| there's nothing garbled about this idea -- not sure about my messaging in this thread, maybe the explanations are a bit looser today A computable function is a function from naturals to the naturals typically specified as an algorithm: a sequence of steps by which input numbers are transformed into output numbers. Eg., consider sorting: 101, 001, 111, etc. Now any physical system can have any component part associated with 0 or 1. There is no reason, a priori, to suppose that voltage flux on a CPU is a "1" or a "0" any more than to associate a photon emission. If one associates a photon emission at some location with a 0, and another with a 1, then displaying content on a screen is a form of sorting. Likewise a planet orbiting the sun is implementing a while(true) i = -1*i, if one associates -1/1 with position of the planet orbiting the sun. This is the heart of 'reversible computing'. The only reason we associate some microscopic part of a CPU with 0, 1, etc. is by design it is something we as observers bring to bare on our interpretation of the physical system. But there's an infinite number of such attributions. We would only ever come to conclude that voltage flux across transitiors was relevant to the operation of a laptop via physics experiments --- no hope via computer science. This is very important for understanding why csci is presently useless and misinformative as far as the brain is concerned. There are an infinite number of 0/1 attributions to make, and infinite number of algorithms being implemented etc. almost all of those are irrelevant. Just, as you detect the absurdity, of using sorting algorithms to understand how an LCD works. This is presently less absurd than people talking about neural networks and equivocating with brain structures |
What makes brain a computer, and the air molecules in your room not a computer, is entropy. The behavior of air molecules is effectively random, the behavior of a brain very much not so.
Also, the universe isn't an uniform temperature soup where everything is equally random. There's energy cost to complexity, and there's a likelihood penalty to complexity. This gives us good confidence that the brain isn't doing something absurdly incomprehensible: it was made by evolution, which is a dumb, brute-force, short-term process. It didn't go out of its way to make things complex - it went with the first random thing that improved survival, which, being random, means generally the simplest thing that could work well enough.
Whatever trickery made brains tick, it must be something that's a) dumb enough for evolution to stumble on it, b) generic enough to scale up by steps small enough for evolution to find, all the way to human level, while c) conferring a survival advantage at every step of the way. Sure, the brain design isn't optimal or made in ways we'd consider elegant, but it's also not actively trying to be confusing. There's literally a survival penalty to being confusing (by means of metabolic cost)!
All to say, we're not dealing with a high-entropy blob of pure randomness. We're dealing with a messy and unusual system, but one that was strongly optimized to be as simple as one could get away with. This narrows down the problem space considerably, and CS is our helpful guide, at the very least by putting lower bounds on complexity of specific computations.