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Oh, they worked really well; they were still used for numerical calculation even after Galileo. But they weren't a "demonstration of knowledge and understanding

Oh, they worked really well; they were still used for numerical calculation even after Galileo. But they weren't a "demonstration of knowledge and understanding" of planetary motion.

sdenton4 3y ago
Understanding is a moving target, though. Newtonian mechanics was incorrect for modeling the solar system as well - as it was eventually superseded - but that doesn't mean it wasn't a scientific understanding of planetary motion. Epicycles gave a better description of the movement of the planets, based on the observations available, which was entirely falsifiable. They were eventually superseded, and that's science at work.
- hyperthesis 3y ago
  Interesting to say it's scientific because falsifiable. The objection is that it wasn't a theory, just fitting a function to data. It did "work" in that it captured some pattern: it was extremely good at generalizing/extrapolating/predicting. And was a "model" of something in the data. But there was no operational model behind it, of what was actually happening. Newtonian mechanics has a model, beyond curve fitting. BTW: I made this analogy between LLM and epicycles as a joke, but it's looking strangely isomorphic... It's funny, because epicycles used to be the poster-child for ad hoc, overcomplex models with no conceptual basis... which is an exact match for LLM... but I don't recall the analogy being made. Not even in https://norvig.com/chomsky.html https://norvig.com/chomsky.html
  - sdenton4 3y ago
    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...
    - YeGoblynQueenne 3y ago
      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.
      - deleted 3y ago
        [deleted]
    - hyperthesis 3y ago
      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 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"). What to think? 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 https://youtube.com/watch?v=XKC-4Tosdd8 3 hours!) 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. BTW Chomsky's point E (which I'd never heard of), the last and most minor, was based on Gold's work.

Oh, they worked really well; they were still used for numerical calculation even after Galileo. But they weren't a "demonstration of knowledge and understanding" of planetary motion.

sdenton4 3y ago

Understanding is a moving target, though. Newtonian mechanics was incorrect for modeling the solar system as well - as it was eventually superseded - but that doesn't mean it wasn't a scientific understanding of planetary motion. Epicycles gave a better description of the movement of the planets, based on the observations available, which was entirely falsifiable. They were eventually superseded, and that's science at work.

hyperthesis 3y ago
Interesting to say it's scientific because falsifiable. The objection is that it wasn't a theory, just fitting a function to data. It did "work" in that it captured some pattern: it was extremely good at generalizing/extrapolating/predicting. And was a "model" of something in the data. But there was no operational model behind it, of what was actually happening. Newtonian mechanics has a model, beyond curve fitting. BTW: I made this analogy between LLM and epicycles as a joke, but it's looking strangely isomorphic... It's funny, because epicycles used to be the poster-child for ad hoc, overcomplex models with no conceptual basis... which is an exact match for LLM... but I don't recall the analogy being made. Not even in https://norvig.com/chomsky.html https://norvig.com/chomsky.html
- sdenton4 3y ago
  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...
  - YeGoblynQueenne 3y ago
    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.
    - deleted 3y ago
      [deleted]
  - hyperthesis 3y ago
    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 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"). What to think? 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 https://youtube.com/watch?v=XKC-4Tosdd8 3 hours!) 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. BTW Chomsky's point E (which I'd never heard of), the last and most minor, was based on Gold's work.