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For further information contact Paul Grobstein.
Summary by Paul Grobstein
(presentation notes available)
In reflecting on our conversations to date, my aim was two-fold: to draw some general conclusions about the kind of methdology that might be successful in developing a new and more useful theory of information and to point to some features that ought to be incorporated in such a theory. The former was better developed in the presentation (see notes) and received more attention in the discussion. The latter will be the subject of a future discussion.
My basic assertion (see notes) was that the limits/problems of formal axiomatic systems (FAS's) and Turing computability were well-established and that, given this, one ought to try and develop forms of inquiry/exploration that transcended those limits. One way to do so, I suggested, was to look closely at the "givens" of FAS's/T-computability, change some of them, and see what happened. In particular, one might note the strict insistence on "consistency" and wonder if relaxing the insistence on consistency might enhance "completeness" (consistency-relaxing is in fact being explored; see eg Paraconsistent Logic). There are also presumptions about the finite character of symbol sets, about the importance of "halting", about the relation between production of sentences/computation and proof/verification, and about determinacy that might be usefully subjected to to the same kind of exploration. Another way to "get out of the box", I suggested, was to look at how the human brain, perhaps the most successful "information processor" ever to exist, works and use that as a guide. In this regard, it seemed to me relevant that irreversibility, inconsistency, and indeterminacy are all key aspects of brain function, as is recusion/self-referentiality.
Among the issues discussed was the degree to which science/humans are actually dependent on formal axiomatic systems (or Turing-computability). In this context, a distinction was made between "description" and "explanation" as in the classic debate about the status of quantum mechanics. One way to view "explanation" is that it is simply compressed "description". From this perspective, the formalisms of quantum mechanics are not regarded as at all a description of any "underlying thing" but are simply a useful compression of the description of .... observations made. One might adopt the same posture toward FAS's and Turing-computability, contending that they don't in fact constitute "boxes to be broken out of" since no one actually lives in them. In addition to some disagreement about the degree to which people do/do not live in them, the possibility was raised that there may in fact be something more to "explanation" than simply compressed description. And there was extended discussion of the extent to which recent mathematical proofs by exhaustive enumeration were "elegant" and/or satisfying in some not fully specified sense.
There was equally rich discussion about the brain, including concerns expressed about whether it was in fact a good information-processor (can it ACTUALLY do things that FAS's/Turing-computers can't? what about the demonstrations that Turing-computers do some things better? that people would LIKE their brains to do better than they do?) and whether its bi-partite, self-referential character was being portrayed in a way that had adequate observational basis. Most discussion focused on the issue of whether one needed BOTH the bipartite organization AND indeterminacy in order to get inconsistency (and the asserted, but debated) advantages thereof. It was suggested that the bipartite structure might itself suffice to assure inconsistency by providing a substrate for "conflict" (which could occur between "levels of organization" or between modules at one level of organization). It was acknowledged that indeed modularity would fulfill this specific requirement; whether it would suffice for all aspects of human capability to "break out of the box" (including "free will" and its consequences for exploration) was left open. An interesting additional open question was whether a FAS itself suffices to generate inconsistency given self-referentiality.
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