15 ms·

How Copernicus took down Ptolemy's Almagest

43 points by Hooke 3y ago

rurban 3y ago
Arguably Aristotle made a worse error in his definition of mechanics, particularly of motion. For him friction ruined acceleration. "Continuation of motion depends on continued action of a force".
- canjobear 3y ago
  Aristotle’s physics is correct for objects immersed in a fluid. https://arxiv.org/abs/1312.4057 https://arxiv.org/abs/1312.4057
  - pdonis 3y ago
    More precisely, it is a good approximation for objects immersed in a fluid that is sufficiently dense relative to the density of the objects, on time scales long enough for the effects of the fluid to be significant given the relative densities. Rovelli fails to point out this critical factor, although it is implicit in the equations he gives, and fails to recognize that this factor invalidates his criticisms of high school textbooks and teachers who, he claims, mislead students by telling them that heavy and light objects fall with the same acceleration. In fact, what high school textbooks and teachers tell students is that if we neglect the effects of air, heavy and light objects fall with the same acceleration. That's what I was taught in high school, and it's perfectly correct. (Note that this phrasing already eliminates cases like motion in water, for which the Aristotelian model is a much better approximation.) Some high school textbooks and teachers (like the one I was fortunate enough to have) will even go on to point out that, for a wide range of objects falling in air, the effects of air are negligible for a significant enough amount of time to make feasible, for example, the famous (but probably apocryphal) experiment of Galileo dropping two cannon balls of different weights from the top of the Leaning Tower of Pisa and seeing them hit the ground at the same time. And Rovelli's equations, when you plug in the relevant numbers for such a case, say the same thing--but Rovelli himself doesn't. While this in itself does not invalidate the actual math in the paper, which is fine, I found it very disappointing that Rovelli went beyond what his math actually justifies in making the criticisms of high school textbooks and teachers in the paper. He should have known better.
    - pdonis 3y ago
      > While this in itself does not invalidate the actual math in the paper, which is fine Actually, on going back and re-reading, I realized that even the math in the paper has an error. The formula for buoyancy force is wrong! Rovelli's formula for buoyancy force is V rho (in the upwards vertical direction), where rho is the density of the fluid in which the object is immersed. But this is wrong; it doesn't even have the right units. This formula says that the buoyancy force is equal to the mass of the displaced fluid; but mass is not force. The correct formula is V rho g, where g is the acceleration due to gravity; in other words, the buoyancy force is equal to the weight of the displaced fluid. (To check against your intuition, you can plug in numbers and realize that, according to Rovelli's formula, an ordinary helium balloon of the kind you get for birthday parties would not rise in air!) This just makes the paper even more disappointing.
- lo_zamoyski 3y ago
  I will add as a footnote, and I know you likely did not mean this, but it happens often enough, that one should distinguish between Aristotle's scientific works and philosophic works. That is, while his physics may be obsolete (though we should show gratitude, as this was an early attempt from which our later traditions drew), his metaphysics is not, for example.
  - pdonis 3y ago
    > his metaphysics is not It isn't?
deleted 3y ago
[deleted]
chipsdip 3y ago
[flagged]
- noahtallen 3y ago
  [flagged]
visarga 3y ago
Can we say humans also hallucinate and continue parroting a bad idea for 1500 years? How does this support the concept that humans have real understanding unlike AI? Looks to me we have hallucinated theories that eventually get invalidated. We don't really understand, we're like hallucinating LLMs testing their outputs in the world. Similarly to this we had no idea about the germ theory of disease even when 30% of our population was dying (Black Death). A life and death scenario and we couldn't figure it out, that's how intelligent we are in reality - not enough to save our asses. Our intelligence is social, an environment based discovery process not something coming from a single brain. All we know comes from the environment, and no agent is too smart alone. We should reexamine intelligence as a property of the brain, better see it as a property of language.
- koliber 3y ago
  Coming up with a plausible but incorrect theory of how something works is not hallucination. Hallucination is seeing something that is not there. In terms of LLMs, they don’t come up with with any original theories. When they hallucinate, they make things up that are easily shown to be untrue using current and present methods.
  - visarga 3y ago
    There is no difference between real understanding and integrating feedback into a hallucinating model. We're adjusting based on feedback to reign hallucination in.
    - marketneutral 3y ago
      A and B are not the same thing if they can sometimes generate the same output to a particular query.
- mihaic 3y ago
  What you're doing seems to be the opposite of anthropomorphization (is there a term for that?) You seem to be considering humans by forcing them to fit into the observations of LLM outputs. > Our intelligence is social, an environment based discovery process not something coming from a single brain. Germ theory didn't come from the group, there were individuals that came up with new inventions (the microscope)_and concepts that later were approved by a community. I think you're trying to oversimplify our society, and that loses some important truths along the way.
dave333 3y ago
So which of today's accepted theories are in error? Quantum Mechanics and General Relativity do not agree so at least one must be incorrect yet both are widely if not completely accepted.
- FredPret 3y ago
  We're certainly zero-ing in on the truth though, which is extremely exciting
  - _a_a_a_ 3y ago
    Are we though? All I see is a lot of effort followed by a lot of reaching (yet again) for the aspirin and/or whiskey. Have you any examples showing recent convergence between quantum & relativity?
    - FredPret 3y ago
      Pessimism much? We have GPS satellites orbiting, we can land a robot on a specific spot on Mars, and we can make a ton of predictions about how the universe should look on both huge and tiny scales and have those pan out. Sure we don't have a single theory of everything yet, but our mental model is asymptotically converging to our observations.
      - _a_a_a_ 3y ago
