My point is that the laws of physics work just fine in a wide variety of mathematical framings. It's sensible to pick a framing that keeps the complexity of the equations as low as possible, but you're not incorrect if you pick a frame that puts the moon in the center or any other point. The accuracy of the theory's predictions are completely separate from where it applies labels like "center".
> you're not incorrect if you pick a frame that puts the moon in the center or any other point
I think you're conflating different things. Yes, we can predict motion from the view of any point and that would likely involve epicycles. But that's not what people were after. Causality matters, a lot. It's kinda the whole point of physics (and what makes it so expressive and powerful).
What classical relativity does not allow you to do is place yourself at an arbitrary point and call that the center of mass of the system (i.e. things orbit around you). That's not invariant. It's a very different thing than predicting the motion of objects from your vantage point.
100% agreed, but Ptolemy and Copernicus weren't talking about mass or causality, they were just looking for somewhere to put the origin, and making predictions without reference to gravity. Picking an origin such that it happens to align with a barycenter would be in good taste for an audience with our modern understanding of gravity, but picking one elsewhere would not be incorrect so long as the predictions held up.
And that's the part that I'm suggesting AI might be unable to solve. Even if it can effortlessly generate theories that are consistent with both evidence and specification, there's still a lot of thinking to do about which ones we should specify for use in different situations.
Even if a "Theory of Everything" can exist, it may not be suitable for all situations for squishy human reasons besides anything having to do with correctness.
> but Ptolemy and Copernicus weren't talking about mass or causality
Except they were
My critique is that there's a difference between "x is the center" and "motion looks like y when sitting at x".
Those are different claims with very different consequences. You're dismissing this as minutia but that minutia is the critical point. In a geocentric model you need to explain why things revolve around the earth. In a heliocentric model you need to explain why things move around the sun. Predicting the motion of the planets doesn't answer these. But answering these *correctly* allows you to build a generalized model in which you can predict the motion of planets, in any arbitrary system.
I'll also add that I love the geocentric model as a good illustration of why observation alone can't give you causality. There's far more to science than data fitting. In fact, that's why all the mathematicians are getting upset and what Tao has been talking about this whole time
I don't think Copernicus did any explaining why at all. That took another 150 years.
We now bind our physics to our astronomy, but they didn't then. That's what I mean by it being a matter of taste, not of truth.
If you were prompting a godlike LLM for a theory of the heavens in the 1540's you probably wouldn't have used words like "mass" at all, and the theory that it spit out would be similarly absent that concept.
> I don't think Copernicus did any explaining why at all.
He did. I mean even ask yourself, why would he do what he did if he was just concerned with motion? Ptolemy's model was accurate for predicting motion. If it was just about motion, then the viewer's position doesn't matter.
But Copernicus's enables us to say more. It is more elegant (it was not simpler though). Copernicus was seeking realism. He was the person annoyed with how complex a system was while everyone around him was saying "who cares, it works".
> That's what I mean by it being a matter of taste, not of truth.
There is no taste to truth, only taste in how you convey truth
I was taught that Copernicus's work was a more elegant predictive system: these equations work and are nicer than those, without attempting to address causation. Nothing about gravity in there. I guess I'll have to read his work and find out.
As for your second point, it seems we agree. They're orthogonal. Even if a machine can give you one, the other still needs doing.
Note that Copernicus's system still has epicycles. So it was still fairly complicated. More elegant, but still complicated. It also, importantly, gives order to the planets. Distinguishablity matters
