Probability Theory Quotes & Sayings

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

General relativity is in the old Newtonian framework where you predict what will happen, not the probability of what will happen. And putting together the probabilities of quantum mechanics with the certainty of general relativity, that's been the big challenge and that's why we have been excited about string theory, as it's one of the only approaches that can put it together. — Brian Greene

Probability theory is nothing but common sense reduced to calculation. — Pierre-Simon Laplace

On the one hand, a central part of this theory is the introduction of probability measures which describe what associations and deductions we are likely to make. — Ulf Grenander

An aphorism is an extreme synthesis of thesis and antithesis, theory and practice, it's a mixture of intuition and observation, hypothesis and illusions of certainty and probability, history and stupidity. — William C. Brown

Say your boss has been taking longer than usual to respond to your e-mails. Many people would take that as a sign that their star is falling because if your star is falling, the chances are high that your boss will respond to your e-mails more slowly than before. But your boss might be slower in responding because she is unusually busy or her mother is ill. And so the chances that your star is falling if she is taking longer to respond are much lower than the chances that your boss will respond more slowly if your star is falling. The appeal of many conspiracy theories depends on the misunderstanding of this logic. That is, it depends on confusing the probability that a series of events would happen if it were the product of a huge conspiracy with the probability that a huge conspiracy exists if a series of events occurs. The effect on the probability that an event will occur if or given that other events occur is what Bayes's theory is all about. To — Leonard Mlodinow

But the stupidity which is common to all such "explanations" is, of course, simply that of proceeding as though the merits of a theory - such things as truth, or probability, or explanatory power - could not possibly be among the reasons for its currency. — David Stove

Mathematically speaking, the probable (that in 6,000,000,000 throws with a regular six-sided die the die will come up proximately 1 ,000,000,000 times) and the improbable (that in six throws with the same die the one will come approximately up six times) are not different in kind, but only in frequency, whereby the more frequent appears a priori more probable.
But the occasional occurrence of the improbable does not imply the intervention of a higher power, something in the nature of a miracle, as the layman is so ready to assume. The term "probability" includes improbability at the extreme limits of probability, and when the improbable does occur this is no cause for surprise, bewilderment or mystification.
Cf. Ernst Mally's Probability and Law, Hans Reichenbach The theory Probability, Whitehead and Russell's Principia Mathematica, von Mises' Probability, Statistics and Truth — Max Frisch

If skeptic can weakly force E, then he can force E. — Glenn Shafer

I am convinced that it is impossible to expound the methods of induction in a sound manner, without resting them upon the theory of probability. Perfect knowledge alone can give certainty, and in nature perfect knowledge would be infinite knowledge, which is clearly beyond our capacities. We have, therefore, to content ourselves with partial knowledge-knowledge mingled with ignorance, producing doubt. — William Stanley Jevons

A scientist worthy of a lab coat should be able to make original discoveries while wearing a clown suit, or give a lecture in a high squeaky voice from inhaling helium. It is written nowhere in the math of probability theory that one may have no fun. — Eliezer Yudkowsky

In no other branch of mathematics is it so easy for experts to blunder as in probability theory. — Martin Gardner

I am no friend of probability theory, I have hated it from the first moment when our dear friend Max Born gave it birth. For it could be seen how easy and simple it made everything, in principle, everything ironed and the true problems concealed. Everybody must jump on the bandwagon [Ausweg]. And actually not a year passed before it became an official credo, and it still is. — Erwin Schrodinger

I may finally call attention to the probability that the association of paternal and maternal chromosomes in pairs and their subsequent separation during the reducing division as indicated above may constitute the physical basis of the Mendelian law of heredity. — Walter S. Sutton

You know that, according to quantum theory, if two particles collide with enough energy you can, in principle, with an infinitesimal probability, produce two grand pianos. — Isidor Isaac Rabi

We come finally, however, to the relation of the ideal theory to real world, or "real" probability. If he is consistent a man of the mathematical school washes his hands of applications. To someone who wants them he would say that the ideal system runs parallel to the usual theory: "If this is what you want, try it: it is not my business to justify application of the system; that can only be done by philosophizing; I am a mathematician". In practice he is apt to say: "try this; if it works that will justify it". — John Edensor Littlewood

Maybe we should teach schoolchildren probability theory and investment risk management. — Andrew Lo

Probability theory is nothing more than common sense reduced to calculation. -1819 — Pierre-Simon Laplace

At least some of them, I suspect, have turned to probability theory in the hope that it would give them what they had originally expected from a subjectivist or epistemological theory of the attainment of truth through verification; that is, a theory of rational and justifiable belief, based upon observed instances. — Karl Popper

