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by roaur 2175 days 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?
2 comments
wdevanny 2175 days ago
Normal 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

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morelisp 2175 days 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.

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morelisp 2175 days ago
It 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

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