Can you please stop posting unsubstantive comments and definitely please not post in the flamewar style to HN? You've done that a lot in this thread and it's not what this site is for.
You could define the Big Bang to be at any value of t, i.e., pick t0 > 0. Such a shift changes nothing and won’t fix any singularities in the dynamics.
You, by definition, cannot. Our best science suggests that `t` ceases to be a linear value at t=0. It's why we define t=0 to be there.
The problem is the absurdity of the idea that `t` could ever cease to be a linear value. Causality is a fundamental truth. To lose the idea of "before" and "after" is to lose causality.
If your fundamental theorem of the universe requires you to forego causality, you should consider looking elsewhere.
Fair. I misstated my premise. "Find the math that allows zero to be treated like any other number, or, find the math that treats it like it's definitely the wrong answer."
Consistency is the key. What we have now is only locally consistent. You can break it into pieces with set theory, geometry, etc. You're never going to find a unifying equation in a version of mathematics where geometry and algebra don't mesh.
No, those are fine. Well, almost. They're not uniquely broken, at least.
Mathematics would have me believe "the sum of all positive integers" is a negative number. They can provide glorious proofs of that fact. When you insert the result into the physics equations, the equations work.
But the idea is, on its face, stupid. Any child would tell you as much. The equations only "work" on that premise because they're almost right.
But that's not a problem with infinity, it's a problem with something we're assuming when we go to write the proof in the first place. And whatever that problem is... it's almost certainly the thing stopping us from solving the Riemann hypothesis.
Goedel, Russell, and Frege proved from first principals that our understanding of basic arithmetic cannot be both complete and consistent. One or the other, but not both.
If children's arithmetic cannot be proven complete and consistent, what does that say about the sort of math used to define the universe?
Building upon a broken structure is how you get broken results.
