Strong Law of Small Numbers
"The Strong Law of Small Numbers" is the humorous title of a popular 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."[1]
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 paper gives 35 examples in support of this thesis. This can lead inexperienced mathematicians to conclude that these concepts are related, when in fact they are not.
Guy's observation has since become part of mathematical folklore, and is commonly referenced by other authors.[2][3]
See also
- Insensitivity to sample size
- Law of large numbers (unrelated, but the origin of the name)
- Law of small numbers (disambiguation) (other meanings of similar phrase)
- Mathematical coincidence
- Pigeonhole principle
- Representativeness heuristic
- Amos Tversky; Daniel Kahneman (August 1971). "Belief in the law of small numbers.". Psychological Bulletin 76 (2): 105–110. doi:10.1037/h0031322.
people have erroneous intuitions about the laws of chance. In particular, they regard a sample randomly drawn from a population as highly representative, I.e., similar to the population in all essential characteristics.
Notes
- ↑ Guy, Richard K. (October 1988). "The Strong Law of Small Numbers" (PDF). American Mathematical Monthly 95 (8): 697–712. doi:10.2307/2322249. ISSN 0002-9890. JSTOR 2322249. Retrieved 2009-08-30.
- ↑ Wells, David (2005). Prime Numbers: The Most Mysterious Figures in Math. Hoboken: John Wiley & Sons. p. 31.
- ↑ Dudley, Underwood (1998). Numerology: Or, What Pythagoras Wrought. The Mathematical Association of America. p. 87.
External links
- Caldwell, Chris. "law of small numbers". The Prime Glossary. External link in
|work=(help) - Weisstein, Eric W., "Strong Law of Small Numbers", MathWorld.
- Carnahan, Scott (2007-10-27). "Small finite sets". Secret Blogging Seminar, notes on a talk by Jean-Pierre Serre on properties of small finite sets. External link in
|work=(help)
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