All,
One of the running arguments I have with one of my favorite colleagues here in
Santa Fe is about whether Mathematics is (or isn't) different from all other
intellectual enterprises, such as psychology or philosophy. in that, unlike
them, mathematics "adds up," in the long run. Contrary to psychologists and
philosophers like me, who are besotted with ephemeral traditions and
ideologies, and keep changing the rules of the game, mathematicians have built
a structure that is not subject to vicissitudes and whims of intellectual
history. (I hope I have represented this argument fairly.) Although I have
tried to give him as little comfort as possible, I confess that I have been
impressed more and more by this argument as I continue to read accessible works
on the history of mathematics.
For this reason, I was startled to find a contrary argument in a powerful book
written by the Music Critic of the New York Times, Edward Rothstein on the
relation between music and mathematics, EMBLEMS OF THE MIND [Times books, NY:
1995]. I am curious to know what anybody thinks of it. I will key in a brief
passage (from page 43-4) below for comment:
Begin quote from Rothstein =====>
"Because context is so important, aspects of mathematical truth may alter over
time. ...
.... Paradoxically, this is one reason why so few mathematicians ever study the
history of their own discipline. The apparent uniformity of truth through time
might seem to suggest that a geometer might as profitably study Descartes as
Lobachevsky, or a number theoretician might as usefully read Euler as Hardy. In
fact, the language of mathematics today bears so little resemblance in style
and form to the languages of the past that it would take a great deal of effort
to "translate" the mathematics of the past into contemporary terms. ...
One example of shifting context and the transformation of mathematical styles
was discussed by the mathematicians Philip J. Davis and Reuben Hersh in THE
MATHEMATICAL EXPERIENCE, [Boston: Birkhauser, 1981]. They present a simple
theorem of arithmetic that has been generally known as the Chinese remainder
theorem."
<===== End quote from Rothstein.
Davis and Hersh (according to Rothstein) then summarize the presentations of
this same theorem in mathematicians from Fibonacci to E. Weiss.
Rothstein now concludes.
Begin quote from Rothstein =====>
"Mathematical style is far more important than it usually seems. It is
intimately connected to the essence of mathematical work. It defines conditions
and expectations. It presents a set of rules, of course, but it also does
something more: it reflects what is considered important at a particular
historical moment and shapes the evolution of future inquiries. It resembles,
in this way, musical style."
<===== End quote from Rothstein.
So I am wondering: Is this a bridge too far????
Nick
This discussion is posted in the Noodlers' Corner, at
http://www.sfcomplex.org/wiki/MathematicsAndMusic
Nicholas S. Thompson
Emeritus Professor of Psychology and Ethology,
Clark University ([EMAIL PROTECTED])
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