This principle is just applying Turing equivalence to the hypothesis that there is nothing in nature that is effectively computable but exceeds the Turing computable (which would be the "maximal level of computational power")

Given we have no evidence of the existence of anything effectively computable that is not Turing computable, it's a reasonable hypothesis, with no evidence pointing towards falsifying it, nor any viable theories for what a "level of computational power" that exceeds this hypothetical maximum would look like.

And, yes, if that hypothesis holds, then life is equivalent, to the point of at least being indistinguishable from when observed from the outside, computation.

A lot of people get upset at this, because they want life to be special, and especially human thought. If they want to disprove this, a single example of humans computing a function that is outside the Turing computable would be a very significant blow to this hypothesis, and the notion of life as a computation (it wouldn't conclusively falsify it, as to do that you'd need to also disprove that there might we ways to extend computers to compute the set of newly discovered functions that can't be computed by a Turing machine, but it would be a very significant blow)

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TheOtherHobbes 2 days ago | parent | next [-]

This is a poor argument, because the universe is uncomputable. We have models that apply on short time scales, but it's fundamentally not computable either in practice or in principle.

On long enough scales - and they're not that long when you're talking about billions of years - we don't even know if the solar system is stable.

Bio-computability has the same issue at smaller scales. There are islands of conceptual stability in a sea of noise, but good luck to you if you think you can compute this sequence of comments on Hacker News given the position of every atom in the original primordial soup.

The universe is not clockwork. The concept of computability is essentially mechanical, and it's essentially limited - not just by conceptual incompleteness theorems, but by the fact that any physical system of computation has physical limits which place hard bounds on precision and persistence.

	▲	vidarh 2 days ago \| parent [-]
		> because the universe is uncomputable We have no evidence to suggest that is true. If no individual process in the universe exceeds the Turing computable - and we have no evidence it does, or that anything exceeding the Turing computable can even exist - then the universe itself would be existence-proof that it is computable. Now, we can't be 100% sure, because we'd have to demonstrate that every physical interaction everywhere is individually Turing computable. But we also have nothing that even hints of evidence to the contrary. Note that it is possible the universe is not computable from within with full precision due to e.g. lack of compressibility. > On long enough scales - and they're not that long when you're talking about billions of years - we don't even know if the solar system is stable. That has zero relevance to whether or not it is computable. If it is computable, then any such instability is simply an effect of a computation. In other words you're committing the logical fallacy of begging the question - your conclusion rests on your premise, as you're trying to argue that the universe is computable by using processes as evidence that can only be uncomputable if the universe as a whole is uncomputable. > The universe is not clockwork. That is irrelevant to whether or not it is computable. > but by the fact that any physical system of computation has physical limits which place hard bounds on precision and persistence. This is also in general irrelevant to whether or not a system is computable. We can operate symbolically on entities that requires any arbitrary (including infite) precision and persistence within various constraints. E.g. we can do math with 1/3 to infinite precision for a whole lot of calculations. Unless you can show specific processes that demonstrably happens with a precision that is impossible to simulate without the computation becoming infinite, this argument doesn't get you anywhere. Note that it would be insufficient to show a process that appears to have infinite precision in a way that would take infinite time to calculate unless there is demonstrably no way to lazily calculate it to whatever precision you actually try to observe in a finite amount of time, as such a system can be simulated. Length of time would also not be a problem unless you can show why such a simulation needs to run at full speed to work, rather than impose a subjective time on the inside of the simulation that can vary with computational complexity. Space complexity is also irrelevant unless you can show limits on the theoretical maximum capacity of an outside simulator. Now to the question of whether life is computable, then if the universe is computable, then life is too, but if the universe is not, life might still be, and so this is largely a digression from the original point I made.

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seanhunter 2 days ago | parent | prev [-]

Firstly the crux of that hypothesis seems completely undecidable. Secondly it seems to me that applying something like Turing equivalence to things which are not computer programs is a category error which leads to him talking very obvious total nonsense.

1. Complexity != computation. How does a weather system compute anything at all for example? By any standard definition of these words it doesn’t. Since Wolfram never defines his terms rigourously, this statement is prima facie meaningless.

2. Computational complexity != equivalence. He’s talked about implementing the universe in 4 lines of mathematica code when clearly mathematica itself is in the universe and takes more than 4 lines of code to implement. What he (actually his staff) has implemented in 4 lines is a cellular automaton that is Turing equivalent. That’s cool but it’s not the universe. If you’re not drinking the kool-ade it’s just nonsense.

3. How does any of that make life indistinguishable from computation? All life that I’ve observed seems to be very easily distinguishable from computation, and I would suggest that anyone who finds this confusing should probably get out more.

	▲	vidarh 2 days ago \| parent [-]
		> Secondly it seems to me that applying something like Turing equivalence to things which are not computer programs is a category error which leads to him talking very obvious total nonsense. Turing equivalence applies to all computation. "Computer programs" has nothing to do with it. > How does a weather system compute anything at all for example? By any standard definition of these words it doesn’t By every normal definition of these words it does. Any computation with a digital computer is us applying an interpretation onto physical computation in the form of basic physical interactions that carry out operations that we interpret in terms of logic. And we have computing devices that makes this link more explicit, such as e.g. the Soviet "water integrator". Using physical interactions to compute is trivial, e.g. ranging from the trivial, with two pools of water merging is the computational equivalent of addition, to the slightly less trivial classic demonstration of Pythagoras theorem with tree interconnected triangles filled with fluid. Every physical system carries out computations with every interaction, but most of them are useless to us. But every digital computer can carry out computations that are useless to us too, if we let them run chaotic programs on chaotic data. > That’s cool but it’s not the universe. It's not the universe, but that is irrelevant unless you can either disprove Turing equivalence or prove that the universe contains computation that exceeds the Turing computable. If you could, there'd likely be a Nobel prize with your name on it. > 3. How does any of that make life indistinguishable from computation? All life that I’ve observed seems to be very easily distinguishable from computation, and I would suggest that anyone who finds this confusing should probably get out more. If life does not exceed the Turing computable, then it can be fully simulated, to the point of giving identical responses to identical stimuli when starting from the same state and at that point if there is any distinction at all, it would need to require observing the internal processes of the entities involved. Put another way: If life does not exceed the Turing computable, then you don't know whether or not you are simply a simulation, nor do you know whether or not the universe itself is.