Information?: An InquiryThursdays, 9:30-11 amScience Building, Room 227 Schedule | On-line Forum | Evolving Resource List For further information contact Paul Grobstein. |
Summary by Paul Grobstein
(presentation notes available
see also An Exchange on Bayesian Inference and Formal Axiomatic Systems)
In our last discussion for the summer, I tried to connect recent discussions about formal axiomatic systems and Turing computability back to our opening thoughts about the nature of information using a brief introduction to Bayesian inference as a bridge. The basic idea (see presentation notes for elaboration) was that Bayesian inference might potentially serve as an alternative to FAS's as a basis for inquiry, in that it made no presumptions about "reality" and simply operated iteratively on "degree of uncertainty". At the human level, one might take "information" as anything that changes "degree of uncertainty". In its dependence on an "observer" this is consistent with our earlier considerations of "information" as something that is transformed by a decoder and evaluated using randomness as a baseline, but presumes an appreciation of "counter-factuals", and so cannot be a general (HUMAN observer independent) characterization of information. I suggested one might bridge between the bottom and top level consideration of information by assembling decoders into models (that have some "predictive" capability), into model makers (which have the capacity to be modified by their own decoding/predicting activity) and finally by the addition to a model making assembly of story telling (with its inherent capacity to appreciate counter-factuals). And posed a series of further questions if this line of thinking was to be pursued further (including the problem of "quantification" of information and that of whether there were "laws of information).
Discussion focused largely on a series of questions about Bayesian inference (with which most participants were only vaguely familiar) and related matters. One, also considered at our last session, was whether it is possible (or meaningful) to try and go beyond the limits of FAS's. It was pointed out that humans tend to use "gut feelings", that may or may not reflect FAS's, and that these intuitions often lead to "logical" errors. At the same time, it was shown that some "intuitions" may not only conflict with what one understands "logically" but be demonstrably "better" in dealing effectively with certain situations. It was also noted that one can't PROVE that there is no "foundational logic". But that there were reasons to suspect humans could do things hard to account for in systems that operate fully under the constraint of rigorous consistency ("intuition", right or wrong in any given case, can demonstrably come up with predictions different from those arrived at "rationally", ie consciously).
Mark provided an interesting concrete example for discussion, adapted from a paper by Tversky and Kahneman (1983). In this case, the issue related to the existence of two different strategies for dealing with observations. One can use a set of observations to develop a complete "story" which one then uses for the purpose of prediction. Alternatively (and with different resulting predictions) one can undertake a "logical" analysis of the pieces of information themselves and their relatedness. It was suggested that each of the two strategies was relatively more advantageous in different contexts and that being able to do both achieved a degree of "completeness" that neither had alone. It was further suggested that "humanities" in general took the approach of trying to create something quite specific and individual from bits of observations, while "social science" regarded individual cases as unrepresentative and so worked in a way that didn't have the same focus on filling out individual sets of observations.
The notion of co-existing (potentially conflicting/inconsistent) "multiple representations" seemed appealing to many and has potentially interesting parallels in linguistics (where "type languages" cross cut semantic distinctions). It is also worth thinking about in relation to computer languages, all of which might be thought of as equivalent activities on different basis sets (raising the question of whether one could overcome the Turing limitations by expanding language dimensionality). Perhaps one can't fully escape FAS's in general, but can perpetually transcend particular ones by revisions of their axiomatic base?
An extended discussion of Bayesian inference and FAS's and their escapability continued after the meeting and is appended to this summary.
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