        > Pessimism much I'm asking for facts, hope doesn't come into it. > ...our mental model is asymptotically converging Which is not what I'm picking up, so have you any evidence to change my mind? TIA
        FredPret 3y ago
        If you're able to look at the modern world and all it's marvels - none of which are possible without a testable and provable understanding of an increasing fraction what's out there - and you'd still rather be down in the dumps, there's no amount of evidence anyone can offer that would change your mind.
bcaxis 3y ago
How mach of our current understanding is just as wrong?
- Certhas 3y ago
  Nothing. At least not for any precise definition of "just as wrong" that would be useful. There is, today, not a single terrestrial observation in contradiction to GR and QM. We have an incredibly good understanding of the fundamental nature of our reality. Our understanding is so good that it takes decades of work by brilliant scientists and engineers, to build machines that could show even the slightest evidence of something else going on. It's easy to overlook how stunning this situation is. It is utterly unprecedented in the history of science. This does not mean that there are no deeper truths to discover, but Newtonian mechanics does correctly describe how the apple falls, even if it is not the final word.
- lcuff 3y ago
  "We don't know what we don't know", comes to mind as an answer. Quantum Mechanics and General Relativity explain a Whole Lot, but since they haven't yet been "meshed", there's more to come. The James Webb Space Telescope is providing data that is upending many things in cosmology. Dark Matter: As a phrase, it's not even clear that it's "matter". There's some phenomenon that causes stars to be attracted to one another independent of our current notion of mass. Richard Feynman said "Science is the belief in the ignorance of experts", and Carl Sagan said the "Science is a way of thinking more than it is a body of knowledge". Both of these point to the reality that our current understanding of the universe is riddled with errors and omissions. We do our best with the data we have, and try to transcend our own prejudices and history. How much or our current understanding is "just as wrong?": Well, like most things, it's on a continuum, and to some extent a matter of opinion. Was Newtonian mechanics "just as wrong" as Ptolemy, when considering Relativity? I wouldn't say so, but maybe you would. Ptolemy's conception explained almost nothing and glossed over contradicting facts. Newton put mathematics around observations available to him, but named the reality that he had no understanding of how action-at-a-distance happened. "I make no hypothesis".
- stareatgoats 3y ago
  Depending on what the future might bring, maybe all of it - or at least some aspect of everything. Since we base much, if not all of of our understanding on what we think we know: when those beliefs get thrown out then it will affect everything. This is admittedly not very useful in everyday life since we can't know beforehand exactly how earthshattering the new knowledge will be. Except, useful perhaps as a certain antidote to the potential suppressive damage done by those who are absolutely certain of the things we know now to be true for ever. Example: what if it turned out that time itself had qualities no-one had suspected before? Time is one of those fundamental things in existence that may (or likely will) still reveal some previously unknown aspect. Which in turn would likely affect our perception of all things in existence. Which means our "primitive" concept of time (and everything in it) would perhaps not be wrong, but incomplete. Or plainly wrong, for that matter.
Jun8 3y ago
The premise of this article is wrong: heliocentric was not rejected because ancient scientists were foolish or they were afraid to speak up to established theory. It was not accepted because egocentrism produced better results! They correctly understood that heliocentrism predicted a parallax but failed to measure that with the primitive observational equipment they had. I thought this was a commonly known fact, together with the myth that the ancient believed Earth was flat, but evidently not. For further reading: https://physics.stackexchange.com/questions/26291/why-did-the-ancients-fail-to-discover-that-the-earth-orbits-the-sun https://physics.stackexchange.com/questions/26291/why-did-th...
- canjobear 3y ago
  Furthermore Copernicus’s system had lower accuracy and more epicycles. There wasn’t any real reason to prefer heliocentric models until Kepler.
  - mistercheph 3y ago
    Kepler makes Copernicus look like a tool.
- sorokod 3y ago
  A neat example of how the predictive power of a theory does not guarantee its correctness. Even if the theory and its predictions were incremental refined and improved over time.
  - mistercheph 3y ago
    What measure is there for assessing the correctness of a theory aside from predictive power?
    - sorokod 3y ago
      Here we have a theory which turned out to be fundamentally wrong while having predictive power. Maybe every physical theory is just a model approximating something that can at any time be replaced by by a better model that is still just that, a model.
rs_rs_rs_rs_rs 3y ago
And Kepler "took down" whatever Copernicus did.
herodotus 3y ago
This article is wrong on many levels. A very good article to read about this is '"Crisis" versus Aesthetic in the Copernican Revolution' by Owen Gingerich https://dash.harvard.edu/bitstream/handle/1/4258973/Crisis%20vs%20Aesthetic%20OGingrich.pdf?sequence=2&isAllowed=y https://dash.harvard.edu/bitstream/handle/1/4258973/Crisis%2...
- wolverine876 3y ago
  When they disagree, how do you know which article is accurate about what? How do we know? People say these things about almost every OP on HN; the claim itself isn't a signal.
  - herodotus 3y ago
    The article I cited above is well argued, includes citations and evidence, and is written by one of the top scholars in the field (https://en.wikipedia.org/wiki/Owen_Gingerich https://en.wikipedia.org/wiki/Owen_Gingerich).
clausecker 3y ago
Also worth reading on this subject: The great Ptolemaic smackdown (https://tofspot.blogspot.com/2013/10/the-great-ptolemaic-smackdown-table-of.html https://tofspot.blogspot.com/2013/10/the-great-ptolemaic-sma...).
oglop 3y ago
This is mostly fantasy. It was accepted because it worked. There was no grand cultural or religious reason. Just boring old “it works”. You can still use the algamest if you’d like to plot the paths of planets. John Conway pointed this out to me in one of his wonderful books. It’s pretty good actually. Which is why it was used for so long. Fun to suggest it was some weird religious thing though. I’m sure the author felt good about sticking it to those stupid Christian’s, though Copernicus was a Christian so that train of thought seems nonsensical.

