Ockham's razor and astronomy

[johnjoe]

Hi
I am writing a book about the role of Ockham’s razor in science and one of the topics is the successive simplification of the solar system from the Ptolemaic system through Copernicus to Kepler.

Both Copernicus and the young Kepler (before he worked out the correct system) and Galileo and Tycho Brahe claimed that the Copernican system was simpler than the Ptolemaic and simplicity was the reason for their preference for heliocentricity. It is well known that the heliocentric Copernican system provided no more accurate predictions than Ptolemy's geocentric system. So despite their lack of evidence, Copernicus, (the young) Kepler and Galileo were all convinced the heliocentric system was true solely on the simplicity criterion – Ockham’s razor. Galileo additionally gave erroneous proofs, such as the tides but, apart from these, the only argument the Copernicus, Kepler and Galileo could muster for heliocentricity was that the Copernican system was simpler than the Ptolemaic.

Yet historians of science such as Thomas Kuhn and Arthur Koestler, who have counted the orbits and epicycles (circles) in both systems and come to roughly the same number, so they claim that Copernicus, Kepler and Galileo were deluded as both systems were equally complex. But then why had these great scientists been convinced by geocentricity without any other evidence? I find it hard to believe that they were deluded themselves.

The reason i believe is that the Copernican system, despite having a similar number of circles, was actually simpler because it only had to correct for Copernicus' two errors: his insistence on perfect circles and uniform motion. The deviations of the actual planetary orbits from perfect circles to ellipses and uniform motion to variable motion is relatively minor compared to the deviation of a geocentric from a heliocentric system. So i am guessing that Copernicus' correcting epicycles are much smaller than Ptolemy's. But all the diagrams i can see online are not drawn to scale so i cannot compare them.

Does anyone have scaled diagrams of the two system? Or is it possible to calculate the relative size of the circles in both systems?

[michael.h.f.wilkinson]

Note that Galileo had direct evidence from the phases, and relative sizes at different phases of the inner planets that they orbited the sun. Having one set of planets orbit the sun and the rest the earth would be a bit of an odd mix (that didn't stop Tycho Brahe, of course). You can get rid of the deferents of Venus and Mercury (and rid yourself of the fine tuning that these deferents have the exact same period of that of the sun), and the major epicycles of the outer planets, but to correct for the ellipticity of the orbits you will have to retain a bunch. So the number of removed circles might be roughly the same, but removing just one, or the aforementioned fine tuning makes the Copernican system simpler. For Galileo, the additional evidence that the inner planets move around the sun made a system in which the earth and outer planets also orbit the sun simpler than the odd mixture of the Tychonean system.

[johnjoe]

Thank you Michael

I believe that it was the phases of Venus that Galileo cited  in his Dialogue  as evidence for the heliocentric system.  But, as you say, they were compatible with Tycho Brahe's system that still had the Earth at its centre. Galileo's other evidence was earthshine on the moon - but that didn't prove geocentricity, only that the Earth  is another heavenly  body. He also claimed that the earth's tides were caused by the Earth's annual rotation , but that was clearly erroneous. 

I agree that it was specific simplifications, such as a rational explanation for retrograde motion, that convinced these great astronomers. However, in loads of history of science books the authors claim that the simplicity argument - Ockham's razor - was erroneous  because of the circle count criterion. I'd just like to knock it on the head as it kind of implies that some of the greatest scientists were deluded when they cited simplicity as their reason for supporting heliocentricity.  i think  that the relative simplicity of the Copernican would be obvious in a scaled diagram of the Ptolemaic vs Copernican  because the Copernican circles are correcting for smaller errors. But i don't  where there is one or how to make one. Anyone know?

 

[michael.h.f.wilkinson]

I will check out the books I had for the course "The History of Cosmological Thought" taught by John North, which I still have, somewhere at home. Note however that the fact that the number of circles is roughly the same is not enough to say the simplicity of the models is similar. The Ptolemaic system needed epicycles simply to explain major features such as retrograde motion, and further lesser epicycles to account for deviations from circular motion, whereas the Copernican needed no epicycles for the former, only for the latter. Besides, the fine tuning mentioned before was not needed in the Copernican system

[johnjoe]

thanks Michael. I agree with all you points but, as the historians do a circle count, i'd like to dismiss them on their own ground, if possible..  Surely someone somewhere drew both the Copernican and Ptolemaic system to the same scale?

