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Topic: math query
Replies: 10   Last Post: Oct 26, 1995 6:40 PM

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John Conway

Posts: 2,238
Registered: 12/3/04
Re: math query
Posted: Oct 25, 1995 12:32 PM
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> Bonnie Leitch asked:

> > I am a high school math teacher with a historical question. Bill Dunham
> >suggested I ask you. Why in both the Romance and Germanic languages are
> >eleven and twelve so different from the rest of the teens, ...>

I'm trying to remember the book that I regard as "the standard
reference" on these things.

It's something like "Number words and Number symbols", and may be by
Karl Menninger. (Unfortunately, my memory for the names and authors of
books is not as good as that for their contents - which is by no means
perfect, but not TOO bad)

I talked about the English names for 11 and 12 in my last message.
These words implicitly refer to a break at 10, and so plainly they
themselves don't come from the habit of counting in dozens. Again,
"thirteen" &c explicitly mention "ten", so the same is true for these
words. However, the reason why we change from one form to the other
may well be connected with this habit.

The break at 60 is much more interesting. The germanic languages
(including English) had a special name for 60 ("shock" is the English
one), and people certainly did count in 60s, dividing each group of 60
into groups of 10 or 20. It is not unlikely, though opinions are
divided, that this habit comes down all the way from Babylonian times.
It's certainly true that it's because the oldest trigonomentric tables
date from a time when counting in 60s was habitual that we still use
degrees, minutes and seconds. (It was just too big a job to change
such tables into a "more modern" notation.)

This is certainly the reason why in modern French one has
"soixante-dix", "quatre-vingt" and "quatre-vingt-dix", although I
gather that the regular forms such as "nonante" have some currency
in French Canada. However, it was true in all the major European
languages, not just French, as the biblical expression "three
score and ten years" indicates.

The word "score" here, by the way, is really the same as the
other word "score", meaning "cut". [At 20, one used to score an extra
large notch in one's counting stick.] A "skirt" or "shirt" is a
garment that is cut off - these words are etymologically the same
as each other, and as "scored". The "score" in a game is also the
same word, since originally it would be cut into a marking stick.

John Conway

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