Re: K.W. Regan • The Graph Of Math
Re: Artem Kaznatcheev • Three Types Of Mathematical Models
What — if anything — is the common sense that connects the different senses of the word model, as it has been used over the years in logic, mathematics, and the special sciences? It’s a problem I’ve been running into for several decades now and I think I can trace the roots of it going back as far as Aristotle’s treatment of analogy. Just by way of creating a bit of trans-disciple-ary interaction, here’s a link to a link of the issue’s most recent arising in my own roll of blogs.
How far can we reverse engineer or devolve the idea of a physical model? Molecules like DNA and much simpler chemicals act as models that store information in various ways. One method, though probably not the most basic, is shape matching or fitting. Anything that has a non-random association with any other thing becomes a model of some kind of relation. The association seems like the most fundamental unit (for our purposes anyway) of any model. To understand what an association is maybe we can look at the simplest associations in nature. It seems to me that they always involve some type of what we call “force” and most often also some type of “fit.” Higher orders of model encode/embody more complex relations.
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