Just don't believe at all the shitty marketing that AI companies are creating to make you believe that they have found the Holy Grail
It's quite a good method for approximating any arbitrary smooth periodic function.
My best guess is that the originators of this model (perhaps as early as Hipparchus, but at any rate someone by the time of Ptolemy) didn't think there were literally circles being combined, but had a pretty clear idea that they were trying to make an approximate model to fit the data. A previous model, from Eudoxus, was also probably pretty accurate but more cumbersome to compute with, involving approximation of the visible planetary motion by the combination of uniform rotations of some imagined sphere(s) centered on the earth. (We don't know exactly because the books about it don't survive, so all we have are vague descriptions by other people.)
Any number of things can serve as a basic vocabulary to postulate entities, and do so in a textured way that matches some parts of underlying physical reality.
It's tempting to look at this and make the tragic jump into anti-realism because of the interchangeability of so many forms of representation. But I think as long as you have a combination of pragmatic attitude, treat knowledge claims as provisional and converging on truth, there's a cash value to descriptions that makes them legitimately truth tracking regardless of how they're formed.
I think you might be underestimating how transformative an "advance search function" could be. If the search engine knows how to design and carry out experiments in order to synthesize new evidence that allows it to ensure that the answers it provides are well supported, then humans are essentially out of the "truth" part of science, leaving them only to advice on the "beauty" parts, which might be ok, but it's a pretty big shift.
It's possible to come up with an "unnecessarily complex model" for why someone accused of a crime did the crime, but that has completely no bearing on whether the defendant is actually guilty. If the defendant is, in fact, innocent, then the prosecution's model is, in fact, untrue - no matter how well it fits the evidence.
Are you proposing that an explanation can be true even though there's a different explanation which better fits the evidence?
Or are we talking about cases where both candidate explanations fit the evidence equally, and you have access to some kind of intuition which tells you which of the two are true?
Such a proposition would be correct; compare the concept (and name!) of "overfitting" in statistics.
That’s another way of saying it’s untrue.
> Judge a model based on its accuracy, not its point of reference.
Something can be both accurate and wrong, in the manner of a model that pinpoints the cause of death from cancer as admission to a cancer ward.
Are you sure there will always be just one simplest theory? Or are you using some other criteria to pick it?
There's a basic principle called Ockham's Razor that I'm sure you're aware of, which proposes that the simplest theory is the most likely candidate, but that's a heuristic, not a rule.
Another relevant concept here is that the map is not the territory. All theories are attempts to express some kind of underlying truth via some sort of formal system. Some of those theories map much more closely to the truth than others, in a way that's independent of accurately predicting observed behavior to date.
All you have is the different theories, so there's no definitive way to assess their closeness to truth other than by their predictive accuracy. If you don't have the physical capacity to leave the room and observe the world, all you've got is the maps themselves and how well they predict travel times and features found along the way.
The only tool you have is the inductive strength of a big pile of observations in which correlations emerge. You can do experiments to prune certain causal stories, but there's never time to eliminate all possible stories. You end up with something that makes sense for you, in terms of the equipment that you have, and the theories that you and your peers use, and it's good enough, so we move forward with it.
I can see how it might be useful to document a particular explanation as "the" explanation, especially if you're communicating why a drug works because it will lead to useful conclusions about who should or shouldn't take the drug.
But when it comes to speculation about whether a given astronomical body will be visible at a particular time, I think science would have progressed much more quickly if we had not held so tightly to the notion that one explanation is intrinsically correct, and we're probably holding ourselves back now in other domains by doing the same.
there is no "actual truth" - there is only what you can measure reliably
Either state your argument coherently so as to address my completely valid objection, or move on if you're not interested in having a discussion.
Arguing by sending bare links to wiki articles isn't productive and doesn't make you look particularly good.
Would you say the continuum hypothesis (or its negation) is "actual truth"? Or does the "actual truth" become something closer to "actually, there are models of ZFC where CH holds as well as models where it doesn't hold, or maybe ZFC is already inconsistent; we don't really know, nor can we."?
