A computational system is classically formulated as a sequential system. A dynamical system has always been a parallel system. However, there is no reason why a computational system can also be formulated as a parallel system.
Biological brains are more like parallel computational system than they are like dynamical systems. This is because biological systems have to interpret their environments and interpretation implies language translation.
A classic computer system is obviously built on the physics of a dynamical system. However, it is designed with constraints and error correction at many scales. Its design is also a reflection of the cognitive capabilities of its designers.
A biological computer in contrast does not have a designer with a mind. It employs evolution to drive its design. The constraints and error correction mechanism it selects in its design are fined tuned over eons of evolution. But it still designs (or evolves) at multiple scales.
As a consequence, the constrains and error correction mechanisms are of a decentralized (also parallel) construction and do not rely on the cognitive simplification required by a designer with a mind. As a consequence, its design is obfuscated in complex parallel processes.
How can we best reason about the construction of biological minds? Are the use of equations of dynamics in physics (i.e. principle of least action) useful in this domain? Does this principle convey to the domain of evolution? What evidence do we have that it does?
If we treat complex systems as intertwined and layered virtual machines. Each virtual machine with its own encapsulation and instruction set. We need to ask, are the equations of dynamics preserved in these virtual machines? What argument do we have that they must?
Must the 2nd law of thermodynamics be present in each encapsulated virtual machine? It is likely not and by extrapolation, any other dynamical law may not be sufficient. The simulations in a virtual machine do not have to abide by the laws of physics.
Therefore, the mathematical tooling that we've developed for physics (i.e. variational principles) has its limitations in the realm of biological brains. Analytic equations are at best descriptions of a physical system, they are not the mechanism of the actual physical systems.
Furthemore, analytic equations are limited in their modeling of computational systems. This is a well-established limitation introduced by Turing and Church. Biological minds are governed by the same laws of computation.
Biological brains exhibit irreducible computation and this is the constraint on equations of dynamics can be used for its analysis.
I guess this is implied from the thread: https://twitter.com/OpenAI/status/1273323325431754753
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