Approximating spatial structure with the Ohtsuki-Nowak transform

Can we describe reality? As a general philosophical question, I could spend all day discussing it and never arrive at a reasonable answer. However, if we restrict to the sort of models used in theoretical biology, especially to the heuristic models that dominate the field, then I think it is relatively reasonable to conclude that no, we cannot describe reality. We have to admit our current limits and rely on thinking of our errors in the dual notions of assumptions or approximations. I usually prefer the former and try to describe models in terms of the assumptions that if met would make them perfect (or at least good) descriptions. This view has seemed clearer and more elegant than vague talk of approximations. It is the language I used to describe the Ohtsuki-Nowak (2006) transform over a year ago. In the months since, however, I’ve started to realize that the assumptions-view is actually incompatible with much of my philosophy of modeling. To contrast my previous exposition (and to help me write up some reviewer responses), I want to go through a justification of the ON-transform as a first-order approximation of spatial structure.
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