Nick,
Concerning the following quote from your email one could easily replace
musical style with painting style or writing style or clothing style
or............ style.
Orlando
*"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." *
Nicholas Thompson wrote:
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] <mailto:[EMAIL PROTECTED]>)
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Orlando Leibovitz
[EMAIL PROTECTED]
www.orlandoleibovitz.com
Studio Telephone: 505-820-6183
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Meets Fridays 9a-11:30 at cafe at St. John's College
lectures, archives, unsubscribe, maps at http://www.friam.org
