“To every event defined for the original random walk there corresponds an event of equal probability in the dual random walk, and in this way almost every probability relation has its dual.”

— William Feller

Source: An Introduction To Probability Theory And Its Applications (Third Edition), Chapter III, Fluctuations In Coin Tossing And Random Walks, p. 92.

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William Feller 30

Croatian-American mathematician 1906–1970

William Feller (1906–1970) Croatian-American mathematician

Source: An Introduction To Probability Theory And Its Applications (Third Edition), Chapter IX, Random Variables; Expectation, p. 212.

“[Market outcomes] depends on the cumulation of random events.”

W. Brian Arthur (1946) American economist

Source: Competing Technologies, Increasing Returns and Lock-in by Historical Events, (1989), p. 124; as cited in: Tobias Georg Meyer (2012) Path Dependence in Two-sided Markets. p. 244

“Teachers were both blamed for everything that went wrong with kids and turned to for their every salvation. This dual role of scapegoat and savior was downright messianic but even Jesus was probably paid better.”

Lionel Shriver book We Need to Talk About Kevin

Source: We Need to Talk About Kevin

“From the beginning I could not believe that the “efficient market” hypothesis was dependent on a pure Brownian motion white noise or any truly random random walk. Place a minuscule colloidal molecule on a horizontal table that covers unlimited acres. Bombard it from every direction with thousands of minute atoms; and then if you wait long enough that original molecule can have traveled a billion miles in one direction. That’s truly a random Bachelier-Einstein walk, but not my notion of economic fluctuations.”

Paul A. Samuelson (1915–2009) American economist

New millennium, An Enjoyable Life Puzzling Over Modern Finance Theory, 2009

“The first attempts to consider the behavior of so-called "random neural nets" in a systematic way have led to a series of problems concerned with relations between the "structure" and the "function" of such nets. The "structure" of a random net is not a clearly defined topological manifold such as could be used to describe a circuit with explicitly given connections. In a random neural net, one does not speak of "this" neuron synapsing on "that" one, but rather in terms of tendencies and probabilities associated with points or regions in the net.”

Anatol Rapoport (1911–2007) Russian-born American mathematical psychologist

Anatol Rapoport. "Cycle distributions in random nets." The bulletin of mathematical biophysics 10.3 (1948): 145-157.
1940s

“In American culture the coin toss is the paradigm of the random event. A coin toss decides who kicks off the Super Bowl. Looked at another way, a coin toss is not random at all. It is physics.”

William Poundstone (1955) American writer

Part One, Entropy, Toy Room, p. 46
Fortune's Formula (2005)

“A hundred years ago, it became clear that most events at the level of the subatomic are random, uncaused, indeterministic quantum events—merely matters of probability. Locate an electron on one side of a steel barrier it doesn't have the energy to penetrate. There is some probability that the next time you detect it, the electron will be on the other side of the barrier it can't penetrate. But there are no facts about the electron that explain why sometimes it does this and sometimes it doesn't. At the basement level of reality, there are just probabilities.”

Alexander Rosenberg (1946) American philosopher

The Atheist's Guide to Reality (2011)

“A distinguished writer (Siméon Denis Poisson) has thus stated the fundamental definitions of the science:
:"The probability of an event is the reason we have to believe that it has taken place, or that it will take place."
:"The measure of the probability of an event is the ratio of the number of cases favourable to that event, to the total number of cases favourable or contrary, and all equally possible" (equally like to happen).
From these definitions it follows that the word probability, in its mathematical acceptation, has reference to the state of our knowledge of the circumstances under which an event may happen or fail. With the degree of information which we possess concerning the circumstances of an event, the reason we have to think that it will occur, or, to use a single term, our expectation of it, will vary.”

George Boole (1815–1864) English mathematician, philosopher and logician

Source: 1850s, An Investigation of the Laws of Thought (1854), p. 243-4; As cited in: "George Boole (1815–64)" in: Oxford Dictionary of Scientific Quotations, Edited by W. F. Bynum and Roy Porter, January 2006

“It is the event that is the immediate entity of perception; Nature is the sum-total of events, and every instrument of thought that our minds employ can be traced back to its ultimate origin in events.”

Herbert Dingle (1890–1978) British astronomer

pages 12–13 https://books.google.com/books?id=hwpKAAAAIAAJ&pg=PA12
Relativity for All, London, 1922

“Every habit and faculty is preserved and increased by correspondent actions,—as the habit of walking, by walking; of running, by running.”

Epictetus (50–138) philosopher from Ancient Greece

How the Semblances of Things are to be combated, Chap. xviii.
Bartlett's Familiar Quotations, 10th ed. (1919)

“To every event defined for the original random walk there corresponds an event of equal probability in the dual random walk, and in this way almost every probability relation has its dual.”

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