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Wednesday, April 15, 2009

 

Tycho Brahe gets a Shave

Back in March I wrote a post “Occam's Razor and the Two World Systems”, where I discussed the idea propounded by William Wallace that Occam’s razor failed when applied to the transition from the Ptolemaic geocentric solar system to the Copernican heliocentric solar system. Mr Wallace replied on that post and I promised to respond, but life (and various asteroids and comets) got in the way. Rather than add new comments there. I’ll take this up as a new post.

The starting point of the old post was Mr Wallace’s contention:
I have a counter example, from science, fully described here, where Occam's razor fails. The idea that the "simplest explanation is probably right" was falsified when Tycho Bryhe [sic] rejected heliocentricism for geocentricism, based on his analysis of the best available data.
Once again, I must emphasise that Occam’s razor is not the simplest explanation is probably right, but let’s pick up on Mr. Wallace’s comments. I’m going to do this slightly out of order, so as to address particular issues that arise from the quotes more logically
There were three systems, Copernicus, classical Ptolemaic, and neo-Ptolemaic (or Tycho's). Both Ptolemy's and Tycho's could be accurately described as geocentricism. I just want to clarify that I don't think I ever claimed--and I certainly never intended to claim--that Tycho held a purely Ptolemaic view of the solar system. He held a geocentric view, more consistent with Ptolemy's than Copernicus's (though Kepler's was arguably more akin to Copernicus's than Tycho's was to Ptolemy's.)
This is so very, very wrong. Tycho’s system was not a neo-Ptolemaic system, as I describe below, Tycho explicitly rejected the Ptolemaic system based on observational evidence. Tycho accepted most of Copernicus’s system, but balked at a moveable Earth and produced a Heliocentric-geocentric system (not a geocentric system, for another animation of the respective systems see here). Indeed it is an “inverted Copernican” system, basically a remapping of the Copernican system into a reference frame centred on Earth. Tycho’s system contains nothing of Ptolemy; there are no equants, no great epicycles and so on[1]. I’ll emphasise that again, Tycho’s system was not a re-jigging of Ptolemy, it was an inversion of Copernicus’s system.

The only point of similarity between Ptolemy’s system and Tycho’s system was the Earth was immobile in both systems, but in Tycho’s, everything but the Moon rotated around the Sun. Again, the key features of Ptolemy’s system, the equant and the great epicycles were absent from Tycho’s formulation. This may seem like mere pettifoggery, after all, both Ptolemy and Tycho had the Earth as the centre of the solar system, but Ptolemy’s system was not just “everything goes around the Earth”. Tycho had explicitly rejected the Ptolemaic system, all the key features of the Ptolemaic system, taken all the planets and placed them around the Sun and grounded his system on a reformulation of the Copernican system.
Tycho's system required fewer calculations and was consistent with all known measurements. Copernicus's was not consistent with observations.
Tycho's system required roughly the same number of calculations as Copernicus’s, as it was basically Copernicus’s translated into Earths reference frame [2]. Tycho fully accepted Copernican geometry, used Copernican planetary models, and where he did not explicitly do his own calculations, he used planetary tables based on Copernican models. Where Tycho was more accurate than Copernicus, it was through his greater observational accuracy, not any superiority of his model. Indeed, when he talks of his system, he notes that he has kept all the superior features of the Copernican system. Ironically, it was Tycho’s own measurements of the opposition of Mars in 1582 that showed that the Copernican model was in better agreement with the observed retrograde motion of Mars than the Ptolemaic model.
And yet Copernicus' model defied experimental verification, using the best astronomical apparatus of the time (Tycho's).
Actually, that’s not true. There was a key test of the Ptolemic vs Copernican system and the Copernican system came through with flying colours. It was one of the key results that forced Tycho to reject the Ptolemaic system. However, that test tends to be ignored these days because of modern commentators focusing on the issue of stellar parallax.