Similarly, on the subject of astronomical reference frames, I'd argue the "actual truth" is closer to this:
> Any reference frame that locally obeys Newton's law of inertia is equally valid. Some are more useful than others depending on the problem you are studying. The notion of an "absolute center" is purely semantic, and a meaningless human construct, until one places bounds on the system under study, wherein the center of mass becomes the most reasonable choice at sub-cosmological scales.
If I say "there are countries with an access to a sea, and there are also countries without an access to a sea" does it mean that there is no truth about whether seas exist or not?
a reasonable person would at least peruse the literature before making such strong claims as
> Either state your argument coherently so as to address my completely valid objection, or move on if you're not interested in having a discussion.
i'm not interested in educating you on thousands (literally dating back to plato) of years of scholarship/philosophical discourse on the topic of epistemology. that's not my responsibility because you are not paying me for this - typically people charge large amounts of money for this kind of work (uni professors are well compensated).
lucky for you others have done lots of work making this information available to you for the low low price of "reading". that's why i provided the link.
Like I said in a different thread: thousands of years from now, it might literally not be possible to prove that you ever existed, but that wouldn't change the "actual truth" - the fact that you did exist, and do things. Stuff happens outside of your person, in the real world, without regard for our ability to perceive/articulate/"know" it. It's only possible to say things like "actual truth doesn't exist" if you think your mind is the only thing that really exists.
> i'm not interested in educating you on thousands (literally dating back to plato) of years of scholarship/philosophical discourse on the topic of epistemology.
Cool. Then don't start a discussion with me.
My man forget thousands of years in the future you don't know whether I exist today lololol
> Cool. Then don't start a discussion with m
I didn't? I told you were wrong and that's it (and then you got pissy). I know that's what happened because each of ours responses are recorded on this indelible/irrefutable medium lololol
Predictive power on the other hand, gives you a framework to decide which story is more useful.
I think that sort of proves the point that the OP was making, which is that you can create a functional model around any arbitrary location and it can be valid (as long as valid means: it can make useful predictions). When you put the center of the Sun at the center of the model, you still need your models to account for the "orbital wobble" happening as a result of the Sun doing a little dance with Jupiter (and all the other masses that orbit it) in the equations for the determining the relative positions of the Sun and Earth.
Using the Sun as the center versus the solar systems barycenter are both somewhat "arbitrary" in that way, and depend on what you're trying to do with the information - how accurate you need it to be, and how complicated you're willing to make the calculations to hit higher accuracies.
Sure, it depends on what you're trying to do. Fit an equation or understand it. Yes, you can use a reduced mass to simplify the equations and make it more accurate, which usually isn't necessary when the new center is at less than 1% of the radius of the Sun (note ellipses have 2 foci from Kepler/Newton). Even Jupiter's center of rotation is at the surface of the Sun, and both have eccentricities <1%.
Of course, if you're using epicycles, you're never going to get Einstein's elliptical precession correction to the orbit of Mercury. Simpler, is usually better for models, even when you need greater and greater accuracy, overfitting is the enemy of explanation (to coin a phrase).
All models are wrong, some are useful. - Box
Dealing with people wanting to do this is story of my current professional life lol I would love to get them onto the same page that chasing down a final <1% improvement isn't (always) worth it
"All models are wrong, some are useful" - this is what I was trying to say, I was just being a bit snarky/pedantic because the commenter above seemed to be trying to pull a "gotcha" saying that the "truth" of something overrides the utility of it.
> you're not incorrect if you pick a frame that puts the moon in the center or any other point
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.
And that's the part that I'm suggesting AI might be unable to solve. Even if it can generate consistent explanations effortlessly, there's still a lot of thinking to do about which one is right for humans to use in which situations.
> but Ptolemy and Copernicus weren't talking about mass or causality
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
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.
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.
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.
While you're technically correct, everyone already understood
Put differently, would you say a heliocentric reference frame is also "wrong" since the sun is actually orbiting around Sagittarius A*?
