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Topic: [HM] question about term "normal"
Replies: 13   Last Post: Dec 7, 2006 4:19 PM

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William C Waterhouse

Posts: 655
Registered: 12/3/04
Re: [HM] question about term "normal"
Posted: Oct 23, 2006 4:27 PM
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On Mon, 16 Oct 2006, judith grabiner <>
passed on the following question:
> A colleague has asked me the following:
> Someone said that some digits
> were "normally" distributed when he clearly meant
> "uniform." And when I say that, I mean that he used the two terms
> incorrectly according to my "statistician's"
> vocabulary. However, he has pointed out
> to me (see below) that Number Theorists actually do use "normally
> distributed" to mean "uniform":
> The term "normal" is clearly inappropriate in this
> situation (i.e. the number theorists are really talking about uniform
> distributions).
> Does anyone know the history about why, or
> who came first?
> Thanks,
> Judith Grabiner

I think there is a slight confusion here. Emile Borel
(according to Hardy and Wright) introduced the term
"normal number" in 1909, proving that the non-normal
numbers were a set of Lebesgue measure zero. So we
can speak of normal numbers, or the normality of a
number; but this is not the same as a "normal
distribution" of digits (whatever that might mean).
Note that the website mentioned does not use the phrase
"normally distributed."

There are also many other uses of "normal" in
mathematics: normal vectors to surfaces, normal
subgroups, normal complex matrices, and so on.
Clearly confusion is bound to be normal.

William C. Waterhouse
Penn State

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