He claims to have an argument that P=NP. He’s a philosopher, so “argument” != proof. Although approaching P=NP as a philosophical argument does strike me as kooky.
Better proof of kookhood is that he was at AGI mainly to present his work on hypercomputing, which he claimed was a computational system with more power than a Turing machine. One element of his argument was that proofs using hyperset logic (which he said is an entire field of logic nowadays; I wouldn’t know) use a notation that can not even theoretically be represented by a Turing machine. These proofs were published in two-dimensional journal articles, in black-and-white print. I did not notice any fractal fonts in the proofs.
He claims to have an argument that P=NP. He’s a philosopher, so “argument” != proof. Although approaching P=NP as a philosophical argument does strike me as kooky.
If it’s this argument, it’s wrong. It is based on the claim that soap films solve the Steiner problem, which they don’t. I tried this myself for four pins; here is a report of six-pin soap-film configurations. The soap film, obviously, only finds a local minimum, not a global one. But finding a local minimum is computationally easy.
Elsewhere, in a paper that detracts from the credibility of the journal it appears in, he argues that people can perform hypercomputation, on the grounds that we can imagine people performing hypercomputation. (Yes, I read all 24 pages, and that’s what it comes down to.)
One element of his argument was that proofs using hyperset logic (which he said is an entire field of logic nowadays; I wouldn’t know)
Judging by Google, the only wide use of the word “hyperset” in mathematics is in non-well-founded set theory. If that is what he was talking about, it’s equiconsistent with the usual sort of set theory and has no more significance for AI than the choice of programming language (which, in my view, has no significance for AI).
What is it with AI? Does it attract the insane, or does it drive them insane? ETA: Or attract the people that it can drive insane?
Oh… This is sad work (Bringsjord). His argument for hypercomputation by people seems remarkably similar to Alvin Plantinga’s Modal Ontological Argument for God.
I am also suspect of much of what Penrose has to say about Computationalism, although I am not yet sufficiently knowledgeable to be able to directly confront his work in any meaningful way (I am working to rectify that problem. I seem to have a knack for formal logic, and I am hoping that when I get to upper division logic classes that I will be able to more directly confront arguments like Penrose’s and Bringsjord’s)
It would be nice though, if outsiders could show some respect by demonstrating, as is probably demonstrable but difficult, that its object of study is incoherent, not just imaginary.
I’m not really sure it makes sense to talk about mathematical objects as being imaginary but not incoherent.
I’d be very surprised if this Universe was super-Turing, but you think it’s actually incoherent? I can definitely conceive of a hypercomputational cellular automata, what is it about the idea of our Universe being hypercomputational that seems incoherent to you?
I think that it is very common for things that we casually think we can definitely conceive of to actually be incoherent. I also think that almost everyone else underestimates how common it is.
I think I’m correcting for that. Do you agree that the halting oracle function itself is well-defined? If so, what seems inconceivable about a cellular automaton whose rules depend on the output of that oracle? OK, you have to stretch the definition of a cellular automaton to allow it, perhaps by allowing cells to have unbounded state, but the result is a wholly defined and therefore surely in-principle-conceivable Universe which is super-Turing. No?
It’s not incoherent. There could be such a thing as Hypercomputation.
However, nobody has found any evidence that it exists so far—and maybe they never will.
Hypercomputation enthusiasts claim that its existence doesn’t matter too much—and that it’s a valuable concept regardless of whether it exists or not. Maybe.
And, now I see why I am skeptical of hypercomputation. It seems to all necessitate some form of computation over an infinite number of steps. This would require some severe bending of the rules or constraints of physics, wouldn’t it?
timtyler’s comment below mine seems to be appropriate:
He claims to have an argument that P=NP. He’s a philosopher, so “argument” != proof. Although approaching P=NP as a philosophical argument does strike me as kooky.
Better proof of kookhood is that he was at AGI mainly to present his work on hypercomputing, which he claimed was a computational system with more power than a Turing machine. One element of his argument was that proofs using hyperset logic (which he said is an entire field of logic nowadays; I wouldn’t know) use a notation that can not even theoretically be represented by a Turing machine. These proofs were published in two-dimensional journal articles, in black-and-white print. I did not notice any fractal fonts in the proofs.
If it’s this argument, it’s wrong. It is based on the claim that soap films solve the Steiner problem, which they don’t. I tried this myself for four pins; here is a report of six-pin soap-film configurations. The soap film, obviously, only finds a local minimum, not a global one. But finding a local minimum is computationally easy.
Elsewhere, in a paper that detracts from the credibility of the journal it appears in, he argues that people can perform hypercomputation, on the grounds that we can imagine people performing hypercomputation. (Yes, I read all 24 pages, and that’s what it comes down to.)
Judging by Google, the only wide use of the word “hyperset” in mathematics is in non-well-founded set theory. If that is what he was talking about, it’s equiconsistent with the usual sort of set theory and has no more significance for AI than the choice of programming language (which, in my view, has no significance for AI).
What is it with AI? Does it attract the insane, or does it drive them insane? ETA: Or attract the people that it can drive insane?
Oh… This is sad work (Bringsjord). His argument for hypercomputation by people seems remarkably similar to Alvin Plantinga’s Modal Ontological Argument for God.
I am also suspect of much of what Penrose has to say about Computationalism, although I am not yet sufficiently knowledgeable to be able to directly confront his work in any meaningful way (I am working to rectify that problem. I seem to have a knack for formal logic, and I am hoping that when I get to upper division logic classes that I will be able to more directly confront arguments like Penrose’s and Bringsjord’s)
I came across a wikipedia article on hypercomputing a while back, http://en.wikipedia.org/wiki/Hypercomputation , the whole theory doesn’t seem at all well supported to me.
It is a field with an imaginary object of study.
It would be nice though, if outsiders could show some respect by demonstrating, as is probably demonstrable but difficult, that its object of study is incoherent, not just imaginary.
I’m not really sure it makes sense to talk about mathematical objects as being imaginary but not incoherent.
I’d be very surprised if this Universe was super-Turing, but you think it’s actually incoherent? I can definitely conceive of a hypercomputational cellular automata, what is it about the idea of our Universe being hypercomputational that seems incoherent to you?
I think that it is very common for things that we casually think we can definitely conceive of to actually be incoherent. I also think that almost everyone else underestimates how common it is.
I think I’m correcting for that. Do you agree that the halting oracle function itself is well-defined? If so, what seems inconceivable about a cellular automaton whose rules depend on the output of that oracle? OK, you have to stretch the definition of a cellular automaton to allow it, perhaps by allowing cells to have unbounded state, but the result is a wholly defined and therefore surely in-principle-conceivable Universe which is super-Turing. No?
Respectful outsiders?
Is that a reference to the inner sanctum of the Hypercomputation sect? ;-)
It’s not incoherent. There could be such a thing as Hypercomputation.
However, nobody has found any evidence that it exists so far—and maybe they never will.
Hypercomputation enthusiasts claim that its existence doesn’t matter too much—and that it’s a valuable concept regardless of whether it exists or not. Maybe.
I don’t disagree (i.e., I don’t see any positive reason to doubt the coherence of hypercomputation – though Michael sounds like he has one), but remember not to confuse subjective conceivability and actual coherence.
And, now I see why I am skeptical of hypercomputation. It seems to all necessitate some form of computation over an infinite number of steps. This would require some severe bending of the rules or constraints of physics, wouldn’t it?
timtyler’s comment below mine seems to be appropriate:
Doesn’t Newtonian gravity require computation over an infinite number of steps?