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Sunday, April 10, 2011

Is it true that Ptolemaic models gave better predictions than Copernican models until 50 years after the publication of "De revolutionibus orbium coelestium" in 1543 ?

I have recently noticed that this claim is sometimes made by economists. The appeal is simple. The fact that decades of effort by macroeconomists have not yielded models which give better predictions than an IS(with accelerator) LM adaptive expectations augmented Phillips curve model is frustrating. If, indeed, the same was true of the Copernican revolution, we can believe that we have made great progress.

I know that the Wikipedia is not edited, but no one has objected to this claim

"Copernicus' theory was at least as accurate as Ptolemy's but never achieved the stature and recognition of Ptolemy's theory."

A serious problem with the claim of fact is that the Copernican model was not improved in the 50 years which followed 1543. In fact, it wasn't improved at all.

Rather it was replaced by Kepler's model (which yields excellent predictions). Also Tycho Brahe noted that one could reconcile the Copernican model with the belief that the Earth stood still by assuming that the sun orbits the Earth and the other planets orbit the Sun. Brahe's model can not be distinguished from Copernicus's model by astronomical observations.

I think I understand the origin of the claim. Galileo obtained evidence which proved that the Ptolomaic model was not close to correct. In 1610 Galileo observed the phases of Venus. This made it possible to determine the angle between the line from the Sun to Venus and the line from Venus to the Earth. That angle corresponded to the angle predicted by Copernicus and not to the angle predicted by any Ptolomaic model.

Note 2: In planetary astronomy, predictions are made from a model of the solar system as a whole. This important because the Ptolemaic and Copernican models of the whole solar system makes different predictions about the phases of Venus, for example, even if they made the same predictions about the angular positions of the planets. Therefore, Ptolemaic and Copernican models are not predictively equivalent in any unrestricted sense.

The change in relative performance was due to the invention of the telescope not due to the relatively rapid improvement of successive models of of a new type.

This does not sound like a reasonable basis for hope for contemporary macroeconomists. It would change nothing if new data were observed which don't correspond at all to the implications of our models (IS-LM included). Many such data are available already. The economist's response to such data is that models are false by definition and the interesting question is whether they help us predict the variables of interest.

Nor is it true that further research based on the set of core assertions made by Copernicus was fruitful. The idea, old in Ptolomy's time (first written down by Plato) was that eternal motion must be circular. A hard core position was that the rate of motion around the circle must be constant and the largest circle (deferent) must be centered at the Earth (the epicycles were centered on that circle). Of course Copernicus put the Sun at the center. But he was a hard line circle guy rejecting off center deferents and insisting that motion around the deferent and epicycles had to be at a constant rate.

As noted by Kepler, the Sun is not at the center of the orbits of the planets (the center of an ellipse is halfway between the foci) but rather at a focus. Also angular momentum is constant so the speed at which planets move is not. In other words, on two of three issues which divided Copernicus from Ptolomaic astronomers, we now believe that the Ptolomaic astronomers were right. On two key points of agreement, that orbits must be made of circles and that there are deferents and epicycles, we disagree with both.

I am actually interested in whether non economists (other than Van Jacobson) make the claim that Ptolomaic predictions were better than Copernican predictions for 50 years. I suspect not. The belief seems to follow from the conviction that we have achieved a scientific revolution combined with the fact that our theories have had no empirical success.


Hans Suter said...

I've commented on facebook suchly: Robert succeeds in explaing something I don't understand at all using examples I simply don't understand.

Bruce Webb said...

I suspect you could find that claim/admission in Kuhn's original book Copernican Revolution

it would certainly be consistent with Kuhn's development of the idea of successive scientific paradigms as explicated in the even more influential Structure of Scientific Revolutions and the subsequent Popper-Kuhn debates that. Certainly Kuhn didn't equate scientific progress via models in quite the rigid way Popper's Falsificationism requires. Instead fundamental advances could go hand in hand with less precise results, there being more to science than just tacking on the next couple of decimal points.

And backing up the fundamental problem with Ptolemaic theory was not its lack of precision, it had that in plenty, but its continual development of ad hoc explanations to save it (epicycles, pericycles etc).

But in terms of the overall 'Is Economics science' I think it more fruitful to start with 'Structure' rather than recreating the wheel with 'Copernican Revolution'

Robert said...

Dear Hans

Thanks (I think).

Dear Bruce

Copernicus's model had more epicycles that Ptolomy's model.

The question of which model gave more accurate predictions from 1543 through 1593 can be answered unambiguously. Current models are so close to exact that we can tell where the planets were during that period much much better than astronomers cold tell tehn (notably without using telescopes). A current effort to determine which data were available at the time is imperfect almost entirely because we can't know about their measurement error.

The wikipedia entry to which I linked is just a Wikipedia entry, but the claim is very very definite that Copernicus's model was at least as accurate as Ptolomy's.

I haven't read Kuhn's book on the Copernican Revolution and I don't plan to. I don't recall reading any such claim in "The Structure of Scientific Revolutions" and I definitely do recall that Kuhn asserted that, at the time of a Scientific revolution, the revolution is not won because of evidence (in fact I recall that he only added the qualifier "at the time of a scientific revolution" later when challenged). He is close to asserting that different paradigms are incommesurable -- that one can only discuss truth within a paradigm. I rather doubt he would neglect to mention a fact which so strongly supported his view. I wouldn't be so surprised if I had forgotten the claim in the book, which I read decades ago.

