Complexity_ A Guided Tour - Melanie Mitchell [92]
I began working on this project at MIT in the summer of 1984. That fall, Hofstadter started a new faculty position at the University of Michigan in Ann Arbor. I also moved there and enrolled as a Ph.D. student. It took a total of six years of working closely with Doug for me to construct the program he envisioned—the devil, of course, is in the details. Two results came out of this: a program that could make human-like analogies in its microworld, and (finally) my Ph.D.
How to Do the Right Thing
To be an intelligent copycat, you first have to make sense of the object, event, or situation that you are “copycatting.” When presented with a situation with many components and potential relations among components, be it a visual scene, a friend’s story, or a scientific problem, how does a person (or how might a computer program) mentally explore the typically intractably huge number of possible ways of understanding what is going on and possible similarities to other situations?
The following are two opposite and equally implausible strategies, both to be rejected:
Some possibilities are a priori absolutely excluded from being explored. For example, after an initial scan of mrrjjj, make a list of candidate concepts to explore (e.g., letter, group of letters, successor, predecessor, rightmost) and rigidly stick to it. The problem with this strategy, of course, is that it gives up flexibility. One or more concepts not immediately apparent as relevant to the situation (e.g., group length) might emerge later as being central.
All possibilities are equally available and easy to explore, so one can do an exhaustive search through all concepts and possible relationships that would ever be relevant in any situation. The problem with this strategy is that in real life there are always too many possibilities, and it’s not even clear ahead of time what might constitute a possible concept for a given situation. If you hear a funny clacking noise in your engine and then your car won’t start, you might give equal weight to the possibilities that (a) the timing belt has accidentally come off its bearings or (b) the timing belt is old and has broken. If for no special reason you give equal weight to the third possibility that your next-door neighbor has furtively cut your timing belt, you are a bit paranoid. If for no special reason you also give equal weight to the fourth possibility that the atoms making up your timing belt have quantum-tunneled into a parallel universe, you are a bit of a crackpot. If you continue and give equal weight to every other possibility ... well, you just can’t, not with a finite brain. However, there is some chance you might be right about the malicious neighbor, and the quantum-tunneling possibility shouldn’t be forever excluded from your cognitive capacities or you risk missing a Nobel prize.
The upshot is that all possibilities have to be potentially available, but they can’t all be equally available. Counterintuitive possibilities (e.g., your malicious neighbor; quantum-tunneling) must be potentially available but must require significant pressure to be considered (e.g., you’ve heard complaints about your neighbor; you’ve just installed a quantum-tunneling device in your car; every other possibility that you have explored has turned out to be wrong).
The problem of finding an exploration strategy that achieves this goal has been solved many times in nature. For example, we saw this in chapter 12 in the way ant colonies forage for food: the shortest trails leading to the best food sources attain the strongest pheromone scent, and increasing numbers of ants follow these trails. However, at any given time, some ants are still following weaker, less plausible trails, and some ants are still foraging randomly, allowing for the possibility of new food sources to be found.
This is an example of needing to keep a balance between exploration and exploitation, which I mentioned in chapter 12. When promising possibilities are identified, they should be exploited