This "naive reductionism" looks to me like the difference between the way that analysts and algebraists work on problems [1]: "If I have to wave my hands and e

This "naive reductionism" looks to me like the difference between the way that analysts and algebraists work on problems [1]: "If I have to wave my hands and explain it, I would explain it like this. In algebra there are sequences of operations which have proven to be important and effective in one circumstance. Algebraists try to reuse these operations in different contexts in the hopes that what proved effective in one situation will be effective again. By contrast an analyst is likely to form an idiosyncratic mental model of specific problems. Based on that mental model you have intuitions that let you carry out long chains of calculations that are, in principle, obviously going to lead to the right thing. Typically your intuition is correct to within a constant factor, and you're only interested in some sort of limiting behavior so that is fine." How else is a person supposed to intelligently explore the solution space of a problem other than through some kind of "naive reductionism"? [1] http://bentilly.blogspot.com/2010/08/analysis-vs-algebra-predicts-eating.html http://bentilly.blogspot.com/2010/08/analysis-vs-algebra-pre...