multiplied by the area of initial triangle) then So The final calculation exploits the binomial expansion. This is the famous Koch snowflake, first described in 1904, and is an example of a fractal. The doors There are one hundred closed doors in a corridor. The first person who walks along the corridor opens all of the doors. The second person changes the current state of every second door starting from the second door by opening closed doors and closing open doors. The third person who comes along changes the current state of every third door starting from the third door.

The Vanishing Face of Gaia: A Final Warning
by James E. Lovelock
Published 1 Jan 2009

May found that computer models of population growth showed similar chaotic behaviour, especially in biological systems containing more than two species; these discoveries stirred great interest among mathematicians and scientists in the nature of deterministic chaos. Practical applications in communications and to new art forms have emerged, for example those stunning illustrations of fractal mathematics such as the Mandelbrot set. It was so human and apparently understandable that neither of these eminent scientists made much of the fact that the appearance of chaos suggested that something might be wrong with their hypotheses about the world. Lorenz and May were both looking at the Earth system from within separated scientific disciplines that took cause‐and‐effect determinism for granted.

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Systems like the weather, the motion of more than two astronomical bodies linked by gravitation, or more than two species in competition, are exceedingly sensitive to the initial conditions of their origin, and they evolve in a wholly unpredictable manner. The study of these systems is a rich and colourful new field of science enlivened by the visual brilliance of the strange images of fractal geometry. It is important to note that efficient dynamic mechanical systems, such as the autopilot of an aircraft, are essentially free of chaotic behaviour, and the same is true of healthy living organisms. Life can opportunistically employ chaos, but it is not a characteristic part of its normal function.

The Musical Human: A History of Life on Earth
by Michael Spitzer
Published 31 Mar 2021

You might have come across Calista and the Crashroots’ ‘Deepdream’, the first music video created by this programme.52 It is a swirling, psychedelic sea of surreal images in which humans turn into dogs, mountains into buildings, eyes appear everywhere, and the camera zooms through layer upon layer of detail, like the fractal iterations of a Mandelbrot set (see Figure 11.2). It is either a dream or a nightmare, depending on your taste. In any case, DeepDream has gone viral since Google released the source code to developers, and it became an app anyone can use to spice up their videos.53 Figure 11.2 A DeepDream Fractal The point is that DeepDream reveals human creativity in the raw, stripped down to its own source code, as it were: the phenomenon called ‘pareidolia’.

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On an acoustic level, for music of many styles, the spectral density of the audio signal is inversely proportional to its frequency according to a 1/f distribution.58 Even more extraordinary, 1/f ratios have been detected in many biological systems, and the neuroscientist Daniel Levitin has even reported that human sensory and brain systems have evolved around 1/f pink noise.59 There is an even tighter link between pink noise and music: fractals.60 Noise is fractal because it exhibits self-similarity across orders of magnitude. Whether you increase or decrease magnification, the noise waveforms look the same, as do coastlines, mountains, trees, clouds, even the turbulent clouds of gas and dust in the Orion nebula.61 The patterns are infinitely recursive. The only human art form that has this feature (other than visualisations of fractals, obviously) is music, the stereotypical art of repetition. Music endlessly repeats at every level, and the reason why we don’t find this boring is that the repetitions are subtly different each time.62 We find such recursion not only in octaves but in rhythm and form: the pattern of beats in a bar mirrored by the pattern of bars in a phrase, of phrases in a section, of sections in a movement, of movements in a symphony, and so on.

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Coming at the problem from an opposite direction (themes, not tonality), he thought of music as an endless cycle of variations (‘developing variation’), repeating the same ‘basic shape’ (Grundidee) at rising structural levels.64 His is the most convincing analysis of Beethoven’s musical logic that we have. Fractals have also been taken up by contemporary composers. Ligeti, Xenakis, Grisey and Haas, four of the greatest composers of the late twentieth century, all embraced fractal principles self-consciously, deliberately absorbing the contours of natural processes.65 Reciprocally, computers have been fed pink noise as a raw material to produce music, and fractals have inspired a new breed of algorithmic composition based on ‘cellular automata’ – discrete dynamic systems formed of simple computational units that behave like living cells.66 While the results are not very polished, this musical simulation of artificial life is perhaps the most promising direction for AI composition.

Ways of Being: Beyond Human Intelligence
by James Bridle
Published 6 Apr 2022

On each measurement, the reading would get more accurate, with more and more of the coastline accounted for. But the result, as Richardson realized, was not that the measurement converged on the correct answer but rather, the more closely it was measured, the longer it got. What Richardson had discovered was what the mathematician Benoit Mandelbrot would later term ‘fractals’: structures which repeat to infinite complexity. Instead of resolving into order and clarity, ever-closer examination reveals only more, and more splendid, detail and variation.26 The Richardson effect applies to biology, archaeology, evolution and, it seems, to life itself. As our archaeological and biological tools get better, as we unravel the web of life, the result is not an ordered tree, with measurable branches and clear delineations between forms and types, but a whirling dance of encounters and interrelationships.

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Richardson explicitly discusses the coastline paradox in Lewis F. Richardson, ‘The Problem of Contiguity: An Appendix to Statistics of Deadly Quarrels’, General Systems: Yearbook of the Society for the Advancement of General Systems Theory, 6(139), 1961, pp. 139–87. 26. Mandelbrot built directly on Richardson’s work, inspired by his work on coastlines. See B. Mandelbrot, ‘How Long is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension’, Science, new series, 156(3775), 5 May 1967, pp. 636–8. 27. For Woese and Fox’s original paper, see C. R. Woese and G. E. Fox, ‘Phylogenetic Structure of the Prokaryotic Domain: The Primary Kingdoms’, Proceedings of the National Academy of Science, USA, 74(11), November 1977, pp. 5088–90; DOI: 10.1073/pnas.74.11.5088.

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Ross 181–3, 185 aspens 77 astrobiology 87 atomic bomb 224–5 Augustin, Regynald 156 Australopithecus 88 Author of the Acacia Seeds, The 169–71 automatic machine see Turing machine Autonomous Trap 26–7, 26, 204 autonomous vehicles 23–6, 65, 275 avocados 108 Babbage, Charles 30 baboons 32, 52–55, 64, 74 bacteria 17, 87–8, 104–10, 236–7, 248, 300 badgers 291 Barabási, Albert-László 81 Barad, Karen 84–6, 130, 249 Basilicata 138, 140–43 bears 1, 89–90, 92, 266, 290–91, 293–4 beavers 256 BeeAdHoc (computer programme) 262 beech 125, 142 Beer, Stafford 184–91, 211, 214–15, 230 bees 145, 187, 258–62 Bergson, Henri 279 Berners-Lee, Tim 81 birch 60, 118, 124, 138, 279 Black Language 168 Black Lives Matter 155 Blake, William 16 Blas, Zach 208 Boeing X-37 136 Bonner, John Tyler 238–9 bonobos 37, 50, 98 Boran (people) 146 Bornmuellera tymphaea 309 Boulez, Pierre 229 Boulle, Marcellin 90 Bouvet, Joachim 234 bow-wow theory 148 Brainfuck (programming language) 161–2 Brassica juncea 310 Bruniquel cave 92 buen vivir 268 cacti 64, 235, 294 Cage, John 227–35, 241, 242, 312 Cambridge Analytica 155 cantu a tenòre 148 capuchin monkeys 163 Caputo, Francesco 143 Caputo, Matteo 143 caribou 120 Carrol, Lewis 180 Carson, Rachel 12, 15 Castro, Eduardo Viveiros de 18 caterpillars 65 Cecilia (chimpanzee) 265 cedars 138 cephalopods 47–51 CERN 81 Charlotte (gibbon) 32 Chassenée, Bartholomew 252 Chaucer, Geoffrey 152 Chernobyl 293 Chesapeake Bay Model 202, 203, 204 chestnuts 61, 118 Children of Time 49 chimpanzees 36–37, 50, 55–6, 88, 98, 145 choice machine see oracle machine Christ Stopped at Eboli 140 Christmas Island 293, 295 Chua, Leon O. 194 Chucho (bear) 266 Churchill, Winston 18 Citizens’ Assembly 243–5 Clarke, Arthur C. 158 climate change 5–6, 121–4, 242–5, 282, 301–2 climate modelling 78–9 Cloud (computing) 111–12, 158–9 Cochran, William 285, 297 cockatoos 163 Cockroach Controlled Mobile Robot see Roachbot cockroaches 212, 258 cognitive diversity 246–8 Colossus (computer) 220 ‘Computing Machinery and Intelligence’ 29 Conway’s Game of Life 161 corn 75 Corraro, Rosina 143 cougars 290 Covid-19 114 cows 140, 143, 149, 265, 302 crabs 48, 195–7, 256, 293, 293–5, 293, 307, 312 cuckoos 118 cuttlefish 47, 49 Cybernetic Factory 185, 186, 189–90 Cybernetic Serendipity 231 cybernetics 181–90, 214 Dallol see Danakil Depression Danakil Depression 86–8, 104 Daphnia 188–9, 191, 198 Darwin, Charles 12, 34–6, 72, 89, 127–30, 129, 235, 239 Darwin, Francis 127–30, 129 De Anima 122 de Martino, Ernesto 141–2 de Waal, Frans 39 Debord, Guy 24 decentralization 49, 208–10, 213, 280 DeepMind 8, 275 deer 65, 77, 258, 290–93, 298–9, 299 Delphi 174, 177 demilitarized zone (DMZ) 292 Denisova Cave 96 denisovans 96–8, 100 Denny (denisovan) 97, 100 Descartes, René 16 Descent of Man, The 36 Dimkaroski, Ljubem 90 ding-dong theory 147 Dinkinesh (Australopithecus) 88 distributed computing 209 Divje Babe 90–91, 91 DNA 95–7, 103–7 dodder vine 75 dogs 147–8, 163, 302 spinal dog 184, 212 Dolphin Embassy 165–6, 165 dolphins 37–8, 41–2, 145, 166, 170, 263, 286 Doolittle, Ford 109–10 Duchamp, Marcel 128–31, 129 ducks 256 earthquakes 302–3 Ebonics 168 EDVAC (computer) 223, 230 Eglash, Ron 156 elephants 34, 38–9, 40–44, 41, 64, 250–51, 263–5, 278, 291–2, 296, 312 Elmer (robot tortoise) 180 Elsie (robot tortoise) 180 email apnea 155 Emojicode (programming language) 161, 173 endosymbiosis 108 ENIAC (computer) 225, 230 Epirus 1–5, 308–9, 311 Epstein, Jean 138 ERNIE (computer) 220–22, 221, 222, 226, 236 Euglena 188–91 Euler, Leonhard 81 European Green Belt 292 evolution 12, 54, 67, 71, 96, 102, 146, 164, 235, 241, 247, 311 of computers 222 convergent evolution 42, 51, 231, 262 Darwin’s theories 36, 89, 128, 132, 235, 256 process 107–12 randomness 235–40 tree of evolution 47, 50–51, 96, 100 Explanation of Binary Arithmetic 234 Facebook 154, 275 ethics 277 gender categories 111–12, 208 language applications 167–9, 173 Fensom, Harry 220 finches 132, 235, 239 firs 60, 142, 279 Flowers, Tommy 220 Folding@home 209 Forte, Giovanni 143, 144 fossil fuels 3–6 Franklin, Benjamin 248 Fredkin, Edward 195 Frisch, Karl von 259 fungi 11, 17, 60–63, 78–82, 106–8, 128, 192, 290 Gagliano, Monica 71–5, 127, 303, 319 Gaia (goddess) 174, 190, 215 Gaia theory 190 Gallup, Gordon G., Jr 36, 39 Ganges River 266 gannets 132 Gates, Bill 8, 275 Gaup, Ingor Ántte Áilu 150 Gebru, Timnit 277 geese 164, 170 General Morphology of Organisms 11 ghost populations 88, 98 gibbons 32–4, 33, 38–9, 42, 52, 64, 312 goats 1, 140, 143, 148, 293, 302 Göbekli Tepe 93–4, 93 Godfrey-Smith, Peter 50 Gombe Stream National Park 55 gomphotheres 108 Goodall, Jane 55–6, 263 Google 8, 111, 154, 211, 241, 269, 275 ethics 156, 277 oil and gas applications 5–6 language applications 163, 167, 169 gorillas 44–7, 44, 98 Grant, Peter 236 Grant, Rosemary 236 graph theory 81 Great Chain of Being 123 Greece 1–5, 114, 216 Greenpeace 5 Griffith, Frederick 105 grouse 150 Grumpy (elephant) 40 Guantánamo Bay 296 Gudynas, Eduardo 268 gulls 133, 256 habeas corpus 41, 264–6, 270, 296 Hadza (people) 146 Haeckel, Ernst 11–12, 105, 239–40, 240 Hagenback, Karl 254 Half-Earth Project 305–6 Happy (elephant) 39–41, 41, 263–5, 273, 296 Haudenosaunee see Iroquois Confederacy Hawira, Turama 267 hawks 256 hawthorn 118 Heritage Foundation 277 Herodotus 3 Hertz, Garnet 212–13 Hilbert, David 178 Hiller, Lejaren 230–31, 233 Hofstadter, Douglas 262 Holmes, Rob 203 homeostat, 181–3, 182, 187, 206, 215 honey 143–6 honeyguides 143–6, 164 horizontal gene transfer 105–7 hornbeam 118 Hotbits 222 HPSCHD (composition) 230–32 Hribal, Jason 253–5 Hubble Space Telescope 135 HUGO Gene Nomenclature Committee 154 Humboldt, Alexander von 239 Huxley, Aldous 113, 208 hyenas 257 hyperaccumulators 308–10 I Ching 228–231, 228, 234, 242 IBM 4–5 ICARUS (animal tracking) 284, 300, 302–3 ICHING (computer programme) 230–31 iguanas 296 ILLIAC (computer) 230 IM see instant messaging Inky (octopus) 48 instant messaging 152–3, 172–3 Institute of Contemporary Art 231 International Meridian Conference 116 International Space Station (ISS) 284 internet 80–82 Iroquois Confederacy 248 Island (novel) 113 Israeli Defense Forces 295 jackdaws 163 jaguars 294 jaguarundi cats 294 James Webb Space Telescope 135 jellyfish 180 Jenny (orang-utan) 34–6, 35 joik 149–50, 312 Keyhole (satellite) 136 Khan-Dossos, Navine 140 khoomei 149 Kidder, Tracy 117 King, William 89 King Solomon’s Ring 163 klepsydra 216–17, 217 klerotereion 218–19, 243 Koko (gorilla) 44, 45, 47 Konstantinou, Maria 309 Kowalsczewski, Bruno 91 Kropotkin, Peter 256–7, 279 Kunstforum der Natur 239, 240 Lack, David 132–3, 285 Land Art 203 Landsat 137, 137–9, 139 lapwing 256 laurel 174 Lavarand 222 Le Guin, Ursula 13, 169–71 Leakey, Louis 56 Lederberg, Esther 105 Lederberg, Joshua 105 Legg, Shane 8, 275 lemurs 163 Leptoplax emarginata 309 Levi, Carlo 141 lichens 107, 171 Liebniz, Gottfried 234 Lindauer, Martin 259–60, 284 lions 77, 257 Lord, Rexford 285, 297 Lorenz, Konrad 163–4 Lovelace, Ada 30 Lovelock, James 190 LUCA (last universal common ancestor) 103 Lucy (Australopithecus) see Dinkinesh Lukyanov, Valdimir 199–200, 199 lynx 290 macaques 42–4, 64, 254 machine learning 30, 63 Mandelbrot, Benoit 102 mangroves 138 Mansfield, Lord (William Murray) 264 Margulis, Lyn 108, 110, 112 Marino, Lori 38 Marsham, Robert 118 Marsham record 118–21 Matera 140 Maxine (elephant) 39 Maxwell, Sarah 301 McLuhan, Marshall 18 memristors 124–5 Merleau-Ponty, Maurice 150 Metropolis, Nick 225 mice 187 Michael (gorilla) 45, 47 Microsoft 5, 8, 154 Million Random Digits with 100,000 Normal Deviates, A 226, 226 mimosa 71–4, 127–8, 192, 195, 303 Mimosa pudica see mimosa Ministry for the Future, The 282 mirror test 36–46, 181 Mississippi Basin Model 201–2, 204 Mondrian, Piet 161 MONIAC 205, 205–7 Monte Carlo 225–7, 242 Moore, Michael 135 Morgan-Mar, David 161 moths 180 mouse-eared cress see rock cress Muir, John 11 Müller, Max 146–8 Müller, Urban 161 Museum of the Ancient Agora 216–18 Musk, Elon 8, 158, 275 Mutual Aid: A Factor in Evolution 256 mycorrhiza 60–62, 77–9, 81–2, 194 mynah birds 113 NASA see National Aeronautics and Space Administration Nasser, Ramsey 160–61 National Aeronautics and Space Administration (NASA) 135, 137–9, 284, 286 National Oceanic and Atmospheric Administration (NOAA) 137–8, 286 National Reconnaissance Office (NRO) 135 neanderthals 89–92, 94–8, 100 network theory 81 neural networks 24–5, 25, 82, 166, 275, 312 NEXRAD (Next-generation radar) 133, 134 Niassa National Reserve 143 nightingales 118 nightjars 118 non-binary activism 208 computing 208–9, 213, 312 identity 112 Nonhuman Rights Project 41, 263–5, 296 nutation 128, 197 oak 118–19, 124 ocelots 294 octopuses 111, 47–51, 73, 197, 209 oil industry 4–6 oleander 174 On the Origin of Species 11, 36, 89 Ook!

