It is indeed surprising to me that @stephen_wolfram 's AKNS which has been around for around 2 decades isn't as commonly accepted. It seems I still need to re-explain the ideas in that book. Here's a recent interview by @lexfridman
It's a 4-hour interview and there's a lot of newer ideas discussed here. But essentially, all reality is computation. I had assumed that this to be true for a very long time, but it didn't occur to me that this needed to be stated and explained.
Wolfram believes that he is finally beginning to understand quantum mechanics in an intuitively graspable way. This is indeed a bold assertion, but I do think he is on the right path.
His theory involves a general theory of computation that involves parallel computation and a notion of causal invariance. Causal invariance is that massively parallel computations arrive at the same state regardless of the timing of the computation of individual nodes.
All of nature as well as the brain is massively parallel and the fact that we see a definite reality is a consequence of invariant features emerging out of the computation.
The explanation of how the brain works may likely be the same explanation how the universe evolves. There is apparently a connection between quantum mechanics and the brain in that they are driven by common principles. medium.com/intuitionmachi…
The interesting thing is that Wolfram revealed the computational underpinnings of quantum mechanics and this may lead to new ideas of how to explain how evolution and the brain operate.
Therefore, all theories of the brain using classical physics methods are likely to be obsolete and we need to transition to a more modern framework that Wolfram is proposing.
Dynamics is essentially motion along a geodesic (path of least distance) in a space. General relativity is motion in physical space, Quantum mechanics is motion in 'branchial' space ( a space of causal relations ).
Analogously, the brain is in motion in its own mental space that perhaps involves several spaces that are structured like spacetime and causality.
The double-split experiment in quantum mechanics is a consequence of the interaction of the two spaces. That is, the physical setup in space time leads to a condition where branchial space diverges and thus there are no photons every arriving at parts of a sensor.
In a similar manner, the brain maintains a causal graph (classical, not quantum mechanical) that explores a limited set of possibilities to arrive at a conclusion as it navigates in space and time.
Deep Learning is based on calculus, a mathematics that is based on infinitesimal change in integer space. However, we need math that describes infinitesimal motion in fractional and dynamical dimensional space.
The uncertainty principle is a consequence of curvature in branchial space.
Fermions follow the exclusion principle, are involved in the branching in Branchial space Bosons merging in Branchial space and that the spin might have to do with how is possible for one but not the other. Fascinating!
In this interview, Wolfram goes even deeper and explains the Rulial space (the space of all possible rules). The conclusion (which I like) is that the universe is computational (and not hyper-computational) and that aliens may see causality differently given different rule frame.
Extending this idea to biological cognition is that branchial space is constrained by the umwelt of the organism (what it can perceive and what it can do). That is, its causality graph is generated by the possibilities of its agency.
Causal graphs are like second-order category theory. Morphisms are like paths in hypergraphs. What's the equivalent of black holes in mathematics? It looks like non-constructive proofs!
Excellent interview by @lexfridman . I'm looking forward to the next time he interview @stephen_wolfram for newer discoveries in his Physics project.
Wait, did I forget again the crux of the theory? Here it is: "The Universe is computational".
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