Three types of mathematical models

Whenever asked to label myself, I am overcome by existential dread: what am I? A mathematician? A computer scientist? A modeler? A crazy man with a blog? Each has its own connotations and describes aspects of my approach to thought, but none (except maybe the last) represents my mindset accurately. I have experienced mathematical modeling in three very different setting during my research and education: theoretical computer science, physics, and modeling in social and biological sciences. In the process, I’ve concluded that there are at least three fundamentally different kinds of modeling, and three different levels of presenting them. This is probably not exhaustive, but I have searched for some time and could not find extensions, maybe you can suggest some. Since this post is motivated by names, let’s name the three types of models as abstractions, heuristics, and insilications and the three presentations as analytic, algorithmic, and computational.
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