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The question is whether what causes us to understand things is a computational process. See my comment to the other reply, an others in this thread about chaos

The question is whether what causes us to understand things is a computational process. See my comment to the other reply, an others in this thread about chaos/non-determinism to see why I doubt. Ie., I dont think our organic growth and adaption to our environment, in being profoundly chaotic (and via QM, thef. non-deterministic) is likely to be describable as a computable function.

tsimionescu 5y ago
Non-determinism is a red herring. It's trivial to model and produce a non-deterministic computer given a deterministic one and since source of non-determinism (it's in fact impossible to produce a truly deterministic computer in real life). Conversely, you can interpret QM to mean that the universe evolves perfectly deterministically, except that no particular observer can predict in which branch they will find themselves. Also, non-determinism has little to do with computability. All known rules of physics are computable, even if you include the Born rule for non-determinism. A quantum computer is computable by a Turing machine (in exponential time, as far as we know).
- mjburgess 5y ago
  All laws of physics aren't computable. None of them are, they are all defined over the reals. You've a bigger issue with talking about the computability of those laws. I am assuming that somehow the reals can be ditched (which, incidentally, seems unlikely). And in that reality, we still have a problem: the role the reals play is to make reality infinitely precisely measurable. Without this chaotic systems become non-deterministic over realtively short time horizons. Nearly all actual systems are chaotic in many of their properties. It isnt a matter of just adding an RNG to a CPU. A trivial object has 10^30 atoms, in organic stuff, much of that is behaving chaotically on environmental boundaries. The engery to simulate this, assuming 10^30 RNGs (etc.) is vastly greater than the target system and "cannot outrun" that system. Not only this but I think simulation of such things quickly surpasses physical bounds on physically possible computers, not least as the RNGs have an energy cost.
  - tsimionescu 5y ago
    The real numbers used in physics are all computable (pi [0], e, sqrt(2) etc are all computable numbers). There are non-computable real numbers, but so far those have never been necessary for describing physical systems (e.g. Chaitin's constant). When talking about computability in the absolute, theoretical sense, the size of the universe is irrelevant - all we ask is if there exists some arbitrarily large, but finite, Turing machine that performs that computation and then halts after an arbitrarily large but finite amount of time. If we're taking about practical computability, than my base assertion that the physical world is itself a computer also implies that this computer is exactly fast enough to simulate physics. Since we know that the laws of physics are computable in the theoretical sense above, and since we know that the universe is accurately simulating itself, we have proven my assertion. Your other points about chaos and non-determinism I have addressed in another thread. [0] https://stackoverflow.com/questions/4134282/is-pi-a-turing-computable-number https://stackoverflow.com/questions/4134282/is-pi-a-turing-c...

tsimionescu 5y ago

Non-determinism is a red herring. It's trivial to model and produce a non-deterministic computer given a deterministic one and since source of non-determinism (it's in fact impossible to produce a truly deterministic computer in real life). Conversely, you can interpret QM to mean that the universe evolves perfectly deterministically, except that no particular observer can predict in which branch they will find themselves. Also, non-determinism has little to do with computability. All known rules of physics are computable, even if you include the Born rule for non-determinism. A quantum computer is computable by a Turing machine (in exponential time, as far as we know).

mjburgess 5y ago
All laws of physics aren't computable. None of them are, they are all defined over the reals. You've a bigger issue with talking about the computability of those laws. I am assuming that somehow the reals can be ditched (which, incidentally, seems unlikely). And in that reality, we still have a problem: the role the reals play is to make reality infinitely precisely measurable. Without this chaotic systems become non-deterministic over realtively short time horizons. Nearly all actual systems are chaotic in many of their properties. It isnt a matter of just adding an RNG to a CPU. A trivial object has 10^30 atoms, in organic stuff, much of that is behaving chaotically on environmental boundaries. The engery to simulate this, assuming 10^30 RNGs (etc.) is vastly greater than the target system and "cannot outrun" that system. Not only this but I think simulation of such things quickly surpasses physical bounds on physically possible computers, not least as the RNGs have an energy cost.
- tsimionescu 5y ago
  The real numbers used in physics are all computable (pi [0], e, sqrt(2) etc are all computable numbers). There are non-computable real numbers, but so far those have never been necessary for describing physical systems (e.g. Chaitin's constant). When talking about computability in the absolute, theoretical sense, the size of the universe is irrelevant - all we ask is if there exists some arbitrarily large, but finite, Turing machine that performs that computation and then halts after an arbitrarily large but finite amount of time. If we're taking about practical computability, than my base assertion that the physical world is itself a computer also implies that this computer is exactly fast enough to simulate physics. Since we know that the laws of physics are computable in the theoretical sense above, and since we know that the universe is accurately simulating itself, we have proven my assertion. Your other points about chaos and non-determinism I have addressed in another thread. [0] https://stackoverflow.com/questions/4134282/is-pi-a-turing-computable-number https://stackoverflow.com/questions/4134282/is-pi-a-turing-c...