From: Will Wagers (wagers@computek.net)
Date: Tue Oct 03 1995 - 00:09:14 EDT
In addition to writing the words for numbers out in full, in ancient texts,
there are three primary classes of numerical notation system:
1. sign systems (conventional symbols - including simple straight
marks for ones),
2. acrophonic systems (initial letter of the name of a number
represents number),
3. alphabetic system (alphabetic characters serve as numbers, e.g.
deka -> delta = 10).
In Sumerian and Babylonian, ideographic symbols are used a bit like
wedge-shaped, Roman
numerals.
In Ugaritic and Phoenician, ideographic symbols (like Sumerian and
Babylonian) and written
words are used.
In Egyptian hieroglyphic texts, ideographic symbols are used, as in
cuneiform texts.
In Hebrew texts, the words are written out in full. There is some evidence
of symbolic
numbers. Around the second century BCE, the alphabetic notation appears.
In the Old Covenant, Hebrew and Aramaic numbers are written out in word
form. Alphabetic
systems are not used. (However, there is some evidence of its use
and subsequent
misinterpretation).
In Greek, we find the achrophonic system, which yields to the alphabetic
system about
300 BCE. Possibly a Greek invention, the alphabetic system requires
special
punctuation, e.g. spaces on boths sides of the number, an overline
over it, or some
other special punctuation symbol. (Minoan also uses modified
symbols to represent
powers). Of couse, numbers can also be written out in full.
Regarding Mr. Bushnell's criticism, I was trying to use "numerals" in the
same sense as the questioner. (You can see that it is in quotes.) In the
query, "numeral" appears to mean special symbols for numbers which are
distinguishable from alphabetic characters. To my knowledge, the combined
Greek signs {like pente (5) overstrike delta (10) = 50} are not used in any
other way and are therefore distinguishable from alphanumerals. Certainly,
the early sign systems contain symbols which are not (purely) alphabetic.
If one restricts the enquiry to the classical Greek alphabet, then Mr.
Bushnell appears correct.
Sincerely,
Will
------------------------------------------------
> From: Will Wagers <wagers@computek.net>
>
> No, they did have some "numerals", but it is true that the letters have
> numerical values and are even found in computations.
>
>They did have numerals: the letters of the Greek alphabet were used as
>numerals.
>
>They did not have any numerals except for letters; there were two
>numerals that are not part of the classic Greek alphabet, but that's
>only because they had fallen out of use in spelling words (much like
>English thorn and yodh).
>
>For example, the Greek text of Euclid uses letters as numerals.
>
>Michael
Will wagers@computer.net
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