In my perception Sabine’s quality degraded over the last year or so.
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.
_zoltan_ · 7h ago
I don't know if it's just the persona she plays in these videos, but it's so so so creepy and cringe.
schuyler2d · 10h ago
Agree in general -- I think the tiktok/shorts wave is biasing strongly for shorter video and then the time format kills any followup/2nd iteration-explanation
But this one was pretty good.
jakeinspace · 12h ago
Agreed, she's pumping out too many videos I think. Perhaps she's succumbed a bit to the temptation of cashing in on a reputation, ironically one built on taking down grifters.
naasking · 10h ago
As far as I've seen, her position is only that AGI is pretty much inevitable. What's so fantastical about that?
Alive-in-2025 · 6h ago
I think plenty of people don't think it's inevitable. I'm no ai researcher, just another software engineer (so no real expertise). I think it will keep getting better but the end point is unclear.
naasking · 5h ago
The reason it's inevitable is because because it follows from physics principles. The Bekenstein Bound proves that all physical systems of finite volume contain finite information, humans are a finite volume, ergo a human contains finite information. Finite information can be fully captured by a finite computer, ergo computers can in principle perfectly simulate a human person.
This + continued technological development entails that AGI is inevitable.
baxtr · 4h ago
Although the reasoning is clear, you (and her) jump from "possible in principle" to "inevitable in practice".
Just because something is physically possible doesn't make it "inevitable". That's why it's just a fantasy at this point.
naasking · 1h ago
As I said above:
> This + continued technological development entails that AGI is inevitable.
Everyone takes the above as a given in any discussion of future projections.
Can someone explain what's groundbreaking about this? Maybe it's not done so very rigorously, but pretty much every plasma physics textbook will contain a derivation of Boltzmann equation, including some form of collisional operator, starting from Liouville's theorem[1] and then derive a system of fluid equations [2] by computing the moments of Boltzmann equation.
may you please elaborate on why it is important, why hasn't been solved before and what new applications may you imagine with it, please?
dawnofdusk · 23h ago
The short answers:
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 · 18h ago
> 3. There are no applications outside of potentially other pure math research.
I would feel remiss not to say: such statements rarely hold
jerf · 11h ago
In this case, what the research says is that the approximations we have already been using for a long time are correct. "You're already right, keep doing what you're doing!" is not generally something people consider a "practical application".
franktankbank · 14h ago
That's high praise!
killjoywashere · 23h ago
David Hilbert was one of the greatest mathematicians of all time. Many of the leaders of the Manhattan Project learned the mathematics of physics from him. But he was famous long before then. In 1900 he gave an invited lecture where he listed several outstanding problems in mathematics the solution of any one of which would change not only the career of the person who solved the problem, but possibly life on Earth. Many have stood like mountains in the distance, rising above the clouds, for generations. The sixth problem was an axiomatic derivation of the laws of physics. While the standard model of physics describes the quantum realm and gravity, in theory, the messy soup one step up, fluid dynamics, is far from a solved problem. High resolution simulations of fluid dynamics consume vast amounts of supercomputer time and are critical for problems ranging from turbulence, to weather, nuclear explosions, and the origins of the universe.
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.
gnubison · 7h ago
> the solution of any one of which would change not only the career of the person who solved the problem, but possibly life on Earth. Many have stood like mountains in the distance, rising above the clouds, for generations.
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.
bawolff · 21h ago
This kind of misses the point. The problem isn't interesting because its on hilbert's list; its on hilbert's list because it is interesting.
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.
That video s very light and doesn't explains at what point (or intuitively) where the arrow of time comes in.
LudwigNagasena · 23h ago
So where and how does a jump from nice symmetric reversible equations to turbulent irreversibility happen?
rnhmjoj · 8h ago
This has been known for a long time: the irreversibility comes from the assumption that the velocities of particles colliding are uncorrelated, or equivalently, that particles loose the "memory" of their complete trajectory between one collision and another. It's called the molecular chaos hypothesis.
I've been puzzling about this as well. The best answer I have (as an interested maths geek, not a physicist, caveat lector) is that it sneaks in under the assumption of "molecular chaos", i.e. that interactions of particles are statistically independent of any of their prior interactions. That basically defines an arrow of time right from the get-go, since "prior" is just a choice of direction. It also means that the underlying dynamics is not strictly speaking Newtonian any more (statistically, anyway).
whatshisface · 7h ago
It comes about when the deterministic collision process is integrated over all the indistinguishable initial states that could lead into an equivalence class of indistinguishable final states. If you set the collision probability to zero it's time reversible even with molecular chaos, and if the particles are highly correlated (like in a polymer) there can still arise an arrow of time when the integral is performed.
bubblyworld · 3h ago
Interesting, so if I understand right you are saying that coarse-graining your states can produce an arrow of time on its own? Given some fixed coarse-graining, I can see that entropy would initially increase, since your coarse-graining hides information from you. The longer you evolve the system under this coarse graining the less certain you will be about the micro-states.
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.
MathMonkeyMan · 20h ago
Even three bodies under newtonian gravity can lead to chaotic behavior.
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.
LudwigNagasena · 20h ago
But even millions of bodies under Newtonian gravity lead to reversible behaviour unlike Navier-Stokes.
kgwgk · 14h ago
You lose the reversible behavior when you describe the system ignoring almost every degree of freedom.