43 points by Hooke 3y ago

Arguably Aristotle made a worse error in his definition of mechanics, particularly of motion. For him friction ruined acceleration. "Continuation of motion depends on continued action of a force".

canjobear 3y ago
Aristotle’s physics is correct for objects immersed in a fluid. https://arxiv.org/abs/1312.4057 https://arxiv.org/abs/1312.4057
- pdonis 3y ago
  More precisely, it is a good approximation for objects immersed in a fluid that is sufficiently dense relative to the density of the objects, on time scales long enough for the effects of the fluid to be significant given the relative densities. Rovelli fails to point out this critical factor, although it is implicit in the equations he gives, and fails to recognize that this factor invalidates his criticisms of high school textbooks and teachers who, he claims, mislead students by telling them that heavy and light objects fall with the same acceleration. In fact, what high school textbooks and teachers tell students is that if we neglect the effects of air, heavy and light objects fall with the same acceleration. That's what I was taught in high school, and it's perfectly correct. (Note that this phrasing already eliminates cases like motion in water, for which the Aristotelian model is a much better approximation.) Some high school textbooks and teachers (like the one I was fortunate enough to have) will even go on to point out that, for a wide range of objects falling in air, the effects of air are negligible for a significant enough amount of time to make feasible, for example, the famous (but probably apocryphal) experiment of Galileo dropping two cannon balls of different weights from the top of the Leaning Tower of Pisa and seeing them hit the ground at the same time. And Rovelli's equations, when you plug in the relevant numbers for such a case, say the same thing--but Rovelli himself doesn't. While this in itself does not invalidate the actual math in the paper, which is fine, I found it very disappointing that Rovelli went beyond what his math actually justifies in making the criticisms of high school textbooks and teachers in the paper. He should have known better.
  - pdonis 3y ago
    > While this in itself does not invalidate the actual math in the paper, which is fine Actually, on going back and re-reading, I realized that even the math in the paper has an error. The formula for buoyancy force is wrong! Rovelli's formula for buoyancy force is V rho (in the upwards vertical direction), where rho is the density of the fluid in which the object is immersed. But this is wrong; it doesn't even have the right units. This formula says that the buoyancy force is equal to the mass of the displaced fluid; but mass is not force. The correct formula is V rho g, where g is the acceleration due to gravity; in other words, the buoyancy force is equal to the weight of the displaced fluid. (To check against your intuition, you can plug in numbers and realize that, according to Rovelli's formula, an ordinary helium balloon of the kind you get for birthday parties would not rise in air!) This just makes the paper even more disappointing.
lo_zamoyski 3y ago
I will add as a footnote, and I know you likely did not mean this, but it happens often enough, that one should distinguish between Aristotle's scientific works and philosophic works. That is, while his physics may be obsolete (though we should show gratitude, as this was an early attempt from which our later traditions drew), his metaphysics is not, for example.
- pdonis 3y ago
  > his metaphysics is not It isn't?

