One of the necessary conditions here is that the three objects return to their exact initial position, and so does the centre of mass. Initial conditions with non-zero momentum must trivially be ruled out. But this doesn't stop them from having velocities perpendicular to the initial plane that cancel out perfectly, so this doesn't refute the assertion that the planes keep changing.
They presumably meant non-zero total momentum. If the total momentum were non-zero, then the center of mass will be moving in a straight line, and will not return to where it began, and therefore the orbit would not be periodic.
Big picture the center of mass momentum is concerned and it does not matter if the system as a whole is moving up or down or to the right or the left. Like the Earth is basically orbiting the sun in an ellipse [1] so far as the sun is concerned and from the viewpoint of the solar system not care so much that it is moving around the galaxy unless we are interested that orbit being perturbed by other stars that we pass near over millions and milions of years.
[1] ignoring the parameters of that ellipse changing slightly and slowly thanks to the other planets
Oh sorry, yeah - I wasn't fully awake yet when I wrote it. As a sibling comment mentioned, I was talking about the total momentum. Anyway, it was in response to GP's assertion that GGP may be correct if "we're centered on the CG", which doesn't make sense because the CG can't move.
IMO this isn't necessarily bad (it's one way to get data), but the numbers are meaningless without a control. Unfortunately, I think we missed that bus by ~20 years. Had the same study been conducted every few years over the last two decades, I think it would have been valuable. Maybe it is still valuable to do this once every few years? (I think that everyone in 2026 is maximally addicted to mobile phones, but maybe I'm wrong and it can get worse).
Just as more successful machine learning fields distanced themselves from the term during the AI winter, I suppose we will (and perhaps are?) be seeing them adopt it again, now that we are in an "AI summer".
As always, it's a matter of funding. Both inside academia and outside of it. I remember when nanotechnology was all the rage. Everyone flocked to writing grant proposals about their "nano" technology that was thousands or millons of nanometers, aka micrometers or even millimeters. Stupid but if it works it's not stupid. The old joke is what do you call AI that works? Machine Learning.
The real question is how much compute do you need. With LLMs getting popular, so is compute. That's the real win for non-LLM technologies. The sheer availability of GPU capacity. Yes, it's expensive, but time in a GB300 supercomputer isn't even possible if they don't exist.
Alexnet succeeded for many reasons but a big reason is that computers got good enough to apply those algorithms and techniques in practice. Outside of LLMs, what new AI/ML systems await us in the future? The LLM bubble popping, if it ever does, is going to leave us with supercomputer capacity going unused and available for cheap, meaning experiments that were once infeasibly expensive become practical. I can't afford $10 million to run a weather simulation, but at $1,000 for the same amount of compute, a lot more experimentation becomes practical.
Not a biologist but IIRC, male ants develop from unfertilized eggs (and are 'haploid'), and the sperm has no role in the production of male ants. Any fertilized egg produces a female ant. This would proably mean that the queen has means to produce two kinds of eggs, which is quite interesting.
This is likely just Journalism, but the title (that of the original article) is slightly misleading. This appears to be a programming language for modelling soft materials... although I am not sure (having looked only at the Github repo and RTD) I understand what kind of research this targets... the roadmap and API makes it seem fairly general purpose - IMO it would be nice to see some (atleast potential) usecases directly in the repository.
Definitely not. (He may do that, I just hadn't ever heard of that book before today.) I think it was one of Isaacs, Herstein, or Artin, but I'm a bit too lazy to dig through my old books at the moment.
> Definitely not. (He may do that, I just hadn't ever heard of that book before today.) I think it was one of Isaacs, Herstein, or Artin, but I'm a bit too lazy to dig through my old books at the moment.
"I left it at home" is common, but doesn't have the exact same meaning. Tbh, I don't think there really is a way to say that succinctly in British English—we would probably say "I left it at home", "I forgot to bring it", or—if the full meaning is strictly necessary—"I forgot it, it's at home".
Really, "I forgot it at home" is short for "I forgot to bring it; I left it at home".
If they aren't distinct, you wouldn't have 4 clean buttons, but just 3 - in which case we also know the repeating digit repeats exactly once and we get 12x3 (36) possible combinations. With two clean buttons, it's 6 (if both repeat) + 4 (if only one repeats) = 10 and if there's 1 that's just one, and a terrible password.
