How Copernicus took down Ptolemy's Almagest
atlasobscura.com
atlasobscura.com
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-th...
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.
What makes you think so? How is Ptolemaic theory "fundamentally wrong" where our best current physical theories are not?
> 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.
This is indeed our current view of physical theories. But you realize, don't you, that once you accept this, it invalidates your criticism of Ptolemaic theory? Ptolemaic theory was a model. For centuries it was the best model known in terms of the accuracy of its predictions, which were accurate enough to predict things like eclipses years in advance. We now have better models, but none of that invalidates Ptolemaic theory's achievements. It just means we have now found better approximations.
In fact, our modern viewpoint, specifically relativity, even helps us to understand why the Ptolematic model worked as well as it did: it is one way of describing what you get if you use an inertial frame centered on the Earth to analyze the motions of the Sun, Moon, and planets! IIRC Steven Weinberg, years ago, wrote a paper that expounded this in some detail.
Maybe wrong / right are endpoints of a sliding scale of accuracy, and maybe certain quantities on that scale become qualitative in my perception .
Or did we just find another model that:
1. Accurately predicts phenomena the old model predicted accurately and predicts things we hadn't expected from the previous model or from our data that we later measure to be correct.
2. Effectively describes phenomena previously thought to be unrelated to the problem of interest.
3. We appreciated the simplicity of. (i.e. We could come up with more ad-hoc silliness that makes the old model accommodate our new data, but why?)
What's interesting about Ptolemy is that in a sense there is nothing inaccurate about his model. In my reading, it could hardly be called a model so much as a technique for creating models. Extending it to account for any deviations from our empirical measurements is trivial: just add another epicycle. The modelling technique Ptolemy demonstrates in his Almagest, seems to me to just be the Fourier transformation of a periodic function.
For some years I gave talks about this (Germany), it is astonishing how many people think that the idea of a spherical earth is a new one.
"The myth of the flat Earth, or the flat-Earth error, is a modern historical misconception that European scholars and educated people during the Middle Ages believed the Earth to be flat."
And wacky ideas like fundmentalism are likewise very new historically, but eagerly seized upon by our modern sophists who, again, have an ax to grind.
Lol.
> By straw manning the Middle Ages (especially the Middle Ages, as many of these types had an ax to grind against the Church) or the ancients as superstitious imbeciles, it makes them look better, these true men of reason, in the eyes of the ignorant whom they sought to impress.
This is a great point - and still relevant. Academia does this to this day, attacking researchers like Jared Diamond, pooh-poohing the work of (very) ancient mathematicians and astronomers, or diminishing the insanely impressive craftsmanship shown in, eg, 30-50 thousand year old flutes, carved with perfect pentatonic scales.
Pentatonic scales! Well over 30,000 years ago! The implications of that are astounding.
Aristotle in De Caelo (Book II, part 14):
> The earth, then, also, whether it move about the centre or as stationary at it, must necessarily move with two motions. But if this were so, there would have to be passings and turnings of the fixed stars. Yet no such thing is observed. The same stars always rise and set in the same parts of the earth.
* http://classics.mit.edu/Aristotle/heavens.2.ii.html
* https://en.wikipedia.org/wiki/On_the_Heavens
See also:
> In the mathēmatikoi tradition of Pythagoreanism the Earth was removed from the center of the universe. The mathēmatikoi believed that the Earth, along with other celestial bodies, orbited around a central fire. This, they believed, constituted a celestial harmony.[24]
* https://en.wikipedia.org/wiki/Pythagoreanism#The_mathēmatiko...
Also, they didn’t have a theory of gravity so the lack of a sensation of moving with the earth and the fact that objects fall straight down were not expected unless the earth was stationary. There were also other more philosophical arguments for geocentrism that were compelling given the cosmology and science of the time.
> I thought this was a commonly known fact… evidently not.
Especially given how this is tied up with the common use of the Galileo affair as an example of faith vs science despite faith being common between Galileo and the Church Authorities to which he ran afoul.
The Church was not nearly as closed-minded about heliocentric theories in Galileo's time as is commonly thought. Their position was that if empirical evidence clearly showed that the universe did not work the way the Church thought that the Bible said it worked then the Church must have misinterpreted the Bible.
The problem with Galileo's heliocentric theory was that it was empirically not correct. If some observation didn't fit in with his theory and changing the theory to accommodate it would make the theory ugly or inelegant Galileo would dismiss that observation as observational error. God, he believed, would not make an inelegant universe.
What got him in trouble with the Church wasn't that he proposed a heliocentric theory. It was a combination of 5 things.
1. His theory wasn't better than the best current geocentric theories at actually predicting things.
2. He had a very big ego.
3. He was an asshole. If he saw you are a rival or as an inferior he was intolerant and rude to you. Because of his big ego, "inferior" included pretty much everybody.
