"I’d like to talk to her, but first I have to cover half the distance between where we are and where she is, then half of the distance that remains, then half of that distance, and so on. The series is infinite. "
I get it’s a joke but that’s a bad joke. That’s a convergent series. It’s not infinite. Any 1st year calculus student would know that.
"it’s that in theory analog carries infinite information. "
But in reality it can’t. The universe isn’t continous, it’s discrete. That’s why we have quantum mechanics. It is the math to handle non contiguous transitions between states.
How much of that fidelity can you lose before it’s not your consciousness?
That can be tested with c elegans. You can measure changes until a difference is propagated.