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| date | 2001-02-13:13:34 |
| Software |
Not all representations are created equal. This is something that formal methods miss completely, yet the essence of good conceptual design is finding an optimal representation. Most approaches to AI take it as an axiom that any set of propositions implies its deductive closure. And I guess that is axiomatic, isn't it? Which demonstrates conclusively that propositions are not knowledge, because nothing could be further from the truth with regard to knowledge. And part of the reason for that is that knowing some facts is completely different from knowing the deductive closure--the set of all true implications--of those facts. The reason for this is that truth is a property of meaning, and meaning is a matter of intention, and no one ever intends the deductive closure of a set of propositions as its meaning. It follows from this that practical approaches to AI--insofar as we want to build intelligences rather than just machines that simulate intelligent behavior--must have a way of representing knowledge and meaning that violates this particular axiom. This was brought home to me yesterday by a problem I worked on last year that I've recently been doing some further work on to create the new and improved impossible thing. Some of the math in the old implementation was really awkward and clunky, and I could see that the new and improved version would be even more awkward and clunky. But one of the tools I use to generate the inputs to the new version puts out its data in a different form than the old version used. The same information is conveyed--only the format is different. This sort of thing comes up in computational geometry all the time; for example, a plane can be represented as a point and a normal, or a parameterized set of lines. The thing is, some of these mathematical forms are far more tractable for certain problems than others. This is because math has almost nothing to do with formal manipulation of abstract symbols, and almost everything to do with understanding what things those symbols represent, and how operations on those symbols represent behaviors of those things. Great weight is often put on the formal identity of different descriptions of nature--Heisenberg's and Schro"dinger's quantum mechanics, for instance--as if it was the formalism rather than the concepts that were important. Don't get me wrong: I like formalism. It keeps us out of a lot of trouble. But if we treat formalism as overly important--or worse yet as the only thing that's important--we lose almost everything that matters in our understanding, to the extent that our failure to grasp deductive closures becomes mysterious, when it should be the most obvious thing in the world. There is a strange flip-side to this desire to see all formally idendical descriptions as "identical as such". This is a desire to reify the most tractable of the formal descriptions, which is precisely the opposite mistake. So at different times one can find the same people saying that "A and B are formally identical, therefore we don't have to be bothered that they are totally different in every other respect", and "The terms of description in A are what is Real." It's as if people are aware that formally identical descriptions are not, in fact, identical, but because they have removed the knowing subject from their epistemological horizons they have nothing but realism to fall back on when it comes to account why one description is better than its formally identical cousins. |
| Creatures |
I heard coyotes yipping outside the house in the small hours of the night a couple of days ago. My hearing is not so good, and I was pretty tired, and at first I couldn't figure out what the the noise was. It sounded almost like a babble of children's voices, high pitched and happy. But the kids were fast asleep. Then the dog woke up and got interested, running about and barking, so I got up to investigate. Jan came half awake and told me that a neighbor had heard coyotes a few days before, and the children's voices suddenly resolved themselves into the sounds of fighting or more likely mating. I've heard them a couple of times since, and it's good to know they're out there, if for no other reason than realizing that if it weren't for them we'd be neck-deep in bunnies by now. |