When one looks at a title “Beauty: a Mathematical Aesthetics” one never
expects to get into a discussion at the beauty parlor level. Near IADE
there is a school of aesthetics “Escola Internacional de Est?tica” EIT,
where people learn about creams and powders, maquillage, what so ever… I
some times nag one of our colleagues that teach aesthetics submerged in
Tarkovski, Deleuze, Plato, Kant and other ugly guys that she should go there
(to the EIT) and learn something about real aesthetics.
I guess Pythagoras is one of the first guys that reflected upon mathematics
and Aesthetics. ( I must stress this, like Ranulph did: Aesthetics deals
with sensible perception in which beauty MAY be encompassed. Aesthetics is
not about deciding what is Beautiful or Ugly, like Ethics is not about
deciding what is Good or Evil.
Well, back to Pythagoras, by associating dimensions, numbers and aesthetical
appreciation in dividing cords in proportionate intervals, the Greek
footballer established a relation between geometric, numeric, and aesthetic
entities. The proportioned subdivision of the cords conducted to agreeable
chords. Other subdivisions not according to that subdivision of cords
produced not agreeable chords.
This would make guys like Alban Berg, Arnold Schonberg, even the final Aaron
Copeland, Luciano Berio and so forth laugh to the tears, not because they
had not found the validity of the Greek proportions but because their
musical aesthetics was being really aesthetical by manipulating the human
capacity of sensible perception in all possible directions.
Well, the title conjures a different question by making Beauty = to
Mathematical Aesthetics or Beauty =» Mathematical Aesthetics or probably
Mathematical Aesthetics «=» Beauty. In any case one must know what a
Mathematical Aesthetics is.
By replacing Aesthetics by sensible perception we get: Mathematical sensible
perception. By replacing sensible by “through sentiments” and perception by
“immediate apprehension” we get: Mathematical immediate apprehension through
sentiments. Now let’s replace Mathematical. Not that easy, but we would risk
to say that all mathematics lies on abstract reasoning so we will have:
“abstract reasoning immediate apprehension through sentiments” =
Mathematical Aesthetics. This sounds very much like an oxymoron… Let’s move
through another path: Mathematical Aesthetics is the set of theories that
study the qualification of mathematical expressions by its aesthetical
value, say by categories long established resulting from sensible
perception: beautiful, gorgeous, attractive, repulsive, nauseous, ugly,
perfect, unperfected, imperfect, ooohhh, ghghgghh, elegant, etc, etc. This
make sense, we hear a lot of times, “well done that’s a beautiful solution,
that’s an elegant formulation" or “your calculus seem a bit chubby”.
Well, both paths are far from establishing the expression “Beauty: A
Mathematical Aesthetics” as a valid matter illustrated by good looking girls
becoming even more good looking and not so good looking guys staying not so
There is still another path to move through: Aesthetics with a capital A
turn out to be in the last two centuries the Academic discipline that
studies Art in the sense that Art Objects are made specially FOR sensible
perception (and social acclamation as superlative we might add). In that
sense none of the examples of face lifting and notions of average beauty are
of any interest since they are not Art although there is a mathematical
study of Art and even mathematical production of art as we have seen since
Pythagoras. The conspicuous relations between Mathematics and Music and
Mathematics and Architecture (and consequently with Design) are too
fastidious, but are all that matters when we use the word “Aesthetics”.
Well, it’s a great thread like Ido said,