“This faulty intuition as well as many modern applications of probability theory are under the strong influence of traditional misconceptions concerning the meaning of the law of large numbers and of a popular mystique concerning a so-called law of averages.”

—  William Feller

Source: An Introduction To Probability Theory And Its Applications (Third Edition), Chapter X, Law Of large Numbers, p. 250.

Adopted from Wikiquote. Last update June 3, 2021. History

Help us to complete the source, original and additional information

Do you have more details about the quote "This faulty intuition as well as many modern applications of probability theory are under the strong influence of tradi…" by William Feller?
William Feller photo
William Feller 30
Croatian-American mathematician 1906–1970

Related quotes

“The results concerning fluctuations in coin tossing show the widely held beliefs about the law of large numbers are fallacious. They were so amazing and so at variance with common intuition that even sophisticated colleagues doubted that coins actually misbehave as theory predicts.”

William Feller (1906–1970) Croatian-American mathematician

Note on the Use of this Book, p. xi-xii.
An Introduction To Probability Theory And Its Applications (Third Edition)

Leonard Mlodinow photo

“The law of small numbers is not really a law. It is a sarcastic name describing the misguided attempt to apply the law of large numbers when the numbers aren't large.”

Leonard Mlodinow book The Drunkard's Walk

Source: The Drunkard's Walk, Chapter 5, The Dueling Of Large And Small Numbers, p. 99

“Imaginary numbers are not imaginary and the theory of complex numbers is no more complex than the theory of real numbers. Complex numbers are as intuitive for an electronics engineer as -100 is for the average person with an overdrawn bank account.”

Mordechai Ben-Ari (1948) Israeli computer scientist

Source: Just a Theory: Exploring the Nature of Science (2005), Chapter 3, “Words Scientists Don’t Use: At Least Not the Way You Do” (p. 56)

Felix Adler photo

“There is no difference in the law. But so long have they quarreled concerning the origin of law that the law itself has fallen more and more into abeyance.”

Felix Adler (1851–1933) German American professor of political and social ethics, rationalist, and lecturer

Founding Address (1876)
Context: The Hebrew prophets said of old, to serve Jehovah is to make your hearts pure and your hands clean from corruption, to help the suffering, to raise the oppressed. Jesus of Nazareth said that he came to comfort the weary and heavy laden. The Philosopher affirms that the true service of religion is the unselfish service of the common weal. There is no difference among them all. There is no difference in the law. But so long have they quarreled concerning the origin of law that the law itself has fallen more and more into abeyance. For indeed, as it is easier to say. "I do not believe," and have done with it, so also it is easier to say, "I believe," and thus to bribe one's way into heaven, as it were, than to fulfill nobly our human duties with all the daily struggle and sacrifice which they involve.

“Simple methods will soon lead us to results of far reaching theoretical and practical importance. We shall encounter theoretical conclusions which not only are unexpected but actually come as a shock to intuition and common sense. They will reveal that commonly accepted notions concerning chance fluctuations are without foundation and that the implications of the law of large numbers are widely misconstrued.”

William Feller (1906–1970) Croatian-American mathematician

Source: An Introduction To Probability Theory And Its Applications (Third Edition), Chapter III, Fluctuations In Coin Tossing And Random Walks, p. 67.

Siméon Denis Poisson photo

“In many different fields, empirical phenomena appear to obey a certain general law, which can be called the Law of Large Numbers. This law states that the ratios of numbers derived from the observation of a very large number of similar events remain practically constant, provided that these events are governed partly by constant factors and partly by variable factors whose variations are irregular and do not cause a systematic change in a definite direction.”

Siméon Denis Poisson (1781–1840) French mathematician, mechanician and physicist

Statement of Poisson's law also known as the Law of Large Numbers (1837), as quoted by [Richard Von Mises, Probability, Statistics and Truth, Allen and Unwin, 1957, 104-105]

Jacques Derrida photo

“No text in the tradition seems as lucid concerning the way in which the political is becoming worldwide. concerning the irreducibility of the technical and the media in the current of the most thinking thought-and this goes beyond the railroad and the newspapers of the time whose powers were analyzed in such an incomparable way in the Manifesto. And few texts have shed so much light on law. international law. and nationalism.”

Jacques Derrida book Specters of Marx

Injunctions of Marx
Specters of Marx (1993)

Duncan Gregory photo

“There are a number of theorems in ordinary algebra, which, though apparently proved to be true only for symbols representing numbers, admit of a much more extended application. Such theorems depend only on the laws of combination to which the symbols are subject, and are therefore true for all symbols, whatever their nature may be, which are subject to the same laws of combination. The laws with which we have here concern are few in number, and may be stated in the following manner. Let a, b represent two operations, u, v two subjects on which they operate, then the laws are
(1) ab(u) = ba (u),
(2) a(u + v) = a (u) + a (v),
(3) am. an. u = am + n. u.
The first of these laws is called the commutative law, and symbols which are subject to it are called commutative symbols. The second law is called distributive, and the symbols subject to it distributive symbols. The third law is not so much a law of combination of the operation denoted by a, but rather of the operation performed on a, which is indicated by the index affixed to a. It may be conveniently called the law of repetition, since the most obvious and important case of it is that in which m and n are integers, and am therefore indicates the repetition m times of the operation a.”

Duncan Gregory (1813–1844) British mathematician

That these are the laws employed in the demonstration of the principal theorems in Algebra, a slight examination of the processes will easily shew ; but they are not confined to symbols of numbers ; they apply also to the symbol used to denote differentiation.
p. 237 http://books.google.com/books?id=8lQ7AQAAIAAJ&pg=PA237; Highlighted section cited in: George Boole " Mr Boole on a General Method in Analysis http://books.google.com/books?pg=PA225-IA15&id=aGwOAAAAIAAJ&hl," Philosophical Transactions, Vol. 134 (1844), p. 225; Other section (partly) cited in: James Gasser (2000) A Boole Anthology: Recent and Classical Studies in the Logic of George Boole,, p. 52
Examples of the processes of the differential and integral calculus, (1841)

“The engine driving the Kelly system is the "law of large numbers." In a 1713 treatise on probability, Swiss mathematician Jakob Bernoulli propounded a law that has been misunderstood by gamblers (and investors) ever since.”

William Poundstone (1955) American writer

Part Two, Blackjack, The Kelly Criterion Under The Hood, p. 102
Fortune's Formula (2005)

Aron Ra photo

“Laws never become theories! The theory of gravity includes a number of Newtonian laws. There is not one law of gravity; there are several laws included within the theory. The same goes for Relativity and even for evolution for that matter.”

Aron Ra (1962) Aron Ra is an atheist activist and the host of the Ra-Men Podcast

Patheos, Orwellian Legislative Duplicity on HB 1485 http://www.patheos.com/blogs/reasonadvocates/2017/05/05/orwellian-legislative-duplicity-hb-1485/ (May 5, 2017)

Related topics