William Feller - Collected Quotes

"An unbelievably large literature tried to establish a transcendental ‘law of logistic growth’. Lengthy tables, complete with chi-square tests, supported this thesis for human populations, for bacterial colonies, development of railroads. etc. Both height and weight of plants and animals were found to follow the logistic even though it is theoretically clear these two variables cannot subject to the same distribution. […] The only trouble with the theory is that not only the logistic distribution, but also the normal, the Cauchy, and other distributions can be fitted to the material with the same or better goodness of fit. In thig competition the logistic distribution plays no distinguished role whatever; most theoretical models can be supported by the same observational material. Theories of this nature are short-lived because they open no new ways, and new confirmations of the same old thing soon grow boring. But the naïve reasoning has not been superseded by sense." (William A Feller, "An Introduction to Probability Theory and Its Applications" Vol. 2, 1950)

"Historically, the original purpose of the theory of probability was to describe the exceedingly narrow domain of experience connected with games of chance, and the main effort was directed to the calculation of certain probabilities." (William Feller, "An Introduction To Probability Theory And Its Applications", 1950)

"In stochastic processes the future is not uniquely determined, but we have at least probability relations enabling us to make predictions." (William Feller, "An Introduction To Probability Theory And Its Applications", 1950)

"Infinite product spaces are the natural habitat of probability theory." (William Feller, "An Introduction To Probability Theory And Its Applications", 1950)

"It is a common fallacy to believe that the law of large numbers acts as a force endowed with memory seeking to return to the original state, and many wrong conclusions have been drawn from this assumption." (William Feller, "An Introduction To Probability Theory And Its Applications", 1950)

"It is seen that continued shuffling may reasonably be expected to produce perfect 'randomness' and to eliminate all traces of the original order. It should be noted, however, that the number of operations required for this purpose is extremely large."  (William Feller, "An Introduction To Probability Theory And Its Applications", 1950)

"Physical irreversibility manifests itself in the fact that, whenever the system is in a state far removed from equilibrium, it is much more likely to move toward equilibrium, than in the opposite direction." (William Feller, "An Introduction To Probability Theory And Its Applications", 1950)

"Probability is a mathematical discipline with aims akin to those, for example, of geometry or analytical mechanics. In each field we must carefully distinguish three aspects of the theory: (a) the formal logical content, (b) the intuitive background, (c) the applications. The character, and the charm, of the whole structure cannot be appreciated without considering all three aspects in their proper relation." (William Feller, "An Introduction to Probability Theory and Its Applications", 1950)

"The bewildered novice in chess moves cautiously, recalling individual rules, whereas the experienced player absorbs a complicated situation at a glance and is unable to account rationally for his intuition. In like manner mathematical intuition grows with experience, and it is possible to develop a natural feeling for concepts such as four dimensional space." (William Feller, "An Introduction To Probability Theory And Its Applications", 1950)

"The classical theory of probability was devoted mainly to a study of the gamble's gain, which is again a random variable; in fact, every random variable can be interpreted as the gain of a real or imaginary gambler in a suitable game." (William Feller, "An Introduction To Probability Theory And Its Applications", 1950)

"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, "An Introduction To Probability Theory And Its Applications", 1950)

"The notion of conditional probability is a basic tool of probability theory, and it is unfortunate that its great simplicity is somewhat obscured by a singularly clumsy terminology." (William Feller, "An Introduction To Probability Theory And Its Applications", 1950)

"The painful experience of many gamblers has taught us the lesson that no system of betting is successful in improving the gambler's chances. If the theory of probability is true to life, this experience must correspond to a provable statement." (William Feller, "An Introduction To Probability Theory And Its Applications", 1950)

"The philosophy of the foundations of probability must be divorced from mathematics and statistics, exactly as the discussion of our intuitive space concept is now divorced from geometry." (William Feller, "An Introduction To Probability Theory And Its Applications", 1950)

"To the untrained eye, randomness appears as regularity or tendency to cluster." (William Feller, "An Introduction to Probability Theory and its Applications", 1950) 

"The perfect die does not lose its usefulness or justification by the fact that real dice fail to live up to it." (William Feller)