Maybe it’s also the topics she covers. I’m not sure why she is getting into fantasies of AGI for example.
I liked the skeptical version of her better.
But this one was pretty good.
This + continued technological development entails that AGI is inevitable.
Just because something is physically possible doesn't make it "inevitable". That's why it's just a fantasy at this point.
> This + continued technological development entails that AGI is inevitable.
Everyone takes the above as a given in any discussion of future projections.
(Less jokingly, nothing strikes me as particularly AI about the comment, not to mention its author addressed the question perfectly adequately. Your comment comes off as a spurious dismissal.)
Giving a short summary of Hilbert's biography & his problem list, does not explain why this particular work is interesting, except in the most superficial sense that its a famous problem.
(For the record, if I had attempted to answer the earlier question, I probably would have laid out a similar narrative. The asker's questions were of a kind asking for the greater context, and the fact that Hilbert (mentioned in the submission title) posed the question is pretty important grounding. But, that's beside the point.)
We detached this comment from https://news.ycombinator.com/item?id=44439647 and marked it off topic.
https://mathstodon.xyz/@johncarlosbaez/114618637031193532
He references a posted comment by Shan Gao[^1] and writes that the problem still seems open, even if this is some good work.
The neat part (assuming that the result is valid) is that precisely the equations of fluid dynamics result from their billiard ball models in the limit of many balls and frequent collisions.
It's just hard to figure out what the functions are for a set of boundary conditions.
F = mx''(t) = mx''(-t) since d/dt x(-t) = -x'(-t), and d/dt (-x'(-t)) = x''(-t)
Navier-Stokes is only time-reversible if you ignore viscosity, because viscosity is velocity-dependent and you can already see signs of that being a problem in the derivation above (velocity pops out a minus sign under time reversal). From my reading the OP managed to derive viscous flow too, so there really is a break in time-symmetry happening somewhere.
I wonder if "t -> -t" is lost in the Boltzmann step or in the hydrodynamic step.
Besides that, I don't think anybody is really arguing that the correlations are actually lost after a collision, just that it's usually a good approximation to treat them as if they are.
Note that the solutions x(t) are not generally time symmetric. We aren't saying that x(t)=x(-t), we are saying that x(t) is a solution to the differential equation if and only if x(-t) is, which is a weaker statement.
It's hard to take full reversibility seriously given Newton's equations are not actually deterministic. If they're not deterministic, then they can't be fully reversible.
Of course maybe these non-deterministic regimes don't actually happen in realistic scenarios (like Norton's Dome), but maybe this is hinting at the fact that we need a better formalism for talking about these questions, and maybe that formalism will not be reversible in a specific, important way.
But I would expect this to eventually reach an equilibrium where you are at "maximum uncertainty" with respect to your coarse graining. Does that sound right at all? And if so, then there must be something else responsible for the global arrow of time, right?
> If you set the collision probability to zero it's time reversible even with molecular chaos
Is this true for boring reasons? If nothing interacts then you just have a bunch of independent particles in free motion, which is obviously time-reversible. And also obviously satisfies molecular chaos because there are no correlations whatsoever. Maybe I misunderstand the terminology.
Chaos isn't even necessary, it just gets you there faster.
The collisionless case is that way for boring reasons: the map aligns with the coarse graining.
[1]: https://en.wikipedia.org/wiki/Liouville%27s_theorem_(Hamilto...
whatshisface•7mo ago
https://arxiv.org/abs/2408.07818
itsthecourier•7mo ago
makk•7mo ago
bravesoul2•7mo ago
killjoywashere•7mo ago
This team seems a bit like Shelby and Miles trying to build a Ford that would win the 24 hours of LeMans. The race isn’t over, but Ken Miles has beat his own lap record in the same race, twice. Might want to tune in for the rest.
bawolff•7mo ago
This is not my field, but i also don't think this would help with computational resources needed for high resolution modelling as you are implying. At least not by itself.
gnubison•7mo ago
Whether or not this is AI, this comment is not true. An axiomatic derivation of a formula doesn’t change how it’s used. We knew the formulas were experimentally correct, it’s just that now mathematicians can rest easy about whether they were theoretically correct. Although it’s interesting, it doesn’t change or create any new applications.
dawnofdusk•7mo ago
1. It answers how macroscopic equations of e.g., fluid dynamics are compatible with Newton's law, when they single out an arrow of time while Newton's laws do not.
2. It was solved in the 1800s if you made an unjustified technical assumption called molecular chaos (https://en.wikipedia.org/wiki/Molecular_chaos). This work is about whether you can rigorously prove that molecular chaos actually does happen.
3. There are no applications outside of potentially other pure math research. For a physics/engineering perspective the whole theory was fine by assuming molecular chaos.
pizza•7mo ago
I would feel remiss not to say: such statements rarely hold
franktankbank•7mo ago
jerf•7mo ago