Re: maple or derive -Reply
Greg Armstrong (ARMSTROG@GATE1.SBCC.CC.CA.US)
Wed, 22 May 1996 13:44:50 -0800
This discussion of "the universal language of mathematics" seemed
off the thread to me, so Lou Talman and I exchanged posts off list;
however, as it seems not to want to die, let me go ahead and make
public my reply to him, plus an addendum.
What I meant, though perhaps didn't express clearly, is that if you look
at a paper from any country, in any language, that uses mathematics, the
algebraic syntax is [almost] indistinguishable. When students come to our
school from all over the world, they may know little English, but have no
trouble communicating mathematics because we all speak the same
language. It seems a shame to lose that universality for a Babel of
different program syntaxes.
I don't mean to discourage computer systems such as Mathematica
(which I don't know, by the way; we use DERIVE here); however, the
suggestion that we teach a program syntax and NOT teach algebraic
language, which your [Talman's] original post seemed to suggest, seems
pretty short sighted.
RWW Taylor then adds (after a very nice argument about the benefits
of translating between syntaxes, by the way), "As far as "the universal
language of mathematics" goes, I doubt that anyone who has taken more
than a superficial look at the history of mathematical notation believes in
such an animal. I have already seen a number of changes
(improvements) in accepted notation in my lifetime, and I certainly believe
that in 100 years mathematics, when written, will be written more
logically and consistently than it is today."
I do not mean to suggest that the language of mathematics is static,
any more than any natural language is (have you looked at Chaucer
lately)? After all, we have a name for languages that don't change: they
are dead languages. Mathematics evolves for the same reason that it is
studied, namely because it is used. The universality I referred to is in the
sense noted above, that people from all over the world, speaking
different tongues, can read the same mathematics. And, again repeating
myself, my original remark was prompted by the implied suggestion that
we teach a computer syntax, varying from system to system, IN PLACE
of algebraic language. In doing so, we would be losing the lingua franca
of scientific discourse. By all means the language should evolve, and
undoubtedly towards something that accomodates the needs of
software systems; but, if the evolution is driven by people with no
shared algebraic language, I fear we would see a Balkanization of
mathematical tongues rather than the more logically and consistently
written mathematics that Taylor envisions.
Greg Armstrong, Santa Barbara, CA
armstrog@gate1.sbcc.cc.ca.us