Subject: Re: [HM] Marcel Duchamp and Mathematics
From: Bill Everdell (Everdell@aol.com)
Date: Mon Jan 10 2000 - 23:59:53 EST
On 1/9/00, Gordon Fisher questioned my aside:
<<the relationship between mathematics and visual art -- which is always
closer than the one between mathematics and poetry.>>
asking:
<<There is, I suggest, broadly speaking, and according to some of us, a
kind of bounded linear continuum, a closed line segment, of classifications
of mathematicians with pure (let's call them that) algebraists (and
mathematical logicians) at one end and pure geometers (and topologists) at
the other. Would you say that those of us who tend to fall toward the
algebraic end would be more apt to feel akin to poets and prose stylists, and
those of us who tend to fall toward the geometric end would be more apt to
feel akin to visual artists of one kind or another?>>
That's a provocative and interesting thought, but I'm not so sure it's right.
Pascal, I think, was nearer the "geometric end" in his mathematical
thinking, but he made no pictures, other than geometry or physics diagrams,
and his writing form (and diction) is close enough to poetry to have been
imitated repeatedly by poets. The problem is that these poets -- and other
commentators -- almost never connect Pascal's mathematics with the sources of
his thought and style. I've had occasion to think of that today, since I've
just had a bangup discussion of Pascal and the _Pens/ees_ with my students.
Gordon added:
<<I like to think of Euclid as a person in the middle, so to speak, who
wrote a prose masterpiece (it was, after all, written in a language) in which
he translated or transformed some geometry into prose. Similarly later with
Descartes and other founders of algebraic and analytic geometry>>
Euclid did indeed put geometry into stellar prose -- and maybe so did Plato
in the Meno. As for Descartes, he was a superb writer. I often suggest that
the irony in the _Discourse on Method_ #1 is a fair model for a college
application essay -- at least if the student is as gifted as Descartes
insists ironically that he isn't. And Descartes, too, illustrated only his
geometry and physics.
<<In such work, and to some degree in all mathematical work, there is,
don't you think, an interaction between what one might call the literal and
the visual? When beauty or utility are involved, especially in connection
with communication, there are, are there not, analogies, and aesthetic and
perhaps even syn(a)esthetic crossovers?>>
I would plump for synaesthesia as the right word here. I find that some
mathematicians, like Pascal, can see beauty, bare or ornamented, in a whole
range of forms of thought. It is hard to make it clear to some of my less
mathematically inclined students how and why mathematics itself is beautiful;
but I find it to be worth the effort, even (or perhaps especially) in an age
where the strongest trend in philosophy undermines the very idea of ideal
beauty.
Bill Everdell, Brooklyn
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