Solomonoff induction is not in fact infinite due to the Occam prior, because a minimax branch pruning algorithm eventually trims high-complexity possibilities.
You started out by saying, in essence, that general AI is just a matter of having good enough hardware.
You were wrong. Dead wrong. The opposite is true: it is purely a matter of software, and sufficiently good hardware. We have no idea how good the hardware needs to be. It is possible that a general AI could be programmed on the PC I am currently using, for all we know. Since we simply do not know how to program an AI, we do not know whether it could run on this computer or not.
You supported your mistake with the false claim that AIXI and Solomonoff induction are computable, in the usual, technical sense. You spoke of this as though it were a simple fact that any well educated person knows. The truth was the opposite: neither one is computable, in the usual, technical sense. And the usual technical sense of incomputable implies that the thing is incomputable even without a limitation on memory or clock speed, as long as you are allowed to execute a finite number of instructions, even instantaneously.
You respond now by saying, “Solomonoff induction is not in fact infinite...” Then you are not talking about Solomonoff induction, but some approximation of it. But in that case, conclusions that follow from the technical sense of Solomonoff induction do not follow. So you have no reason to assume that some particular program will result in intelligent behavior, even removing limitations of memory and clock speed. And until someone finds that program, and proves that it will result in intelligent behavior, no one knows how to program general AI, even without hardware limitations. That is our present situation.
You started out by saying, in essence, that general AI is just a matter of having good enough hardware.
Ok this is where the misunderstanding happened. What I said was “if you had the luxury of running with infinite compute resources and allow some handwavery around defining utility functions.” Truly infinite compute resources will never exist. So that’s not a claim about “we just need better hardware” but rather “if we had magic oracle pixie dust, it’d be easy.”
That’s fine. As far as I can see you have corrected your mistaken view, even though you do have the usual human desire not to admit that you have done so, even though such a correction is a good thing, not a bad thing. Your statement would be true if you meant by infinite resources, the ability to execute an infinite number of statements, and complete that infinite process. In the same way it would be true that we could solve the halting problem, and resolve the truth or falsehood of every mathematical claim. But in fact you meant that if you have unlimited resources in a more practical sense: unlimited memory and computing speed (it is evident that you meant this, since when I stipulated this you persisted in your mistaken assertion.) And this is not enough, without the software knowledge that we do not have.
Sorry, no, you seem to have completely missed the minimax aspect of the problem—an infinite integral with a weight that limits to zero has finitely bounded solutions. But it is not worth my time to debate this. Good day, sir.
I did not miss the fact that you are talking about an approximation. There is no guarantee that any particular approximation will result in intelligent behavior. Claiming that there is, is claiming to know more than all the AI experts in the world.
Also, at this point you are retracting your correction and adopting your original absurd view, which is unfortunate.
Solomonoff induction is not in fact infinite due to the Occam prior, because a minimax branch pruning algorithm eventually trims high-complexity possibilities.
Ok, let’s go back and review this conversation.
You started out by saying, in essence, that general AI is just a matter of having good enough hardware.
You were wrong. Dead wrong. The opposite is true: it is purely a matter of software, and sufficiently good hardware. We have no idea how good the hardware needs to be. It is possible that a general AI could be programmed on the PC I am currently using, for all we know. Since we simply do not know how to program an AI, we do not know whether it could run on this computer or not.
You supported your mistake with the false claim that AIXI and Solomonoff induction are computable, in the usual, technical sense. You spoke of this as though it were a simple fact that any well educated person knows. The truth was the opposite: neither one is computable, in the usual, technical sense. And the usual technical sense of incomputable implies that the thing is incomputable even without a limitation on memory or clock speed, as long as you are allowed to execute a finite number of instructions, even instantaneously.
You respond now by saying, “Solomonoff induction is not in fact infinite...” Then you are not talking about Solomonoff induction, but some approximation of it. But in that case, conclusions that follow from the technical sense of Solomonoff induction do not follow. So you have no reason to assume that some particular program will result in intelligent behavior, even removing limitations of memory and clock speed. And until someone finds that program, and proves that it will result in intelligent behavior, no one knows how to program general AI, even without hardware limitations. That is our present situation.
Ok this is where the misunderstanding happened. What I said was “if you had the luxury of running with infinite compute resources and allow some handwavery around defining utility functions.” Truly infinite compute resources will never exist. So that’s not a claim about “we just need better hardware” but rather “if we had magic oracle pixie dust, it’d be easy.”
The rest I am uninterested in debating further.
That’s fine. As far as I can see you have corrected your mistaken view, even though you do have the usual human desire not to admit that you have done so, even though such a correction is a good thing, not a bad thing. Your statement would be true if you meant by infinite resources, the ability to execute an infinite number of statements, and complete that infinite process. In the same way it would be true that we could solve the halting problem, and resolve the truth or falsehood of every mathematical claim. But in fact you meant that if you have unlimited resources in a more practical sense: unlimited memory and computing speed (it is evident that you meant this, since when I stipulated this you persisted in your mistaken assertion.) And this is not enough, without the software knowledge that we do not have.
Sorry, no, you seem to have completely missed the minimax aspect of the problem—an infinite integral with a weight that limits to zero has finitely bounded solutions. But it is not worth my time to debate this. Good day, sir.
I did not miss the fact that you are talking about an approximation. There is no guarantee that any particular approximation will result in intelligent behavior. Claiming that there is, is claiming to know more than all the AI experts in the world.
Also, at this point you are retracting your correction and adopting your original absurd view, which is unfortunate.