At the moment I'm not sure about the alleged adding of epicycles to Ptolomaic models. I am going to try to find out the history of models of the solar system pre-Copernicus.

Noah Smith said...

Wow. This post is amazing.

Larry Headlund said...

I think that you will find that for reasons of computational efficiency orbits are not calculated directly as ellipses but often instead using Fourier series.

Which are, in a sense, epicycles.

Exl Blogger said...

According to The Book That Nobody Read, which was about the book Copernicus wrote describing his theory, the Copernican model produced almost identical results to the traditional model using slightly simpler calculations.

I think your comments on the speeds of the planets misses the point that both models were parametric, and the motion of a planet actually did vary in orbital speed, just that there was no point in computing that velocity. It wasn't used in predicting the important and testable thing, the location.

Similarly, the issue of the center of each orbit is a red herring. Copernicus used a computational kludge typical of the era that actually moved the center of the orbit around. As noted, all of these calculations were parametric, so once this pseudo-center was computed, you moved on to the next round of cycles and epicycles.

The power of a scientific theory is not necessarily its raw predictive power. It should do at least as well as any existing model, but it doesn't have to be better if it predicts more different things or provides the basis for a more advanced theory. For example, the Ptolemaic or Copernican model could have been adapted through the age of telescopes, but the Copernican model would have been more useful when faced with discrepancies in Mercury's orbit. Why, of all orbits, should the one closest to the sun, not the earth, have this error? Of course, Kepler and Newton's theories let Einstein come up with an answer.

Nowadays, the general power of an astronomical theory seems to correlate with how few bodies it can easily predict orbits for. Kepler and Copernicus's models had no real limits as it was strictly empirical and would add cycles as needed, just as one can always expand the spectrum of an FFT. Newton's model breaks down with the two body problem. Einstein's model breaks down with the one body problem. Quantum gravity, as best we can tell, breaks down with the zero body problem.

mulp said...

The point about the Ptolemaic v Copernican model in regard to economics is that economist insist the world revolves around their economic model.

When economic models disagrees with reality, economists patch their model with "externalities" just like the Ptolemaic model had all sorts of patches to account for the the earth and planets revolving around the sun.

See the essay "Needed: A Copernican Shift" by Lester Brown.

As in...
"In 1543, Polish astronomer Nicolaus Copernicus published “On the Revolutions of the Celestial Spheres,” in which he challenged the view that the sun revolved around the earth, arguing instead that the earth revolved around the sun. With his new model of the solar system, he began a wide-ranging debate among scientists, theologians, and others. His alternative to the earlier Ptolemaic model, which had the earth at the center of the universe, led to a revolution in thinking, to a new worldview.

"Today we need a similar shift in our worldview, in how we think about the relationship between the earth and the economy. The issue now is not which celestial sphere revolves around the other but whether the environment is part of the economy or the economy is part of the environment. Economists see the environment as a subset of the economy. Ecologists, on the other hand, see the economy as a subset of the environment."

Robert said...

Dear mulp

I assert that the Ptolemaic model did not have all sorts of patches. It had 10 free parameters per planet (I forgot that the direction earth to eccentric was always equal to earth to equant). But wait as noted by Exl there is one dimension of observational equivalence (Ptolemy did not try to predict the distance earth to planet at all). So really 9 parameters per planet. Then a disturbance term (no parametric distribution) of oh a degree or two.

With those 9 parameters if fit a huge amount of data. It was being confronted with data more than a milenium after publication (and doing about as well with the predictions as with fitting in sample). It appears not to have been fiddled or modified in over a milenium.

Comparing economics to Ptolemaic astronomy is grossly unfairly monsterously slandering Ptolemaic astronomy.

The Ptolemaic model is an example (by far the oldest example) of an excellent useful model which summarizes a huge amount of data. The claim that it was fudged and fiddled when it didn't fit the data is extremely extremely common in the secondary literature. There is no historical evidence for this claim.

Robert said...

Exl blogger

It is very hard to measure simplicity of a model. I am not convinced that Copernicus's model was simpler than Ptolemy's.

Notably Copernicus's model was not widely perceived to be an improvement (consider the title "The Book that Nobody Read"). Frankly, I'd say this makes sense. I don't think that sensible people should have been convinced by Copernicus*.

His model is better because it is much closer to the truth. We know this, because it correctly predicts the phases of Venus. It would not make sense to

*I am losing perspective. I mean that literally. One advance between Ptolemy's time and Copernicus's is that they had figured out perspective. In Ptolemy's model the distance from the earth to the moon varies by a factor of 2. The apparent size of the moon is constant. It is ironic that the model fails exactly for the object which we still think has a geocentric orbit (well really around the center of mass of the earth moon system).

I have no idea why the Ptolemaic model has this implication for distances. It seems to me that Ptolemy should just have said the moon orbits the earth with a period around 28/27ths of that of the stars.