[andrew s]

In some ways neither is right or wrong. The are just a phemenogical description from different reference frames. Until you add physical content e.g. Newton's gravity or GR it's a matter of choice and  even here you can choose different reference frames. Clearly some make the maths simpler than others.

Regards Andrew 

[johnjoe]

Thanks Andrew  you are absolutely right. In GR you can choose either heliocentric or geocentric frame. But, if You choose the geocentric then you get pretty much Tycho Brahe's systems with lots of epicycles.  You can work with this but it's much more complicated that Kepler's heliocentric.

Ultimately, all we have are models and their predictions. When we have two or more models whose predictions all fit the data then science chooses the simplest. That, I believe, is key to what science does and why it is so successful.

[ollypenrice]

I've always been troubled by an issue closely related to Johnjo's curiosity about Occam's razor. Galileo makes much of the beautiful simplicity of the heliocentric system in his dialogues - and yet the heliocentricity of De Revolutionibus is not simple at all. Indeed it isn't even heliocentric. Or it isn't, 'strictly speaking,' and there might be the rub. I always get the feeling that Galileo was writing about the Copernicanism of the Commentariolus before it all went pear-shaped (or failed to go ellipse-shaped) in De Revolutionibus. I don't think Galileo was particularly attentive to the details in other people's work and, although he said nature was written in the language of mathematics, he also thought like a physicist. Perhaps some blend of these two characteristics allowed him to see the movements of the Commentariolus through the tangled mesh of the gears making up De Revolutionibus. I like the point about the counting of epicycles being a poor indicator of simplicity because, with the single alteration brought by the ellipse, the Commentariolus can be restored. No equivalent operation could be performed upon  Ptolemy's system. Perhaps Galileo simply 'felt' this. (Or perhaps he never bothered to read De Revolutionbus! I'm half serious. Did he leave an annotated copy or detailed commentary?)

Olly

[andrew s]

Simplicity is in the eye of the beholder.  It is a judgement of personal taste.

Of course,  the "best" answer is not always the simplest. QM is based on the second simplest generalised probability theory not the first (classical probability as per rolling dice)

Regards Andrew 

[Ouroboros]

6 minutes ago, andrew s said:

Simplicity is in the eye of the beholder.  It is a judgement of personal taste.

Of course,  the "best" answer is not always the simplest. QM is based on the second simplest generalised probability theory not the first (classical probability as per rolling dice)

Regards Andrew 

Yes. Sorry if this has already been stated, but did Copernicus, Galileo etc use Okham's razor or similar arguments in support of their hypotheses? If not then this is all somewhat academic. I assume the intention of those scientists back then, as now, was to develop an accurate understanding of the universe as it actually is. Simplicity might be aesthetically pleasing but if it doesn't reflect reality then it's not worth a hill of beans. 

[Ouroboros]

PS perhaps to slightly contradict my previous post .... wasn't Kepler obsessed initially that the orbits should be round or egg shaped because these were 'divine' in some sense or other? He only accepted the ellipse because it fitted the measured data better.  Crudely you might argue that that is an example of science in action. So you might also say that Kepler accepted the in his eyes the less simple or aesthetic model.  

Edited January 20, 2020 by Ouroboros

[andrew s]

13 minutes ago, Ouroboros said:

PS perhaps to slightly contradict my previous post .... wasn't Kepler obsessed initially that the orbits should be round or egg shaped because these were 'divine' in some sense or other? He only accepted the ellipse because it fitted the measured data better.  Crudely you might argue that that is an example of science in action. So you might also say that Kepler accepted the in his eyes the less simple or aesthetic model.  

I certainly don't  know the answer to that. For a mathematician in Newton's era it would have made sense to work through the conic sections looking for a fit. Circle, eclipse,  parabola and hyperbola. These were the bread and butter of geometry of that era.