Taking your argument to its logical conclusion, one would conclude that the [comoving reference frane](https://en.wikipedia.org/wiki/Comoving_and_proper_distances) is the only "true" one. And at last there is real validity to this claim, since the CMB does pick out a preferred velocity at each point in spacetime. But it is pretty impractical to use comoving coordinates to study problems outside of cosmology.
Ultimately, it stops being a matter of "right" or "wrong" but rather one of picking the right tool for the job you're working on.
And yes, of course some reference frames make calculations easier for certain areas of study. See my last sentence in the comment you replied to. But that doesn't make one universally "right" and the other "wrong".
Then Newton came along and blew all of the models out of the water. Nobody's at the center of the universe [0]. A single theory of gravity models both planetary motion and why we don't get flung off the earth. And we can "feel" the rotation of the earth by experiments which came along later such as Foucault's pendulum and the Coriolis force.
[0] A puzzle I like to taunt my friends with: The earth is in fact equidistant from the edges of the observable universe in all directions, so we must be in the center after all. ;-)
Knowledge can be framed as information compression (this actually applies to LLMs as well, amusingly). The heliocentric model plus Newton's gravity are an amazing compression of information related to dynamics of celestial bodies, which then enables related predictions that would be much more difficult to arrive at if you start from epicycles.
Also, most models are lossy compression. The heliocentric model is amazing because it is wrong. Complications are simply ignored.
Now that we have LLMs, those that are hard for people but easy for LLMs will get cleared out, leaving those that are still hard for both.
Yes some of them were clearly like that but there are probably 5-10 which many mathematicians have said were massive results and would all but guarantee a Fields Medal to any human that had solved them. Navier Stokes, Quasi Riemann, etc.
that's not how physics works. epicycles weren't wrong. there is no wrong/right - modern scientists don't believe in platonism. physics is a collection of models which are empirically tested. if epicycles makes predictions to more decimal places than relativity then epicycles are "right" and relativity is "wrong".
now think about how this translates to LLMs...
Most models have relation to each other so it does not suffice to take one in isolation. It's one continuous world (in our knowledge) so almost everything relates to one other. The truthiness of something is not whether it fits some particular phenomena, but how does it generalize.
You don't know what you're talking about (most people on here do not).
> https://en.wikipedia.org/wiki/Ansatz
After an ansatz, which constitutes nothing more than an assumption, has been established, the equations are solved more precisely for the general function of interest, which then constitutes a confirmation of the assumption. In essence, an ansatz makes assumptions about the form of the solution to a problem so as to make the solution easier to find
yes it does. that's exactly what it means.
I feel like there's a lot of "humans are special" in this thread. There's a good chance we're not.
I think this is a fantastic point and this kind of complexifying can and will happen. And I think future of online debating and propaganda is going to complexify in a similar way.
I will say though, I think that can be controlled by building in principles that prefer competing theories on the grounds of cogency, and that cancel out competing theories by reducing them to the parts between them that are equivalent.
My hard disagree will be with this: I don't think at all that we would "never" have got to the theory of relativity. It reminds me a bit of the "embodied cognition" argument against simulated brains. That argument suggests you can't "just" simulate brains, because actual brains are the totality of their embodiment in bodies and environments. Regardless of whether you agree with that line of thinking (I don't), we can assume it's true, and change the target of our simulation to brains + bodies + environments. The problem is bigger, but still perfectly amenable to the same methods.
I think the same is true of theorizing about science and imposing metatheoretical constraints. I think you can optimize for healthy hypothesis production just like you can for first-order reasoning about data. It's definitely harder but not necessarily a difference in kind.
But this need not be a permanent state of affairs. The model labs are probably already examining the elegance problem, since it is such a common complaint of researchers reading these machine generated proofs and papers. And I haven't seen anything disproving the notion that elegance can be RL'd.
> If we were using [humans] to analyze astronomy, we might just get increasingly complicated epicycles and never realize that the Sun is the real center of the solar system.
If we were using LLMs to analyze astronomy, we might just get increasingly complicated epicycles and never realize that the Sun is the real center of the solar system. We then never learn about the anomalies in Mercury's orbit that led to the theory of relativity.
So I agree. I seriously question how valuable LLMs can be in science/math beyond working as advanced search functions.