[s-shellfish]

I haven't done all the math for this (I've deeply investigated the pattern for 2x+1) but it seems like this would be an obvious and intuitive result of primes. You are still generating primes from primes. Yes, you find more primes, but the computation is still dependent on primes. I'm still of the opinion that there is no complete pattern to the primes.

I'm assuming the researchers do not have the intent of confusing a crystal lattice structure with an actual mathematical lattice, because while they possibly may share similar influences in their models, one is math, the other is physics.

#keepmathpure

[calibas]

I've heard this sentiment before and I don't really understand it. There's no separating physics and math. Keeping math "pure" really means keeping it "purely abstract", so it resists any kind of practical application.

[throwawaymath]

> There's no separating physics and math.

There is. Even though most physics research is extremely mathematical and abstract these days, it's still ostensibly grounded in empirical science. Math is not science, it just provides useful tools and insights for studying science. Unlike physics, the disciplinary imperative of math is not to provide us with truths about this world or any other world. Its imperative is to tell us what must follow as a consequence from a given set of assumptions and definitions. This is a very important philosophical dichotomy because it means that even the most lackadaisical, abstract problems in physics (such as moonshine in high energy physics) are still grounded in something "real." Math need not be grounded to anything real; it can be decoupled from what is real or even possible entirely.

> Keeping math "pure" really means keeping it "purely abstract", so it resists any kind of practical application.

I'm not one to be elitist with regards to pure versus abstract mathematics so I sympathize with your point here. That being said, purely abstract mathematics can be extremely useful even if it doesn't ultimately relate to the real world. Consider what G.H. Hardy wrote nearly a century ago in A Mathematician's Apology:

"...both Gauss and lesser mathematicians may be justified in rejoicing that there is [number theory] at any rate...whose very remoteness from ordinary human activities should keep it gentle and clean."

If only Hardy had lived long enough to see his pure and beautiful number theory sullied with the applications to error-correcting codes and cryptography.

[calibas]

While I certainly understand that math and physics are separate concepts, physics as we know it wouldn't be possible without math. I'm sure in your mind you can separate them, but if you took math away from physics, we wouldn't have modern physics.

Math is how physics is given practical application, if anything, that means science is more abstract than math is.

[s-shellfish]

It's about direction of influence.

Physics should not influence math. Math has to be a consequence of it's own axioms, or have it's properties tested against it's own constructions.

Otherwise math falls apart. Then it's useless for physics.

Practical application is wonderful for math. But the direction math is crafted and interpreted matters a lot.

[s-shellfish]

I don't agree with this. And honestly, I really think that depends on what foundation you rely on to think with, work with, create with, test with, and check your own tests with. Physics does not have to use itself to understand itself. Math does.

[Numer]

> Physics does not have to use itself to understand itself.

Could you explain what you mean by that?

[s-shellfish]

It's simple. Physics uses mathematics to construct equations that describe properties of physics.

The difference is physics has reality to test against - observations that can be measured. Math does not have this. Math's only metric against itself is itself.