The theory of probabilities is at bottom nothing but common sense reduced to calculus; it enables us to appreciate with exactness that which accurate minds feel with a sort of instinct for which of times they are unable to account. — Pierre-Simon Laplace

Once we see, however, that the probability of life originating at random is so utterly miniscule as to make it absurd, it becomes sensible to think that the favorable properties of physics on which life depends are in every respect deliberate ... It is therefore almost inevitable that our own measure of intelligence must reflect ... higher intelligences ... even to the limit of God ... such a theory is so obvious that one wonders why it is not widely accepted as being self-evident. The reasons are psychological rather than scientific. — Fred Hoyle

I failed math twice, never fully grasping probability theory. I mean, first off, who cares if you pick a black ball or a white ball out of the bag? And second, if you're bent over about the color, don't leave it to chance. Look in the damn bag and pick the color you want. — Janet Evanovich

You can't talk to thermodynamics and you can't pray to probability theory. You — Eliezer Yudkowsky

The quantum theory is based on the idea that there is a probability that all possible events, no matter how fantastic or silly, might occur. — Michio Kaku

The final story of randomness - utter chaos - has not yet been told to us by the mathematicians. It seems remarkable that something so fundamental for probability theory has not been defined and even more remarkable that we can go so far in mathematics lacking a definition. By simply assuming randomness exists, mathematicians assign elementary probabilities to events, and that is their starting point. But they have not captured chaos and looked it in the eye. — Heinz R. Pagels

The puzzle of time, the mystery of creation, the problem of evil, the enigma of knowledge, the state of soul, the vexations of probability theory of the nature of God's grace, all reduced to a single question. What does it mean, in a world of God's creation, that man is free to choose between the paths of good and evil? — Bernard Beckett

It was our use of probability theory as logic that has enabled us to do so easily what was impossible for those who thought of probability as a physical phenomenon associated with "randomness". Quite the opposite; we have thought of probability distributions as carriers of information. — Edwin Thompson Jaynes

The situation today is, we haven't got a good model to explain partial reflection by two surfaces; we just calculate the probability that a particular photomultiplier will be hit by a photon reflected from a sheet of glass. I have chosen this calculation as our first example of the method provided by theory of quantum electrodynamics. I am going to show you "how we count the beans"-what the physicists do to get the right answer. I am not going to explain how the photons actually "decide" whether to bounce back or go through; that is not known. (Probably the question has no meaning.) I will only show you how to calculate the correct probability that light will be reflected from glass of a given thickness, because that's the only thing physicists know how to do! What we do to get the answer to this problem is analogous to the things we have to do to get the answer to every other problem explained by quantum electrodynamics. — Richard Feynman

The theory of probability is the only mathematical tool available to help map the unknown and the uncontrollable. It is fortunate that this tool, while tricky, is extraordinarily powerful and convenient. — Benoit Mandelbrot

The incomplete knowledge of a system must be an essential part of every formulation in quantum theory. Quantum theoretical laws must be of a statistical kind. To give an example: we know that the radium atom emits alpha-radiation. Quantum theory can give us an indication of the probability that the alpha-particle will leave the nucleus in unit time, but it cannot predict at what precise point in time the emission will occur, for this is uncertain in principle. — Werner Heisenberg

One of the most striking and fundamental things about probability theory is that it leads to an understanding of the otherwise strange fact that events which are individually capricious and unpredictable can, when treated en masse, lead to very stable average performances. — Warren Weaver

On any pure theory of causality or statistical probability, organization would be completely improbable without the external aid of a divine organizer. — Lewis Mumford

If a lack of empirical foundations is a defect of the theory of logical probability, it is also a defect of deductive logic. — David Stove

To leave the atom constituted as it was but to interfere with the probability of its undetermined behaviour, does not seem quite so drastic an interference with natural law as other modes of mental interference that have been suggested. (Perhaps that is only because we do not understand enough about these probabilities to realize the heinousness of our suggestion.) Unless it belies its name, probability can be modified in ways which ordinary physical entities would not admit of. There can be no unique probability attached to any event or behaviour; we can only speak of 'probability in the light of certain given information,' and the probability alters according to the extent of the information. It is, I think, one of the most unsatisfactory features of the new quantum theory in its present stage that it scarcely seems to recognize this fact, and leaves us to guess at the basis of information to which its probability theorems are supposed to refer. — Arthur Stanley Eddington

Entropy theory, on the other hand, is not concerned with the probability of succession in a series of items but with the overall distribution of kinds of items in a given arrangement. — Rudolf Arnheim