| There are an uncountable number of atoms in the universe. There are nondeterministic occurrences in many natural processes. Even if the universe is a simulation, that doesn’t mean that it’s able to be represented or formalized from within the simulation. Math is possibly one of the best tools of the scientific method to make logical sense of the universe, but that doesn’t mean that we can compute any given thing due to the scales involved. Gödel was likely familiar with the unknowable nature of the universe given certain hard limits of calculation, computation, and measurement. Physics is the tool we use to move the world, yet we may never be able to build a lever or fulcrum long enough to actually do so - physics and math only give us a place to stand and means to orient ourselves. Everything else is engineering, I’d say. > Give me a place to stand and with a lever I will move the whole world. https://en.wikiquote.org/wiki/Archimedes I would like to hear your thoughts, however. I think you’re right in a sense, that physics and math are possibly inseparable syntactically, similar to the identity property. If a thing is what it does, physics is math as much as it is logic, or vice versa. Like math, logic is what we understand it to be, regardless of correspondence to reality. Physics rather seeks to represent and model more than the abstract truths of math and logic, and physics has an element of necessary utility and correspondence to hypothetical or actually existing realities, possibilities, and observable phenomena, whereas math and logic are not burdened by testability, but are rather proven or disproven via internal consistency and formalisms. Like many tools, their proper usage comes down to holding them correctly, both in hand and in mind. |