a note by Misha Gromov on category theory

a note by Misha Gromov on category theory

[Micha Gavrilovich]

Dear All,

I thought the list members may be interested in the following
recent note of Misha Gromov which *very* carefully uses ideas of category theory
to talk about entropy. Particuarly, his point of view on category theory
may be appealing.

In a Search for a Structure, Part 1: On Entropy. June 19, 2012
http://www.ihes.fr/~gromov/PDF/structres-entropy-june-2012.pdf

At the end of the paper, he says:

Yet, I hope that I managed to convey the message: the mathematical language  d
eveloped by the end of the 20th century by far exceeds in its expressive
power anything, even imaginable, say, before 1960. Any *meaningful* idea coming
from science can be fully developed in this language.

In the paper, he also says:


To see this, you
just need to realize that ”something” of a physicist, is a covariant
functor from
a suitable ”category of protocols” to the category of sets – outcomes  of exper-
iments; all you have to do afterwards is to follow the guidelines prescribed by
the syntax of category theory.
(Arguably, the category language, some call it ”abstract”, reflects mental
undercurrents that surface as our ”intuitive reasoning”; a comprehensive math-
ematical description of this ”reasoning”, will be, probably, even
farther removed
from the ”real world” than categories and functors.)

Sincerely, Misha



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