This is incorrect: Epicycles were a model of planetary motion - the theory was that the planets moved around the earth, but also had additional circular motion as they moved along their path around the earth. This model explains the apparent geocentric motion of the planets, much as Newtonian gravity explains the apparent heliocentric motion of the planets (but is also wrong). Finding the exact parameters for the epicycles was the curve fitting part.

We now discount that model because it's based on an incorrect geocentric model of the solar system, but that doesn't mean that the model wasn't a model...

[edit] The CHomsky link is interesting - I just listened to an interview where he pooh-poohs LLMs at great length.

This point: "Statistical models have been proven incapable of learning language; therefore language must be innate, so why are these statistical modelers wasting their time on the wrong enterprise?" is interesting in that context - in the recent interview, Chomsky is now unhappy that LLMs can learn /any/ language, even unnatural ones, and therefore aren't good tools for understanding human language. Quite the reversal. I personally think it's a 'science progresses one funeral at a time' kind of situation...

At some point I'd like to carefully study the history of that early era of science because I don't know it as well as I'd like. But I believe I understand that the epicyclical model (and it was a model, rather than a theory) did not in any way depend on geocentrism. For one thing, Coppernicus' model itself, while heliocentric, retained the epicycles of the earlier, geocentric model. Instead, the assumption on which the epicyclical model depended was the shape of the planets' orbits and of the planets themselves, which were considered to be necessarily circular, and spherical, respectively. I think this had to do with assumptions about the geometric perfection of the universe, as a creation of the gods. In any case, assuming that planetary orbits were circular an explanation was needed for the apparent "retrograde" motion of the planets (meaning it looks like they double back and turn against their original heading). Explaining this apparent motion was why epicycles were hypothesised in the first place.

The first time this necessarily circular model was abandoned was with Kepler's laws of planetary motion, which correctly identified the motion of the planets as elliptical, that for the first time explained their apparent retrograde motion without the need for epicycles. Then Newton's theory of universal gravitation explained how the planets could possibly be moving on elliptical orbits. In fact, I believe Newton's theory of universal gravitation explained how the planets could be turning around the sun without crashing down, despite not having anything to hold them up. I think this was the first big mystery that the ancients tried to answer- hence the name of "firmament" for the universe.

And Newton's theory was not the end of the story of course.

I realize I've been repeating shibboleths from my postgrad without full understanding.

A problem with epicycles is they are harder to falsify. If the model doesn't match new observations, just adjust it, or add another epicycle. In contrast, Newtonian gravity can hardly be tweaked at all. So when Mercury's orbit was slightly off, they knew something was wrong.

I'm not quite clear on how I feel about this. Geocentricity is a theory, in broad terms. It seems disrespectful to say adding epicycles makes it "not a theory". As you say, there was a theory that the planets actually moved in epicyclic motion. It wasn't just calculation to them.

(I want to stress that the idea of epicycles, the mechanical craftsmanship, and actual prediction of the planets are all amazing genius.)

Yet, having more parameters than data means the model doesn't explain in simpler terms, only restates. In this sense, it's "not a theory" (by Occam's razor). It seems enough epicycles can model anything: (3Blue1Brown Fourier Series) https://youtube.com/watch?v=bL0LV0Huj1s OTOH the epicycles did predict planetary motion, so they did capture some regularity... not sure what to think.

RE Chomsky: You can see it's like epicycles: with enough parameters, an LLM is like a numerical method for curve fitting, that doesn't explain the data (any more than a fourier transform does). Curiously, they do seem to predict very accurately... yet also generalize strangely ("hallucinate").

But it seems it's got to help! Even if only as a device, like a telescope. Also, from this interview with Terry Sejnowski (https://youtube.com/watch?v=XKC-4Tosdd8) there's instances where a technique was developed for a problem with Neural Nets, and an equivalent was found in the brain.

He also gives a Chomsky-like view: if you duplicated the human brain and it worked perfectly, you wouldn't have done any science if you didn't understand anything.

>> RE Chomsky: You can see it's like epicycles: with enough parameters, an LLM is like a numerical method for curve fitting, that doesn't explain the data (any more than a fourier transform does). Curiously, they do seem to predict very accurately... yet also generalize strangely ("hallucinate"). What to think?

Well, that's the fundamental problem of modelling: that for any set of observations there's an arbitrary number of models that fit the data with great accuracy and even predict future observations well; and we don't know which one is the best in the long term.

The answer is that we should prefer not predictive models, but explanatory theories, that not only predict future observations but also explain why those observations should be expected to be made.

For example, the epicyclical model did not explain anything: it said nothing about why the planets should move on circular orbits with epicycles. Kepler's laws didn't explain anything because they didn't say why the planets should move on ellpitical orbits. Newton's law of universal gravitation explained it all in one stroke: because gravity. And that's why we consider Newton the greatest scientist of his era, not Kepler, not Coppernicus, not Gallileo, but Newton, because he explained the world and didn't just describe it.

