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

 Messages: [ Previous | Next ]
 William C Waterhouse Posts: 655 Registered: 12/3/04
Re: [HM] question about term "normal"
Posted: Oct 23, 2006 4:27 PM

On Mon, 16 Oct 2006, judith grabiner <jgrabine@pitzer.edu>
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":
> http://mathworld.wolfram.com/NormalNumber.html
> 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

Date Subject Author
10/23/06 Tummers P (FDCW)
10/23/06 jim farned
10/23/06 Dr A W F Edwards
10/28/06 Fred Shapiro
10/23/06 William C Waterhouse
10/28/06 Fernando Q. Gouvea
11/14/06 Gunnar Berg
11/22/06 cl.marti
11/22/06 Joao Filipe Queiro
11/22/06 Jean-Luc Gautero
11/22/06 William C Waterhouse
12/7/06 Bruand Francois
12/7/06 JUHEL Alain