Valerii K.

My work happens to consist of two things: writing code and doing math. That means that periodically I produce a very abstract thing, and then observe reality agree with its predictions. While satisfying, it has a common adverse effect of finding oneself in a deep philosophical confusion. An effect so common that there is even a paper about the "Unreasonable Effectiveness of Mathematics." For some reason, noticing this gap is not something I can forget about and unthink back into non-existence. That leads to not-so-productive time spent roughly from 1 to 5 AM on questions even more abstract and philosophical compared to ones I typically work on. Sometimes it even results in something satisfying enough to go to sleep. This post is the example of such a result. Maybe, if you also tend to circle around the philosophical question of why the bits are following the math, and why reality agrees with the bits, you'd find it useful. The question I inadvertently posed to myself last time was about predictive power. There are things which have it, namely: models, physical laws, theories, etc. They have something in common: 1. They obviously predict things. 2. They contain premises/definitions which are pretty abstract and used for derivations. 3. They don't quite "instantiate" the reality (at least to the extent I can see it). The third point in this list is something which made me develop an intellectual itch over the terminology. We have quite an extensive vocabulary around the things which satisfy first and second points. Formal systems. Models. We can describe relationships between them - we call it isomorphism. We have a pretty good idea of what it means to create an instance of something defined by an abstract system. But the theories and laws don't quite instantiate the things they apply to. Those things just exist. The rocks just "happen to have the measurable non-zero property which corresponds to what we define in form