I Am a Strange Loop
by Douglas R. Hofstadter
Published 21 Feb 2011

My explorations did not teach me that any shape whatsoever can arise as a result of video feedback, but they did show me that I had entered a far richer universe of possibilities than I had expected. Today, this visual richness reminds me of the amazing visual universe discovered around 1980 by mathematician Benoit Mandelbrot when he studied the properties of the simple iteration defined by z → z2 + c, where c is a fixed complex number and z is a variable complex number whose initial value is 0. This is a mathematical feedback loop where one value of z goes in and a new value comes out, ready to be fed back in again, just as in audio or video feedback.

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Machine Z machines: with beliefs about free will; confused; conscious; creative; dedicated; downloading of; emulating other machines; with linguistic capacity; as necessarily unconscious; with opinions; reading and interpreting description of own structure; with souls; universal; who think vs. that think Machines Who Think (McCorduck) Macintosh, emulating Alienware machine MacLaine, Shirley macroscopic boundaries, irrelevant to particles macroscopic forces as patterns Madurodam Magellan, Ferdinand magic genie for all mathematical questions magic square, ill-definedness of the notion magical realism magical thinking connected with “I”-ness “magical” vs. “ordinary” entities magnanimity; etymology of the word “Mahatma”, etymology of “main brain” of a given soul Malagasy language, presumed opacity of Mallory, George Malraux, André mammals as dividing line for food Mandelbrot, Benoit Mann, Lois Mantle, Mickey mapping: of colors to color sensations; at core of life; giving rise to meaning; of PM patterns into the world of numbers “marbelous”, too much for words marble, illusory, in envelope box; see also Epi Margolin, Janet marital bond, tightness of Marot, Clément marriage: of Carol and Doug; as soul merger; as third patient in counseling for a couple Married People: Staying Together in the Age of Divorce (Klagsbrun) Mars, teleportation to Martin, Mary Martin, Richard M.

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When we symbol-possessing humans watch a video feedback system, we naturally pay attention to the eye-catching shapes on the screen and are seduced into giving them fanciful labels like “helical corridor” or “galaxy”, but still we know that ultimately they consist of nothing but pixels, and that whatever patterns appear before our eyes do so thanks solely to the local logic of pixels. This simple and clear realization strips those fancy fractalic gestalts of any apparent life or autonomy of their own. We are not tempted to attribute desires or hopes, let alone consciousness, to the screen’s swirly shapes — no more than we are tempted to perceive fluffy cotton-balls in the sky as renditions of an artist’s profile or the stoning of a martyr.

Accelerando
by Stross, Charles
Published 22 Jan 2005

Back in the real world at last!" She can hardly contain her excitement, even forgetting to be pissed at Sadeq for thinking she was just an actor in his Cartesian theatre's performance of Puritan Hell. "Look! It's the DMZ!" They're standing on a grassy knoll overlooking a gleaming Mediterranean city. It snoozes beneath a Mandelbrot-fuzzy not-sun that hangs at the center of a hyperbolic landscape, which dwindles into a blue yonder that seems incomprehensibly distant. Circular baby-blue wells open in the walls of the world at regular intervals, connecting to other parts of the manifold. "How big is it, ghost? In planetary simulation-equivalents."

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And the first meat the new AIs get to know will be the uploaded lobsters. Manfred stumbles back to his hotel, bone-weary and jet-lagged; his glasses are still jerking, slashdotted to hell and back by geeks piggybacking on his call to dismantle the moon. They stutter quiet suggestions at his peripheral vision. Fractal cloud-witches ghost across the face of the moon as the last huge Airbuses of the night rumble past overhead. Manfred's skin crawls, grime embedded in his clothing from three days of continuous wear. Back in his room, the Aineko mewls for attention and strops her head against his ankle. She's a late-model Sony, thoroughly upgradeable: Manfred's been working on her in his spare minutes, using an open source development kit to extend her suite of neural networks.

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"Their own fault; If they hadn't participated in antibiotic abuse they wouldn't be in the isolation ward," harrumphs a twentysomething with mutton-chops and the manner of a precocious paterfamilias. He raps his walking stick on the pavement for punctuation, and they pause for a flock of cyclists and a rickshaw before they cross the road onto the Meadows. "Degenerate medication compliance, degenerate immune systems." Manfred pauses to survey the grass, brain spinning as he ponders the fractal dimensionality of leaves. Then he lurches after them, nearly getting himself run down by a flywheel-powered tourist bus. Club. His feet hit the pavement, cross it, thud down onto three billion years of vegetative evolution. Something about those people. He feels a weird yearning, a tropism for information.

The Death of Money: The Coming Collapse of the International Monetary System
by James Rickards
Published 7 Apr 2014

Extraordinary Popular Delusions and the Madness of Crowds. New York: Farrar, Straus and Giroux, 1932. McKinnon, Ronald I. The Unloved Dollar Standard: From Bretton Woods to the Rise of China. Oxford: Oxford University Press, 2013. Mandelbrot, Benoit. The Fractal Geometry of Nature. New York: W. H. Freeman, 1983. Mandelbrot, Benoit, and Richard L. Hudson. The (Mis)Behavior of Markets: A Fractal View of Risk, Ruin, and Reward. New York: Basic Books, 2004. Martines, Lauro. Furies: War in Europe, 1450–1700. New York: Bloomsbury, 2013. Marx, Karl. Selected Writings. Edited by David McLellan. Oxford: Oxford University Press, 1977.

The Age of Spiritual Machines: When Computers Exceed Human Intelligence
by Ray Kurzweil
Published 31 Dec 1998

Tokyo: Springer-Verlag, 1985. Malcolm, Norman. Ludwig Wittgenstein: A Memoir, with a Biographical Sketch by Georg Henrik Von Wright. Oxford: Oxford University Press, 1958. Mamdani, E. H. and B. R. Gaines. Fuzzy Reasoning and Its Applications. London: Academic Press, 1981. Mandelbrot, Benoit B. The Fractal Geometry of Nature. New York: W H. Freeman, 1988. ─. Fractals: Form, Chance, and Dimension. San Francisco: W H. Freeman, 1977. Mander, Jerry. In the Absence of the Sacred: The Failure of Technology and the Survival of the Indian Nations. San Francisco: Sierra Club Books, 1992. Margulis, Lynn and Dorion Sagan. Microcosmos: Four Billion Years of Evolution from Our Microbial Ancestors.

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London: Oxford University Press, 1927. Peat, F. David. Artificial Intelligence: How Machines Think. New York: Baen Enterprises, 1985. ________. Synchronicity: The Bridge Between Matter and Mind. Toronto: Bantam Books, 1987. Peitgen, H. O., D. Saupe, et al. The Science of Fractal Images. New York: Springer-Verlag, 1988. Peitgen, H. O. and P. H. Richter. The Beauty of Fractals: Images of Complex Dynamical Systems. Berlin: Springer-Verlag, 1986. Penfield, W The Mystery of the Mind. Princeton, NJ: Princeton University Press, 1975. Penrose, R. and C. J. Isham, eds. Quantum Concepts in Space and Time. Oxford: Oxford University Press: 1986.

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Babbage’s Calculating Engines: A Collection of Papers by Henry Prevost Babbage (Editor). Vol. 2. Los Angeles: Tomash, 1982. Bailey, James. After Thought: The Computer Challenge to Human Intelligence. New York: Basic Books, 1996. Bara, Bruno G. and Giovanni Guida. Computational Models of Natural Language Processing. Amsterdam: North Holland, 1984. Barnsley, Michael F. Fractals Everywhere. Boston: Academic Press Professional, 1993. Baron, Jonathan. Rationality and Intelligence. Cambridge: Cambridge University Press, 1985. Barrett, Paul H., ed. The Collected Papers of Charles Darwin. Vols. 1 and 2. Chicago: University of Chicago Press, 1977. Barrow, John. Theories of Everything.

