timelets

On the suggestion of my AI assistant, I'm reading Yuval Harari's "Nexus". Here's its summary of how the author defines information:

In "Nexus," Yuval Noah Harari defines information as something that creates new realities by connecting different points into a network. Unlike the naive view, which sees information primarily as an attempt to represent reality, Harari emphasizes that information's defining feature is connection rather than representation. Information can take many forms, such as music, DNA, or stories, and its primary role is to connect and form networks, rather than merely represent preexisting realities.

Essentially, he says that information is a graph or more precisely, it comprises edges of a graph. Therefore, we can represent it as a homset of all arrows in the graph and apply the Yoneda Lemma to understand the power structure of information.

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

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

Watch on YouTube

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.

https://www.youtube.com/watch?v=RPuWHN0BTio

https://arxiv.org/abs/2008.02394

Need to play with the idea. We can probably glue together narratives as graphs.

upd: The Algebra of Open and Interconnected Systems.

https://arxiv.org/pdf/1609.05382

--- 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).

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.

On the other hand, if business cycles are caused by unanticipated shifts in the entire pattern of tastes and technologies across sectors, we might call that uncertainty noise. I believe that these shifts are significant for the economy as a whole because they do not cancel in any meaningful sense. The number of sectors in which there is a match between tastes and technology varies a lot over time.

When it is high, we have an expansion. When it is low, we have a recession.

...the diversity in a more complex economy means that a single crop failure or demand shock cannot have such a devastating effect; but on the other hand, the specialization in a more complex economy means that when there is a mismatch between tastes and technology, it is costly to move skills and machines between sectors to correct the mismatch.
...
Unanticipated shifts in tastes and technology within and across sectors is what we call information in discussing financial markets.

Noise. Fisher Black, 1986.

https://onlinelibrary.wiley.com/doi/full/10.1111/j.1540-6261.1986.tb04513.x
https://doi.org/10.1111/j.1540-6261.1986.tb04513.x

...dynamic processes give rise to particular growth patterns: branching out whilst foraging (to maximize coverage of territory) and forming networks once nodes have been established (to strengthen connections and facilitate the transfer of information). Branching is a fundamental strategy within myriad biological organisms and physical phenomena, from the bifurcation of river deltas, lightning strikes, tree roots and branches, to mycelial networks and in our own bodily systems including blood vessel networks and the cross channelling of neural pathways. Branching facilitates ‘the transmission and parsing of information, no less than the transfer and dissipation of energy’ and, according to philosopher Stephen Shaviro, ‘is an essential process of Nature’ (Shaviro, 2016: 220).

Drawing Processes of Life, 2024.

Again, branching and consolidation can be represented as critical points in Morse-Smale theory. https://timelets.dreamwidth.org/1568281.html

In a narrative, a character can create a branch, thus diverting the flow of events to their advantage or disadvantage. For example, in the LRRH fairy tale the Wolf diverts the girl's attention to beautiful flowers and gains power over her future. It takes magic to undo his villainy.
An example of a positive diversion would be Царевна-Лягушка, where the ugly frog bride tells the prince to get some sleep while she takes care of the king's challenge.

In social theory, topology-based approach to agency can help model the difference between democratic elections and sociological polling for potential course corrections in authoritarian regimes, like the Putin's (see, e.g. Spin Dictators, by Guriev and Treismann).

M&A narratives and consequences can be treated the same way.

upd. Kan extensions/lifts can be used to represent branching/consolidation patterns.

upd 1. Does it apply to Lawvere's Hegelian Taco?

Because the epistemic value of drawing in science is generally understood in terms of the drawing as an object and not, as is argued at various points in this volume, in the drawing process itself, the unique epistemological value of drawing has become increasingly under-appreciated (Anderson 2014; Tversky 2010; Wittmann 2011). Educationally, this has had costs in terms of student engagement, a deeper understanding of the conventions of scientific representations, and the development of ‘creative reasoning’ (Ainsworth et al. 2011).... A unique advantage of drawing is its double nature as a tool for deepening understanding and for communication. Drawing helps to consolidate ideas, clarify concepts and bring visibility to thought. Drawing can extract and highlight salient information from what is discussed, observed and witnessed, and can be used to communicate and analyze an idea or a concept within a research team or to the broader public.

Drawing Processes of Life, 2024.

The development of computerized simulations and techniques for real-time imaging at microscopic scales provides a partial solution to the problem of visu- alizing such n-dimensional entities, by providing, in effect, 4D projections of them. With these techniques, the scientist or any other viewer of the imagery is removed from the production of the representation, however, which negatively affects the quality of insight and inference.

Quoted from Drawing Processes of Life, 2024.

One purpose of going from viewing to insight development would be discovery of transition points in the process of change, see e.g.

