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>Then everything humanity will ever reach or know has Kolmogorov complexity no larger than this X. Only if it is deterministic, which certainly seems not very

>Then everything humanity will ever reach or know has Kolmogorov complexity no larger than this X. Only if it is deterministic, which certainly seems not very plausible. (You could say everything is a probability distribution, but to me it seems to get extremely complex after that, collapse?) >Because we already know the laws of physics are relatively simple, I would put my bets on the initial conditions having most of the entropy. Just because the laws are simply expressible does not imply they are simple. A variational minimization problem can be very easy to state (certainly that seems a good candidate for a "true" law of nature), but it can easily be as hard as a PDE!

PartiallyTyped 4y ago
It’s also possible that our __models__ are simple, but the underlying reality is not, so as long as there exists some error after sufficient evaluations it is safe to say that our model’s complexity is less than the universe’s.
- constantcrying 4y ago
  Yes, I agree. It is definitely possible that the underlying laws are extremely complex and there is absolutely no simple way to state them. But what I think is really interesting that this extreme complexity can only be found in extremely large and small scales. E.g. Newtons laws are phenomenal at predicting the universe at "human scales". The systems which can arise in Newtonian physics can be extremely complex, but their descriptions are usually very simple. Deviations from Newtonian predictions either are very small or arise only at large/small scales.
  - PartiallyTyped 4y ago
    > Newtonian physics can be extremely complex, but their descriptions are usually very simple IIRC Constructor theory builds on this, in a way, it defines some very basic and simple building blocks out of which the rest of the laws that govern our universe. https://en.wikipedia.org/wiki/Constructor_theory https://en.wikipedia.org/wiki/Constructor_theory
d_tr 4y ago
> Only if it is deterministic, which certainly seems not very plausible. A collapsing quantum state is so far the only proposed process which would result in a nondeterministic universe. The problem is that absolutely nothing is known about it, and everything around it is fishy. I personally think that the concept of the universal wavefunction makes more sense.
machina_ex_deus 4y ago
The point about determinism is correct, but since wavefunction evolution is unitary, the universe is fully deterministic. Only if you take some interpretation that there's real physical process of measurement which we don't understand and is indeterministic you can get randomness. But maybe if you subscribe to multiple worlds interpretation then the hardest part might be specifying which universe you're in, which would require number of bits proportional to the time since the big bang.
- mistermann 4y ago
  > The point about determinism is correct, but since wavefunction evolution is unitary, the universe is fully deterministic. A problem: if you consider the contents of the universe (and the precise state of the contents at a given snapshot in time) to be part of "the universe", you have the hard problem of consciousness to tend with (in that humans are a part of the universe, and they rearrange its contents on a regular basis). > Only if you take some interpretation that there's real physical process of measurement which we don't understand and is indeterministic you can get randomness. Randomness is not the only means to achieve a non-deterministic universe, there is also the possibility of non-deterministic forces being in play, like human activity. Of course, one can assert that human cognition is deterministic (no other option may even be available in some cases!), but science strongly suggests that simply asserting something to be true does not necessarily cause it to be true (though it does often cause it to appear to be true to pre-trained instances of human consciousness, a phenomenon which science has well demonstrated). Abstractly(!), humans seem to be in a very similar cognitive state as they were when they ran on sub-perceptual religious axioms. https://ell.stackexchange.com/questions/155593/meaning-of-the-phrase-meet-the-new-boss-same-as-the-old-boss https://ell.stackexchange.com/questions/155593/meaning-of-th...

PartiallyTyped 4y ago

It’s also possible that our __models__ are simple, but the underlying reality is not, so as long as there exists some error after sufficient evaluations it is safe to say that our model’s complexity is less than the universe’s.

constantcrying 4y ago
Yes, I agree. It is definitely possible that the underlying laws are extremely complex and there is absolutely no simple way to state them. But what I think is really interesting that this extreme complexity can only be found in extremely large and small scales. E.g. Newtons laws are phenomenal at predicting the universe at "human scales". The systems which can arise in Newtonian physics can be extremely complex, but their descriptions are usually very simple. Deviations from Newtonian predictions either are very small or arise only at large/small scales.
- PartiallyTyped 4y ago
  > Newtonian physics can be extremely complex, but their descriptions are usually very simple IIRC Constructor theory builds on this, in a way, it defines some very basic and simple building blocks out of which the rest of the laws that govern our universe. https://en.wikipedia.org/wiki/Constructor_theory https://en.wikipedia.org/wiki/Constructor_theory

d_tr 4y ago

> Only if it is deterministic, which certainly seems not very plausible. A collapsing quantum state is so far the only proposed process which would result in a nondeterministic universe. The problem is that absolutely nothing is known about it, and everything around it is fishy. I personally think that the concept of the universal wavefunction makes more sense.

machina_ex_deus 4y ago

The point about determinism is correct, but since wavefunction evolution is unitary, the universe is fully deterministic. Only if you take some interpretation that there's real physical process of measurement which we don't understand and is indeterministic you can get randomness. But maybe if you subscribe to multiple worlds interpretation then the hardest part might be specifying which universe you're in, which would require number of bits proportional to the time since the big bang.

mistermann 4y ago
> The point about determinism is correct, but since wavefunction evolution is unitary, the universe is fully deterministic. A problem: if you consider the contents of the universe (and the precise state of the contents at a given snapshot in time) to be part of "the universe", you have the hard problem of consciousness to tend with (in that humans are a part of the universe, and they rearrange its contents on a regular basis). > Only if you take some interpretation that there's real physical process of measurement which we don't understand and is indeterministic you can get randomness. Randomness is not the only means to achieve a non-deterministic universe, there is also the possibility of non-deterministic forces being in play, like human activity. Of course, one can assert that human cognition is deterministic (no other option may even be available in some cases!), but science strongly suggests that simply asserting something to be true does not necessarily cause it to be true (though it does often cause it to appear to be true to pre-trained instances of human consciousness, a phenomenon which science has well demonstrated). Abstractly(!), humans seem to be in a very similar cognitive state as they were when they ran on sub-perceptual religious axioms. https://ell.stackexchange.com/questions/155593/meaning-of-the-phrase-meet-the-new-boss-same-as-the-old-boss https://ell.stackexchange.com/questions/155593/meaning-of-th...