Strong Law of Small Numbers
Encyclopedia
"The Strong Law of Small Numbers" is a humorous paper by mathematician Richard K. Guy
and also the so-called law that it proclaims: "There aren't enough small numbers to meet the many demands made of them." In other words, any given small number appears in far more contexts than may seem reasonable, leading to many apparently surprising coincidences in mathematics, simply because small numbers appear so often and yet are so few. Guy's 1988 paper gives 35 examples in support of this thesis, and is thus an example of proof by intimidation
. Confirmation bias
can lead inexperienced mathematicians to conclude that these concepts are related, which in fact they are not.
Guy's observation has since become part of mathematical folklore, and is commonly referenced by other authors.
Richard K. Guy
Richard Kenneth Guy is a British mathematician, Professor Emeritus in the Department of Mathematics at the University of Calgary....
and also the so-called law that it proclaims: "There aren't enough small numbers to meet the many demands made of them." In other words, any given small number appears in far more contexts than may seem reasonable, leading to many apparently surprising coincidences in mathematics, simply because small numbers appear so often and yet are so few. Guy's 1988 paper gives 35 examples in support of this thesis, and is thus an example of proof by intimidation
Proof by intimidation
Proof by intimidation is a jocular term used mainly in mathematics to refer to a style of presenting a purported mathematical proof by giving an argument loaded with jargon and appeal to obscure results, so that the audience is simply obliged to accept it, lest they have to admit their ignorance...
. Confirmation bias
Confirmation bias
Confirmation bias is a tendency for people to favor information that confirms their preconceptions or hypotheses regardless of whether the information is true.David Perkins, a geneticist, coined the term "myside bias" referring to a preference for "my" side of an issue...
can lead inexperienced mathematicians to conclude that these concepts are related, which in fact they are not.
Guy's observation has since become part of mathematical folklore, and is commonly referenced by other authors.
See also
- Finite geometryFinite geometryA finite geometry is any geometric system that has only a finite number of points.Euclidean geometry, for example, is not finite, because a Euclidean line contains infinitely many points, in fact as many points as there are real numbers...
– includes study of structures on small, finite sets - Law of large numbersLaw of large numbersIn probability theory, the law of large numbers is a theorem that describes the result of performing the same experiment a large number of times...
(unrelated, but the origin of the name) - Mathematical coincidence
- Pigeonhole principle