4. He was a celebrity. The rich and powerful would regularly invite him to attend their gatherings.
5. He had a terrible sense of politics. #4 regular brought him in contact with people who could make his life miserable if he annoyed them too much, and #2 and #3 ensured the he did so.
However, the church forbade heliocentric theories up until the middle of the eighteenth century, long after Kepler and Newton. So clearly it wasn’t a question of evidence.
https://dash.harvard.edu/bitstream/handle/1/4258973/Crisis%2...
People say these things about almost every OP on HN; the claim itself isn't a signal.
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.
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.
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.
It isn't?
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.
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".
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.
"All models are wrong, but some are useful" [1]
The validity of Newtonian mechanics didn't change because we discovered relativity just like the equations of motion don't become invalid because there's friction. It's still useful, we're just more familiar with the boundary conditions where it breaks down. It's unlikely we'll ever throw it away because it is the simplest model with a lot of predictive value at low energies.
I don't think getting to the point of throwing anything out is necessary, if (some adequate subset of) humans could even get to the point of seriously wondering if our models and beliefs (across all domains, including those outside of science, particularly those which science sits on top of) contain zero fundamentally important flaws, I believe we would be well on the path to sorting the mess we've made out. Science and engineering are excellent examples of how capable humans are when they really set their minds on trying to understand something.
Which ones? I don't know of settled science that has been found to be false, but maybe I just don't know.
Sometimes a new theory might eclipse another theory - cover all that ground and more, but that doesn't make the prior theory wrong in any way. My new, faster laptop doesn't mean the old one didn't work.
Phlogiston theory is post-Baconian. To me, Bacon was the first to articulate the method of thoughts that characterize good modern science: Observations, theory, prediction, experiments to verify the predictions. So I don't think saying we've thrown out pre-Baconian theories is germane to the conversation.
There is a Wikipedia page for Superseded theories in science. https://en.wikipedia.org/wiki/Superseded_theories_in_science
If that's the best you have, we agree! :)
In fact, astronomers today don't even use a "heliocentric" frame--they use a barycentric frame, i.e., the spatial origin is the barycenter of the solar system. The Sun is of course much closer to the barycenter than any other body, but it's not exactly at it.
What we do have in our current physics is a reasonably good understanding of the limitations of our theories: we know that none of them are theories of everything, they all have limited domains of validity, even if for some of them those domains are very wide. That is the key thing that systems like those of Aristotle and Newton did not have.
Have you any examples showing recent convergence between quantum & relativity?
Sure we don't have a single theory of everything yet, but our mental model is asymptotically converging to our observations.
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
I said our overall mental model of reality is converging with reality. We're zeroing in on the truth. One day that might include a unified theory.
> 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.
You (FredPret) responded
> We're certainly zero-ing in on the truth though, which is extremely exciting
I had to read that as you implying closing in on some resolution of QM with relativity. Hence my confusion.
Isaac Asimov wrote a really great essay about this, in which he pointed out that some people thought the Earth was flat. And it is flat, on a local scale. Then people thought it was round. And it is round, just not exactly. Then it was considered an oblate sphere. And it is an oblate sphere - just not exactly.
The main theme of his essay is to point out that a theory can be wrong, but pretty accurate. Enough for rough work. And the one that replaces it can also be wrong, but even closer. Etc. So all theories in succession can be wrong. The real question is how wrong a theory is, and how useful it is.
Here's the essay:
And whilst one can say these, one may note something like say letting blood can cure disease it is not. Hence talking is ok. But actually using it …
It's not the same kind of error. Because science is based on factual observation, it tends to agree with the facts of reality.
> Quantum Mechanics and General Relativity do not agree so at least one must be incorrect
That's not so. It's not a binary choice at all. Both are accurate - both accurately predict certain phenomena and they will continue to do that. Someday, hopefully, someone will come up with an explanation that encapsulates both of them.
More precisely, they are incompatible if you treat them as fundamental theories of everything. But neither QM nor GR claims to be any such thing.
That is a key difference between our current theories and schemes like Aristotelian physics, or for that matter Newtonian physics. Both Newton and Aristotle thought their theories were theories of everything. We know that neither the QM we currently have nor the GR we currently have are theories of everything; they are just models valid within particular domains. Those domains are very wide, but (a) neither one covers everything, and (b) there is virtually no overlap between them, and where there is (for example, quantum field theory in curved spacetime) we have ways of meshing them that work well enough.
That seems more likely than the thing that happened last time repeating itself. Basically we just need Grothendieck’s ideas to percolate to the physics people.
Or not.
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.
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.
> 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.