Is Mathematics the Operating System of Reality?

The differences between mathematics, physics, and logic.

The difference between true mathematics and speculative mathematics.

Mathematics is a language, and like natural language, it can encode real patterns that describe reality. However, also just like natural language, mathematics also contains a bunch of speculative, paradoxical bullshit. I am deeply suspicious of all mathematical “models” of the world that try to predict behavior (i.e. mathematical physics); they can be useful, but it’s ultrahubris to think we’ve discovered any final laws of physics. All of them, in my mind, are up for grabs -- literally all of them, including conservation laws, etc.

Logic on the other hand is, in some sense, part of the operating system of reality, but that’s saying less than it might initially seem. That just means “the system is however it is; it operates however it operates” which isn’t even a “constraint” per se, because it couldn’t even be otherwise -- unlike any law of physics, which we can imagine revising without contradiction.

The true parts of mathematics are built on logic, as an extension of logic -- so arithmetic can be understood as the logic of quantity. 2 + 2 = 4 is going to be true always and forever, but it’s not really a “model” of the world; it’s just a true way of describing a quantitative relation. Since reality contains multiplicity (i.e. there is more than one thing), arithmetic can tell us some true aspects of reality.

I’ve been saying for many years that we’ve been living in a dark age since at least the early 20th century -- lots of people seem to resonate with that idea. But then I’ve also been saying: and the philosophy of mathematics is the domain in most need of revision, and people are much less excited about that. [Bob] is one of the few people I’ve spoken with who seems to have read and thought enough about this subject to see why that’s a plausible position, because we really went through massive revolutions at the foundations of our thought between ~1870-1945.

In discovering wonderful and important things about math and its relation to the universe (e.g. Euclidean geometry is not necessarily true), we wound up throwing out the baby with the bathwater -- that is, logic.