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Comment by VirusNewbie | Hacker News Reader

>. Turing machines specifically are not required to preserve anything about the initial state and so information can be destroyed and created ex nihilo, violating the main principle of physics which requires that all matter and energy be conserved. The equations have to balance out at the beginning and the end, whatever you start with can not be greater or less than what you end with (at least in physics).

can you explain this more rigorously? I don't see how computation 'destorys' information, unless you are using "destroy" loosely and you just mean exploding the state space?

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I think something like this. Imagine a computer with two memory cells x and y, and a program that maintains the invariant x+y=5. That is information about the program and about the state of the machine: if x=2 then y=3, if x=20 then y=-15, etc.

Now replace that program with an arbitrary Turing machine that can do pretty much anything with those memory cells, like set both of them to zero. You no longer have the information encoded in the former invariant. I.e. That information has been destroyed.

The machinery of quantum mechanics (the standard kind with Hilbert spaces) maintains certain invariants that you can compute things from, but Wolfram's stuff can do pretty much anything. Thus, same idea.

That's a good example and demonstration. The unitary invariance basically requires that the norm of the vector is preserved so that if we start with a unit vector then unitary evolution of that vector will always keep it that way. This is not the case for arbitrary programs because they don't have to preserve any invariants which makes them ill-suited for physical theory building. This is why Wolfram's approach is too open-ended, hypergraph evolution is way too lax of a framework for describing physical reality and conforming to existing experimental results.

I think there is a flaw in your logic here. The physics we know has certain features-e.g. unitary evolution. But, it is possible that there is a “deeper level” of physics we haven’t discovered yet. There are some major proposals for what that “deeper level” (or levels) might look like - e.g. M theory or loop quantum gravity - but for all we know maybe the underlying “real physics” is something nobody has even thought of yet, maybe something completely out of left field whose discovery is centuries away.

Whatever that “deeper level” is, should we assume it shares the “surface level” features such as unitary evolution? Well, there are two possibilities (a) yes it does (absolutely or universally so), or (b) in the most general case, no it doesn’t, but in the normal situation those features emerge.

Suppose, in the “ultimate physics”, unitary evolution is actually violated, but only at very extreme energy levels we are nowhere near being able to test? Or maybe it is conserved locally, but in distant regions of the universe (say a googolplex parsecs away) it isn’t? Or maybe it is conserved in the present, but in the very distant future (say a googolplex years from now) it won’t be any more? Do we have any way of knowing those possibilities won’t turn out to hold?

But if we don’t, then using the fact that cellular automata lack that feature as an argument against Wolfram’s hypothesis - it seems to me rather weak. That’s not to say that his hypothesis is actually true - I’d be rather surprised if it were. But I just don’t think this is a very convincing argument against it

I wasn't providing an argument to convince anyone of anything. Study the mathematics and if you have a way of making progress in constructing better physical theories based on Wolfram's foundations then more power to you. In general, talk is cheap and the proof is in the pudding. Wolfram never provides any testable results of possible experiments to validate his theories. He is mostly theorycrafting with rewrite systems and hoping something useful comes out. It's a lot like an evolutionary search over the space of possible rewrite systems to make some nice looking graphs. Whatever he's doing is not science in any meaningful sense of the word because there are no predictive and falsifiable experiments based on his theories.

so you're saying you can't work backwards at an arbitrary point without the initial IO and that's the problem?

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