Regards Andrew 

Edited January 20, 2020 by andrew s

[ollypenrice]

2 hours ago, Ouroboros said:

Yes. Sorry if this has already been stated, but did Copernicus, Galileo etc use Okham's razor or similar arguments in support of their hypotheses? If not then this is all somewhat academic. I assume the intention of those scientists back then, as now, was to develop an accurate understanding of the universe as it actually is. Simplicity might be aesthetically pleasing but if it doesn't reflect reality then it's not worth a hill of beans. 

Galileo certainly did. Throughout the dialogue on the world systems Salviati (speaking for Galileo) appeals to qualities like elegance and simplicity in urging heliocentrism over Ptolemy. A quick dip into the book produced this quotation regarding the length of the day in the heliocentric model: 'So you see how appropriately the extremely rapid motion of 24 hours is taken away from the universe, and the fixed stars (which are so many suns) enjoy perpetual rest like our sun. Notice also how elegant this first sketch is for explaining why such significant phenomena appear in the heavenly bodies.'

In preferring to see a small Earth spinning than a vast universe, and in preferring the nearest star to have the same properties as the rest, Galileo is showing that the principle of Occam's razor informed his thinking.  The Dialogue contains countless examples of the same thing. This is not the same as arguing that simplicity equates to proof, however, and I don't think Galileo says it does. Rather it is an instinct of his (and others) to feel that a simple explanation beats a complicated one when both satisfy the observations. This instinct has been a productive one in the history of science. Trust quantum theory to make an exception!

Olly

Edited January 20, 2020 by ollypenrice

[andrew s]

Spot on @ollypenrice but it is as well to recall that a spinning, orbiting earth was obviously wrong as we sense no such motion. One man's simplification is another complication. 

Regards Andrew 

[Ouroboros]

1 hour ago, ollypenrice said:

Galileo certainly did. Throughout the dialogue on the world systems Salviati (speaking for Galileo) appeals to qualities like elegance and simplicity in urging heliocentrism over Ptolemy. A quick dip into the book produced this quotation regarding the length of the day in the heliocentric model: 'So you see how appropriately the extremely rapid motion of 24 hours is taken away from the universe, and the fixed stars (which are so many suns) enjoy perpetual rest like our sun. Notice also how elegant this first sketch is for explaining why such significant phenomena appear in the heavenly bodies.'

In preferring to see a small Earth spinning than a vast universe, and in preferring the nearest star to have the same properties as the rest, Galileo is showing that the principle of Occam's razor informed his thinking.  The Dialogue contains countless examples of the same thing. This is not the same as arguing that simplicity equates to proof, however, and I don't think Galileo says it does. Rather it is an instinct of his (and others) to feel that a simple explanation beats a complicated one when both satisfy the observations. This instinct has been a productive one in the history of science. Trust quantum theory to make an exception!

Olly

Yep. Fair points. Although one might argue that in the example you cite Galileo was as much using the 'incredulity argument'. 

[ollypenrice]

6 hours ago, Ouroboros said:

Yep. Fair points. Although one might argue that in the example you cite Galileo was as much using the 'incredulity argument'. 

I've never heard of the 'incredulity argument' as such but if I were to guess at what it might be I'd say it had something in common with Occam's razor and something alien to it.

While the attraction of simplicity has served science well, the same cannot be said for the attraction of what seems reasonable to us. It seemed unreasonable for the earth to be in rapid motion and Galileo's greatest contribution (it seems to me) was to show that, in truth, it was perfectly reasonable. It seemed reasonable to assume that time and space were constants. It seemed axiomatic to physics that it be deterministic. God does not play at dice, said Einstein, to which Bohr gave the sublime reply, 'Stop telling God what to do.'

I've never thought of this before but perhaps incredulity is the enemy of simplicity; does our sense of what is unreasonable prevent us from seeing what is actually quite simple? Relativity, for example, is not difficult to understand, when first you meet it. It's just difficult to accept. Historians and philosophers of science and evolutionary biologists seem to be converging on the notion that our sense of what is reasonable may, ultimately, put a cap on our comprehension. This because our sense of what is reasonable has been a tool essential to our survival - and our survival takes place in a local set of conditions, not a cosmological set.

Doomed to die in ignorance. Aaaarrrgggh!

Olly

[Ouroboros]

An  incredulity argument is one which says something is most likely so because it is impossible or difficult to imagine the opposite might be true.  An example is the argument that goes something like: alien life must surely exist out there somewhere because the universe is so big and there are so many planets blar blar blar .....  It's a fallacious argument of course. 

