If anyone has meta-advice for me, I'm open to it.
Well, this website was actually created around a long sequence of posts trying to teach people how to think more clearly and avoid making precisely this kind of mistakes.
Consider modular arithmetic with modulo 1. It is true that 0+0=0, 1+1=1, and indeed 0=1. What is this describing? A theory of complete nothingness.
I'm working on something on these lines, there is much more structure that one would expect at first. Feel free to reach out privately.
There is a tendency of people to bring QM into everything they find fuzzy and mysterious. Best avoid it. QM is unitary evolution of a vector in a Hilbert space, basically linear algebra with complex numbers.
I think that 0 = 1 hints towards a unifying theory for epistemology, math, consciousness, states of enlightenment, and physics.
BS detector overloaded... There is some mathematical structure in that modulo 1 arithmetic, as the other comment says, but far from the answer to everything. That would be mod 42.
Of course, 0 is not equal to 1. But certain interpretations of quantum mechanics imply that a thing can be one way and be the opposite way at the same time. Any mathematical proof rests on axioms. What I'm looking for is a proof that 0 = 1 which rests on axioms that are being actively debated by mathematicians. (Then, I'll argue that the truth of 0 = 1 is in a quantum superposition with the debates being held by mathematicians.) Feel free to create your own proof, or to direct me to existing works. I may quote your answers in a soon-to-be-published post on this topic.
This doesn't feel frivolous to me; I think that 0 = 1 hints towards a unifying theory for epistemology, math, consciousness, states of enlightenment, and physics. It also has implications for AI. If anyone has meta-advice for me, I'm open to it. I think the benefits balance the negatives of sharing these ideas, especially for ensuring that they're debated more widely and openly. But I could be wrong. (There are keywords I'm not using to be careful.)