chaostaco

I spent ages staring at Milkdrop in the Winamp days. Thanks for the links.

I believe a core element of the smoothness problem solution is that it does blow up in finite time, even with viscosity.

Perhaps an expert could provide a more accurate response, but here is how ChatGPT tried to explain it to me: "In this construction, the viscous term becomes large along with the acceleration, pressure-gradient, and nonlinear momentum-transfer terms, but they balance/cancel in a very precise way. That allows the velocity in the concentrating vortex core to grow without bound even though ν is nonzero."

I'm no expert in this field, but my understanding is that it would occur in the concentrating vortex core. The orange part would become narrower and narrower (the OpenAI article says "like spaghetti"), and the velocity in that concentrating region would grow without bound as the finite blowup time is approached. The rendered flow never literally shows "infinity" because every snapshot before the blowup time is still finite.

I was making a web project about some of my 1996 era 386 graphics code when I saw the visualizations related to the recent solution to the smoothness problem of Navier-Stokes and thought "that would look cool as a 90s-era demo". So here you go, a palette cycler and a particle animation, both using the real equations and both as sub-1kB binaries, rendered online via js-dos/DOSBox as well as JavaScript ports with knobs to go far beyond 386 quality. All source and pre-compiled 386 binaries included and free in every way.

And since I know this is divisive on HN, I should be up front that this effort was AI-assisted, but hey, so was OpenAI's solution of the Millennium problem that inspired my effort.

You already hit the important part with "as long as the premises are logical". Since the premises here are flawed, the proof falls apart. It isn't a flaw in formalized proofs. Getting flawless premises is the challenge for trying to use this for philosophical proof - the concepts are typically not as well defined as, say, what you see in geometry class.

It is fun to see these historical arguments formalized like this, but they should remember to mention how flawed these arguments have proven to be over time.

P3 has the same flaw as Zeno's paradoxes, where there is a false assumption that the sum of infinite things must itself be infinite. If this were true, calculus class would be much easier, as all of those infinite sums would have the same answer. Since we know that the sum of an infinity achieved by infinite division of a finite is a finite itself, we are unable to tell whether it would take infinite or finite power to move these infinite things.

P1 fails to account for the possibility of multiple gods or gods other than the one this proof is presumably about. No evidence is provided for the claims of incorporeality or infinite power, either, without which the proof could well be proving that something more powerful than god exists, but not necessarily that god does.

The entire proof, flaws aside, only endeavors to prove that something god-like once existed, but not that it still exists or has any relation to what people historically have called god.