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> Pi itself is not a random number, for example, but the digits of pi are believed to be random in this way (what mathematicians describe as “normal”): Every in
by roaur 6y ago
> Pi itself is not a random number, for example, but the digits of pi are believed to be random in this way (what mathematicians describe as “normal”): Every integer from 0 to 9 appears about the same number of times.
Does this not make the digits of Pi discreetly distributed (an equal chance for each integer?)? Is the meaning of 'normal' here not referencing a normal distribution?
- morelisp 6y agoIt is not. They are so-named because in any base, almost all reals have this property, i.e. reals which do not are abnormal. https://en.wikipedia.org/wiki/Normal_number https://en.wikipedia.org/wiki/Normal_number
- wdevanny 6y agoNormal has myriad uses in mathematics. See [1]. Somewhat annoyingly there is no common thread to their meanings (Or at least not one that I am aware of). The article intends normal number, not normal distribution. [1] https://en.wikipedia.org/wiki/Normal https://en.wikipedia.org/wiki/Normal
- morelisp 6y ago> Somewhat annoyingly there is no common thread to their meanings The common thread is the Latin word "norma" for a carpentry square. This gets taken literally in cases like "normal vector", figuratively in cases like "Euclidean norm" (i.e. to measure) then increasingly distant as the word is a root to mean usual/ordinary/average (i.e. according to standard measure) in many languages and thereby ends up in "normal number", "normalized vector", etc. "Normal distribution" inherits it doubly, Gauss used it in the orthogonality sense and later authors in the ordinary sense.