Newsgroups: sci.lang
Path: cantaloupe.srv.cs.cmu.edu!das-news2.harvard.edu!news2.near.net!news.mathworks.com!news.alpha.net!uwm.edu!math.ohio-state.edu!howland.reston.ans.net!pipex!uknet!festival!edcogsci!iad
From: iad@cogsci.ed.ac.uk (Ivan A Derzhanski)
Subject: Re: Eleven & Twelve
Message-ID: <D4BG87.79z@cogsci.ed.ac.uk>
Organization: Centre for Cognitive Science, Edinburgh, UK
References: <3hj9ca$mfc@igor.rutgers.edu> <D43Jut.9Gw@cogsci.ed.ac.uk> <Bm06EWg.whl44@delphi.com>
Date: Mon, 20 Feb 1995 20:43:17 GMT
Lines: 103

In article <Bm06EWg.whl44@delphi.com> William Lemay <whl44@delphi.com> writes:
>In Japanese, the native number words (hitotsu, hutatsu, ...) seem to
>stop at "ten" (to).

That should be _to=_ or _to^_.  And they haven't always stopped there.
Cf. _hata-chi_ `20 years (of age)', _hatsu-ka_ `20th (day of the month)';
_miso-ka_ `30th (day of the month)'.

>One old approach, found in the Levant and borrowed into Greek along with
>the Cadmean alphabet, was to use the first ten letters to stand for
>"one" through "ten," the next ten letters for "twenty," "thirty," ...,
>up to "hundred," and the next ten letters for hundreds up to "thousand."

Old as this approach may be, it is clearly much younger than systems
such as the Egyptian one and the slightly more complex Sumerian one.

>This is, let it be emphasized, a writing convention which is
>independent of the names given to any quantity.

This needs to be proven before any emphasis can be put on it.
I should say that the central ro^le of the number 10 (as opposed
to any other) in this approach has the most direct connexion to the
fact that the number names in both Phoenician and Greek were decimal.
After all, 10 is a very awkward number if you have 22 letters to use.

>The Romans had the well-known Roman numerals; these represent
>a "base 5" system of arithmetic, [...]

Not at all.  `25' is "10+10+5", not "5^2".  `100' is "10^2", not "4*5^2".

>For the "small" numbers up to a hundred, the traditional number names
>were not necessarily supplanted,

Up to a hundred?!  Name a language with `traditional' number names
up to one hundred.

>"Twenty" may appear in IE for no more profound a reason than that IE
>languages early on had a dual, so that there was a word ready to hand
>for "twenty" as soon as there was one for "ten."

But in which IE languages is `20' merely the dual of `10'?  And why
were the duals of `6' to `9' not used as number names?

>This is still visible in the Semitic family, where the Arabic word
>for "twenty" is precisely the dual of "ten," although acutally it has
>the form of a plural.

Which seems to imply that this is *not* visible in Arabic.

>In Punjabi, a rather eastern IE language, /barang/ "twelve" is based on
>a different root from /do/ "two", which seems to suggest something like
>the Germanic pattern, until one discovers that the /ba/ root is the one
>that appears in twenty-one, thirty-one, etc.

Not `twenty-two' and `thirty-two'?

>A later post by Anthea F Gupta (ellgupta@leonis.nus.sg):
> 
>= Many ancient West Asian systems (e.g. in Mesopotamia) used base 12
>= and we have inherited remnants of this.

Hm.  I'm wondering why none should count as many.

>= Think of dozens, 360 degrees in a circle, 60 seconds in a minute,
>= and (once upon a time) 12 pence in a shilling.
> 
>again confuses number words (shared by all or most speakers of a
>language, at least for "small" numbers) with the arithmetical system
>(confined mostly to those having special training).

Actually, it does not.  It is hard to tell what it confuses with what,
however, since neither the number words in the languages of Mesopotamia
nor the arithmetic systems used there were base 12.

>First of all, I don't know of any evidence that West Asian languages
>had number names based on 12.  Perhaps students of Akkadian, Elamite,
>and Sumerian can contribute the respective number names to this discussion.

In both Akkadian and Sumerian `12' is "10+2", just as `11' is "10+1"
and `13' "10+3", and the next `significant' number is 20, not 24.
12 is no more than one of the twelve divisors of 60, and as such it
is no more interesting than 15.

>Second, Neugebauer relates that the base-60 notation was only used for
>mathematical purposes.  Mundane uses like ages, dates, commerical
>quantities, etc., were represented in a strictly decmimal system.

This is true for Akkadian, but not for Sumerian, where the only word
for `100' is "60+40" and where `3600' is not "3*1000+6*100".

>I note that the cuneiform *symbols* are "base 10" from one up to
>fifty-nine.  This says a lot about early West Asian arithmetic,
>but nothing about the number words.

Yet the number names are occasionally written phonetically, and thence
it can be seen that the correlation between them and the number symbols
was very close indeed, in both Sumerian and Akkadian.

-- 
`I'm sendin a flood tae pit an end tae it aw.  But dinny worry yersel, Noah.'
Ivan A Derzhanski (iad@cogsci.ed.ac.uk)    (J Stuart, _Auld Testament Tales_)
* Centre for Cognitive Science,  2 Buccleuch Place,   Edinburgh EH8 9LW,  UK
* Cowan House E113, Pollock Halls, 18 Holyrood Pk Rd, Edinburgh EH16 5BD, UK
