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harshhpareek comments on Reinforcement Learning: A Non-Standard Introduction (Part 1) - Less Wrong
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I'm just wondering whether it's true that the Markov property holds for minds. I'm thinking that a snapshot of the world is not enough, but you also need to know something about the rate at which the world is changing. Presumably this information would require the knowledge of states further back.
Also, isn't there an innate element of randomness when it comes to decision making and how our minds work. Neurons are so small that presumably there are some sort of quantum effects, and wouldn't this mean again that information from one step previous wasn't enough.
I don't know, but just some thoughts.
(Assuming Mind=Brain, i.e. the entire mind is just the physical brain and no "soul" is involved. Also, Neurons aren't really all that small, they're quite macroscopic -- though the processes in the neurons like chemical interactions need quantum mechanics for their description)
In Newtonian Mechanics, it is sufficient to know the positions and velocities (i.e. derivaties of position) of particles to determine future states. So, the world is Markov given this informatio.
In Schrodinger's equation, you again only need to know \Psi and it's time derivative to know all future states. I think the quantum properties of the brain are adequately described just with Schodinger's equation. You do need to include nuclear forces etc in a description of the brain. You may need quantum electrodynamics, but I think Schrodinger's equation is sufficient.
My physics education stopped before I got here, but Dirac's equation which may be necessary to model the brain seems to require the second time-derivative of the wavefunction -- so you may need the second order time-derivatives to make the model Markov. Can someone who knows a bit more quantum physics chime in here?
EDIT: Reading the wiki article more carefully, it seems Dirac's equation is also first order