[Automata, Recursion, and Chomsky Linguistics] - A New Kind of Science: The NKS ForumA New Kind of Science: The NKS Forum
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Automata, Recursion, and Chomsky Linguistics
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Posted by: Ray C. Dougherty
Hauser, Chomsky, and Fitch wrote an article in Science claiming that the distinction between human and animal intelligence is that humans have recursion but animals do not. I have written a short essay discussing the relevance of Cellular Automata to their study. You can see it at:
www.nyu.edu/pages/linguistics/CA
and print it out at:
www.nyu.edu/pages/linguistics/CA/HCF.pdf
I would appreciate any comments and feedback.
Posted by: Jason Cawley
Fun, thanks for that. Sounds like you are having a good time with all this, that is good to see.
I note in preface that people have considered language as the paradigm of complexity from simple elements through arbitrary rearrangement of those elements at least since the Epicureans. Lucretius has a nice passage about it: when he wants to argue that a finite number of atoms would suffice to account for all entities, he does so on the analogy of letters in his own writing.
On specifically human vs. animal intelligence, I don't claim to be any sort of expert on how limited the latter typically is. But it seems to me at least possible the questions "what makes humans smart" and "what makes humans different" don't necessarily have the same answer.
The results of the NKS book show the formal threshold for universality is really quite low. Might not the formal machinery required be rather easy to get, but making any sufficiently general and half way reliable use of it be distinctly harder?
Formal systems as simple as the Spencer Brown form or Rule 110 are formally universal. Brains have enourmous memory capacities if they make any significant use of their overall connectivity. So we've got a very low formal threshold on one side, and a whole lot of hardware on the other side. Moreover, much of that brain structure we share with other mammals.
I see you've noticed how people look for human specialness in infinities of one kind or another. I'm highly skeptical of the sentiment behind that. You see it even in fascinating and insightful people like CS Pierce (I see you are also a fan), who thought continuity (the big new formal thing, post Cantor) was the basis of human specialness, intelligence, free will, yada yada.
Penrose wants to think something similar. He acknowledges Turing's point that "these theorems say nothing about how much intelligence may be displayed if a machine makes no pretence at infallibility" - but sees "a certain intrinsic implausibility in the idea that what makes the mind superior to an accurate computer is the mind's inaccuracy" (Penrose, Shadows of the Mind p. 129).
What I think he missed was how restrictive a criterion "knowably sound" actual is. Knowably sound requires a certain predictability, which entails a measure of reducibility. It is not that fallibility is an advantage, but that forseeable enough to be known "safe" beforehand implies to some extent simplistic. It is not a problem of finite machines, but the predictability imposed upon them.
As for the question how universal brains might arise in evolution, we don't know how late they actually are. But for the sake of argument assume it is just us, that dogs aren't there yet, and that it is connected to language. Is there a great problem to explain in this apparent discontinuity? I don't see it. You flip one bit in a rule's formulation and it goes from a mundane class 2 to a universal class 4. Or if you prefer, you reverse two elements in some bracket grammar and get combinators. Some formal systems, very much like others in how they are laid out as rules, just have behavior that is universal rather than simple.
So it seems to me quite plausible that single changes in existing formal systems with quite different, much simpler complexity characteristics, can knock you over the universality threshold.
Notice that once you are over it, you still have to do something with it, and it is not at all trivial to do so. If you've just got some learning system with bare universal potential, it needn't actually figure anything out. That is a separate additional hurdle. Perhaps the hard part is getting all the additional systems that make that learning possible or efficient.
The last is pure speculation - just throwing out possibilities because that is what I think philosophy can add to this sort of question. Which of the possibles nature actually does is for the relevant sciences. I hope some of it is interesting.
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