in highschool for ib, we have to take this weird epistemology course on how the different subjects relate to each other, and i found myself pondering about the topic again.
math is built with logic, a system of constructs achieved by a series of logical equivalencies. elegance may exist within mathematics but creativy resides elsewhere. the idea that mathematics was superior to science came upon me. science is logical, but also arbitrararily defined by laws of nature. science is fitting math equations to natural phenomena. scientific equations are equating natural constants with others i.e. the ideal gas law. PV=nRT, the relationship between these values is pre-determined, the equation is merely a restatement of that. Goops makes a good point by saying that this is the world which we live in so it’s only really necessary to learn these laws. Jim makes another point which is math needs physics to develop. It is possible to develop new branches of mathematics completely independently but there isn’t a motivation for it unless it’s to explain some physics.
there’s two important results to demonstrate at this point:
the limitations of logic: godel’s incompleteness theorem and Münchhausen Trilemma
and the idea that it is possible to have universes with other physical laws
this is part of my journey to decide what i want to study more.
but something which i came upon today on a feynman video was the idea that we shouldn’t try to find the one mystic simple elegant answer to explain the world. but we shouldn’t be afraid and just try to find out more about the world.