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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 nonnormal 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



