NetNews Usenet Archive 1993 #3/NN_1993_3.iso/spool/sci/math/18699

Internet Message Format | 1993-01-24 | 3.1 KB

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From: [e-mail] (Andy Bennett)
Newsgroups: sci.math
Subject: Re: Ancient Number Systems (Was: why is pi irrational)
Date: 24 Jan 1993 00:14:27 -0600
Organization: Dept. of Mathematics, Kansas State University
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[e-mail] (Frederick W. Chapman) writes:
>I've heard that letters of the Hebrew alphabet all have numerical
>equivalents, which were used in ancient scriptures as the basis of a number
>system.  I would be interested in knowing more about this, since it must
>surely qualify as a very early example of a number system.  Doesn't some
>ambiguity occasionally arise as to whether a given string of characters
>should be interpreted as a word or as a numerical quantity?
>Didn't classical Greek also assign numerical values to the letters of the
>alphabet and employ a similar number system?  (For example, there is a New
>Testament passage that speaks of "the *number* of his name" in reference to
>the anti-Christ.)

Classical Greek used the letters of the Greek alphabet for numbers.
alpha = 1
beta = 2
gamma = 3
delta = 4
epsilon = 5
digamma = 6
zeta = 7
eta = 8
theta = 9
iota = 10
kappa = 20
...
sampi = 900

You may have noticed digamma and sampi in the above list. They, along with
qoph, dropped out of the Greek alphabet after it was borrowed from the
Phoenicians because the Greeks didn't need them for the language, but they
kept them for the number system where they were useful. Numbers bigger than
1000 start with alpha again. In modern texts of classical greek, diacritical
marks are used to distinguish between alpha 1 and alpha 1000 and also between
letters that make up a number as opposed to a word. I don't know for sure
if such marks appear in the actual classical texts (though my guess would
be not). Since both Hebrew and Greek borrowed their alphabets from the
Phoenicians and both used the letters for numbers, I would suspect that
the idea originated with the Phoenicians, but I've never been curious enough
to do a literature search and find out. As far as being among the oldest
number systems, the Babylonians had a place value system (base 60) with
a fair knowledge of algebra by 1800BC, well before the Greeks adopt their
alphabet (I'm not sure about dates on the Hebrews or Phoenicians). Denise
Schmandt-Besserat has done a lot of work on the origins of the Babylonian
system tracing it back to 8000BC (though in such a primitive form at that
date that I wouldn't call it a number system and neither would she). She
wrote an article for Scientific American some 10-15 years ago that gives
a nice overview without requiring much background.

--
Andrew G. Bennett         [e-mail]         If you count too
Dept. of Mathematics      Voice: [phone]        much you turn
Kansas State University   Fax:   [phone]        purple.  -  SARAH
Manhattan, KS 66502       STRICTLY MY OWN OPINIONS