The n-Category Café

I enjoyed Yuri Manin’s paper, which deeply seemed aware of both Truth and Beauty. It appealed both to my mathematical and poetic experience.

However, on re-reading, I wondered about the apparent opposition (not quite contradiction) between two sentiments:

(1) “Mathematical truth is not revealed, and its acceptance is not imposed by any authority…. it is not a democratic value.”

(2) “the basic ‘left–brain’ intuition of sets, composed of distinguishable elements, is giving way to a new, more ‘right brain’ basic intuition dealing with space–like and continuous primary images, both deformable and deforming.”

The skeptic may wonder why – if mathematical truth decidedly not ascertained by acceptance ‘in the competition of the market’ – it matters to the establishment (not revelation) of Truth, that a community of ‘left–brain’ Bourbakian practitioners is being displaced by a community of ‘right brain’ Category and n-Category practioners?

One of Clifford Pickover’s early books was
called “Computers Pattern Chaos and Beauty”.
My comment pertains to truth and contrived
definitions of complexity: Effective, a term
used by Gell-Mann, “A measure that corresponds much better to what is usually meant by complexity in ordinary conversation, as well as in scientific discourse, refers not to the length of the most concise description of an entity (which is roughly what AIC is), but to the length of a concise description of a set of the entity’s regularities. Thus something almost entirely random, with practically no regularities, would have effective complexity near zero. So would something completely regular, such as a bit string consisting entirely of zeroes. Effective complexity can be high only a region intermediate between total order and complete disorder.”
SH: The contrast of the two definitions of
complexity, randomness is maximally complex,
AIT, or randomness is minimally complex, (EC)
seems to me to transcend scientific limits
of discretion into a choice between grounded,
and in touch with reality, as opposed to the
provenance of a Platonic realm. I think there
is a big consistency problem when there are
diametrically opposed definitions of complexity.
In which camp does Truth reside?
Which has precedence, Theory or Definition?

Isn’t there an error(or omission) in the Cantor diagonalization as it described in the paper ? “Any subset have form S_y for some y **belonging to S**” - that is not following directly from |X| = |P(X)|
Usually both case - y belong to S_y and y is not belong to S_y considered.