MathMonkeyMan · 18h ago
The Navier-Stokes equations are a set of differential equations. The functions that the equations act upon are functions of time (and space), so the system is perfectly reversible.
It's just hard to figure out what the functions are for a set of boundary conditions.
bubblyworld · 16h ago
This is not quite right. Time-reversibility means that solutions to your differential equation are invariant under the transformation x(t) -> x(-t). It's pretty easy to verify that is the case for simple differential equations like Newton's law:
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.
MathMonkeyMan · 15h ago
Now I get it, thanks for the explanation.
I wonder if "t -> -t" is lost in the Boltzmann step or in the hydrodynamic step.
doop · 14h ago
It's lost at Boltzmann's "molecular chaos" or "Stosszahlansatz" step. If f(x1,x2) is the two-particle distribution function giving you (hand-wavingly) the probability that you have particles with position and velocity coordinates x1 and others with coordinates x2, then Boltzmann made the simplification that f(x1,x2) = f(x1) * f(x2), ie throwing away all the correlations between particles. This is where the time-asymmetry comes in: you're saying that after two particles collide, they retain no correlation or memory of what they were doing beforehand.
mannykannot · 13h ago
I assume (on the basis that it has not come up so far in this discussion and my limited further reading) that position-momentum uncertainty offers no justification for throwing away the correlations?
bubblyworld · 13h ago
The systems we're talking about here are classical, not quantum, so the uncertainty principle isn't really relevant. I think the justification is mainly that it makes the analysis tractable. In physical terms it's simply not true that the interactions are uncorrelated, but you might hope that the correlations are "unimportant" in the long-term. In a really hot gas, for instance, everything is moving so fast in random directions that any correlations that start to arise will quickly get obliterated by chance.
doop · 12h ago
I don't think it really helps - you're already working in something like a probabilistic formulation. If you want to use a quantum mechanical justification for it then you need to look at some sort of non-unitary evolution.
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.
kgwgk · 14h ago
The former. Diffusion in gases is similar.
bonvoyage36 · 12h ago
equations can be time-symmetric, or invariant re time reversal. What you're describing is equations being invariant re time reversal.
bubblyworld · 12h ago
You can call this invariance under time reflection if you like, yeah.
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.
bonvoyage36 · 12h ago
I know what you meant; I've just tried to point out an error in your sentence which pops up sometimes, which may have mislead others. It's all about the time reversal invariance of evolution equations, not solutions.
bubblyworld · 12h ago
Oh I see what you mean, it's kinda easy to read my comment as meaning time symmetry. But I do think the phrasing in terms of solutions is correct, provided you interpret it appropriately. As in "is still a solution to the diff eq after transformation" and not "is left unchanged by the transformation".
bonvoyage36 · 11h ago
It's not a good phrasing to express the point, because "solution is invariant under operation O" has an established meaning, that the solution does no change after the operation. What you mean can be properly phrased as "equations are time-reversal invariant".
bubblyworld · 11h ago
You've convinced me =)
naasking · 9h ago
> The Navier-Stokes equations are a set of differential equations. The functions that the equations act upon are functions of time (and space), so the system is perfectly reversible.
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.
bonvoyage36 · 13h ago
Strictly speaking, naturally on its own, it doesn't. Detailed equations remain reversible. Even for very big N, typical isolated classical mechanical systems are reversible. However, typical initial conditions imply transitions to equilibrium, or very long stay in it. The reversed process (ending in Poincare return) will happen eventually, but the time is so incredibly long, it can't be verified.
bonvoyage36 · 12h ago
In derivations of the Navier Stokes equations from reversible particle models, the former get their irreversibility from some approximation, e.g.
a transition to a less detailed state and a simpler evolution equation for it is made. Often the actual microstate is replaced by some probabilistic description, such as probability density, or some kind of implied average.
quantadev · 23h ago
[flagged]
tomhow · 21h ago
Please don't do this here. If a comment seems unfit for HN, please flag it and email us at hn@ycombinator.com so we can have a look.
(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.)
bawolff · 22h ago
To me, it looks like AI because it doesn't really answer the question but instead answers something adjacent, which is common in AI responses.
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.
Twisol · 22h ago
Your second paragraph is a much more thoughtful critique, and posting that below the original answer would focus the subsequent conversation on those points. The issue here isn't whether the comment was AI-generated; it's how we carry the conversation forward even if we suspect that it is.
(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.)
bawolff · 21h ago
To be clear, im not the person who made the original ai accusation. I agree that just yelling its AI, and running away is super rude and not very constructive.
Twisol · 17h ago
I know it wasn't you :) Sorry if I came across that way.
quantadev · 22h ago
I think the last sentence, about Shelby and Miles, was written by a human, because it doesn't fit with the rest at all. Different style and a complete awkward shift of gears non sequitur. He probably recently saw the Amazon movie Ford V Ferrari, and so he threw that in to feel like he was doing more than cut-n-paste from an AI.
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.
[^1]: https://arxiv.org/abs/2504.06297
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.
[1]: https://en.wikipedia.org/wiki/Liouville%27s_theorem_(Hamilto...
[2]: https://en.wikipedia.org/wiki/BBGKY_hierarchy
https://arxiv.org/abs/2408.07818
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.
I would feel remiss not to say: such statements rarely hold
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.
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.
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.
See https://en.wikipedia.org/wiki/Molecular_chaos
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.
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.
We detached this comment from https://news.ycombinator.com/item?id= 44439647 and marked it off topic.
(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.)