ir230@sdcc6.ucsd.edu (john wavrik) (12/03/89)
Leo Brotzman writes:
<a great many things including>
# The key phrase here is "at some point in history". Man was counting for
# thousands of years before the numerals we use today became "standard". There
# were many systems of lines, curves, and dots to describe quantities. Each
# was sufficient to perform the job at hand. The Roman numeral system is only
# useful for quantities numbering in the few thousands. In Roman times, who
# needed to count farther than that? Would it have been a good idea to freeze
# the standard at that point?
Leo raises many points, some of which must be addressed logically, some
historically, and some subjectively. It is quite correct that, while Arabic
numerals were first introduced to the west in the 12th century, Roman numerals
were still in use well into the 18th century. To anyone interested in reading
a well written account of the history of numeration, I recommend "Number the
Language of Science" by Tobias Dantzig (Anchor Books).
Dantzig tells the story of a merchant in the 16th Century who desired the best
possible commerical education for his son. He turned to a professor at a
German university for advice -- and was told that if his son's mathematical
education only required addition and subtraction that he would be able to
get his education at a German university -- but that if he would need to know
the arts of multiplication and division, he would have to go to study in Italy
which was the only place that such advanced subjects were taught.
Dantzig points out that computations which any elementary school can now
perform required, in those times, days worth of effort on the part of
specialists. While this is sometimes taken as a proof of the growth in human
intelligence, Dantzig is quick to point out that it is really the result of a
change in numeration -- that the numeration system (i.e. Roman Numerals) in
use during the 16th century was not able to support simple rules for
multiplication and division.
This is actually the subjective part of my reply:
1. Do you really think that Forth represents the kind of advance
over conventional languages that Arabic numerals represented
over Roman?
Yes
2. Do you see any historical parallels?
I can picture the proponents of Arabic numerals having annual
conferences at Asilomar to argue over the shape of "3" while
the rest of the world says "let's stick to Roman -- they're ugly
but at least they're portable!"
3. What happens in the long run for Forth?
Good ideas don't die, they are just rediscovered (or reinvented)
when the time is ripe (sometimes centuries later).
John J Wavrik
jjwavrik@ucsd.edu Dept of Math C-012
Univ of Calif - San Diego
La Jolla, CA 92093