timelets: (Default)
...space-time cannot in reality be
considered as a self-subsistent entity. It is an abstraction, and its
explanation requires reference to that from which it has been extracted.
Space-time is the specification of certain general characters of events
and of their mutual ordering. This recurrence to concrete fact brings me
back to the eighteenth century, and indeed to Francis Bacon in the
seventeenth century.
...
in order to
understand the difficulties of modern scientific thought and also its
reactions on the modern world, we should have in our minds some
conception of a wider field of abstraction, a more concrete analysis,
which shall stand nearer to the complete concreteness of our intuitive
experience.

whitehead. Science..., 1925
timelets: (Default)
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.)
timelets: (Default)
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.
timelets: (Default)

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.
timelets: (Default)


The image of a unit of "brick vs straw house" causality is life.
timelets: (Default)
This is an important insight: comma categories always have a terminal object. Now, I can relate it to Lawvere's interpretation of Hegel's logic.


"If X is any application of the graphic G , then the "comma" category G/X (whose objects are the elements of X and whose morphisms determine the action via the discrete fibration property of the labelling functor G/X -> G ) is again a graphic. Thus each particular application X of G provides one way G'-> G of expanding the graphic G into a more detailed graphic G' " -- Lawvere, Hegelian Taco.
timelets: (Default)
Is time irreversible? Would that it were! On the contrary, it is reversible-so reversible that it is possible not to have made any progress since the time of the Romans. Now if things stagnate, we can hardly make a distinction between 1871 and 1875, except on the calendar, which does not amount to very much.

--- Bruno Latour. TPoF, 1993.


upd. Compare this to Lawvere's point about being vs becoming. Specifically, space serves as аn arena for becoming, which requires at least two points to be noticeable. Stagnation implies maintaining a given state in a space of states, i.e. just one point, despite changes in calendar time, which is a different space. We can express stagnation vs change as the difference in intensive quantity, e.g. states per an interval of time. Движуха!
timelets: (Default)

The exact sciences elude social analysis not because they are distant or separated from society, but because they revolutionize the very conception of society and of what it comprises. Pasteurism is an admirable example.

--- Bruno Latour. The Pasteurization of France, 1993. p 38.


AI seems to be moving in the same direction.
timelets: (Default)
Similar to the way in which Bergson contrasts time and duration, intellect and intuition, Péguy differentiates between history and tradition, science and experience. To illustrate this difference, for example, in Clio history is compared to a long railway line that runs along the coast and that allows one to stop at any station one wishes. In this metaphor tradition—collective memory—appears as the coast, with its marshes, people, fishes, estuaries of rivers and streams, as life on land and life in the sea.
Read more... )
--- Heoning Schmidgen. Bruno Latour in Pieces, 2014.


In contrast with schoolbook history that treats its subject as tourism, he thinks about it as travel, similar to the original approach introduced by Herodotus more than two thousand years ago.

Also see Lawvere, Categories of Space and Quantity, 1992, wrt the example of a sojourn, as a variable intensive quantity. Peguy's history vs a schoolbook one would have a completely different intensive quantity pattern, while the terminal object in the underlying extensive category, i.e. the total would be the same.
timelets: (Default)
Space and time are a frame, an ordering realm, with the help of which we
establish and indicate the place and time point of the
particular things. It might be, therefore, that each thing,
if it is determined with respect to place and time, is now
just this (je dieses ), not mistakable for any other.

-- Heidegger, What is a thing?. 1967.
Read more... )
timelets: (Default)
Hillary Putnam on Kant's insight into the connection between time, space and causality.

https://youtu.be/DPQZfsAHgSg?t=812
timelets: (Default)
This use of 1, 2, 2 x 2, is based on the insight that these very simple categories are ‘basic figure shapes’ for the analysis of general categories; it is an example of a general
method for analyzing the ‘inside’ of objects in any category

--- Lawvere & Schanuel. Conceptual Mathematics, 2009. p 370.


In the context of Lawvere's 1992 paper "Categories of Space and Quantity", 1 represents being; 2 - becoming; 2x2 – coherent scenarios of becoming, with a natural transformation between them (theories).
timelets: (Default)
A good background video before discussing Lawvere's Categories of Space and Quantity, 1992. Specifically, the material applies to extensive quantities.


timelets: (Default)
“...he [Lincoln] managed polarities: they didn’t manage him.
...
Scale sets the ranges within which experience accrues. If, in evolution, edges of chaos reward adaptation; if, in history, adaptation fortifies resilience; and if, in individuals, resilience accommodates unknowns more readily than rigidity, then it stands to reason that a gradual expansion of edges better equips leaders for the unexpected than those that shock, leaving little time to adapt, or those inherited, which breed entitlement and arrogance, its companion.
..
Space is where expectations and circumstances intersect."
...
Tolstoy suggests, in the last pages of War and Peace, that the interdependence of time, space, and scale simultaneously reflects choice and necessity: the illusion of agency causes us to believe in free will even as inexorable laws deny the possibility. ”

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


We can model this as an interval and/or 10x pushout/pullback.

Creating a new scale, i.e. expanding the range, e.g. via a technology can be viewed as an equalizer.
timelets: (Default)
"Pivoting requires gyroscopes,...

Machiavelli, thinking gyroscopically, advised his prince to be a lion and a fox, the former to frighten wolves, the latter to detect snares. Elizabeth went him one better by being lion, fox, and female, a combination the crafty Italian might have learned to appreciate. Philip was a grand lion, but he was only a lion. Such princes can through conscientiousness, Machiavelli warned, become trapped. For a wise ruler “cannot observe faith, nor should he, when such observance turns against him, and the causes that made him promise have been eliminated. . . . Nor does a prince ever lack legitimate causes to color his failure to observe faith.”

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


This relates to the idea of a pivot space.
timelets: (Default)
The three little pigs in a phase space.
timelets: (Default)
Back to regular programming:

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 07:59 am
Powered by Dreamwidth Studios