Quick Summary So Far…
Posted on April 13, 2008
Filed Under Artificial Intelligence, General |
A quick summary of the (long) description of the Complex Systems Problem that was in the previous post.
The purpose of the argument
My purpose is to explain that if the task of building an artificial intelligence involves trying to engineer a “complex system”, then we are in big trouble because all the methods currently used by AI researchers depend on the fact that intelligent systems are not complex systems.
Step 1 of the argument
Scientists have been trying to explain various aspects of the world for quite some time, and they have noticed that some explanations are longer and more difficult to write down than others. That may seem like an obvious point, but some people find it surprising.
For example, explaining how the wheel works is simpler than explaining why some things float, which is simpler than explaining Newton’s theory of gravitation, which is simpler than quantum electrodynamics, which is simpler than string theory… and so on. Scientists have an informal idea of “theory size” - they don’t bother to talk about it much because it is usually of no importance, but the idea is there nonetheless. Roughly speaking, the size of a theory is the amount of paper that the average person would have to read and understand in order to get from no knowledge of any science, up to the level where they could understand the theory.
But this prompts a question that a scientist might ask. Could it be that there are systems in the universe that can only be explained by a theory that is so huge that we can never discover it? Or, could there be systems in the universe that we cannot explain because no theory can ever be found (of any size whatsoever) that could explain that system? We have encountered many things in the universe that we can explain, but by itself that means nothing: do we have any reason to believe that all systems are explicable in a reasonable amount of human time?
Keep that question in mind while we go to step 2.
Step 2 of the argument
Imagine that one day you go up to a mathematician and tell her that you just constructed a “system” (a bunch of objects that are having effects on one another), and that each of the objects in the system is following a rule that you invented, which you have written down on a single piece of paper. Before handing over the piece of paper, you ask the mathematician if she will be able to predict the behavior of the whole system, given only the description of the object-behavior that you wrote on the piece of paper. You specifically want to know if there is a pretty good chance that she will be able to predict the system, no matter how complicated and ugly the rule is.
The mathematician will laugh and say “Heck no! Unless your rule happens to be really simple, I wouldn’t even touch it”.
You are a bit discouraged, but you press the point. You ask what would happen if you got all the mathematicians in the world, and they did nothing but work on your rule for a thousand years. Would they then be able to say that no matter what the rule was, they’d have a pretty good chance of solving it (i.e. figuring out what the system as a whole would do)?
But her answer is just the same; “No way. The vast majority of rules that you could write down would be so ugly that no mathematician would even want to touch them. We don’t know for sure that they are unsolvable, but probably not.” She would go on to explain that if mathematicians were not allowed to choose their own problems to work on, but instead they were given problems by some outsider who made up systems at random, probably none of these systems would yet have been solved. There might be solutions to some of them, but they would be impossibly difficult to discover, or (more likely) most of the systems would not have any solutions.
But now you have another question. If we start building examples of these “untouchable” systems and actually observe how they behave, wouldn’t most of them just be behaving randomly, with nothing interesting to explain? The answer would again be negative: “Sorry, but no. That would be true of some of them, but you could easily find systems that had untouchable rules and very interesting behavior when you looked at the system as a whole.”
She would add that there is a name for systems that have untouchable rules but which nevertheless have “interesting” behavior: they are called complex systems.
Step 3 of the argument (the last step)
Back to the scientists we left in Step 1, who were wondering if there might be some things in the world that could only be explained by a theory of enormous (and overwhelming) size. A theory so big that we could never, in practice, discover it or write it down.
Now that you have had your chat with the mathematician, you go up to the scientists and say “Hey, there is no need to worry about the possibility of something having a humungous theory-size. I mean after all, you have studied lots of systems since the beginning of modern science, and even though the objects that make up those systems are sometimes following rules that those pessimistic mathematicians don’t like - the horribly nonlinear, tangled, “untouchable” rules - you scientists have still been able to explain how those systems worked. You must have come across plenty of untouchable-rule systems in your time, and if you can work with those systems even when the mathematicians have given up on them, surely you don’t have to worry.”
And then the scientists look at you strangely. “Uh… no, actually not. The overwhelming majority of the systems that we have scientifically explained have been nice and elegant, not “untouchable” at all. Down at the lowest levels, the universe seems to be made only of things that follow reasonably elegant rules. Or, if not elegant, then at least only slightly ugly.”
“So, what” you ask “would count as a really ugly kind of system?”
“Well, imagine that electrons were not all the same, but each one had its own unique characteristics and when it hit some other particle it reacted in a way that depended on which other particles it had hit recently, and what other particles happened to be in the neighborhood right now. If electrons had memory, and if they had individual preferences for particular other electrons which developed over time, that would be seriously ugly. If that were the way the universe worked then we’d probably have to go to the mathematicians and ask them if they have changed their mind about those really nasty, untouchable systems. And if they are right about how bad those untouchable systems are, then we would have to give up: this would be a real, honest-to-goodness example of chasing a theory that was too big to ever discover. Probably there would be no theory at all to explain particle physics, if electrons had complicated memories and preferences, and if they developed over time.”
You try to cheer the scientists up again: “But you have never come across a system like that, so maybe you never will, and there won’t be any theories that are too big. Why worry about something that will probably never happen?”
And then one scientist starts to look worried “Well, there is one example of a system like that.”
“What?”
“An artificial intelligence system. An AI is supposed to be made up of particles called “concepts” or “symbols”, and these symbols interact with each other in ways that seem to be exactly like those hypothetical electrons with memory and preferences, and which develop over time. If that is the way that intelligence works, then those AI folks are probably in deep trouble. It might be impossible to build a theory that explains why a given set of low level mechanisms must give rise to a system that is intelligent. And if they don’t have such a theory, and can never work towards one, I don’t know how they think they are choosing the low level mechanisms that they think will work…”
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