Here’s a technical crossover I’m glad to see. The TH-cam 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.
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.
The diagramming technique Jonathan is using appears to have a tendency to overwrite background annotations with a foreground annotation where two transitions cross. This can be confusing when interpreting the diagram. In the first diagram we see a 3 overwriting a 1, for example, where two transitions cross. The graph rendering software may want to learn how to detect a foreground/background overwrite like this and algorithmically displace them, so the graph is easier to decode for the reader.
Here’s a technical crossover I’m glad to see. The TH-cam 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.
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?
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.
Jonathan Gorard’s mind produces theoretical dynamite 🤯
Lol! I don't even understand how levers work.
The diagramming technique Jonathan is using appears to have a tendency to overwrite background annotations with a foreground annotation where two transitions cross. This can be confusing when interpreting the diagram. In the first diagram we see a 3 overwriting a 1, for example, where two transitions cross. The graph rendering software may want to learn how to detect a foreground/background overwrite like this and algorithmically displace them, so the graph is easier to decode for the reader.
59:33 - Entropy is pretty neat! ^.^
New idea for me: There is no meaning to 'causality' in a deterministic system.
Bisimilarity is a useful equivalence for computations.
Vaugh Pratt's concept of Residuation matches up nicely with the core idea of Covariant computation!