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We define the central notion of a domain as a set of integral dimensions that are separable from all other dimensions.

--- Peter Gärdenfors, Matías Osta-Vélez. Reasoning with Concepts: Conceptual Spaces as a Framework, 2026.

https://direct.mit.edu/books/oa-monograph/6152/Reasoning-with-ConceptsConceptual-Spaces-as-a

Remarkably, business textbooks love two-dimensional diagrams, which allow to define a domain with the minimal number of separable dimensions.

Exercise for the reader: place Putin and Trump on the diagram, wrt the former's war with Ukraine and the latter's war with Iran. Explain.



Conversely, trade-offs allow to collapse a domain into one dimension.

The central notion of conceptual space is defined as a collection of
one or more domains with a distance function (a metric) that represents
properties, concepts, and their similarity relations.



-- ibid.
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.

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