timelets

Here's an interesting way to make a connection between Peirce's pragmatism/logic and the category theory

Link to the paper https://ncatlab.org/davidcorfield/files/Peirce200225.pdf

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

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.

--- Lambek & Scott, Introduction to higher-order categorical logic. 1994.

It looks like the Prince Charming class of narratives can be represented by an algebra category as it relates to the multiplier effect M (example T1).

When you put your money in the bank you (your money) provide(s) a service to the bank, not the other way around like the vast majority of people tend to think.

Similarly, investors serve startups, which explains why hype cycle is similar to Turchin's elite-peasants exploitation pattern.

When in doubt build a model based on the Kan extension. Or at least, use Lawvere's simplified version of it ( determination/choice).

* Questions (A) -> Little Red Riding Hood (B) -> Learning [Wolf Detection] (C)

A -> C maps to False ( A -> Ω), which hints at the idea that marginal knowledge can be modeled as a topos. We can also show the nature of the transition from Google Search to GPT.

* All objects are marginal.

https://www.youtube.com/watch?v=xTVSMJhDoOQ

Technology toolkit re-use is an extension problem. E.g. Julius Cesar's guide for building army camps using common agricultural approaches of the time. The use of steam engine manufacturing toolkit for railroads, steam ships, etc.

Technology choice or development is a lifting problem. E.g. discovery/choice of the right data set for a desired ML application (see IBM's recent failure vs TikTok's success).

In the LRRH narrative we see the failure of an existing solution to the extension problem, i.e. the werwolf destroys the girl's ability to deliver the medicine to her grandma.

By a graphic we will mean any finite category each of whose endomorphism monoids satisfies the identity xyx = xy ; in particular, a graphic monoid is a graphic category with one object.
By an application of a graphic category we will mean any right action of it on finite sets (i.e. any contravariant finite-set- valued functor on it).
-- Lawvere, The Hegelian "Taco", 1989.

I think social networking satisfies this requirement, e.g. Make Use Make = Make Use (a user to Make a new user).

Lawvere & Schanuel, 2009.

Lawvere also asks (and then answers), "What is a space and how can quantities vary over a space?", "spaces actually arise and are used in mathematical science, they have two main general conceptual features: first they serve as an arena for "becoming" (there are spaces of states as well as spaces of locations) and secondly they serve as domains for variable quantity." (1992).

Along the same lines we could consider Aristotle's final cause R to be a space. Then, success of a course of actions, i.e. efficient cause measured using a binary system, can vary over that space. Furthermore, both the material cause and the "labor" aspect of the efficient cause would vary over R as well.

In this model, Fairy Godmother would be a realization for the efficient cause, while Cinderella would play the role of a corresponding material cause, i.e. labor. By analogy, startup founders shape investor capital to succeed in the market.

As a result, we have a space of variable quantity for becoming successful.

It looks like there are two different types of human-animal transmutations in fairy tales: enabling and constraining. The first enables a human-animal hybrid to obtain the powers of both, e.g. a werewolf is clever like a man and is powerful like a wolf. Most of ancient Egyptian and Babylonian chimeras(gods) are of that type too. They are specifically designed to be masters of multiple realms.

The constraining type puts a human into an animal body or vice versa. Probably the best modern example would be Kafka's Gregor Samsa from the Metamorphosis. The Thousand Nights and a Night are full of these too. And so are Russian folk tales.

When it was the Nine Hundred and Eighty-fifth Night,
...
'To content thee, I will not kill them, but I will enchant them.' So saying, she brought out a cup and filling it with sea-water, pronounced over it words that might not be understood; then saying, 'Quit this human shape for the shape of a dog;' she sprinkled them with the water, and immediately they were transmuted into dogs, as thou seest them, O Vicar of Allah."

https://www.gutenberg.org/files/3443/3443-h/3443-h.htm#chap29

[30:2]
...we must first take care  not to commit ourselves to a search, going back to infinity - that is, 

in order to discover 
                     the best method 
of finding truth, there is
               no need of another method 
               to discover such method; 
nor of a third method 
for discovering the second, 
                and so on to infinity. 

(3) By such proceedings, we should never arrive at the knowledge of the truth, or, indeed, at any knowledge at all.

[31] (1) But as men at first made use of the instruments supplied by nature to accomplish very easy pieces of workmanship, laboriously and imperfectly, and then, when these were finished, wrought other things more difficult with less labour and greater perfection; and so gradually mounted from the simplest operations to the making of tools, and from the making of tools to the making of more complex tools, and fresh feats of workmanship, till they arrived at making, complicated mechanisms which they now possess.

--- Benedictus de Spinoza. “Improvement of the Understanding.”

The wolf is a tortilla [functor], while the house is not. Rather, the house is a nullifier. That is,
hwh = hw.

see Burritos for the Hungry Mathematician, by Ed Morehouse April 1, 2015.

The prince is a tortilla.

Prince vs Wolf is like freedom-for vs freedom-from.

Gradations,

--- John Lewis Gaddis. “On Grand Strategy.”

Hegel formalized this approach later in his The Science of Logic. Also, see W.Lawvere's "Display of graphics and their applications, as exemplified by 2-categories and the Hegelian "taco."
https://ncatlab.org/nlab/show/Hegelian+taco

Lawvere's Hegelian Taco https://apps.dtic.mil/sti/pdfs/ADA360121.pdf

Retrieving stored knowledge presupposes some consciousness of the structure it has; this structure is in its particularity fixed by the storage process itself (and in its generality is partly a reflection of the content, i.e. of the nature of the knowledge stored). Thus in both retrieval and storage one needs to be explicitly aware of the kind of structure involved.

Lot's to learn here.

Русский народ - Сизиф. Россия - камень. Русский царь - кара богов.

Back to regular programming:

Watch on YouTube

This course should be a prerequisite for learning CT

Watch on YouTube

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"There is a widespread refusal to let children know that the source of much that goes wrong in life is due to our very own natures—the propensity of all men for acting aggressively, asocially, selfishly, out of anger and anxiety. Instead, we want our children to believe that, inherently, all men are good. But children know that they are not always good; and often, even when they are, they would prefer not to be. This contradicts what they are told by their parents, and therefore makes the child a monster in his own eyes.
The dominant culture wishes to pretend, particularly where children are concerned, that the dark side of man does not exist, and professes a belief in an optimistic meliorism.”

--- Bruno Bettelheim. “The Uses of Enchantment.”

https://theantijunecleaver.com/fairy-tales-with-wolves/

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Charles Peirce, Inference and Category theory

Categorical Algebra with Segal Conditions

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