>> BTW Chomsky's point E (which I'd never heard of), the last and most minor, was based on Gold's work.

Gold's negative learnability result was a huge upheaval that led directly to the current paradigm of machine learning. Chomsky used it to argue about his universal grammar but linguistics was only one of the two fields that Gold's result turned upside down.

And it was a negative result. As I say in another comment, science gives you the tools to know when you're wrong and that's how progress is made, when we find out where we were wrong before.

With epicycles, it took almost two thousand years before we figured out where the model was wrong. Let's hope that it doesn't take that long with LLMs and neural nets also, because I doubt we have another couple thousand years to spare on a wild goose chase.

> Chomsky used it to support his argument about the poverty of the stimulous but linguistics

Do you know where Chomsky refers (directly or indirectly) to Gold? I've been searching for a reference for some time.

No, I'm sorry. I'm not a linguist so I only know the relation between Gold's result and linguistics second-hand. I'm more interested in it from the point of view of inductive generalisation in machine learning; that's my schtick.

Just to make sure I didn't hallucinate all that, I had an admittedly perfunctory search online and I could find this paper:

https://proceedings.neurips.cc/paper/2002/file/04ad5632029cb...

Whose introduction describes how Gold's result is considered to support the arguments for linguistic nativism from the poverty of the stimulus. Then again, the author doesn't seem to be a linguist himself and he doesn't give any more specific references, so I'm now a little worried; and your question remains un-answered.

Have you tried wading through Chomsky's early work on linguistics? I don't have the courage to. The closest I've got to is I have a friend who has read a couple of Chomsky's linguistics books. My friend is making a living as an astrologist now so maybe that's a bit of a warning there :P

(not who you asked) I thought this would be in the linked transcript, but it's not. Norvig must be getting it from elsewhere (maybe in the 404ed video?), but it seems like misrepresentation.

The gravity model is similar though: we posit a force that pulls things together, but we don't know /why/ that force seems to exist, no more than the ancients knew /why/ the planets seemed to move in smaller circles along their circular paths. We're really not /that/ enlightened, after all.

I think that's right, but ultimately all explanations we have are based on prior knowledge that is itself not necessarily complete. It's explanations all the way down, until we hit some primary observations or axiomatic assumptions that are the hardest to get rid of.

"Enlightened" was my bad choice of a word. I get overexcited when I think of how much we have learned in the past couple thousand years and I forget that we mainly learned how little we know. Or can explain!

Yes. A matter of degree?

I'd like to think explaining means giving a model simpler than the observations. But this can be true of a predictive model, that offers no "why". Another commenter pointed out that epicycles do simplify - so they do "explain" in this sense.

> not predictive models, but explanatory theories

Maybe an advantage of an explanatory theory is in revealing more of the "black box", giving more ways to check the theory. (But I'm not sure how this could apply to Newton's gravity, since the only observations were outcomes. And no plausible way to "experiment".)

> If it wasn't for the ancients stumbling and fumbling in the dark for millennia

Is there any evidence that the epicyclic models helped scientific understanding, even indirectly? Later theories didn't seem to build on it. I wonder if it actually detoured understanding, with its misleadingly impressive accuracy, so that understanding would have progressed more quickly without it.

Thinking of pg's "great work" (https://news.ycombinator.com/item?id=36550615): to be the Newton of neural nets would seem the most ambitious aspiration of our times. But it took a bunch of geniuses just to get to Newton... and it seems an even harder problem than planetary motion. Though a difference is neural nets are based on actual neurons (loosely!).

It's looking like working human-level AI will precede understanding... perhaps by those 2000 years?

> BTW Chomsky's point E (which I'd never heard of), the last and most minor, was based on Gold's work.

Do you know where Chomsky says this exactly? I've been looking for how/if his argument is the same as Gold's.

I don't think the problem wasn't that it wasn't a "model" it's that it had lots of unexplained "plug-in" behavior. The heliocentric model had much less; it explained more using less despite being less accurate.

Nobody's arguing that the heliocentric model wasn't better for a variety of reasons... simply that getting superseded doesn't make the previous approach 'not science.' All models are wrong, some are useful, and all that.

And the heliocentric model still has plenty of unexplained parameters: the major and minor radii for each body. (Not to mention those pesky perturbations in mercury's orbit.)

Chomsky hasn't made any reversal, Norvig misrepresents what Chomsky has said.

> Chomsky is now unhappy that LLMs can learn /any/ language, even unnatural ones, and therefore aren't good tools for understanding human language

That's also not what he has said: He said they aren't useful for understanding the human language faculty, in other words, understanding how people are able to have language. As he says it obviously can't be the same way as LLMs because LLMs are able to learn languages humans can't learn.