Overdiagnosed: Making People Sick in the Pursuit of Health
by H. Gilbert Welch , Lisa M. Schwartz and Steven Woloshin
Published 18 Jan 2011

Beiser, et al., “Prevalence and Correlates of Silent Cerebral Infarcts in the Framingham Offspring Study,” Stroke 39 (2008): 2929–35.[back] R. Davis, “The Inside Story,” USA Today, August 25, 2000.[back] C. D. Furtado, D. A. Aguirre, C. B. Sirlin, et al., “Whole-body CT Screening: Spectrum of Findings and Recommendations in 1192 Patients,” Radiology 237 (2005): 385–94.[back] B. Mandelbrot, The Fractal Geometry of Nature, revised edition (New York: W. H. Freeman and Company, 1983), 116. [back] And in Utah (as well as in other states in the intermountain west) you will also have to struggle with the question of when to make this determination. In May, some lakes will still be under snow; by September, some will have dried up.

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In other words, because we can see more, the typical abnormality we see means less. Abnormalities that are detectable only by the new imaging technologies generally include less severe variants, those that are less likely to cause symptoms or death. The basic problem was well illustrated by an expert in fractal geometry who posed the deceptively simple question “How many islands surround Britain’s coast?”13 There is no single correct answer; it depends on how many you can see. The number of islands will increase with the resolution of the map used to identify them. But as the number of islands increases with improved resolution, and many previously undetected islands become apparent, the size of the average island decreases.

The Volatility Smile
by Emanuel Derman,Michael B.Miller
Published 6 Sep 2016

Lewis, Alan. 2000. Option Valuation under Stochastic Volatility. Newport Beach, CA: Finance Press. Malz, Allan M. 1997. “Option-Implied Probability Distributions and Currency Excess Returns.” Federal Reserve Bank of New York, Staff Reports. Available at www.ny.frb.org. Mandelbrot, Benoit. 2004. The (Mis)Behavior of Markets: A Fractal View of Risk, Ruin, and Reward. New York: Basic Books. Merton, Robert C. 1973. “Theory of Rational Option Pricing.” Bell Journal of Economics and Management Science 4 (Spring): 141–183. Merton, Robert C. 1976. “Options Pricing When Underlying Stock Returns Are Discontinuous.”

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Price is simply what you have to pay to acquire a security, or what you get when you sell it; value is what a security is worth (or, more accurately, what you believe it is worth). Not everyone will agree on value. A price is considered fair when it is equal to the value. But what is the fair value? How do you estimate it? Judging value, in even the simplest way, involves the construction of a model or theory. 1 See, for example, Mandelbrot (2004) and Gabaix et al. (2003). Overview 9 A Simple but Prototypical Financial Model Suppose a financial crisis has just occurred. Wall Street is laying off people, apartments in nearby Battery Park are changing hands daily, but large luxurious apartments are still illiquid. How would you estimate the value of a seven-room apartment on Park Avenue, whose price is unknown, if someone tells you the price of a two-room apartment in Battery Park?

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We can use Equation 24.48 to get the approximate formula for the smile in Figure 24.6, which is (√ √ 𝜆 𝜏e−𝜆𝜏 J 𝜋 ) ( ) K 1 + √ ln 𝛴 ≈𝜎+ 2 𝜎 𝜏 S S ( ) K ≈ 0.102 + 0.56 × ln S (24.50) which is a good approximation to the exact results near at-the-money. 416 THE VOLATILITY SMILE FURTHER THOUGHTS AND READING Merton’s model of jump-diffusion regards jumps as “abnormal” market events that have to be superimposed upon “normal” diffusion. The view that the market has two regimes of behavior, normal and abnormal, is regarded as contrived both by Benoit Mandelbrot and by Eugene Stanley and his econophysics collaborators. To paraphrase their view, a single model rather than a mixture of “normal” and “abnormal” models should ideally explain all events. END-OF-CHAPTER PROBLEMS 24-1. Estimate the price of a 24,000 strike put with two weeks to expiration on the Hang Seng Index (HSI).

Planet of Slums
by Mike Davis
Published 1 Mar 2006

"Partly these fires, " Hans Schenk writes, "are said to be organized by slum leaders who can cash (part of) the government compensation money; partly by some political party-affiliated gangs to clear 'unwelcome' categories of the urban poor; partly by private landowners who want their land cleared in an easy way from (illegal) squatters and have it 'developed.'"24 Pathologies of Urban Form If natural hazards are magnified by urban poverty, new and entirely artificial hazards are created by poverty's interactions with toxic industries, anarchic traffic, and collapsing infrastructures. The chaotic form of so many Third World cities — "urban mandelbrots," according to urban theorist Matthew Gandy — annuls much of the environmental 24 Hans Schenk, "Living in Bangalore's Slums," in Schenk (ed.), Living in India's Slums: A. Case Study of Bangalore, Delhi 2001, p. 34. efficiency of city life and breeds the small disasters that constantly terrorize metropolises like Mexico City, Cairo, Dhaka, and Lagos.

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example, in 1992 had an estimated 6.6 million low-income people living contiguously in 348 square kilometers of informal housing.28 Most of the poor in Lima, likewise, live in three great peripheral corns radiating from the central city; such huge spatial concentrations of urban poverty are also common in Africa and the Middle East. In South Asia, on the other hand, the urban poor tend to live in a much larger number of distinct slums more widely dispersed throughout the urban fabric in patterns with an almost fractal complexity. In Kolkata, for instance, thousands of thika bustees — nine hutments of five huts each, with 45square-meter rooms shared, on average, by an incredible 13.4 people — are intermixed with a variety of other residential statuses and landuses 29 In Dhaka, it probably makes more sense to consider the nonslum areas as enclaves in an overwhelming matrix of extreme poverty.

The Education of a Value Investor: My Transformative Quest for Wealth, Wisdom, and Enlightenment
by Guy Spier
Published 8 Sep 2014

Tartakower and J. du Mont Homo Ludens: A Study of the Play Element in Culture by Johan Huizinga Reality Is Broken: Why Games Make Us Better and How They Can Change the World by Jane McGonigal Winning Chess Tactics for Juniors by Lou Hays Wise Choices: Decisions, Games, and Negotiations by Richard Zeckhauser, Ralph Keeney, and James Sebenius Investing A Zebra in Lion Country by Ralph Wanger with Everett Mattlin Active Value Investing: Making Money in Range-Bound Markets by Vitaliy Katsenelson Beating the Street by Peter Lynch Common Stocks and Uncommon Profits by Philip Fisher Fooled by Randomness: The Hidden Role of Chance in Life and in the Markets by Nassim Nicholas Taleb Fooling Some of the People All of the Time: A Long Short Story by David Einhorn and Joel Greenblatt Fortune’s Formula: The Untold Story of the Scientific Betting System that Beat the Casinos and Wall Street by William Poundstone Investing: The Last Liberal Art by Robert Hagstrom Investment Biker: Around the World with Jim Rogers by Jim Rogers More Mortgage Meltdown: 6 Ways to Profit in These Bad Times by Whitney Tilson and Glenn Tongue More Than You Know: Finding Financial Wisdom in Unconventional Places by Michael Mauboussin Of Permanent Value: The Story of Warren Buffett by Andrew Kilpatrick Pioneering Portfolio Management: An Unconventional Approach to Institutional Investment by David Swensen Security Analysis by Benjamin Graham and David Dodd Seeking Wisdom: From Darwin to Munger by Peter Bevelin Short Stories from the Stock Market: Uncovering Common Themes behind Falling Stocks to Find Uncommon Ideas by Amit Kumar The Dhandho Investor: The Low-Risk Value Method to High Returns by Mohnish Pabrai The Manual of Ideas: The Proven Framework for Finding the Best Value Investments by John Mihaljevic The Misbehavior of Markets: A Fractal View of Financial Turbulence by Benoit Mandelbrot and Richard Hudson The Most Important Thing: Uncommon Sense for the Thoughtful Investor by Howard Marks The Warren Buffett Way by Robert Hagstrom Value Investing: From Graham to Buffett and Beyond by Bruce Greenwald, Judd Kahn, Paul Sonkin, and Michael van Biema Where Are the Customers’ Yachts?

Only Americans Burn in Hell
by Jarett Kobek
Published 10 Apr 2019

“The kissing and the cuddling.” HRH went on an inner trip. There was a psychedelic tunnel. HRH went through the psychedelic tunnel. Everything looked like a Mandelbrot set transformed into quivering nerves. HRH turned back and saw himself in the IKEA chair, surrounded by sex workers. HRH continued through the psychedelic tunnel. HRH came through on the other side. HRH found himself in a mystical land, surrounded by elfin creatures, with fractal trees sprouting forth from the earth. The elfin creatures spoke a strange language that sounded more like buzzing than words. HRH tried to talk but his words came out as shattered glass.

Adaptive Markets: Financial Evolution at the Speed of Thought
by Andrew W. Lo
Published 3 Apr 2017

More Money than God: Hedge Funds and the Making of a New Elite. New York: Penguin Books. Maloney, Michael T., and J. Harold Mulherin. 2003. “The Complexity of Price Discovery in an Efficient Market: The Stock Market Reaction to the Challenger Crash.” Journal of Corporate Finance 9: 453–479. Mandelbrot, Benoit B. 1982. The Fractal Geometry of Nature. San Francisco: W. H. Freeman. Markowitz, Harry. 1952. “Portfolio Selection.” Journal of Finance 7: 77–91. Marshall, Alfred. 2009. Principles of Economics: Unabridged Eighth Edition. New York: Cosimo. May, Robert M., Simon A. Levin, and George Sugihara. 2008.

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This unusual term derives from an eighteenth-century gambling strategy in which bettors would double their stakes to cover their previous losses (which is definitely not a good idea, but often too tempting to resist for reasons we’ll get to in chapters 3 and 4). 13. See Bass (1985) and the fictionalized account of Mezrich (2002) for examples. 14. Einstein (1905). 15. In his evaluation of his Ph.D. student’s rather unorthodox thesis, Poincaré highlighted the curious connection between science and financial economics (Mandelbrot [1982, 395]): The manner in which the candidate obtains the law of Gauss is most original, and all the more interesting as the same reasoning might, with a few changes, be extended to the theory of errors. He develops this in a chapter which might at first seem strange, for he titles it “Radiation of Probability.”

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Quarterly Journal of Economics 52: 255–280. Fagnan, David, Jose Maria Fernandez, Andrew W. Lo, and Roger M. Stein. 2013. “Can Financial Engineering Cure Cancer?” American Economic Review 103: 406–411. Falk, Dean. 1990. “Brain Evolution in Homo: The “Radiator” Theory.” Behavioral and Brain Sciences 13: 333–344. Fama, Eugene. 1963. “Mandelbrot and the Stable Paretian Hypothesis.” Journal of Business 36: 420–29. ___. 1965a. “The Behavior of Stock Market Prices.” Journal of Business 38: 34–105. ___. 1965b. “Random Walks in Stock Market Prices.” Financial Analysts Journal 21: 55–59. ___. 1970. “Efficient Capital Markets: A Review of Theory and Empirical Work.”

Dawn of the New Everything: Encounters With Reality and Virtual Reality
by Jaron Lanier
Published 21 Nov 2017

But my daydreams, and probably my dreams at night, were filled with imagining what this new technology would be like. It would be beautiful, expressive, sensitive. It would be Hieronymus Bosch crossed with Bach crossed with chocolate. My hand would be measured, would turn into an unconstrained appendage, maybe a hand, maybe a wing. I’d fly through the Mandelbrot Set on a date, I’d program through dancing; make music with my friends by growing imaginary plants. The terror arose from one word in that paragraph, and it is “measure.” Wiener considered how computers could fit into the world. Up to that time, computers had been mostly used in rather abstract, formal ways, to break secret codes or calculate missile trajectories.

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Not a chance of that, of course. A red H for hillbilly was sewn on my skin. Previously I was aware that I was slightly and weirdly privileged, and I was. After all, it wasn’t me who drowned at the bottom of my neighborhood pool. My skin color had elevated my status a tiny but crucial bit. But I realized that status is fractal; the pattern repeats itself at every scale, small and large. When the titans of industry are gathered in a room, there will always be one who is the designated loser, relatively speaking. When poor tough kids cluster, there’s always one who’s the top dog. I experienced yet other local minima. This is not entirely fair.

