The basics of category theory aren't that difficult to understand. It's
also somewhat easy to see where it applies, but to understand where it's
actually applicable, you have to dig deeper into the theory instead of
speculating from outside, I think.
What you're describing, Max, doesn't seem to hold; it's a very exact
discipline.
That said, there's this - https://kerodon.net/ - which I do not
understand, except that it's based on category theory and is reworking the
foundations of math; I think there was a Quanta article on it (but I may
be mistaken).
Neural network theory's been used by neuroscience of course, as well as
AI; the piece I put up yesterday is based on AI of course, bringing the
circulations and fractal resonances to the surface. I'd be careful about
taking difficult concepts and sending them into territory one knows,
without digging deeply into those concepts and understanding them.
There's a lot of simplified explanations of category theory itself out
there. Then there's topos theory which extends that...
Etc. etc., I am humble before mathematicians! :-)
Best!, Alan, be well!
On Fri, 5 Jun 2020, Rob Myers wrote:
On 2020-06-03 8:27 p.m., Max Herman via NetBehaviour wrote:
Hi Rob,
I've been interested in category theory for a year or so, on a friend's
recommendation.? Where do you see it applying?? For me it relates to
mapping networks and to translating concepts and principles between
disciplines, and by a combination of these possibly art and literature.?
(It's even been applied to neuroscience I think.)
I don't really know. :-)
It seems very popular in computer science at the moment for the most
trivial things that people seem to find mind-blowing, possibly because
it puts them on a better theoretical foundation? So I feel I must be
missing something. And that makes it interesting to me.
I do like it as a way of talking about mappings, the isomorphisms that
you mention.
Other people do also seem to be applying it to interesting things -
https://alpof.wordpress.com/
And then there's -
https://www.youtube.com/watch?v=ho7oagHeqNc
I have a few recent blogs at Leonardo.info about the ML grouped under
"The Mindful Mona Lisa" and a unique "bridge" theory I am trying to sort
out.? I've asked a lot of Leonardo experts and they say it's unique, but
wrong, though I'm not entirely convinced by their reasoning.? ?
I think that to still be generating new theories after all this time
says good things about both Leonardo's painting and the power of
mathematics. :-)
- Rob.
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