We now know that stellar parallax could not be measured with instruments available then. It wasn’t obvious back then, and there were several attempts to measure the stellar parallax. Tycho established that the stellar parallax had to be less than 0.1 degree. However, this did not falsify the Copernican model as negligible parallax was an a priori feature of the Copernican system.

Tycho was well aware of this, and his argument was not that the lack of parallax showed that the Earth did not move, but that if the parallax was so small the distance between Saturn and the stellar sphere would have to be 700 times the distance between the Sun and Saturn. A provident creator would not be so wasteful of space and produce such asymmetry in his creation.
So we can see that the stellar parallax argument as used by Tycho is in the end not a scientific argument.

So what was the measurement that convinced Tycho to reject the Ptolemic system? Ironically, it was a parallax measurement. One of the predictions of the Copernican system was that Mars would be closer to Earth than the Sun at opposition; while in the Ptolemaic system Mars would always be more distant from the Sun. Tycho’s careful measurements of the parallax of Mars showed that Mars was closer to Earth than the Sun. Similar measurement of Venus’s parallax by Tycho also confirmed Copernican predictions. Copernicus was right, Ptolemy was wrong, and Tycho unhesitatingly rejects Ptolemy. But in the end Tycho rejects both Ptolemy and Copernicus.
My ultimate point about Tycho's rejection of Copernican theory was that applying principles of modern science sometimes leads one astray.
Erm. Mr. Wallace. This is what you said:
I have a counter example, from science, fully described here, where Occam's razor fails...
In this case, it was Tycho’s system failed the Occam’s razor test. It requires more assumptions than the Copernican system, introduces two centres of motion, introduces more problems with motions and whilst reproduces the retrograde motions of the planets, it no longer provides these motions as a natural consequence of the orbits of the planets. Altogether it is far less economical than the Copernican system and no longer explains the precession of the equinoxes and is affected by solar eccentricity (and this was pointed out at the time). Occam’s razor doesn’t fail, because Occam’s razor was not used to make the choice between the Copernican and Tychonian systems. What was the basis of Tycho’s rejection of the Copernican system? Let Tycho tell us in his own (translated) words.
Since all these results [parallax measurements of Mars and Venus] did not all agree with the Ptolemaic hypotheses I was urged afterward to put more and more confidence in the Copernican invention. The exceedingly absurd opinion that the Earth revolves uniformly and perpetually nevertheless made up a very great obstacle, and in addition the irrefutable authority of the Holy Scripture maintained the opposite view. [emphasis added]
It wasn’t the principles of modern science that lead Tycho astray.

[1] The equant was seen as a particular drawback to Ptolemy’s system, if one wanted to explain planetary motion in terms of uniform circular motion, and Copernicus reformulation of planetary motion so that the equant was dispensed with. This was seen by contemporary astronomers and mathermaticians and a great benefit of the system. Tycho too saw the equant as something undesirable, and the great epicycles of Ptolemy as unparsimonius.
[2] Tycho got rid of Librations, but generally his scheme was Copernicus’s recast from Earth’s frame of reference.
[3] Ironically, Tycho’s system made the acceptance of the Copernican system easier. It made people familiar with the Copernican system, and smashed key sections of Aristotelian physics which have proved a barrier to acceptance of he Copernican system.

Sources:

The Reception of Copernicus’s Heliocentric Theory 1973 ed Jerzy Dobryzcki, Reidle esp Chapter 3.
Copernicus, On the Revolution of the Heavenly Spheres (translation AM Duncan 1976) Barnes & Nobel
The Copernican Revolution 1957, TS Kuhn Harvard University Press
The Book Nobody Read 2004, O Gingerich, Walker & Company

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Comments:
Now I am busy. Meanwhile, why the adjective "great" in the phrase "great epicycles"? Could you comment on epicycles in general before I respond...
 
To account for the retrograde motion of the planets, Ptolemy made the planets be carried on great epicycles that occupied most (or a large chunk of) of the orbits (again, see the animation here.