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The big gathering would be in a decaying unused factory, an abandoned ferry, or some other eerie Bay Area party environment, and a few people at a time would come in a secret van from there to VPL’s offices by the bay, all through the night. A stable of speakers and bands became established. (My favorite of the bands was called D’Cuckoo. Linda Jacobson was one of my favorite GNFs and VR pundits.) The VR party universe overlapped with the psychedelic one and the Grateful Dead one; it drew from the fractal, endless catalog of utopian crews and cults around the bay. In a sprawling, haunted-beautiful nineteenth-century wooden mansion above a gurgling spring in the Berkeley hills there lived a circle of roommates who published esoteric psychedelic magazines. They adapted to the VR party aesthetic by concocting a tech magazine with a psychedelic style, called Mondo 2000.

Traders, Guns & Money: Knowns and Unknowns in the Dazzling World of Derivatives
by Satyajit Das
Published 15 Nov 2006

Making money didn’t prove anything, it could just be a lucky accident. A good story did not guarantee success, a bad one just meant that the trader was riding his luck, shooting craps. Quants increasingly ‘mine’ vast quantities of data to ‘prove’ their models. You can substantiate anything given enough data. There is ‘chaos’ theory – the world of fractals, the eponymous Mandelbrot set. In popular science, chaos theory is portrayed as the relationship between the perfect storm and the wing beats of a butterfly in the Amazon jungle. In truth, it is a form of non-Euclidean geometry (the stuff you learn at school). It is used to model complex phenomenon including, hilariously, financial markets.

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Selection criteria • You will be able to demonstrate a detailed knowledge of financial markets and trading techniques. (You should wax lyrical about obscure markets (the Zambian Kwatcho and L Key responsibilities DAS_Z01.QXP 8/11/06 2:10 PM Page 315 Epilogue 315 Table E.1 Continued • • • • • Islamic finance techniques) and complex mathematics (field theory; neural networks; fractals). Everybody will think you are a genius or a fool but will be unsure of which.) You will be able to demonstrate detailed knowledge of derivatives, including exotic and non-standard structures. (Everybody knows that derivatives allow highly leveraged positions that are impossible to understand or value accurately.)

Coming of Age in the Milky Way
by Timothy Ferris
Published 30 Jun 1988

Greek Life and Thought from the Age of Alexander to the Roman Conquest. London: Macmillan, 1887. Mainx, Felix. Foundations of Biology. Chicago: University of Chicago Press, 1955. Malthus, Thomas Robert. An Essay on the Principle of Population, ed. Philip Appleman. New York: Norton, 1976. Mandelbrot, Benoit B. The Fractal Geometry of Nature. New York: Freeman, 1983. Introduction to fractal geometry, by its founder. Manier, E. The Young Darwin and His Cultural Circle. Boston: Reidel, 1978. Manuel, Frank E. A Portrait of Isaac Newton. Washington, D.C.: New Republic, 1968. Psychological study. Marchant, James. Alfred Russel Wallace: Utters and Reminiscences. 2 vols.

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It is the boundary condition, then, that provides the essential distinction between mind and the universe: Thoughts and events are bounded, even if the totality is not.* And where did the boundaries come from? Quite possibly from the breaking of cosmic symmetries at the moment of genesis. We look out across a cosmic landscape riven by the fractal lines of broken symmetries, and draw from their patterns metaphors that aspire to be as creative, if not always quite as flawed, as the universe they purport to describe. (All metaphors are imperfect, said the poet Robert Frost, that is the beauty of them.) It may be, then, that the universe is comprehensible because it is defective—that because it forsook the perfection of nonbeing for the welter of being, it is possible for us to exist, and to perceive the jumbled, blemished reality, and to test it against the ghostly specter of the primordial symmetry thought to have preceded it.

The Art of Computer Programming
by Donald Ervin Knuth
Published 15 Jan 2001

Therefore if x and y are arbitrary reals and k > 1, the number Zk = ([16fcccJ + [16fcyjz)/16fc is in S + m + ni for some integers m and n. It can be shown that S + m + ni is bounded away from the origin when (m, n) / @,0). Consequently if \x\ and \y\ are fixed and k is sufficiently large, we have Zk G S, and limfc-^oo Zk = x + yi is in S. [B. Mandelbrot named S the "twindragon" because he noticed that it is essentially obtained by joining two "dragon curves" belly-to-belly; see his book Fractals: Form, Chance, and Dimension (San Francisco: Freeman, 1977), 313-314, where he also stated that the dimension of the boundary is 2 lg cc « 1.523627, where x = l + 2cc~2 s=: 1.69562. Other properties of the dragon curve are described in C.

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Vittorio Griinwald proposed using the digits 0 and l/\/2 in odd-numbered positions, to avoid such a problem; but that actually spoils the whole system [see Commentari dell'Ateneo di Brescia A886), 43-54]. 206 ARITHMETIC +1-* Fig. 1. The fractal set 5 called the "twindragon." Another "binary" complex number system may be obtained by using the base i - 1, as suggested by W. Penney [JACM 12 A965), 247-248]: 4a4 i)a3 - 2ia2 a0 - | _i H In this system, only the digits 0 and 1 are needed. One way to demonstrate that every complex number has such a representation is to consider the interesting set S shown in Fig. 1; this set is, by definition, all points that can be written as Ylk>iQ<k(i — l)~fc5 for an infinite sequence ai, a2, a^, ... of zeros and ones. It is also known as the "twindragon fractal" [see M. F. Barnsley, Fractals Everywhere, second edition (Academic Press, 1993), 306, 310].

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MacPherson, Robert Duncan, 114. 750 INDEX AND GLOSSARY MacSorley, Olin Lowe, 280. Maeder, Roman Erich, 627, 635. Mahler, Kurt, 180. measure, 683. Makarov, Oleg Mikhailovich (MaicapoB, Ojier MnxafijioBHi), 700, 714. Mallows, Colin Lingwood, 74. . Manasse, Mark Steven, 403. Manchester University Computer, 192. Mandelbrot, Benoit Baruch, 606. Mangoldt, Hans Carl Friedrich von, 663. function, 371, 376. MANIAC III computer, 242. Mansour, Yishay (Ti^a >W>), 316. Mantel, Willem, 552. Mantissa, 214, see Fraction part. Marcziriski, R. W., 205. Mariage, Aime, 201. Mark I computer (Ferranti), 3. Mark II Calculator (Harvard), 225.

Aurora
by Kim Stanley Robinson
Published 6 Jul 2015

Jupiter: we came in just past the molten yellow sulfuric black-spotted ball of Io, aimed for a periapsis that was just slightly inside the uppermost gas clouds of the great banded gas giant, all tans and ochres and burnt siennas, with the wind-sheared border between each equatorial band an unctuous swirl of Mandelbrot paisleys, looking much more viscous than they really were, being fairly diffuse gases up there at the top of the atmosphere, but sharply delineated by densities and gas contents, apparently, because no matter how close we came the impression remained. We came in around the equator, above a little dimple that was apparently the remnant of the Great Red Spot, which had collapsed in the years 2802–09.

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There were limits on how many people could leave the shelters at once, so there was a scramble for spots on the schedule during this slack time, because at some point in the early afternoon of the daymonth, the onshore wind would begin, a hard flow of air barreling in off the sea into the interior of Greenland, as the land got hotter than the ocean and its air rose and vacated a space that cooler sea air rushed in to fill, the wind arriving in puffs and faltering breezes, then in a steady gentle push, which strengthened through the afternoon of the daymonth until sunset. This was generally the time of strongest onshore winds, although that varied of course, as storm systems swirled around Aurora in the usual fractal nautiloid motions that occur when gases move around the exterior of a rotating sphere. Although Aurora’s day was also its month, it was still rotating once in that daymonth, and that slow rotation caused the air in the atmosphere to drag a little in relation to both hydrosphere and lithosphere, creating winds that curled and mixed to create the usual trades, polar swirls, and so on.

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Visible around any ship in the intergalactic medium would be galaxies like stars. They would cluster irregularly, as stars cluster within a galaxy. The greater structure of galactic diffusion would become visible; clouds of galaxies like gas clouds, then the Great Wall, then also emptier bubbles where few or no galaxies reside. The universe is fractal; and even when flying inside a galaxy, this vision of galaxies clustering around us out to the universal horizon is available, using certain filters. Granular vision in different registers. Something like a septillion stars in the observable universe, we calculate, but also there may be as many universes as there are stars in this universe, or atoms.

Is the Internet Changing the Way You Think?: The Net's Impact on Our Minds and Future
by John Brockman
Published 18 Jan 2011

This year, I enlisted the aid of Hans Ulrich Obrist, curator of the Serpentine Gallery in London, and the artist April Gornik, one of the early members of the Reality Club, to help broaden the Edge conversation—or, rather, to bring it back to where it was in the late 1980s and early 1990s, when April gave a talk at a Reality Club meeting and discussed the influence of chaos theory on her work, and Benoit Mandelbrot showed up to discuss fractal theory. Every artist in New York City wanted to be there. What then happened was very interesting. When the Reality Club went online as Edge, the scientists were all on e-mail—and the artists weren’t. Thus did Edge, surprisingly, become a science site, whereas my own background (beginning in 1965, when Jonas Mekas hired me to manage the Film-Makers’ Cinematheque) was in the visual and performance arts.

The Food Lab: Better Home Cooking Through Science
by J. Kenji López-Alt
Published 20 Sep 2015

Remove from the oven and allow to rest for 5 minutes. 5. Sprinkle the chicken with the remaining Parmigiano-Reggiano, the basil, and parsley and serve. FRACTALS, PANKO, AND BREAD-CRUMB COATINGS Have you heard of Mandelbrot fractals? They’re computer-generated images that appear on a small scale very much as they do on a large scale. Fractals are something that occur in nature quite often—the outlines of a cloud, for instance, or the leaves on a fern. One well-known fractal effect pertains to coastlines. When you look at a coastline from far away and measure it, you’ll measure a certain perimeter. As you zoom closer and closer, you realize there are tiny inlets or curves in the beach that weren’t visible from far away.

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Standard breading consists of three distinct layers: flour, egg, and bread crumbs. Here’s what they’re for. • Bread crumbs make up the outermost layer, and they perform two functions. First, the many nooks and crannies formed by the crumbs increases the overall surface area of the chicken (see “Fractals, Panko, and Bread-Crumb Coatings,” here). It also serves as an insulator, preventing the chicken from overcooking and drying out. Of course, bread crumbs won’t stick without . . . • Eggs. They form the adhesive layer, and they’re perfect for the job. They start out as a viscous liquid, but as they fry, they form a solid gel, ensuring that the crumbs stay put.

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As far as cooking the chicken goes, I found that shallow-frying it in a wide skillet was less messy and easier to clean up than deep-frying it. I also used panko-style crumbs, which I seasoned myself—far easier than making your bread crumbs, and much better than the sandy “Italian-style” crumbs from the supermarket (see “Fractals, Panko, and Bread-Crumb Coatings,” here). Next up: the sauce and cheese. I opted to use my basic marinara sauce for this dish; its richness and deep flavor stand up nicely to the crunchy chicken. For cheese, a grating of fresh mozzarella applied before baking is traditional. Despite the nomenclature, Parmesan cheese does not always make an appearance in this dish.

Escape From Rome: The Failure of Empire and the Road to Prosperity
by Walter Scheidel
Published 14 Oct 2019

Conversely, the aggregated peninsular and insular shares of China, India, and the Middle East and North Africa region range from 1 percent to 3.6 percent.4 Because of this, Europe’s coastline is much longer than that of East and South Asia: 33,700 kilometers for “Western Europe” as opposed to 6,600 kilometers in China and 7,300 kilometers in India. This in turn means that Mandelbrot’s fractal dimension—an index of complexity bounded at 1 (lowest) and 2 (highest)—is higher for “Western Europe” (1.24 and 1.42 without and with islands, respectively) than for China (1.13 and 1.26) and India (1.11 and 1.19). The latter two are overall more compact than Europe west of Eastern Europe—a landlocked region eventually subsumed within a single very large land empire, Russia.

Surfaces and Essences
by Douglas Hofstadter and Emmanuel Sander
Published 10 Sep 2012

Let’s not forget that between the integers there are plenty of other numbers (for example, 1/2 and 5/17 and 3.14159265358979…, etc.), and mathematicians in the early twentieth century who were interested in abstract spaces — especially the German mathematician Felix Haussdorff — came up with ways to generalize the concept of dimensionality, thus leading to the idea of spaces having, say, 0.73 dimensions or even π dimensions. These discoveries later turned out to be ideally suited for characterizing the dimensionality of “fractal objects”, as they were dubbed by the Franco–Polish mathematician Benoît Mandelbrot. After such richness, one might easily presume that there must be spaces having a negative or imaginary number of dimensions — but oddly enough, despite the appeal of the idea, this notion has not yet been explored, or at any rate, if it has, we are ignorant of the fact.

