"I don't think that the details of which particular Turing machine is or is not universal are all that significant. What is significant, though, is how widespread universality is in general. And currently the only way we have of establishing that is to do the hard work of proving the universality or non-universality of particular Turing machines."
I smell a rat. His "Universality" and how often it occurs is what he has yet to prove.
He proves it in all kinds of examples (I think NKS is full of them). Other than that, he is just putting forward a hypothesis that some people might find interesting to consider. What is wrong with that?
It's very interesting how much elbow room (or is it rope?) these mathematicians give Wolfram regarding his new theory. I've read NKS, but cannot claim to understand it. I am not qualified to judge his other theoretical contributions. Does anyone here have the math chops to explain the, as it were, political situation?
Wolfram was smart once, but has become increasingly wacky lately. Nobody wants to actually come out and say that Wolfram is nuts, but people are treating him that way -- metaphorically speaking, smiling and nodding politely while backing away slowly. Keep in mind that this is a culture where the quality of one's mind is all-important, so accusing someone of being crazy is the worst possible insult.
Maybe it will turn out that Wolfram has been right all along -- but until and unless that happens, I think it's good that people who make wild and utterly unsupported claims are met with great skepticism.
So what wild and unsupported claims does Wolfram supposedly make? Seems to me he went at great lengths to spell everything out, so "unsupported" sounds a bit unfair to me.
He claims that what he's shown in A New Kind of Science is revolutionary, but the revolution has yet to happen. Maybe he's the only one to really get it and he doesn't have enough time to better show "us" the way. It seems unlikely though.
OK, but that is not a mathematical claim. I thought you have a criticism of his mathematical claims.
I think NKS ist at least entertaining, more than what can be said for many other mathematicians work. And people are still wondering about the origin of life, seems to me NKS could do more to show that life is likely to emerge than many other approaches. It seems like a small thing, but maybe it is revolutionary after all, if no other approach is making any headway.
I personally don't have anything to oppose to the maths. Wolfram goes pretty deep, and nothing is obviously wrong, although some of it didn't feel right. This review, however, goes into the details:
http://www.cscs.umich.edu/~crshalizi/reviews/wolfram/
Search for "untrue" if you want to get there directly.
I enjoyed NKS as well. It's good intellectual stimulation, but the hyperbole was still annoying.
http://forum.wolframscience.com/showthread.php?s=c34045c0fea...
Wolfman responds as well:
http://cs.nyu.edu/pipermail/fom/2007-October/012149.html