Copernicus did away with these great epicycles.

But even with the great epicycles, Ptolemy's system still needed additional, much smaller (with respect to the orbit of the planet) epicycles for accuracy. Neither Copernicus nor Tycho could get rid of all these small epicycles (as of course, the orbits of the planets are eliptical, not circular).
 
Wallace is an idiot and a blowhard; don't waste your time.
 
Anonymous wrote Wallace is an idiot and a blowhard; don't waste your time.On the contrary, it's not all a waste of time -- think of the lurkers like me who learn from these posts!
 
Sharing the history of astronomy, especially when it throws light on how science is done, is never a waste of time.
 
I am curious what motivates you to quote:

"was falsified when Tycho Bryhe [sic] rejected heliocentricism for geocentricism, based on his analysis of the best available data.as opposed to:

"was falsified when Tycho [Brahe] rejected heliocentricism for geocentricism, based on his analysis of the best available data.'

You also wrote: "The only point of similarity between Ptolemy’s system and Tycho’s system was the Earth was immobile in both systems"

Hence, the term geocentricsm.

More to come latter. Meanwhile, feel free to gloat if I misspelled any other names or words.
 
William Wallace wrote: I am curious what motivates you to quote:

"was falsified when Tycho Bryhe [sic] rejected heliocentricism for geocentricism, based on his analysis of the best available data.That is the standard quotation practice in my discipline. You don't mess with other people wording. As the Typo king I can't complain about peoples spelling.

William Wallace wrote:
You also wrote: "The only point of similarity between Ptolemy’s system and Tycho’s system was the Earth was immobile in both systems"Hence, the term geocentricsm.

No, it's a heliocentic-geocentric system, all the planets bar one (two if you count the Moon) circled the Sun. If you can't understand the fundamental difference between a geocentric and heliocentric-geocentric system, then you are going to have trouble following the rest. This is not a trivial distinction, but one of fundamental importance (where's the equants in Tycho's system?)
 
"No, it's a heliocentic-geocentric system, all the planets bar one (two if you count the Moon) circled the Sun."

On average, which object is at the *center*, the Earth, or the sun?

"The exceedingly absurd opinion that the Earth revolves uniformly and perpetually nevertheless made up a very great obstacle, and in addition the irrefutable authority of the Holy Scripture maintained the opposite view."--Tycho Brahe

To what extent, in your interpretation, was Tycho Brahe motivated by observations, and to what extent was he motivated by scripture, in concluding the Earth was stationary?

I.e., in your view, was consistency with scripture essential, or just the icing on the cake?

Again, feel free to quibble if it makes you feel good. It makes you look petty, but if that is how you want to look, go for it.
 
William Wallace said:On average, which object is at the *center*, the Earth, or the sun?That question is meaningless. There are Two centres of motion The Sun and the Earth. You can't average them at all.

William Wallace said:To what extent, in your interpretation, was Tycho Brahe motivated by observations, and to what extent was he motivated by scripture, in concluding the Earth was stationary?Why do you need my interpretation. You can read his very own words. He rejected a moving Earth because of a combination of (non-observational) neo-Platonic metaphysics and scripture, with scripure figuring heavily. It's mentioned a lot in his various accounts and letters.
 
"Why do you need my interpretation?"

Because I have one quote, and it's not clear. It appears that it could just be the icing on the cake. Just today I made a design decision for one reason, but the decision had an ancillary benefit: it reduced cost.

I did not consider cost in making the decision, as time is rather critical right now.

But I pointed it out the cost benefit to my boss after I explained the technical reasons for the decision, partly because he always likes to save money where possible.

However, I did take the time to disclose that if it weren't for the technical issues, and considering that I am working on a higher margin device, I would not have made the change I made if it weren't for the technical reason.

Tycho made no such distinction in your quote.

