ActInf MathStream 009.1 ~ Jonathan Gorard: A computational perspective on observation and cognition

Jonathan Gorard
“A computational perspective on observation and cognition”
It has become increasingly clear that a fully computational description of reality must somehow account for the relative computational sophistication of observers (including their processes of measurement, analysis and cognition) and the natural systems that they observe. An ongoing research program, based upon the mathematical formalism first set out in arxiv.org/abs/2301.04690, seeks to use methods from category theory and topos theory to construct a purely compositional version of traditional computational and algorithmic complexity theory, within which an algebraic description of the tradeoff between observer vs. system complexity may be developed. It is claimed that this formalism has implications for the computational foundations of physics, mathematics, and potentially many other fields.
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[@truefaceofevil]

Here’s a technical crossover I’m glad to see. The CZcams video discussion between Karl Friston and Stephen Wolfram was too one-sided and high-level, but I’ve been feeling an intuitive connection between the two theories and I’m glad that’s being explored.

[@truefaceofevil]

Regarding Jonathan’s question about how to separate observer from system in FEP, I heard Karl Friston define it in terms of sparsity, I believe?

[@TheMemesofDestruction]

59:33 - Entropy is pretty neat! ^.^

[@NightmareCourtPictures]

I'm very interested in that question asked at around 1:02:00 which is whether there is a geometrization of the space of rules, and how they are distributed.
When I was looking at game of life and going through each configuration to find out which ones "generate something interesting" there didn't seem to be any consistent reason as to why or when there would be interesting behavior. If I had to make a guess, the complexity of the distribution of rules is probably also computationally irreducible. That understanding that distribution is like the halting problem. We can't know if that geometry will be a pattern, or if it will be randomly distributed, end or not end etc...and that it's complexity is subject to this observer dependence. in this way i don't think the distribution of the computational geometry of a problem is going to be like the mandlebrot set where it has a concrete form, it's going to vary based on how we are parametrizing the problem.
I usually imagine the ruliad object as like a sphere you can rotate around, and that sphere is like an infinitely deep fractal (like some kind of hyperbolic caley graph) but this is just a mere human perception (and also just plain wrong, over-simplified perception) of what would otherwise be an infinitely complex, infinitely large, and maximally symmetric object.
It's worth investigating for sure.

[@Self-Duality]

Jonathan Gorard’s mind produces theoretical dynamite 🤯

[@MikeFuller-ok6ok]

Lol! I don't even understand how levers work.

[@StephenPaulKing]

Bisimilarity is a useful equivalence for computations.

[@StephenPaulKing]

Vaugh Pratt's concept of Residuation matches up nicely with the core idea of Covariant computation!

[@berniethejet]

New idea for me: There is no meaning to 'causality' in a deterministic system.