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Martin’s purchase belongs to, 189–190; of categorizations having opaque mechanisms, 511; of category distinctions never taught in schools, 126, 127; of children’s semantic approximations, 39–41; of chunked items in grocery stores, 92; of cognitive-dissonance reduction situations, 116; of colorful acts of categorization, 510; of common metaphorical uses of words, 62; of compound words in French and Italian, 89; of compound words with “air”, 86; of compound words with rival plurals, 87; of compound words with unnoticed components, 86; of computer concepts used in daily life, 402–404; of concepts at the core of a conceptual space, 79; of concepts close to golfer, 49, 50; of concepts modified by their “children”, 53–54; of concepts tacit in the concept hub, 52, 54; of concepts whose members have great reality to us, 132; of concepts with blurry boundaries, 60; of concepts with labels of ever-greater length, 111; of conceptual broadenings of catchy new concepts, 130; of conceptual-proximity slippage errors, 271–276; of conjunctions that name categories, 55, 70; of consequences of special relativity, 468; of containment situations in everyday life, 333; of conventional metaphorical usages, 232; of cousins of the word “and”, 72; of cousins of the word “but”, 30, 72, 74; of criteria for bird-ness, 55; of “dead” acronyms, 93; of decision-making situations, 330; of definitions of intelligence, 125; of definitions of multiplication, 412; of different ways of eating, 10; of diverse factors influencing categorization, 526; of diverse forms of caricature analogies, 320; of division word-problems concocted by students, 416; of division word-problems that give a larger answer, 418; of doctors who generalize known cures, 463–465; of dog breeds, 238; of English phrases used in French, 122; of entities belonging to rival categories, 191–192; of “equations” in advertisements, 409; of errors mediated by mutually reinforcing analogies, 277–278; of everyday analogies, 507; of everyday concepts of boundless richness, 5; of fairly low-frequency concepts, 81; of familiar concepts, 390; of families of metaphors, 63; of famous golfers of yore, 49; of fancy names used by professionals for familiar things, 421; of fancy technical concepts, 51; of fauxthenticity examples, 176–177, 178; of features of attics, 48–49; of features of offices, 47; of features of studies, 47–48; of four division problems involving photos, 422; of frame-blending Copycat analogies, 359; of French phrases used in English, 122; of French words for “pattern”, 81; of French words for “to get”, 80; of gearshift attributes, 344; of genericized brand names, 217; of generic-male usages, 193; of geniuses of yore who would be astounded by today’s commonplace knowledge, 130; of great commanders, 125; of highly variegated categories, 516; of historical precedents of the Vietnam War, 332; of household-item compound words, 88; of human needs engendering cultural activities, 314; of hypothetical contributions today of yesterday’s geniuses, 132; of hypothetical idioms for “spill the beans”, 96; of idiomatic phrases, 95; of ignored aspects of familiar things, 427; of impenetrable idioms, 105; of inferences made from category membership, 20, 21; of ingrained habit suddenly turns obsolete situations, 149; of items frequently used in division wordproblems, 419; of Jewish-mother jokes, 93; of Jewish-mother traits, 94; of labeled concepts, 20; of levels of abstraction in the speech chain, 25–26; of lexical blends, 260; of life lessons derived from Pac-Man, 303; of lists in this book, 569–570; of lovely spots in San Francisco, 296; of Mandarin verbs for playing instruments, 12; of marginal category-memberships, 56; of marginal members of the category bridge, 67; of marking in language, 193–194; of maternal traits, 34, 38; of meanings of the French word “ciel”, 375; of meanings of the word “band”, 3–4; of meccas, 220; of mechanical experiments, types of, 466–467; of medium-frequency concepts, 81; of members of the bark worse than bite category, 96; of members of the category unfortunate incidents caused by trying to avoid them, 524, 526; of members of the category very, 75; of metaphorical mothers, 38; of metaphorical usages of “to break”, 42; of metaphors casting abstract activities in terms of mundane activities, 63; of metaphors casting complex situations in terms of fights, 63; of metaphors casting moods in terms of heights, 63; of metaphors not belonging to a systematic family, 63; of metaphors used by metaphor-bashing philosophers, 22; of me-too’s featuring subtle conceptual slippages, 146; of me-too’s triggered by a compliment to a spouse, 147–148; of mistaken categorizations, 527; of monosyllabic lexical blends, 267; of morality-as-cleanliness stock phrases, 289; of “much” phrases, 67, 69, 70; of a multitasker’s activities, 403; of mundane, unseen analogies, 23; of negative numerical quantities in everyday life, 441; of 9/11’s, 297–298; of noncountability of members of the simplest of categories, 61; of non-lexicalized categories, 139; of non-subjective analogies, 525; of notions implicit in the category plate, 519; of objective categorizations, 522; of obsessions engendering analogies, 301–302; of office-like categories, 74; of old words with new technological meanings, 396, 398; of once bitten twice shy situations, 103; of opaque French idioms, 97; of operation–result “equations” in daily life, 408; of other cultures’ proverbs for “Once bitten, twice shy”, 105; of pairs of contradictory proverbs, 101; of parameters affecting one’s likelihood to jump to a conclusion via analogy, 307, 309; of Parises of the United States, 16; of parts of an airport, 52; of pasta types, 243–244; of phrases describing space in terms of time, 63; of phrases describing time in terms of space, 63; of phrases modified by “quote unquote”, 64–65; of physics phenomena belonging to electromagnetism, 467; of physics phenomena belonging to mechanics, 466, 494; of pieces of knowledge needed to understand a contemporary phrase, 128; of Platonic animal categories, 56; of plausible contributors to a lexical blend, 266; of pointless analogies, 283; of polysyllabic lexical blends, 267; of popes, 219; of possible meanings of Nick’s Nubian me-too, 151; of potential distinctions between categorization and analogy-making, 503; of potential members of the category bird, 59, 60; of proverbs about the sum of many little things, 109; of proverbs applicable to rationalization situations, 117–118; of proverbs poised halfway between categorization and analogy-making, 100; of pseudo-proverbs, 105; of questionable members of familiar categories, 528; of random thoughts in an airport, 33; of readymade sentences, 98; of reasons division always makes things smaller, 417; of reasons division word-problems cannot give a larger answer, 418; of reasons underlying Greece’s position in the Falkland Islands War, 332; of recent words coined from productive suffixes, 129; of reliable run-of-the-mill analogies, 529; of rival categorizations of a bag-toting woman, 127; of running-race metaphors, 289; of salient entities typically used in caricature analogies, 320; of sample languages that Google Translate offers, 377; of schoolday analogies, 17; of sci-fi fantasies rooted in familiar phenomena, 314; of sentences with the word “normalement”, 82; of similarities underpinning the Carol/Isabel analogy, 313; of single-word categories, 85; of situations defined by proverbs, 174; of sour grapes situations, 113, 114; of spicy one-line analogies, 136; of stock phrases shooting words into the speech chain, 25; of striking events liable to evoke memories, 158; of subcategories of dog, 240; of subjective categorizations, 523; of superordinate categories of dog, 240, 520; of symbols of sadness after a death, 300; of tail wagging the dog situations, 120-121; of thank-you’s of various flavors, 46; of things analogous to asparagus tips, 19; of trivial side show situations, 162–163; of types of analogies used in word- and phrase-retrieval in one’s native language, 376; of types of sandwiches, 214–216; of types of shadows, 204–209; of types of waves, 209–214; of unfamiliar concepts, 390; of unintended name slippages, 224; of universally important concepts, 80; of unstriking events not liable to evoke memories, 158; of unusual professions, 242; of usages of “much”, 70; of varieties of mess, 127; of verb-like phenomena presumably lacking mass, 475; of verbs used as category names, 66; of virtual actions frame-blended with real-world actions, 405–407; of virtual actions we perform daily, 395; of virtual objects we use daily, 395; of ways of missing the gist of a situation, 125; of wildly different-looking animals, 516; of words that start with “multi”, 413; of words with different connotations in English and Chinese, 368; of zeugmas, 6 literal encoding as inadequate, 174–175; see also abstraction literal-mindedness in the Copycat domain, 348–349, 351, 355, 357–360, 363–364 Locke, John, 22 logic: influence on psychologists’ theories of categories, 55, 436; the small role of, in thinking, 258, 288, 392; versus psychologic, 410; see also analogic versus logic loot carried off by thief, 472 “lovely spots” on city streets, as influencing perception, 296–297 lowercasing of categories, 34–35, 44 “lustre”, as possible French analogue to English word “score” in Gettysburg-address translation challenge, 372 —M— Macbeth effect, 289–290 Mach, Ernst, 487 machine translation, see translation Madonna, 223; syllogistic proof of mortality of, 193 magical angel stung by randomly buzzing interplanetary bumblebee, 493 magnet in motion, giving rise to electric field, 493 making distinctions and seeing commonalities, 189, 198 Malevich, Kazimir, 296 “man”, ambiguity of, 193–195 Mandarin, see Chinese Mandelbrot, Benoît, 444 manipulations, routine, in math, 449–450 manipulators versus manipulatees, 382–383 Marceau, Marcel, 322 marking, 186–187, 193–204, 217–218; applied to proper nouns, 227; and category extension, 254; helping to reveal a concept’s essence, 255; list of examples of, 195; in mathematics, 228–232, 419; in metaphor understanding, 229–232; origin of the term, 218 marriage, concept of, in constant evolution, 53 Martin, Mr.: as dog fancier, 238–239; as multi-categorizer, 189–190, 197, 248, 435 Mary, mother of Jesus, 38 Maslow, Abraham, 301 mass: barrier between two varieties of, 476, 478, 484; belonging to immaterial phenomena, 475; conservation of, 472, 475; interconvertibility between two varieties of, 480, 484; loss of, as result of radiation, 470–471, 475; normal versus strange, 476–485; poofing out of existence, 472, 475, 477–479, 481, 482, 484; possessed by energy, 471–478; possessed by heat, 475, 476; possesses energy, 482; two types of, 476, 477–478, 485 mass/energy analogy in Einstein’s mind, 472, 479–481, 482, 484; running aground on a fatal snag, 480, 484 mathematical formulas, mistaken views of, 391–394 mathematicians: arguing over category membership, 392; reluctant to extend categories, 440–444; seeing analogies between analogies, 502; “sniffing” the crux of a problem, 451; thinking by analogy, 439–451; toolkit of, 450 mathematics: ambiguity in, 237; analogy with Monopoly, 450–451; causality in, 411; imagined as lacking blurriness, 233, 392, 439; intuition in, 451; marking in, 228–232; naïve analogies in, 407–434, 439; rooted in everyday experiences, 393, 427; routine situations in, crying out for specific routine techniques, 449–450; spectrum of subtlety of analogy-making in, 451; unusual categorizations of, 510; use of analogy in, 439–451 matter as imbued with energy, 481 Maxwell, James Clerk, 130, 212, 213, 275, 361, 453, 459, 502 Maxwell–Boltzmann distribution, 457, 458; see also ideal gas Maxwell’s equations of electromagnetism, 361, 410–411, 456, 459, 489; both confirmed and undermined by one and the same experiment by Hertz, 460 measurement: contrasted with sharing, 420, 422–426; of energy E in units of size hν, 459; as key concept in division, 420 “Mecca” pluralized to “mecca”, 220 meccas, list of, 220; of wind-surfing, 229 mechanical translation, see translation mechanics: defined, 466; generalized to all of physics, 466–467, 494–495, 499 medium: in producing shadows, 207–208; of waves, 210–214 “melting” of components in compound words, 87, 111 membership in categories: non-black-and-white nature of, 14, 55–57; transitory nature of, 225 memo to office assistant, ambiguity of many words in, 395 memories of the past, as allegedly shackling people, 313–315 memory retrieval: alleged uselessness of, 338, 341; allegedly triggered by irrelevant features, 341; salient features’ dominance in, 342; surface-level features’ alleged dominance in, 337–346; virtuosity in, 110; see also remindings menace, as typical example of a verb naming a category, 66–67 mental blocks, recipes for escape from, 248–249 mental bridges, 183–184; see also analogy-making mental lexicon, 137 mental simulation in math word-problems, 421–425, 427–429 mental spaces, 365; see also Fauconnier mess, as example of a highly protean concept, 5, 127, 510 meta-analogies: in doing theoretical physics, 212; in evolution of wave concept, 211–212; in ordinary conversation, 27 metallurgists appreciating the blurriness of the category metal, 60 metaphorical versus literal meanings, 37–38 “metaphorical” usages: not always metaphorical, 229–230; three types of, 230–232 metaphors: conventional, 229–232; creativity in many, 510; embodiment and, 286–289; families of, 63; as flapdoodle, 22; Glucksberg–Keysar theory of, 228–229; going dead over time, 64; list of common words used as, 62; list of sentences using stock, 232; mixture of abstract and concrete in, 286–290; “mobile army of” (Nietzsche), 21; process of understanding of, 228–232; scorned by Hobbes, 22; used to criticize metaphors, 22 “me too”, unclear halo implicit in the phrase, 145, 150–153 me-too analogies, 143–153; in Copycat’s microdomain, 346–358; marginal members of the category, 147; phrases that often are giveaways of, 143, 152, 507; the ubiquity of, 507–508 métro in Paris, 215; American transculturation of, 377–379 microworlds, 305 “Mighty oaks from little acorns grow”, 109 military-budget arguments mobilizing flow of ideas, 26 military versus non-military analogies in times of war, 333–335 milk carton too heavy for bag, 133 Millikan, Robert, 461 Minkowski, Hermann, 453, 498–499 mistaken-identity scenes, 291–292 “mobile army of metaphors” (Nietzsche), 21, 509 Molière, 186, 248 Mommy as core of concept mother, 34–37 Mona Lisa with mustache, 351 monolithicness of categories, illusory, 3–5, 9–13, 71, 81–83, 241 Monopoly, 11, 450–451 Moon, analogical extension of, leading to the concept moon, 43–45, 64, 147, 210, 217 moonlets in Saturn’s rings, waves in medium of, 21 “morsel of shame”, 140 Moser, David, 89, 150–151, 259, 291–292 mosquito: in nudist colony, 320; perspective on Albert Einstein of, 163, 164–165 mother: abstract extensions of the category, 37–38, 53; development of the category, 34–38, 48, 53; marginal cases of, 37–38; as opposed to the concept mommy, 36 motion, children’s naïve view of, 294–295 Mount Analogy: scaling hardest slopes with and without pitons, 131; trekking on, 126, 131–132 mouse, as tangible gateway to intangible world, 252–253, 509 mouse/limb analogy, 252–253 Mozart, Wolfgang Amadeus, 223; of mushrooms, the, 222, 229 “much”: syntactic slots for, as a category, 68–70 much-situations: nature of, 67–68; role of expectations in, 68 multi-categorizability: of objects, 59, 189–192; of situations, 117–118, 188, 248 multiplication: apparent asymmetry of, 413, 415, 428; commutativity of, 413–416; generalized to abstract objects, 446–447; mental simulation used to solve, 424–425, 427–429; naïve analogies for, 411–416; as necessarily making larger, 413–414, 416; as repeated addition, 412–416, 427–429; tables, patterns in, 446–447 multitasking: concept borrowed without awareness from computer world, 402–403; passage of the concept into the everyday world, 404 Munich conference, 332, 334; pluralization of, 335 Murphy, Gregory, 60, 436 Mussolini, Benito, of mulligatawny, the, 222, 360 music keyboards, electronic, and musicianship, 131 musical instruments and zeugmas, 11–12 mystical characterization of genius, 501 —N— naïve analogies, 31–32; as bases for effective interfaces, 400; coexisting with other views, 389, 409; concerning analogy-making, 451; concerning categorization, 435–436; concerning cicadas, 388; concerning disk ejection, 401; concerning division, 416–421, 425–426; concerning email addresses, 385–387; concerning the equals sign, 407–411; concerning icons, 402; concerning motion, 294–295; concerning multiplication, 411–416; concerning shaving, 385–387; concerning size changes, 295; concerning titmice, 385–387; concerning virtual desktops, 401; deep entrenchedness of, 394, 409; defined, 386; education and, 389–394, 409, 411–434; like groomed-slope skiers, 389; linking cleanliness to morality, 289–290; made by analogy experts, 436–437; in mathematics, 407–434, 439; in mathematicians’ minds, 439, 441; misleading nature of, 400–401; not eliminated by scientific training, 389, 394; permeating today’s computer technology, 400; rooted in everyday experience, 386, 389, 391, 393–394; stemming from the computer world, 402–407; unconscious character of, 386, 389, 512; underlying jargon-creation, 399–400; utility of, 389 naïve equations, 407–411 names: conflated with items they name, 227; retrieved by analogy, 224–225 Napoleon: of fossil bones, the, 222; frame-blended with emperor penguins, 380 nature, cut at the joints by categories, 14, 77, 522–523 N-dimensional spaces, 443–444 nebula, as image for a language’s filling of a conceptul space, 119 necessary and sufficient criteria for category membership, 55, 436 negative numbers: fear of, 439–442; square roots of, 442–443 Neruda, Pablo, 522 nested radicals in polynomial solution-formulas, 445 Newman, Paul, 318 Newton, Isaac, 130, 210, 443, 471, 490, 491, 500; law of gravitation of, 389, 489; second law of motion of, 410, 491; of terrorism, the, 222 New York subway, as translation of Paris métro, 378 Nick’s me-too quip to the Nubian taxi driver, 151–152 Nixon, Richard: of superheroes, the, 222; yearining to be known as “RMN”, 90 Nietzsche, Friedrich, 21, 509 9/11, see September 11th Nobel Prize: citation for Einstein, extreme caution of, 461–462; for creative extensions of categories, 464–465 non-Euclidean geometry, 16, 498–499 non-lexicalized concepts, 30, 137, 139–140, 176–180 normalement, as monolithic concept in French, 82 normal mass/potential energy analogy, 480–481 normal mass/strange mass membrane, broken, 480–481, 482, 484 Norman, Donald, 259, 400 norms as directing word choices, 73 novices: inability to spot depth, 341; versus experts, 236–246, 255, 392–394 Nubians harmed by dam, me-too analogy centered on, 151–152 number : blurriness of the category, 392; relentless conceptual broadening of, 439–443, 447–448 numerical comparisons as analogies, 153–154, 281–282, 285, 331 —O— oars replaced by javelins, 317, 322 object recognition, mediated by analogy, 19, 184 objectivity: of analogies, 522–526; of categorization, 522–526 obsessions engendering analogies galore, 258, 299–305, 524 October 11th crash, 31, 297 “Ode to Constraints” (James Falen), 315 “office” versus “study”, 47–49, 74, 76 office visit as an example of a schema, 336–337 “official” boundaries of categories, 64–65 old town, as metaphor for a category’s core, 61–62, 65 Once bitten, twice shy: as an abstract category, 100, 103–106, 516; as a proverb incarnated in various languages, 105; as analogical pressure in column-translation dilemma, 306–307 “one”, as the name of a category, 75 one-dollar bill, as minimal banknote, 280 one-line analogies, list of, 135 one-member categories, see single-member categories “one smart dude”, as indicative of category of speaker, 75 opacity: of acronyms, 91–93; of compound words, 86–87; of idiomatic phrases, 97–98 operation–result naïve analogy for equations, 407–411; see also cause–effect Oppenheimer, Frank, 275 Oppenheimer, Robert, 275, 507 opposite meaning: produced through biplans, 268; produced through conceptual-proximity slippage errors, 276–277 Orwell, George, 57 —P— “pacifier”, semantic components of, unheard by toddler, 86 Pac-Man, obsession with, 303–305 pantheons, 219–220 paradoxes stemming from the alleged dominance of the superficial in retrieval, 341–344 parallels between parallels, Maxwell’s love of, 502 Paris: being Paris, 522; genericity of, to French people, 378; growth of, over centuries, 61; métro stations in, 215, 377–379; as tourist mecca versus book-writing locale, 163; of the United States, 16, 378; as venue of Marie Antoinette’s dizzy remark, 358 parking places in San Francisco: beauty of, 296–297; surprising availability of, 327–328 particle–antiparticle annihilation, 482 parts hidden inside wholes, 86–93 Pascal, Blaise, 