For example, the emergence of new opportunities and related decision forks can be represented as a critical point within the Morse-Smale theory.

Following our previous collaborations, it had been our intention from the start to make a connected image that would permit us to visual- ize the previously disconnected sequence of changes in topology all at once. This is completely unlike making an animated movie from a sequence of stills, because the movie still unfolds in time, whereas our image is timeless. ‘The whole is no longer subjected to time but rather possesses time within itself’ (Wellmann 2017: 83).

Quoted from Drawing Processes of Life, 2024.

Here, the intent to include time into the whole is articulated so succinctly that I'm going to steal it in its entirety. From now on, all categories should include time by default (see e.g. Lawvere's take on Hegel.)

emphasized communicability:

But a second, especially crucial role of models, drawings, and computer graphics is to make explicit a relationship that you have found, enabling other people to see it as well. This often can be done just by making the relevant part a heavier line or a brighter color, or by deleting most of everything else, but it always requires explicit effort.

Richardson, Jane and Richardson, David C. (1992), ‘looking at proteins’, Biophysics Journal, 63, pp. 1186–209.

quoted from Drawing Processes of Life: Molecules, Cells, Organisms. 2024.

F: CxC --> C

F - lived happily ever after.

C:

D --> J
  \   ^
   \  |
      T

All narratives are Kan extensions ( in this particular case it's a Kan lift problem).

For example, when we consider today's Russian history textbooks*, the ultimate "happily ever after" narrative F:CxC -> C would be the strengthening of a centralized authoritarian state ("сплочение народа").

*https://langobard.livejournal.com/9843723.html
>>
Шорт-лист того, чем гражданин России должен гордиться из истории страны с точки зрения авторов нового вузовского курса "Основы российской государственности".
Цитирую по студенческому конспекту.
1. Освобождение от монголо-татарского ига.
2. Победа над Наполеоном.
3. Победа в Великой Отечественной.
4. Освоение космоса.
5. Восстановление после распада СССР.

...the hierarchy of praxis that Ricoeur presents are (1) practices, (2) life plans and (3) narrative unity of life.

--- Wessel Reijers, Mark Coeckelbergh. Narrative and Technology Ethics.

So far, the AI community, esp. its business leaders, has failed to address these three essential narratives of praxis for people outside of the community itself. If you are a truck driver, there's nothing for you in the AI-powered future. By contrast, the web, the iPhone and even social networks accomplished the task very well.

Schopenhauer ventures into math and concludes that space begets geometry, while time begets algebra. He also trashes Euclides theoretical approach; i'll update the post with some quotes later.

Logic is, therefore, without practical utility; but it must nevertheless be retained, because it has philosophical interest as the special knowledge of the organisation and action of reason.

But it has its real value, in relation to philosophy as a whole, in the inquiry into the nature of knowledge, and indeed of rational and abstract knowledge. Therefore the exposition of logic should not have so much the form of a practical science, should not contain merely naked arbitrary rules for the correct formation of the judgment, the syllogism, &c., but should rather be directed to the knowledge of the nature of reason and the concept, and to the detailed investigation of the principle of sufficient reason of knowing.

-- Arthur Schopenhauer, The World As Will And Idea.
https://www.gutenberg.org/cache/epub/38427/pg38427-images.html

For centuries, if not millennia, logic was mostly useless until computer software came along and took advantage of it.

Что же здесь происходит? Почему нужно избушку повернуть? Почему нельзя войти просто? Часто перед Иваном гладкая стена
— «без окон без дверей» — вход с противоположной стороны. «У этой избушки ни окон, ни дверей, — ничего нет» (17). Но отчего же не обойти избушки и не войта с той стороны? Очевидно, этого нельзя. Очевидно, избушка стоит на какой-то такой види- мой или невидимой грани, через которую Иван никак не может перешагнуть. Попасть на эту грань можно только через, сквозь избушку, и избушку нужно повернуть, «чтобы мне зайти и выйти»

-- В. Пропп. Исторические корни волшебной сказки.

I never thought about избушка as an interface, an airlock, between spaces. We could probably model it as a pushout.

Another interesting observation:

Слеп человек не сам по себе, а по отношению к чeму-нибудь. Под «слепотой» может быть вскрыто понятие некоторой обоюдности невидимости.

...
Герой все это знает, потому что он г е р о й . Геройство его и состоит в его магическом знании, в его силе.
Вся эта система испытания отражает древнейшие представления о том, что подобно тому, как магически можно вызвать дождь или заставить зверя идти на ловца, можно вынудить вход в иной мир. Дело вовсе не в «добродетели» и «чистоте», а в силе.

Watch on YouTube

In the Sirens adventure, Odysseus with some help from the gods solves the diagonal argument.

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