timelets: (Default)


Among other things, the ant solution to the grain sorting problem given to Psyche by Aphrodite can be modeled as a replacement of an Inert with an Active. The same applies to the Trasnsformer solution of the translation problem, etc.

upd. the Odysseus solution to the Sirens problem also fits the pattern
timelets: (Default)
I keep coming back to this video about the relationship between (pre-)sheafs and cohomology. Here he says that "the number one technique in mathematics is turning any problem into a linear algebra problem.

More generally, Lawvere often talks about mapping geometry to algebra.

https://youtu.be/RPuWHN0BTio?si=U0h7YM-3GlcyvnS5&t=1890



D --> J <-- T ( c: D --> T is the solution to a choice problem, per Lawvere).

d: D --> J
e: T --> J
c: D --> T

This diagram is a regular Kan extension problem, with a cohomology twist, i.e. assigning values to both objects and arrows.
timelets: (Default)
The word ‘_perceive_’ is, in our common usage, shot through and through
with the notion of cognitive apprehension. So is the word
‘_apprehension_’, even with the adjective _cognitive_ omitted. I will
use the word ‘_prehension_’ for _uncognitive apprehension_: by this I
mean _apprehension_ which may or or may not be cognitive.

Whitehead. Science..., 1925.

----

If we modeled this prehension as a CT monad we could develop and algebra of prehension, with quantative thresholds that separate the uncognitive and cognitive.

https://ncatlab.org/nlab/show/state+monad

X -> [W, WxY]

Here the operation [W, Wx(-)) is the monad on the type system which is induced by the above adjunction; and this latter function is naturally regarded as a morphism in the Kleisli category of this monad.

Profile

timelets: (Default)
timelets

December 2025

S M T W T F S
  12 3456
78910111213
14 151617 18 19 20
21 222324252627
28293031   

Syndicate

RSS Atom

Most Popular Tags

Style Credit

Expand Cut Tags

No cut tags
Page generated Dec. 25th, 2025 10:51 am
Powered by Dreamwidth Studios