Astroblog

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

Labels: Copernicus, creationism, Galileo