So, if it is not an interpretation, do you have good evidence to assert that Tycho Brahe would have ignored contradictory evidence, and been guided by scripture, based on your quote, or any other quote you want to introduce? That is, if evidence was readily available to Tycho Brahe that the Earth really was moving through space, would he have ignored it?

Regarding the question of whether or not Tycho Brahe's was a geocentric system, we will have to agree to disagree. I do know of others who say it was geocentric.

For example,

"However, Tycho did not completely disbelieve the geocentric model. He developed a system that kept the Earth at the center, but the other planets revolved around the sun in circles, which orbited Earth in a circle. This model became very popular for a while."--From a website largely authored by Stuart Robbins, graduate student in astronomy

"Tycho’s geocentric model put the Earth at the centre (A) of the universe, with the Sun (B) revolving around it, and the planets revolving around the Sun."Encyclopedia Britanica"Believing that the Copernican system with its moving earth defied the laws of physics, Brahe devised a geocentric organization of the solar system.--"Brahe, Tycho - Introduction." Literary Criticism (1400-1800). Ed. Jelena O. Krstović and Marie Lazzari. Vol. 45. Gale Cengage, 1999.

Professor Steven L. Goldman, who has taught the history of science, also refers to it as a geocentric system.

On the other hand, in hindsight it seems obvious to me that you could construct a Brahe system around any of the planets; it would just be a change in reference.

Do you think, or know, if Brahe realized this?

WW

P.S. I just realized that before this latest entry "Tycho Brahe gets a shave", the Bryhe misspelling had already been corrected at my site.
 
William Wallace said: "Because I have one quote, and it's not clear."It's very clear. He has just performed the most precise measurements of parallax of Venus and Mars and has found that they agree with the Copernican, not the Ptolemaic, predictions. It was the combination of scripture and metaphysics, not observation, that made him reject the Copernican system He quotes scriptural reasons several times in his book Opera Omnia (eg see Vol VII, 202-203), letters and especially the correspondence with Caspar Peucer and Christopher Rothmann.

And for your sources, a very short paragraph on the history of Astronomy that doesn't actually call Tycho's system anything, Literary Criticism for heaven's sake and Goldman is a sociologist, not a historian of science (and if he can't understand the distinction between the Ptolemic and Tychonican systems, he's not much of an anything of science).

Tycho's system is heliocentric-geocentric. And Tycho rejected the Ptolemaic geocentric system in no uncertain terms.

William Wallace wrote: "On the other hand, in hindsight it seems obvious to me that you could construct a Brahe system around any of the planets; it would just be a change in reference.

Do you think, or know, if Brahe realized this?"
It is very hard to tell if Tycho realised this. He certainly understood that his system was a remapping of Copernicus's, but it is doubtful if such a radical vision would have occurred to him. It wouldn't have fitted his need to align the solar system with scripture and God's revealed truth (eg see Opera Omnia Vol I 152).
 
"Tycho's system is heliocentric-geocentric. And Tycho rejected the Ptolemaic geocentric system in no uncertain terms."

I agree that he rejected the Ptolemaic system, but he did not reject geocentricism. And using "heliocentric-geocentric" as a description just does not jive with the fact that the sun is moving in Brahe's system. The word centric has a specific meaning, "located at the center". "Heliocentric-geocentric" thus implies that the sun and the Earth are co-located.

"Goldman is a sociologist, not a historian of science (and if he can't understand the distinction between the Ptolemic and Tychonican systems, he's not much of an anything of science)..."

Goldman has a B.S. in physics and a Ph.D. in philosophy, and is very well read, and has taught courses in the history of science and philosophy of science. Wikipedia says "He has a joint appointment in the departments of philosophy and history because his teaching and research focus on the history, philosophy, and social relations of modern science and technology."

Regarding sources, that was just a quick list. I notice you didn't bother mentioning the Encyclopedia Britannica source.
 