deleted 3y ago

[deleted]

chipsdip 3y ago

[flagged]

noahtallen 3y ago
[flagged]

visarga 3y ago

Can we say humans also hallucinate and continue parroting a bad idea for 1500 years? How does this support the concept that humans have real understanding unlike AI? Looks to me we have hallucinated theories that eventually get invalidated. We don't really understand, we're like hallucinating LLMs testing their outputs in the world. Similarly to this we had no idea about the germ theory of disease even when 30% of our population was dying (Black Death). A life and death scenario and we couldn't figure it out, that's how intelligent we are in reality - not enough to save our asses. Our intelligence is social, an environment based discovery process not something coming from a single brain. All we know comes from the environment, and no agent is too smart alone. We should reexamine intelligence as a property of the brain, better see it as a property of language.

koliber 3y ago
Coming up with a plausible but incorrect theory of how something works is not hallucination. Hallucination is seeing something that is not there. In terms of LLMs, they don’t come up with with any original theories. When they hallucinate, they make things up that are easily shown to be untrue using current and present methods.
- visarga 3y ago
  There is no difference between real understanding and integrating feedback into a hallucinating model. We're adjusting based on feedback to reign hallucination in.
  - marketneutral 3y ago
    A and B are not the same thing if they can sometimes generate the same output to a particular query.
mihaic 3y ago
What you're doing seems to be the opposite of anthropomorphization (is there a term for that?) You seem to be considering humans by forcing them to fit into the observations of LLM outputs. > Our intelligence is social, an environment based discovery process not something coming from a single brain. Germ theory didn't come from the group, there were individuals that came up with new inventions (the microscope)_and concepts that later were approved by a community. I think you're trying to oversimplify our society, and that loses some important truths along the way.

dave333 3y ago

So which of today's accepted theories are in error? Quantum Mechanics and General Relativity do not agree so at least one must be incorrect yet both are widely if not completely accepted.

FredPret 3y ago
We're certainly zero-ing in on the truth though, which is extremely exciting
- _a_a_a_ 3y ago
  Are we though? All I see is a lot of effort followed by a lot of reaching (yet again) for the aspirin and/or whiskey. Have you any examples showing recent convergence between quantum & relativity?
  - FredPret 3y ago
    Pessimism much? We have GPS satellites orbiting, we can land a robot on a specific spot on Mars, and we can make a ton of predictions about how the universe should look on both huge and tiny scales and have those pan out. Sure we don't have a single theory of everything yet, but our mental model is asymptotically converging to our observations.
    - _a_a_a_ 3y ago
      > Pessimism much I'm asking for facts, hope doesn't come into it. > ...our mental model is asymptotically converging Which is not what I'm picking up, so have you any evidence to change my mind? TIA
      - FredPret 3y ago
        If you're able to look at the modern world and all it's marvels - none of which are possible without a testable and provable understanding of an increasing fraction what's out there - and you'd still rather be down in the dumps, there's no amount of evidence anyone can offer that would change your mind.

bcaxis 3y ago

How mach of our current understanding is just as wrong?