101, 102 past, as key to understanding the present, 20, 23 pasta, expertise in, 243–244 Pasteur, Louis, 300 patent clerk, Third Class, 457, 460, 463, 470 “pathological” functions, 392 “Patsy is a pig”, see metaphors, “pig” pattern, as monolithic concept in English for which French has no single word, 81–82 patterns in discourse space, 69–76 patterns in multiplication tables of groups, 446–447 “peaks” of concepts poking out above clouds, 50, 52 Pearl Harbor, as category, 298 pedaling in sauerkraut, 248 pedestal, shared, as conceptual skeleton of two different word problems, 433–434 peel, semantic halo surrounding, 126, 270–271 people, analogically conflated, 181, 224–225, 275 perception: context-biased nature of, 299; dependency on concepts, 171; without concepts, 172, 315 perception of grammatical situations, 69–70 permutations, successive, as giving rise to groups, 446 personal celebrities, 222–223 Peter-Defare, Evelyne, 259 Peter miswriting the year every January, 148–150, 174 Phædrus, 112 Phædrus, 522–523 Phelps, Michael, 154–155, 367 philosophy of life, courtesy of Pac-Man, 303–305 phonetic proximity, role of in speech errors, 265 “phonon” as name for sound quantum, 459 photoelectric effect: behavior predicted by Einstein, 460–463; discovered by Hertz, 460; Einstein’s predictions confirmed by Millikan, 461; merely an afterthought in Einstein’s 1905 light-quantum paper, 460, 462 “photon” as name for light quantum, 459, 461, 462, 482 phrase choice constrained by sentence choice, 26 phrases: blended together, 259–265; retrieved by analogy, 93–98 physical world, understood via naïve analogies to computer world, 402–407 physicists: perception of equations by, 410–411; stereotype of, 451–452 physics: naïve analogies in, 410–411; seen as deductive, axiomatic discipline, 452; seen as generalization of mechanics, 467–468 physics problems, as perceived by novices versus experts, 342 physics thinking/political thinking analogy, 337 π, 302, 409, 410, 413, 444, 498 pianist: striking one wrong key, 270–271; striking two keys at once, 263, 266 “pig”, metaphorical use of, 228–232 pinball-machine obsession, 301 ping-pong, thanks to analogies, in discovery process, 500 pinpointing of essence, see essence-spotting Pisa: Galileo’s use of the tower of, 492, 493; prior to its famous tower, 319, 468; with tower not yet leaning, 472: with tower starting to lean, 482 piton-placing as metaphor for concept creation, 131 pizza consumption, as generic bland event that does not trigger remindings of specific events, 158–159 Planck, Max, 456–458, 460–461; disdain for Einstein’s light quanta, 460, 461, 463; likened to thirsty horse, 457; pardoning Einstein’s sins, 461; skeptical of existence of atoms, 460 Planck’s constant h, 456, 459 planet, as category requiring long deliberation to decide about membership in, 60, 512, 514, 528 plans, blending of, see biplans plastic card as a key, 254 plate, as category lacking relationships among non-parts, 518–519 plate-throwing woman, frame blend by, 367 Plato: of freemasonry, the, 222; objectivist vision of, 190, 522–523; warning of analogy’s slipperiness, 21 Platonic concepts, hopefully precise laws of, 56, 58 “play”, zeugmatically exploited, 10–12 pluralization: of Bible, 220; of famous people, 221–222, 254, 297; of friends or relatives, revealed by speech errors, 224; of friends, via strong resemblance, 224; of Hitler, 335; of Jeff, 223; of Mecca, 220; of Mommy, 34–35; of Moon, 44; of Munich, 335; of Pantheon, 219–220; of Pope, 219; of September 11th, 297–298; of signature-botching, 149; of a specific wine, 244 plurals of compound nouns, 87 Pluto, debate over its status as planet, 60, 512, 514, 528 poem learned by rote as member of category boat on tracks, 522 poems in the text: “Arizona Ants” (Kellie Gutman), 160, 381; “The Fox and the Grapes” (Benserade), 112; “The Fox and the Grapes” (La Fontaine), 112; “The Gardener’s Daughter” (Tennyson), 397; “Karnak Caps”, (Kellie Gutman), 160, 381; “La cigale et la fourmi” (La Fontaine), 388; “Ode to Constraints” (James Falen), 315; “Psalm XXX” (Milton), 397; “There Is No Word” (Tony Hoagland), 133 Poincaré, Henri, 132; on flesh of geese and of dogs, 132; letter of reference for Einstein by, 501; on mathematical thinking, 439–440, 509; sudden flash of inspiration of, 16 pointless analogies, see analogies, purposeless Poirot-Delpech, Bertrand, 373 political analogies, 17, 331–337 Polya, George, 507 polynomials: over finite fields, 447–448; imaginary numbers in, 448; search for general solution formula for, 445 pool table/ideal gas explanatory analogy, 457 Pope: of atheism, 219; pluralization of, 219; as salient entity used in caricature analogies, 320; of search engines, 220 positron (= anti-electron), 482 potential analogies, see semantic halos potential energy, 479–481 pressures: to categorize in real time, 258, 261; in creative translation, 371, 380–382; in Einstein’s mind, 477, 480–481, 485; guiding caricature analogies, 323; inducing fluid conceptual slippages in Copycat domain, 350–351, 352, 354–357; to make equations reflect cause and effect, 407–411; pushing for creative analogies, 300–301, 355–356, 458, 477, 480–481; see also cognitive dissonance prime numbers: generalized to “prime groups”, 449; generalized to “prime knots”, 449; generalized to primes inside rings, 448 primitive needs as primeval forces, 314 “prison”, metaphorical use of, 228–229 prison of the known, Krishnamurti’s putative 313–315 privileged category of each entity, 190, 435 probabilities, as hinted by strengths of analogies, 308 problem-solving: led astray by miscategorization, 293–295; mistaken for the raison d’être of analogy-making, 283, 285 Procrustes, bed of, 144–145, 160 productive suffixes “-holic”, “-thon”, and “-ism”, 129 professions, hierarchical structuring of, 242–243 proper nouns, pluralization of, 217–223 proportional analogies, 15–16; as gleaming jewels, 16; unhelpful in devising caricature analogies, 323–324; as unnatural view of most analogies, 144–145 proportionality/analogy proportional analogy, 15 proportionality to mass: of fictitious forces, 488; of gravitational forces, 489–491 prototype theory versus exemplar theory of concepts, 57 proverbs: families of, 109; as filters through which to understand situations, 101, 102; as names of categories, 100–102; non-opacity of, 106; objective reality of instances of, 110, 111, 132–133; overly general interpretations of, 107; recognized in situations, 174, 188; retrieval of, 104–105, 110; scope of, 106–109; surface versus essence of, 106–109; use of, as an act of analogy-making, 100; use of, as an act of categorization, 100 pseudo-proverbs, 105, 106 psychic trauma as a notion foreseen in the proverb “Once bitten, twice shy”, 104 psychological pressures leading one to map oneself analogically onto others, 153, 154–155 “psychology does not recapitulate etymology”, 86 public categories, 100 “pull no stops unturned”, as quintessential lexical blend, 262–264 pumpkins, pastries, plows, and pigs, 66 puns under attack, caricature analogy of, 319 “pure” versus “uncontaminated” analogies, 363–364, 366–367 Pushkin, Alexander Sergeevich, 130, 132; constraints in poetry of, 315; of feminism, the, 222 putting finger on a situation’s essence, see essence-spotting Pythagoras, as a category, 221 —Q— quadratic equation: broken up into six cases, 441; formula(s) for, 438, 441 quadrilaterals, classification of, 233–238, 255 quality control, as explanatory analogy, 329 quantum of energy: of electromagnetic wave, 459; of heat, 461; of sound, 461; of vibrating atom, 456–457, 461 quartic equation: group of symmetries of its solutions, 446; strange formula for, 445 “quatre-vingts” as translation of “four score”, 370–371 quintic equation: search for formula for solutions of, 445–446; unsolvability via radicals proven for, 446 quotation marks: as a convention of this book for words, 34, 110; for honorary category members, 44, 64–65; second-order, 65 “quote unquote”, as way of indicating metaphorical usage, 64–65 quotient groups, 448–449 quotient skyscrapers, 448 —R— Raban, Jonathan, 284 random murder as conceptual skeleton, 248 random resemblances constantly noticed, 284 randomly buzzing interplanetary bumblebee, see magical angel rapid right-on retrieval: as the core of cognition, 127; as the essence of intelligence, 125–126; as needed for survival, 79, 83, 505–506; see also essence-spotting rationalization and sour grapes, 115–118 read ⇒ write conceptual slippage, 276–277 reading, as triggering ideas in a mind, 376–377 ready-made sentences as categories, 98–99 Reagan, Nancy, 358 reality of members of abstract categories, 110, 111, 132–133 reasoning, as opposed to analogy-making, 333; see also logic, analogic versus logic recategorization of situations, 73, 249–252, 327–328 reclothing a stripped-down essence, 153 Recorde, Robert, 408 reduction ad absurdum technique in mathematics, 450 redwood trees, trip to, 310–312 refinement of categories, as reaching a limit, 83 relationships among parts: as crucial for analogy-making, 517–518; as crucial for categorization, 518–519 relativity, Galilean, principle of, 466–468, 485, 486, 492 relativity, general: analogies at root of, 491–495, 499; attempts at, 490–491; experimental confirmation of, 496; goals of, 486–488; rotating disk in, 497–498 relativity, special, 361; analogy at root of, 467–468 remindings: as crucial for survival, 172–173; as a deep mystery of cognition, 159–166, 354; as due to analogousness, 18, 30, 336; idiosyncratic nature of, 525–526; induced by traumatic experience, 225; mediated by faces, 181–184; mediated by identical encodings, 173; mediated by many diverse cues, 171; opacity of mechanisms of, 511; revealing the existence of unsuspected categories, 168; seeming not to need explanation, 18; triggered by simple visual analogies, 169–170 repeated addition: as crux of multiplication, 412–416; as way of solving multiplication problems, 427–429 reporter #1/reporter #2 romantic analogy, 305–306, 308 retrieval of memories, see remindings, triggering reversal: by Einstein, 474, 482–483; as potential source of humor, 280; role of, in creativity, 356–357, 363–364, 371 rhyme, preservation of, in poetry translation, 381 rich and poor zones of a language in conceptual space, 82–83 Richard, Jean-François, 294–295 Riemann, Bernhard, 498 “right” versus “wrong”: in analogy-making, 16; in Copycat domain, 350–351, 352; see also esthetics Ringfinger, Renate, 464 rings, as homes of new types of numbers, 448 ripples, see waves Rips, Lance, 390 rival analogies: in real-time competition, 260–278; in wartime decision-making, 333 rock-climbing as metaphor for creative thinking, 131 rock music, category in the mind of a classical-music lover, 241 role reversal in Grand Canyon episode, 163, 165 Roosevelt, Franklin Delano, 90, 275 roots of polynomials, see solutions of polynomials rope, speaking of, in the house of the hanged, 104, 311 Rosch, Eleanor, 55, 345, 436 Rossi, Mario, 259 rotating disk/non-Euclidean geometry analogy, 498 rotations of a cube, as number-like entities, 446–447; see also groups royalty statement triggering analogies, 153–154 Ruffini, Paolo, 446 rule of thumb separating analogy-making and categorization, 515 Rumelhart, David, 259 Russian language, 9–10, 12, 368; Anna’s dream in, 504; “but” in, 74 Ruth, Babe: of bank robbers, the, 222; 1927 Yankees minus, 468 Ruth, Dan’s image of, contaminated by Jeanine, 225 Rutherford, Ernest, 143 —S— sabbatical year, zooming in on details of, 50 Sagan, Françoise, obituary of, as translation challenge, 373–377 salience: of any feature as subjective, 363–364; of deep features to experts, 342–344 salient features dominate in memory retrieval, 342 salsa: debugging of technique in, 403–404; the pope of, 219 salt/sugar confusion as categorization error, 102, 527 Sander, Emmanuel: as error collector, 259; explaining humps and bottles to his son, 198–200; falling momentarily for categories = boxes, 436; making analogy between co-author’s two blue station wagons, 283; as one-time Pac-Maniac, 303–305; smiling with joy at finally finishing book :), 575; taking coffee break, 185, 317; transculturated to San Francisco, 327–328 Sander, Mica, 40, 198–200, 295 Sander, Talia, 17, 39, 40, 43 Sander, Tom, 40, 126, 233–234, 236 Sandwich, Earl of, the fourth, 214 sandwiches: “A–B–A” form of, 215–216; abstraction of, 214–216; of appointments, 216; blurry boundaries of category, 214–216; bread role in, 214–216; edible, 214, 216; horizontality of, 215; meat role in, 214–216; in Paris métro, 215; in physics, 215–216; of rhymes; 215; sexual, 215; symmetry, as unclear criterion in, 215–216; transistors as, 215; walking, 214–215 sandwichology, burning questions of, 215–216 San Francisco, parking in, 296–297, 327–328 Santa Clara Valley, metamorphosis of, 397 Sapir–Whorf effect, 123–124; cultural version of, 128–131 Saturn’s rings, waves in the medium of, 213 savanna, 71, 364–366 Schank, Roger, 104, 173 schemas: as another name for categories, 336; office visit as an example of, 336–337; versus concrete concepts, 336–337 Schrödinger, Erwin, 453 Schweitzer, Albert, face of, 183–184 science-fiction story as core of a category, 524–526 scientific discoveries: boldness of analogies in, 360–361; mediated by seeing two phenomena as bagels from the same batch, 310 Scott/Thor facial resemblance as an analogy, 181–182 search engines, limited to surface, 115 search, virtual, frame-blended with physical search, 402, 405 secret agent in tunnel category, 167–168 self-monitoring by speakers, 72–73 Selvinsky, Il’ya L’vovich, poem by, 9–10 semantic approximations, 39–43, 270–278 semantic halos: errors caused by, 270–278; as sources of latent analogies, 271, 273 semantic memory, 137 semantic space/nebula analogy, 119–120 semantic space, zones in, 10, 78–81, 83–84, 118–124, 132; see also conceptual spaces senses, physiological, and analogy-making, 286–288 sentence choice constrained by idea choice, 26 sentences: blended together, 268–269; ready-made, 98–99 September 11th: as category, 297; imposing itself on perceptions of events, 31, 297–298; pluralization of, 297–298 sexist default assumption, 293 sexist language and marking, 193–195 shadow: due to absence of light, 204–206; due to absence of mysterious particles, 208; due to absence of rain, 205, 207; due to absence of snow, 205–206; due to absence of vehicles, 207; due to absence of young males, 208; gradual abstraction of, 204–209; in late afternoon, 205; of Nazism, 208 Shakespeare, William, 130, 132; of advertising, the, 222 shallow depth, 346 shallower and deeper aspects of concepts, 203–204 shallow features, experts’ blindness to, 343–344 sharing: contrasted with measuring, 420–426; as key concept in division, 419–426; marked sense of, 419; as necessarily reducing, 419 shells in a conceptual space, 81 shoes: of Albert Einstein, 455; left versus right, 427 showers, used by analogy, 23, 507, 509 sibling, concept of in various languages, 77 silver platters, analogies handed to the reader on, 160, 170 Simmons, Curt, 325 simplification, as key drive in mathematics and physics, 440 simulation, see mental simulation single-member categories as no different from multiple-member categories, 39 “sitting right there”, 140–141 situations: constant real-time encoded of, 161; doing the thinking in math problems, 432; evoking categories, 45–47, 450; lacking clear boundaries, 33, 161; multi-categorizability of, 188; possessing both superficial and deep aspects, 342–344, 515; see also analogy-making, remindings sixty, pointless analogy involving, 281–282, 285 size changes, adults’ naïve view of, 295 size, role of, in encoding of situations, 163 skunk caused by stench, thanks to Maxmell’s equations, 411 slippages, conceptual: between opposite concepts, 276–277, 356–357; in caricature analogies, 321–326; cascade of, 357; due to conceptual proximity, 270–278; engendering conceptual broadening, 150; in level of abstraction, 186; in me-too analogies, 144, 146–148, 151; riding on coattails of other slippages, 276, 357; role of, in creativity, 186–187, 249–256; triggered by esthetic pressures, 350–351, 352, 354, 357; unintended, from one person’s name to another’s, 224 Smith, Peter, see Peter miswriting year smoking causing impotence, 362 smurfs, limited vocabulary of, 108 snag, outflanking of, in Copycat domain, 356–357 “sniffing” the crux of a math problem, 450–451 Snoopy the cat, caricature analogy involving, 319 snow shadow, photo of, 206 snuoiqers versus iggfruders, 11 “so to speak”, to indicate honorary category members, 64–65 soccer played with a bowling ball, 318 Socrates, 16; of snails, the, 222 solutions of polynomials, formal symmetries of, 446–447 sound choice mediated by word choice, 25 sound particles/light particles analogy by Einstein, 461; see also light waves/sound waves analogy sound-quantum hypothesis, 461 sound waves, Doppler effect for, 469–471 sounds versus noises, 126 source–target paradigm in psychology experiments, 339–340 sour grapes situations: category of, 29–30, 113–118, 310; contrasted with silver lining situations, 117–118 space/space-time analogy, 498–499 Spalding, Thomas, 436 Spanish language, 369, 522 speaker/driver analogy, 73 special relativity, see relativity, special spectrum: blackbody, 455–459; defined, 455–456; of ideal gas, 457–459 speech errors: blatant when placed in frames, 261; collecting of, 261; no extra insights in analyzing one’s own, 264; rampant on Web, 261; revealed by hesitations, phonetic distortions, etc., 263, 269, 281; translation of, 379; see also errors, lexical blends spider, as occasional member of category insect, 58 spilling the beans as a category, 96–97 spinning universe, 487 Spitz, Mark, 154–155, 367 square roots of negative numbers: analogy to ordinary numbers, 442; fear of, 442–443 squares, as questionable rectangles, 234–238, 255 staircases, negotiated by analogy, 507, 509, 516 Stargell, Willie, 325–326, 383 statistical approach to machine translation, 372–374 staying on the surface versus going into depth, 344 stealing, conceptual halo around, 106–107 stereotypes: of analogy-making, 135–136, 392, 521, 529; of creativity in physics, 452; efficiency of, 466; as overhasty categorizations, 527–528; shallowness of, 346 Stevens, Wallace, 38 sticks for stirring coffee, absurdity of, 317, 321–322 strange mass: analogous to energy, 479; mutating from one form to another, 479; versus normal mass, 476–485 Streep, Meryl, of spitting, the, 222, 360 strings, alphabetic, 347 string/wire conceptual conflation, 277, 278 “study” versus “office”, 47–49 stupidity, not the same as ignoring most of the world, 426–427 subgroups, nesting patterns of, 447 subjectivity: of analogies, 522–526; of categorizations, 522–526 subscripts/exponents analogy, 169–170, 174 substitutions, Lagrange’s theory of, 446, 447 subtraction word-problems, various strategies for solving, 421–422, 425, 429–434 suburban sprawl likened to marginal or metaphorical uses of a word or phrase, 62, 65–66 Sue (fictional Tim’s fictional mother), 34, 37, 38 sunset, as seen by astronomy students, 389 “superficial”: meaning of, 340; pejorative versus neutral connotations of, 344 superficial features: guiding perception only in one’s domains of incompetence, 340; experts’ blindness to, 343–344; role played by, in memory retrieval, 171, 343; versus deep features, 340 “superfluid” Copycat analogy, 352 superimposing of instances creating more abstract concept, 23, 35, 334, 336–337, 521–522; see also schemas surfaces: bad reputation of, 344; as cues to depths, 345–346; as royal road to essences, 344–346 surfaces versus essences: proverbs about, 102; of certain proverbs, 102, 106–107 surface/depth correlation, 345–346 surface/depth distinction: merely a surface-level contrast, 344; nonexistent for novices, 341–344 surgeon riddle, 293 surgery, mathematical notion of, 426 survival: as dependent on rapid analogy-making, 506–507; as dependent on rapid categorization, 79, 505–506 SUV/search engine analogy, 402 swerves in discourse space, 72–73 swimming pool/black body explanatory analogy, see black body “swimming pool table” analogy, 455, 457–458; see also black body/ideal gas analogy sword of Damocles, as a category, 95–96 syllepses, see zeugmas syllogisms, 15–16, 193, 437 symbol-manipulation recipes, role of analogy-making in the evocation of, 451 symmetry: abstract forms of, 446–447; as an ideal kind of analogy, 357 synopsis of the book, 29–32 syntactic slots as categories, 68–70 —T— tags for photos, as analogues to encodings of experiences, 172 tail wagging the dog concept, 120–121 tango rote memorization as member of category boat on tracks, 521–522 Tartaglia, Niccolò, 438 taste, good versus bad, see good taste technical terms, originating in everyday world, 395–400 technology, understood through homey analogies, 394–400 technomorphism, 404–407 telephone-answering gaffe, 175 “temps”, distinct concepts associated with the French word, 78 Thagard, Paul, 330 Thank you!