William Wallace wrote:I agree that he rejected the Ptolemaic system, but he did not reject geocentricism. He rejected the dominant paradigm, the one that held sway for nearly 2000 years, the one that defined geocentrism to the world. After all, Galileo's "Dialogue concerning the two chief world systems" the classic heliocentric vs geocentric text post Tycho is about the Ptolemaic system vs the Copernican system.

If you can't recognise that in Tycho's system, everything except the Earth and Moon rotates around the Sun, and that there are two centres of motion, then you are missing the point big time.

Wiliam Wallace wrote: Goldman has a B.S. in physics and a Ph.D. in philosophy, and is very well read..... and what he does is sociology. I have a B.AppSc. in Medical Technology, but what I do is try and develop drugs that will unfold misfolded proteins, hopefully to use in Alzheimer's disease.
 
I forgot the most important point.

William Wallace wrote:I agree that he rejected the Ptolemaic system....He rejected the Ptolemaic Geocentric system because his own observations agreed with predictions of the Copernican system. In 1587 he stood on the brink of accepting the Copernican system based on his observations, but in the end he quailed and rejected Heliocentrism, not because of observation, but because of metaphysics and religion.

You can call Tycho's system whatever you like, you can call it pink spotted hufflepuff, but the facts above refute your article and its central point.
 
And yet it's you against the world.

But here's another interesting question: Why did Galileo reject Kepler's explanation of elliptical orbits and non-uniform speeds?
 
So William, rather than attempt to support you claim that Tycho represents a failure of Occam's Razor, you are turning to non-sequiters.
 
It's not a failure, you're just engaging in semantic games, and you've already declared that I can call it whatever I want. We are at a deadlock.

I've clarified my view on Tycho Brahe, and you have attributed to Tycho Brahe a belief in religion for his refusal to model the solar system as a heliocentric system. I suspect that was the icing on the cake.

Meanwhile, you have yet to produce a single piece of evidence that was available to Tycho Brahe that should have led him to model the solar system as a strictly heliocentric model.

On the other hand, I am pointing to such a piece of evidence on the part of Galileo. Kepler's findings.

Clearly, Kepler found in Tycho's data data evidence of elliptical orbits, but Kepler found that after Tycho Brahe died, and many scientists afterward have been unable to agree, from what I understand, whether Kepler's discovery was an act of genius or just an honest look at the data.

It seems to me that many scientists think it was an act of genius, and that the 1/4 or so orbit worth of data that was initially used by Kepler did not scream "elliptical". However, this viewpoint of Kepler's genius is not universal.

Regarding Galileo, I am trying to suggest an interesting topic for another post, as you seem to be interested in the history of astronomy and science. Why did Galileo pit the discredited Copernican model of circular orbits against the discredited model of Ptolemy?

To what do you attribute Galileo's ignoring Kepler's findings in Dialogue Concerning the Two Chief World Systems?

Since Galileo is today held up as a martyr for science against the Church, it seems doubtful that his reluctance to cite Kepler had little to do with a reading of scriptures.

It is an interesting, slightly related, topic. If you don't find it interesting, just say so. You don't need to call it a red herring. The other discussion was already concluded, it seemed.
 
That should have been: ...it seems doubtful that his reluctance to cite Kepler had to do with a reading of scriptures
 
William Wallace wrote: "Meanwhile, you have yet to produce a single piece of evidence that was available to Tycho Brahe that should have led him to model the solar system as a strictly heliocentric model."

Did you actually read the article? What were Tycho's observations of the parallax of the orbits of Mars and Venus, which were incompatible with Ptolemy's system, but were predicted by the Copernican system if not evidence?

Oh, and I haven't attributed a belief in religion to Tycho, he himself does, multiple times in his writings (of which a quotation was given).

So, rather than admit that you statements about Tycho and Occam's Razor are wrong, you are trying to change the subject.
 
So you think that Brahe's belief in the Holy Scriptures led him away from the truth? No, it was Copernicus's unbelief in the Holy Scriptures that led him and the whole modern day Scientific community away from the truth. Brahe was right.
 
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