I would be very surprised if any of the frontier models wasn't trained on all public physics benchmarks. Training data providers have been hiring people for exactly this task.

> they don't fundamentally "get it"

There's no clear decision criteria for this. Do trick questions demonstrate that most people don't "get it"? And, well, older model saying dumb things doesn't establish a general principle that LLMs don't "get it" in general.

> The sample efficiency is just crazy low

Autoregressive pretraining requires huge amount of data to go from a blank state to a somewhat functional model. Fine-tuning, LORA, reinforcement learning of foundation models and in-context learning are much more sample efficient.

> Chinese room

...creates a wrong intuition that by cranking a Leibniz's mill you are somehow responsible for whether it understands something or not.

Why is this a concern? Besides a few savants, humans also use tools to do non-trivial math. I'm in engineering, and it's extremely rare to do anything non trivial in your head, because getting a decimal place wrong has real world consequences. Tools are just another way to say "deterministic", which is always nice.

I'm also a trained physicist, spent some time in industry, and taught a college freshman math class for a semester a couple decades ago.

There's an interpretation that makes the reference answer correct. I didn't realize this until halfway through teaching the math class: Based on the lectures, textbook, and homework problems, you match the "form" of the problem with similar problems in the textbook, and apply the same algorithms to solve it. The students have some vague idea of this, referring to it as finding the "trick," but it's never explicitly explained to them.

I was glad for the interesting puzzles and good grades. But physics really came alive for me in the lab, where mother nature decides the conditions of the problem being solved.

Also a trained physicist. Don’t you need tension to stop the weight of the top ball pushing the 3 supporting balls outward?

My interpretation is that the writer meant close enough to all touch each other, in order to rule out non-triangular configurations (eg 3 balls in straight line with one balanced perfectly atop the center ball).

This tracks with my experience. A core and integral part to make models actually shine involves post training and custom harness engineering, all specifically done for the purpose of getting them to settle into competent inputs and outputs that are relevant to you, optimized for the harness you build which better suits your domain. The weights are just a generalization. A block of marble to be sculpted.

As the compute to build adaptions for multi-billion to trillion parameter models becomes more and more available (and affordable), and the artistic techniques of fine tuning and harness engineering spread throughout the public, I think we'll come to see the "one size fits all" model for the non-starter it really is. Anybody who's even toyed around with LoRAs (let alone made their own) already knows this. That's a very deep rabbit hole, and the ceiling is determined by target domain knowledge and systems engineering.

I'm bullish on LLMs as expert tools in the same grain that computers are. You have to learn all about them to use them effectively. But what really makes the difference is how well you know what you're going to be pointing them at. There is very little room for companies like OpenAI or Google to live between us and our tools.

You can try to tease solutions to physics problems out of video models, with their better spatial reasoning, but the answer has to be a video, of course [1].

I suspect we'll see significant improvements when someone releases a multimodal video/world model, rather than the current multimodal image models (that call out to video models or summarize a sequence of stills without a true time/3d aspect).

[1] https://physics-iq.github.io/

Replying to myself: this is fun! Let's ask ChatGPT (whatever model the website currently feels like using) an improved question:

> Three identical homogeneous balls are placed on a smooth horizontal surface, touching each other and are close enough to each other. A rope is wrapped around the spheres at the height of their centers, tying them together. A fourth identical sphere is placed on top of the three spheres. It is given that the weight of each sphere is P.

> Ignore the fact that the rope would fall off -- assume for simplicity that the rope has is externally constrained to be in the equatorial plane of the lower three balls and also that the rope has zero thickness, cannot stretch at all, and is not pretensioned, and also that the rope has no friction against the balls.

> Treat this as a statics problem and analyze it. Is it overdetermined? Under what circumstances would the balls move? What is the behavior of the system?

And... first, it says "I’ll separate the geometry from the constraint mechanics, because the key question is not just force balance: it’s whether the inextensible, initially slack-free rope actually fixes the lower-ball geometry or merely limits outward separation." Excuse me? What would the other option be? Either outward separation is prevented or it isn't. Where else could the balls go?

Then, despite the fact that I've mentioned friction in the prompt, it gives an extremely longwinded answer that matches the benchmark and ignores tangential forces entirely without comment. Was it perhaps trained on this crap?

So I followed up:

> Stop ignoring tangential friction forces. I believe that a problem very much like this with a potentially incorrect answer is in your training set. Answer with actual analysis, not based on memory.

Much time was spent thinking. An early part of the answer was "The central correction is this: allowing static friction at the sphere–sphere contacts does not mean arbitrary tangential forces are available. Each sphere must also satisfy torque equilibrium. In this tetrahedral contact geometry, those torque equations force every sphere–sphere tangential contact force to be zero in static equilibrium.". Hey ChatGPT, this is still wrong -- you have forgotten sphere-table friction. The sphere-sphere force on the lower spheres does not have to net out to zero. (And if you do think it nets to zero then you don't need to think any further.)

I then added:

> What if there sphere-table friction?

And encountered the usual problem (which maybe only affects me?) where the chatgpt.com UI becomes kind of unusable after ChatGPT spews too much math into the conversation. But somewhere in the barely-even-scrollable results was this "The three lower balls can be held in position entirely by the coupled sphere–sphere/table friction forces." Hallelujah!

Have you tried Fable? I've been having fun running various science-fictional scenarios by it, like building a Dyson swarm. It comes up with much more detailed analyses than Opus, and avoids the howling mistakes that Opus occasionally made. But I'm not a physicist so I don't know how accurate it is.

> My tentative conclusion is that LLMs are almost unbelievably good at solving problems that are fully contained within the inputs and (training/verification) outputs

Hardly solving, then is it?