Edited January 20, 2020 by Ouroboros

[JamesF]

It even has a Wikipedia entry all of its own:

https://en.wikipedia.org/wiki/Argument_from_incredulity

James

[ollypenrice]

10 hours ago, Ouroboros said:

An  incredulity argument is one which says something is most likely so because it is impossible or difficult to imagine the opposite might be true.  An example is the argument that goes something like: alien life must surely exist out there somewhere because the universe is so big and there are so many planets blar blar blar .....  It's a fallacious argument of course. 

 

9 hours ago, JamesF said:

It even has a Wikipedia entry all of its own:

https://en.wikipedia.org/wiki/Argument_from_incredulity

James

Thanks. I hadn't come across this as an established concept though I've long subscribed to the view that the universe has no need whatever to behave in a way which seems reasonable to me. In fact the whole charm of astronomy, cosmology and physics is that they throw our preconceptions out of the window. Didn't Einstein say that common sense was just the name given to that set of prejudices accumulated by age eighteen, or something like that?

Olly

[andrew s]

1 hour ago, ollypenrice said:

Didn't Einstein say that common sense was just the name given to that set of prejudices accumulated by age eighteen, or something like that?

Olly

Indeed he did "exactly" that 😉 although possibly in German. My only prejudice is that I don't have any. Now that's  a self referential paradox ala Bertrand Russell. 

Regards Andrew 

Edited January 21, 2020 by andrew s

[JamesF]

I have occasionally been tempted to suggest to some people that "common sense" is an oxymoron.  Unfortunately I think it would have been lost on most of them.

James

[saac]

On 21/01/2020 at 10:23, JamesF said:

I have occasionally been tempted to suggest to some people that "common sense" is an oxymoron.  Unfortunately I think it would have been lost on most of them.

James

I turn to Mark Twain on those occasions    "Never argue with stupid people, they will drag you down to their level and then beat you with experience".  

I feel I'm having to turn to Mr Twain more often these days.  

Jim  

[JamesF]

I didn't realise that was Mark Twain, though I also admit to having used the quote on a number of occasions.

James

[ollypenrice]

On 20/01/2020 at 23:44, Ouroboros said:

An  incredulity argument is one which says something is most likely so because it is impossible or difficult to imagine the opposite might be true.  An example is the argument that goes something like: alien life must surely exist out there somewhere because the universe is so big and there are so many planets blar blar blar .....  It's a fallacious argument of course. 

Point taken. But if we take the 'billions of stars therefore alien life' argument and add to it the observable fact that the 'laws' of physics and chemistry of the local environment seem entirely consistent with those seen everywhere within observation range, does the argument not gain a dimension? If we found that, not too far from the sun, the local laws did not apply then the 'billions of stars' argument would fail entirely. When we combine the 'billions of stars' with the scientific consistency of the universe should we not then invoke another guiding principle of astronomy, the Copernican principle, which advises us to beware of believing that there is something special about our immediate environment?

Neither Occam's Razor nor the Copernican Principle are arguments and they are certainly not proofs, but rather they are notes of caution which it might be wise to sound at the hypothetical stage of theory-building.

Or am I missing a philosophical point about the 'billions of stars' argument? That's quite likely!

Olly

[andrew s]

On 25/01/2020 at 09:08, ollypenrice said:

Neither Occam's Razor nor the Copernican Principle are arguments and they are certainly not proofs, but rather they are notes of caution which it might be wise to sound at the hypothetical stage of theory-building.

Or am I missing a philosophical point about the 'billions of stars' argument? That's quite likely!

Olly

At best they are an aid to thinking at worst a block.

I am very suspicious of the 'billions of xxx' arguments. Technically you can't define a probability density on an infinite dimensional set. In addition extrapolation from one case to 'billions' again seems unjustified given the circularity at the heart of frequentist probability theory.

Even if one of the infinite typing AI robots did reproduce this post how could you know?

Better to wait for observations. The history of Astronomy has shown that what we thought we new is often totally wrong when new observations are available. E.g. were not all planetary system thought to be like ours?

Regards Andrew 

Edited January 26, 2020 by andrew s