☞ Theme One • A Program Of Inquiry

The program integrated a sequential learning module and a propositional reasoning module that I thought of as *The Empiricist* and *The Rationalist*, respectively.

The learning module was influenced by ideas from the psychologists Thorndike and Guthrie and the statisticians Fisher and Tukey, the reasoning module made use of ideas about logical graphs from C.S. Peirce. There is a kind of phase transition as we pass from finite state adaptation covered by the learning module to context-free hypothesis generation covered by the reasoning module, but it happens that some aspects of the latter are already anticipated in the former.

]]>The interesting thing, that I’ve discussed with other mathematicians, is the existence of various subcultures within mathematics even beyond the pure/applied divisions. In fact it is often pure mathematicians which might appreciate what mathematical biologists do while some applied mathematicians think we don’t prove enough ‘quantitative theorems’ about things like convergence rates etc.

All types are necessary I think. Biology is often so messy that choosing the right (abstract!) ‘Test statistic’ is crucial and helps set the level of abstraction.

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