Certhas 3y ago
Nothing. At least not for any precise definition of "just as wrong" that would be useful. There is, today, not a single terrestrial observation in contradiction to GR and QM. We have an incredibly good understanding of the fundamental nature of our reality. Our understanding is so good that it takes decades of work by brilliant scientists and engineers, to build machines that could show even the slightest evidence of something else going on. It's easy to overlook how stunning this situation is. It is utterly unprecedented in the history of science. This does not mean that there are no deeper truths to discover, but Newtonian mechanics does correctly describe how the apple falls, even if it is not the final word.
lcuff 3y ago
"We don't know what we don't know", comes to mind as an answer. Quantum Mechanics and General Relativity explain a Whole Lot, but since they haven't yet been "meshed", there's more to come. The James Webb Space Telescope is providing data that is upending many things in cosmology. Dark Matter: As a phrase, it's not even clear that it's "matter". There's some phenomenon that causes stars to be attracted to one another independent of our current notion of mass. Richard Feynman said "Science is the belief in the ignorance of experts", and Carl Sagan said the "Science is a way of thinking more than it is a body of knowledge". Both of these point to the reality that our current understanding of the universe is riddled with errors and omissions. We do our best with the data we have, and try to transcend our own prejudices and history. How much or our current understanding is "just as wrong?": Well, like most things, it's on a continuum, and to some extent a matter of opinion. Was Newtonian mechanics "just as wrong" as Ptolemy, when considering Relativity? I wouldn't say so, but maybe you would. Ptolemy's conception explained almost nothing and glossed over contradicting facts. Newton put mathematics around observations available to him, but named the reality that he had no understanding of how action-at-a-distance happened. "I make no hypothesis".
stareatgoats 3y ago
Depending on what the future might bring, maybe all of it - or at least some aspect of everything. Since we base much, if not all of of our understanding on what we think we know: when those beliefs get thrown out then it will affect everything. This is admittedly not very useful in everyday life since we can't know beforehand exactly how earthshattering the new knowledge will be. Except, useful perhaps as a certain antidote to the potential suppressive damage done by those who are absolutely certain of the things we know now to be true for ever. Example: what if it turned out that time itself had qualities no-one had suspected before? Time is one of those fundamental things in existence that may (or likely will) still reveal some previously unknown aspect. Which in turn would likely affect our perception of all things in existence. Which means our "primitive" concept of time (and everything in it) would perhaps not be wrong, but incomplete. Or plainly wrong, for that matter.

Jun8 3y ago

The premise of this article is wrong: heliocentric was not rejected because ancient scientists were foolish or they were afraid to speak up to established theory. It was not accepted because egocentrism produced better results! They correctly understood that heliocentrism predicted a parallax but failed to measure that with the primitive observational equipment they had. I thought this was a commonly known fact, together with the myth that the ancient believed Earth was flat, but evidently not. For further reading: https://physics.stackexchange.com/questions/26291/why-did-the-ancients-fail-to-discover-that-the-earth-orbits-the-sun https://physics.stackexchange.com/questions/26291/why-did-th...

canjobear 3y ago
Furthermore Copernicus’s system had lower accuracy and more epicycles. There wasn’t any real reason to prefer heliocentric models until Kepler.
- mistercheph 3y ago
  Kepler makes Copernicus look like a tool.
sorokod 3y ago
A neat example of how the predictive power of a theory does not guarantee its correctness. Even if the theory and its predictions were incremental refined and improved over time.
- mistercheph 3y ago
  What measure is there for assessing the correctness of a theory aside from predictive power?
  - sorokod 3y ago
    Here we have a theory which turned out to be fundamentally wrong while having predictive power. Maybe every physical theory is just a model approximating something that can at any time be replaced by by a better model that is still just that, a model.

rs_rs_rs_rs_rs 3y ago

And Kepler "took down" whatever Copernicus did.

herodotus 3y ago

This article is wrong on many levels. A very good article to read about this is '"Crisis" versus Aesthetic in the Copernican Revolution' by Owen Gingerich https://dash.harvard.edu/bitstream/handle/1/4258973/Crisis%20vs%20Aesthetic%20OGingrich.pdf?sequence=2&isAllowed=y https://dash.harvard.edu/bitstream/handle/1/4258973/Crisis%2...

wolverine876 3y ago
When they disagree, how do you know which article is accurate about what? How do we know? People say these things about almost every OP on HN; the claim itself isn't a signal.
- herodotus 3y ago
  The article I cited above is well argued, includes citations and evidence, and is written by one of the top scholars in the field (https://en.wikipedia.org/wiki/Owen_Gingerich https://en.wikipedia.org/wiki/Owen_Gingerich).

clausecker 3y ago

Also worth reading on this subject: The great Ptolemaic smackdown (https://tofspot.blogspot.com/2013/10/the-great-ptolemaic-smackdown-table-of.html https://tofspot.blogspot.com/2013/10/the-great-ptolemaic-sma...).

oglop 3y ago

This is mostly fantasy. It was accepted because it worked. There was no grand cultural or religious reason. Just boring old “it works”. You can still use the algamest if you’d like to plot the paths of planets. John Conway pointed this out to me in one of his wonderful books. It’s pretty good actually. Which is why it was used for so long. Fun to suggest it was some weird religious thing though. I’m sure the author felt good about sticking it to those stupid Christian’s, though Copernicus was a Christian so that train of thought seems nonsensical.