Here are a few thoughts on Artificial Intelligence. I have contributed nothing to the field but I know several contributors. I have been around since the early heady days when it seemed to many that a few MIPs should readily suffice. I sort of thought so.

First and informally I think we have a long way to go to catch up with the Darwinian method that has been going for at least 5∙108 years. In the 60’s we could give a nearly convincing story of how we performed “cognition” by mere introspection. It was nearly convincing because the listener shared the same introspective experience. Nagging at the corners of the argument were issues of salience. When people sought proofs for theorems or played games they jumped to conclusions that seem now clearly to be illogical, yet effective. Now it seems that cognition is 90% pattern recognition and only slightly pure logic. We have good theories of logic but not patterns. Kolmogorov patterns are not practical except for an abstract theory of patterns. It is not clear to me that there is any connection between Kolmogorov patterns and the patterns that can be found and recognized by either meat or silicon computing systems. Perhaps the connectionist school will eventually provide some progress here.

Some patterns become social constructs. The modern theory of groups was written down long after many mathematicians and others had effectively used the group pattern in solving problems. After it was written down more people could use the pattern and proofs became shorter and more proofs were possible because people shared the body of knowledge governing groups. You might say that math is a purely a collection of explicit patterns.

Math specializes in patterns that admit no exceptions. Such patterns are a limiting case of patterns that were probably critical in the arms race between predators and prey that began around the Cambrian explosion about 500 million years ago. There was certainly parasitic activity long before this but such relationships were established genetically and not in the nervous system, as there was previously little nervous system. When the predator and prey could see each other and they had a combinatorial nervous system it was possible and incumbent for each to recognize the other. There are at least these advantages of neural learning over genetic learning:

When a mathematician contemplates Gödel’s incompleteness proof he recognizes a pattern that he has not seen formalized before. That is why a conventional proof checking program will not recognize the proof. The proof is convincing to the degree that the pattern in the proof is familiar. The mathematician will presumably stretch his proof pattern to accommodate the new proof. I think that the mathematician is as likely to make an error in studying Gödel’s proof as in multiplying two 10 digit numbers. (Incidentally, I think Gödel’s proof is valid.)

Few species have a theory of mind. (only primates?) Most (all?) vertebrates have elaborate pattern abilities. This indicates that our genes provide support for theory of mind. Perhaps it is merely that our brain has more neurons, but I suspect otherwise.

I think we will get general AI but that it will take a long time and come in many stages. Many problems that are now solved were once ascribed to the realm of AI. When they are solved they are no longer ascribed to AI. “AI” seems to refer to those problems we have not solved. I think that the logicians, Bayesians, connectionists and genetic programmers will all contribute to the solution, as well as several schemes not yet invented. Alas I think that good AI will be an unholy mess.

Further Thoughts

Perhaps there is less difference between intuition and logic, as brain function, than is commonly supposed. This is easily supposed for we understand so little about intuition. Ordinary mathematical logic is a pretty good model of what people do, both trained mathematicians and others. When we invoke logic consciously or even verbally, we require names for things and predicates. I speculate here that intuition may be just as principled, but may deal with unnamed things and predicate. Naming things presumably arose with the evolution of language. Logic, at least intuitive style, came earlier. We are adept at applying logic to unnamed things. Adept but quite possibly unconscious.