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Below are listed some concepts — just a minuscule subset of the concepts that our culture abounds in — the possession of which would seem to give us a substantial leg up on people from previous generations or centuries: Positive and negative feedback, vicious circle, self-fulfilling prophecy, famous for being famous, backlash, supply and demand, market forces, the subconscious, subliminal imagery, Freudian slip, (Edipus complex, defense mechanism, sour grapes, passive-aggressive behavior, peer pressure, racial profiling, ethnic stereotype, status symbol, zero-sum game, catch-22, gestalt, chemical bond, catalyst, photosynthesis, DNA, virus, genetic code, dominant and recessive genes, immune system, auto-immune disease, natural selection, food chain, endangered species, ecological niche, exponential growth, population explosion, contraception, noise pollution, toxic waste, crop rotation, cross-fertilization, cloning, chain reaction, chain store, chain letter, email, spam, phishing, six degrees of separation, Internet, Web-surfing, uploading and downloading, video game, viral video, virtual reality, chat room, cybersecurity, data mining, artificial intelligence, IQ, robotics, morphing, time reversal, slow motion, time-lapse photography, instant replay, zooming in and out, galaxy, black hole, atom, superconductivity, radioactivity, nuclear fission, antimatter, sound wave, wavelength, X-ray, ultrasound, magnetic-resonance imagery, laser, laser surgery, heart transplant, defibrillator, space station, weightlessness, bungee jumping, home run, switch hitter, slam-dunk, Hail Mary pass, sudden-death playoff, make an end run around someone, ultramarathon, pole dancing, speed dating, multitasking, brainstorming, namedropping, channel-surfing, soap opera, chick flick, remake, rerun, subtitles, sound bite, buzzword, musical chairs, telephone tag, the game of Telephone, upping the ante, playing chicken, bumper cars, SUVs, automatic transmission, oil change, radar trap, whiplash, backseat driver, oil spill, superglue, megachurch, placebo, politically correct language, slippery slope, pushing the envelope, stock-market crash, recycling, biodegradability, assembly line, black box, wind-chill factor, frequent-flyer miles, hub airport, fast food, soft drink, food court, VIP lounge, moving sidewalk, shuttle bus, cell-phone lot, genocide, propaganda, paparazzi, culture shock, hunger strike, generation gap, quality time, Murphy’s law, roller coaster, in-joke, outsource, downsize, upgrade, bell-shaped curve, fractal shape, breast implant, Barbie doll, trophy wife, surrogate mother, first lady, worst-case scenario, prenuptial agreement, gentrification, paradigm shift, affirmative action, gridlock, veganism, karaoke, power lunch, brown-bag lunch, blue-chip company, yellow journalism, purple prose, greenhouse effect, orange alert, red tape, white noise, gray matter, black list… Not only does our culture provide us with such potent concepts, it also encourages us to analogically extend them both playfully and seriously, which gives rise to a snowballing of the number of concepts.

