mckee@CORWIN.CCS.NORTHEASTERN.EDU (George McKee) (05/26/89)
David Kristofferson wants more people to contribute to the list, so here's a tidbit (less than 2 cents worth, but US coinage doesn't go below 1...) The greatest difficulty in representing scientific knowledge is that there's no single representation possible for anything. Multiple representations are superficially redundant, so researchers are very reluctant to dilute their work by representing facts more than once. (Logicist AI is an extreme example of this, trying to fit all thought into first order logic.) The great strength of the matrix approach is that it has multiple representations as a fundamental principle. But viewing each dimension of the matrix as a linear vector of properties doesn't work, though it would be nice if it did. The urge to derive explanations from "first principles" seems to me to be an attempt to find some fundamental axiom set from which everything can be deduced. But even in physics "it's no use, it's turtles all the way down" as the builders of particle colliders are busily finding out. It seems to me that each dimension of the knowledge matrix should be viewed as a continuum that can be sampled at varying resolutions, producing a hierarchy of theory-slices that need to link together only the observations at a particular scale. The theory-slices are connected by metatheories that show how the whole picture fits together. Evolution, for instance, is one of the metatheories, while population genetics is one of the theory-slices within the evolutionary dimension. In neuroscience, Terry Sejnowski has constructed a very nice diagram showing how important classes of neural structures can be identified at 7 of the 8 orders of magnitude in size between molecules and human CNS (fig.1 in P.S.Churchland and T.J.Sejnowski, Science 242,p.741, 4 Nov.1988). Counting planetary ecology, biology includes 6 more orders of magnitude simply in physical scale. I think it was Laplace who wanted to do things like predict species extinctions by enumerating the molecules in the Amazon jungle, but who can collect that kind of data? Theories of knowledge have to accept the fact that some facts are in principle knowable, but the data is simply inaccessible. - George McKee NU Computer Science Disclaimer: I'm not an expert in anything, particularly this stuff.