Quantum Biology and the Puzzle of Coherence

[Joseph8th]

49. Not sure why I'm bothering, but...

... interesting synopsis that doesn't advance any position that I can discern, as it is full of contradictory positions. I'm aware of these debates, but again assert that they are completely secondary and only interesting from a philosophy of science POV. Naturally, they're quite interesting to mathematicians, who regularly deal with both the unimaginable and the physically impossible. (Just try visualizing an N-dimensional sphere.) But physicists are constrained by additional considerations that are uninteresting to most mathematicians. Things like the boring ole laws of physics. I mean, really. I have no desire to whip out some maths so astronauts can poo in space. Often, we don't even understand each other's notation on the same exact subject (just look in Lie groups by math ppl vs. physicists). And, of course, there is a famous historical animosity between pure and applied math, even within the single department.

For math, Godel's thm is great because it's job security. We'll always have interesting problems to work on.

But only a tiny percentage of those will be found to be useful in the sense that they somehow model behavior of observables. For instance, string-theory asserts that nature has a minimum size -- that means that if we want to apply that model, we can no longer assume (as we normally do in the analysis underlying almost all physics) the Archimedean Principle holds in nature. That's pretty big, and that's why string theory math is hairy. If you start shrinking down to Planck scale, you will just start getting bigger, again. That's completely unintuitive when we're used to assuming that we can always find another point between any two points. So here's an example of a really really fundamental mathematical principle that physicists assume all the time, but which physicists cavalierly tossed aside to even begin to reconcile QM and relativity at the Planck scale.

So insofar as Godel's says there's an infinite pools of math problems (of a certain sort), then yeah, there's plenty of maths for physicists to exploit. Doesn't mean any of it accurately models nature.