Probability

Probability is the measure of the likelihood that an event will occur. Probability is quantified as a number between 0 and 1 (where 0 indicates impossibility and 1 indicates certainty). The higher the probability of an event, the more certain that the event will occur.

• This statistical regularity in moral affairs fully establishes their being under the presidency of law. Man is now seen to be an enigma only as an individual; in the mass he is a mathematical problem.
  • Robert Chambers, Vestiges of the Natural History of Creation (1844).

• Probability is the very guide of life.
  • Cicero, De Natura, 5, 12; reported in Hoyt's New Cyclopedia Of Practical Quotations (1922), p. 634. Quoted by Bishop Butler. Also used by Richard Hooker, Ecclesiastical Polity, Book I, Chapter VIII., and, Book II, Chapter VII. Found in John Locke, Essays, Book IV, Chapter XV. Also in Hobbes' Leviathan.

• It is a truth very certain that, when it is not in our power to determine what is true, we ought to follow what is most probable
  • René Descartes, (1596–1650), reported in S.H. Wearne, Control of Engineering Project (1989), p. 125.
• There is no Algebraist nor Mathematician so expert in his science, as to place entire confidence in any truth immediately upon his discovery of it, or regard it as any thing, but a mere probability. Every time he runs over his proofs, his confidence increases; but still more by the approbation of his friends; and is raised to its utmost perfection by the universal assent and applauses of the learned world.
  • David Hume, A Treatise of Human Nature (1739), Part IV, Section I.

• Al right. I already see you turning off. I can see you say you don't understand me. You can't understand that it could be chance. "I don't like it!" Tough! I don't like it either, but that's the way it is! Ok? I don't understand it either. ..."It must be that Nature knows that it's going to go up or down." No, it must not be that nature knows! We are not to tell Nature what she's gotta be! That's what we found out. Every time we take a guess as how she's got to be, and go and measure... She's clever. She's always got better imagination than we have, and she finds a cleverer way to do it than we have thought of. And in this particular case, the clever way to do it is by probability, by odds. ...[L]ight works by probability.
  • Richard Feynman, Lecture 1. "Photons: Corpuscles of Light" (1979) Sir Douglas Robb Memorial Lectures, University of Auckland.

• My thesis, paradoxically, and a little provocatively, but nonetheless genuinely, is simply this :

  PROBABILITY DOES NOT EXIST.

  The abandonment of superstitious beliefs about the existence of Phlogiston, the Cosmic Ether, Absolute Space and Time, ... , or Fairies and Witches, was an essential step along the road to scientific thinking. Probability, too, if regarded as something endowed with some kind of objective existence, is no less a misleading misconception, an illusory attempt to exteriorize or materialize our true probabilistic beliefs.

  • Bruno de Finetti, Theory of Probability (1970), Preface

• Probability is too important to be left to the experts. [...] The experts, by their very expert training and practice, often miss the obvious and distort reality seriously. [...] The desire of the experts to publish and gain credit in the eyes of their peers has distorted the development of probability theory from the needs of the average user. The comparatively late rise of the theory of probability shows how hard it is to grasp, and the many paradoxes show clearly that we, as humans, lack a well grounded intuition in the matter. Neither the intuition of the man in the street, nor the sophisticated results of the experts provides a safe basis for important actions in the world we live in.
  • Richard Hamming, The Art of Probability for Scientists and Engineers (1991), p. 4 [emphasis in original]

• How often have I said to you that when you have eliminated the impossible, whatever remains, however improbable, must be the truth?
  • Sherlock Holmes, Sign of the Four Chap. 6, p. 111, written by Arthur Conan Doyle

• R. A. Fisher, J. Neyman, R. von Mises, W. Feller, and L. J. Savage denied vehemently that probability theory is an extension of logic, and accused Laplace and Jeffreys of committing metaphysical nonsense for thinking that it is.
  • E. T. Jaynes; G. Larry Bretthorst (10 April 2003). Probability Theory: The Logic of Science. Cambridge University Press. p. 293. ISBN 978-0-521-59271-0. 

• They should have known better. The probability of a train derailment was infinitesimal. That meant it was only a matter of time.
  • N. K. Jemisin, Non-Zero Probabilities - Originally published in Clarkesworld magazine Issue 36, September 2009

• No human being can give an eternal resolution to another or take it from him; If someone objects that then one might just as well be silent if there is no probability of winning others, he thereby has merely shown that although his life very likely thrived and prospered in probability and everyone of his undertakings in the service of probability went forward, he has never really ventured and consequently has never had or given himself the opportunity to consider that probability is an illusion, but to venture the truth is what gives human life and the human situation pith and meaning, to venture is the fountainhead of inspiration, whereas probability is the sworn enemy of enthusiasm, the mirage whereby the sensate person drags out time and keeps the eternal away, whereby he cheats God, himself, and his generation: cheats God of the honor, himself of liberating annihilation, and his generation of the equality of conditions.
  • Søren Kierkegaard, Four Upbuilding Discourses (31 August 1844) in Eighteen Upbuilding Discourses p. 382.