The Master and His Emissary: The Divided Brain and the Making of the Western World
by Iain McGilchrist
Published 8 Oct 2012

Braudel, 2001, p. 344. 150. L’Orange, 1965, p. 3. 151. ibid., pp. 3–8. 152. ibid., pp. 9–11. 153. Fractality is the property of forms as diverse as plants, river systems, coast lines, snowflakes and blood vessels that dictates that their form at higher levels of magnification replicates their form at lower levels. Although the term is modern, and derives from the mathematics of Benoît Mandelbrot in the mid-1970s, Leibniz may already have intuited, possibly on the basis of microscope findings, that nature is fractal: see Leibniz, 1992, §67–8, pp. 25–6, and commentary on pp. 41 & 234 ff. Elsewhere in this aphoristic late work, Leibniz relates his description of these worlds within worlds that formed part of his monadology to two further concepts of relevance for the theme of this book: the way that each body mirrors its environing universe, and each soul mirrors its environing body (and consequently the entire universe) (§61–2); and the way in which ‘all bodies are in a perpetual flux, like rivers, and some parts enter into them and some pass out continually’ (§71–2). 154.

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There was an organic beauty which pervaded the whole conception and could be found in its smallest detail: ‘in the same way that the individual type of a living being determines the form of each single part of it, so the principle for the whole structure of the classical building is contained within each single element of it.’152 The phrase reminds one of the way in which, in living forms, the structure of DNA within every cell contains information about the whole organism, or of the fractality of organic forms.153 Thus, he continues, often on sacred sites the classical temples stand ‘with peculiar recalcitrance’ beside one another, each with its own orientation determined by its god or cult, by sacred portents and signs in the temple ground. Each building defies superior order of axiality, symmetry, or unity of direction … This organic and autonomous life, this supreme development from within of each part, of each ornament of the building, was lost during the Hellenistic-Roman evolution that followed.

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Edgard Varese became obsessed with mathematics at the time of composing Intégrales (1925), writing in the programme note for its New York premiere: ‘there is more musical fertility in the contemplation of the stars – preferably through a telescope – and in the high poetry of certain mathematical exposition than in the most sublime gossip of human passions’. Amongst contemporary musicians, the American composer Elliott Carter read mathematics at Annapolis University, Pierre Boulez studied applied mathematics before turning to composition, and György Ligeti discovered fractal geometry in the early 1980s, after which his music was influenced by the complex, many-layered structure of this branch of mathematics. Karlheinz Stockhausen, who displayed many characteristics of a schizotypal personality, used confessedly inappreciable mathematical series to structure his works. 95.

The Sum of All Fears
by Tom Clancy
Published 2 Jan 1989

It has a long and distinguished history that has benefited from another traditional Russian strength, a fascination with theoretical mathematics. The relationship between ciphers and mathematics is a logical one, and the most recent manifestation of this was the work of a bearded, thirtyish gnome of a man who was fascinated with the work of Benoit Mandelbrot at Harvard University, the man who had effectively invented fractal geometry. Uniting this work with that of MacKenzie's work on Chaos Theory at Cambridge University in England, the young Russian genius had invented a genuinely new theoretical way of looking at mathematical formulae. It was generally conceded by that handful of people who understood what he was talking about that his work was easily worth a Planck Medal.

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Golovko hung up and looked at the major standing in front of his desk. "That mathematician who figured this all out - good God, I wish we'd had him five years ago!" "He spent ten years devising this theory on ordering chaos. If it's ever made public, he'll win the Planck Medal. He took the work of Mandelbrot at Harvard University in America and MacKenzie at Cambridge, and -" "I will take your word for it, Major. The last time you tried to explain this witchcraft to me I merely got a headache. How is the work going?" "We grow stronger every day. The only thing we cannot break is the new CIA system that's starting to come on line.

Accessory to War: The Unspoken Alliance Between Astrophysics and the Military
by Neil Degrasse Tyson and Avis Lang
Published 10 Sep 2018

Cunliffe points out that Pytheas would have been measuring in the unit known as the stade, equivalent to 125 paces and amounting to 8.0 or 8.3 stades to the Roman mile, depending on who was doing the measuring. Ignoring fractals, the long and the short of it is that Britain’s coastline, as given in Encyclopaedia Britannica and cited by Cunliffe, measures 4,548 miles—and Pytheas’s approximation amounted to something in the neighborhood of 4,400 miles. Today (presumably taking into account only some of the ins and outs), according to the Ordnance Survey, Britain’s national mapping agency, “The coastline length around mainland Great Britain is 11,072.76 miles,” www.ordnancesurvey.co.uk/oswebsite/freefun/didyouknow/ (accessed May 17, 2010). But as Benoit Mandelbrot famously proposed in “How Long Is the Coastline of Britain?”

Shantaram: A Novel
by Gregory David Roberts
Published 12 Oct 2004

His hands squeezed tighter. My neck was strong and the muscles were well developed, but I knew he had the strength to kill me. My hand reached, groping for the pistol in my pocket. I had to shoot him. I had to kill him. That was all right. I didn’t care. The air in my lungs was spent, and my brain was exploding in Mandelbrot whirls of colored light, and I was dying, and I wanted to kill him. Vikram crashed a heavy wooden stool into the back of the big man’s bald head. It’s not as easy to knock a man out as it seems in the movies. It’s true that a lucky hit can do it in one shot, but I’ve been hit with iron bars, lumps of wood, boots, and many hard fists, and I’ve only ever been knocked out once in my life.

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Lin,’ Khaderbhai said, smiling graciously as Farid removed the hookah and set about cleaning the ash-filled bowl. ‘It is also our custom for the guest to give us the theme for discussion. This is usually a religious theme, but it need not be so. What would you like to talk about?’ ‘I … I … I’m not sure what you mean?’ I stammered, my brain soundlessly exploding in fractal repetitions of the pattern in the carpet beneath my feet. ‘Give us a subject, Lin. Life and death, love and hate, loyalty and betrayal,’ Abdul Ghani explained, waving a plump hand in effete little circles with each couplet. ‘We are like a debating society here, you see. We meet every month, at least one time, and when our business and private matters are finished, we talk about philosophical subjects and the suchlike.