• The epistemological value of probability theory is based on the fact that chance phenomena, considered collectively and on a grand scale, create non-random regularity.
  • Andrey Kolmogorov, Limit Distributions for Sums of Independent Random Variables (1954), as translated by K. L. Chung

• As is known, the question of the objectivity or the subjectivity of probability has divided the world of science into two camps. Some maintain that there exist two types of probability, as above, others, that only the subjective exists, because regardless of what is supposed to take place, we cannot have full knowledge of it. Therefore, some lay the uncertainty of future events at the door of our knowledge of them, whereas others place it within the realm of the events themselves.
  • Stanisław Lem, "De Impossibilitate Vitae and De Impossibilitate Vitae Prognoscendi", in A Perfect Vacuum (1971), tr. Michael Kandel (1978).

• Feeling threatened is not the same as being threatened, but the difference gets lost. The danger from low levels of radiation is quite low, as expressed as morbidity statistics or probabilities, but there is an unfortunate lack of connection to probability in the average person. Low probabilities are a particular problem of perception. If they were not, then nobody would play the lottery and the gambling industry would collapse.
  • James Mahaffey (2015). Atomic Accidents. Pegasus Books. p. xix. ISBN 978-1-60598-680-7. 

• In applying dynamical principles to the motion of immense numbers of atoms, the limitation of our faculties forces us to abandon the attempt to express the exact history of each atom, and to be content with estimating the average condition of a group of atoms large enough to be visible. This method... which I may call the statistical method, and which in the present state of our knowledge is the only available method of studying the properties of real bodies, involves an abandonment of strict dynamical principles, and an adoption of the mathematical methods belonging to the theory of probability. … If the actual history of Science had been different, and if the scientific doctrines most familiar to us had been those which must be expressed in this way, it is possible that we might have considered the existence of a certain kind of contingency a self evident truth, and treated the doctrine of philosophical necessity as a mere sophism.
  • James Clerk Maxwell, "Introductory Lecture on Experimental Physics," The Scientific Papers of James Clerk Maxwell (1890) Vol. 2.

• Einstein's supreme greatness was in transforming physical thinking from that of the culmination of classical physics about 1900 to that of quantum mechanics starting about 1925. ...far more than anyone else, he caused physicists to think in terms of probabilities. He began to do this in his early work in thermodynamics, and he brought such thinking to its first great fruition in 1905 in his work on Brownian movement and in his first work on radiation, in which he introduced the concept of light quanta or photons. Its second, even greater fruition was in his famous paper on the quantum theory of radiation in 1917.
  That paper illustrated methods that have been in use almost without change ever since, even though the majority of the users have no knowledge that it was Einstein who propounded them. It was in this paper that Einstein postulated the various transition possibilities between two states of a quantized system. ...quantum theory has existed ever since precisely for the purpose of evaluating these probabilities. In this paper of 1917 Einstein postulated in particular the process known as stimulated emission, and inferred the properties of this process. This is the process employed in the... light maser or laser.
  • W. H. McCrea, as quoted by G. J. Whitrow, Einstein, the Man and His Achievement (1973)

• The theory of probability combines commonsense reasoning with calculation. It domesticates luck, making it subservient to reason.
  • Ivars Peterson (1997). The Jungles of Randomness. John Wiley & Sons. p. 19. ISBN 0-471-29587-6. 

• Why do [people] confuse probability and expectation, that is, probability and probability times payoff? Mainly because much... schooling comes from examples in symmetric environments... the... bell curve... is entirely symmetric.
  • Nassim Nicholas Taleb, Fooled by Randomness: The Hidden Role of Chance in Life and in the Markets (2001) Six: Skewness and Symmetry | The Median is Not the Message

• Since the end of World War II, I have been working on the many ramifications of the theory of messages. Besides the electrical engineering theory of the transmission of messages, there is a larger field which includes not only the study of language but the study of messages as a means of controlling machinery and society, the development of computing machines and other such automata, certain reflections upon psychology and the nervous system, and a tentative new theory of scientific method. This larger theory of messages is a probabilistic theory, an intrinsic part of the movement that owes its origin to Willard Gibbs and which I have described in the introduction.
  • Norbert Wiener, The Human Use of Human Beings (1950; 1954)

• At a purely formal level, one could call probability theory the study of measure spaces with total measure one, but that would be like calling number theory the study of strings of digits which terminate.
  • Terence Tao, Topics in Random Matrix Theory (2012), also on his blog

• Randomness
• Statistics

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