A misleading illustration.



The difference between an easy model and a complicated one.

The gif above, from Malin Christersson’s  Website, has been making the rounds of the Internet to much acclamation but it is in my opinion severely misleading in what it claims to represent. Some people have pointed out that the heliocentric model is false because the orbits should be elliptical. This is my opinion an irrelevance because the eccentricity of the planetary orbits, that is the degree by which the ellipses differ from a circle, is so small that in a diagram of this sizel it wouldn’t be really detectable. In fact illustrations of the heliocentric system tend to exaggerate the eccentricity to make it clear that the orbits are in fact ellipses. My problem is another. The two models are presented side by side as if they were directly comparable but in fact they are two radically different representations.

The heliocentric system is displayed from a bird’s eye, or perhaps a god’s eye, view from a position directly above the sun perpendicular to the plane of the planetary orbits somewhere a couple of billion kilometres out in space. One should point out the sizes of the orbits are not to scale. Opposed to this the presentation of the geocentric system is not something one could actually view in reality. It is a fictitious birds eye view of the system as reconstructed by the astronomers in antiquity based on the activities they saw in the heavens and herein lies the crux of the problem.

Viewed from the earth the moments of the celestial bodies is not the lovely regular circles depicted in the heliocentric model above but a bizarre dance of confusing movements. The sun appears to go around the earth once a year and the moon once every approximately twenty-nine days. The so-called inner planets mercury and venus both also appeared to take a year to orbit the earth never wandering far from the sun, at times to one side and at other times on the other. Often both disappeared for periods of time. This behaviour led some people in antiquity to speculate that they orbit the sun and not the earth, the so-called Egyptian or Heracleidian model. It is however the so-called outer planets mars, jupiter and saturn that display the most puzzling behaviour. They role along in one direction for a lengthy period of time and then appear to stand still for a short period before turning tail and heading back in the opposite direction after a short time remaining stationary again before resuming in the original direction. These apparent loops in the planets progress are known technically as retrograde motion. We now know that this is an illusion created within the heliocentric system as the earth moving faster overtakes one or other of the outer planets. Given the seemingly stationary condition of the earth this was a difficult conception leap for astronomical observers to make. In fact in two thousand or more years of astronomy only two people appear to have made that leap, Aristarchus of Samos in the third century BCE and Copernicus in the fifteenth century CE. Both of these visionaries still had to cope with the very obvious empirical evidence that the earth doesn’t move.

The gif above creates a false impression because it seems to imply that the simplicity of the heliocentric system makes its an obvious choice over the geocentric model but as should be obvious from my description of what you actually see as an observer on the earth, and all observers in the past were on the earth, making that choice is anything but simple or obvious. The creator of the gif includes a short history of the journey from geocentricity to heliocentricity, which unfortunately contains various errors and misconceptions, which I will now highlight.

≈ 350 BC, Aristotle 

Aristotle a pupil of Plato, becomes the tutor of Alexander the Great. Aristotle’s views of the world shape science for centuries. His influence lasts until the enlightenment. In his book On the Heavens (part 14), Aristotle asserts that:

From these considerations then it is clear that the earth does not move and does not lie elsewhere than at the centre.

Aristotle is just one of many scholars from antiquity whose views influenced the future views of the world. He in fact inherited and modified the homocentric geocentric views and models of Eudoxus and Callippus. These models could explain retrograde motion fairly well but not the observable variation in brightness of the planets. This was not the system that medieval Europe inherited from antiquity. See below Ptolemy.

 ≈ 250 BC, Aristarchus

Aristarchus estimates the size of the sun to be much larger than the size of the earth. Based on this observation he then presents the heliocentric model.

The geometrical text, which is attributed to Aristarchus, is for determining both the distance of the sun from the earth and its size relative to the moon. It is a purely geocentric text and has nothing to do with his speculation about a heliocentric cosmos. There are no direct accounts of Aristarchus’ heliocentric model so we don’t actually know what caused him to adopt it.

 ≈ 250 BC, Archimedes

In The Sand-Reckoner, Archimedes estimates the number of sand corns in the universe using the heliocentric model of Aristarchus.

In the Sand Reckoner Archimedes wishes to demonstrate his system for recorded extremely large numbers. He uses Aristarchus’ heliocentric model, which he sketches, because Aristarchus argued that the stars were much further away than hypothesised in the normal geocentric model in order to explain why there was no observable stellar parallax. Archimedes used this model because it would require many more grains of sand to fill thus giving him a much greater number to express with his system. It is only one of two accounts of Aristarchus’ heliocentric system both of which are uninformative.

≈ 150 AD, Ptolemy

In his book Almagest, Ptolemy introduces so called epicycles to explain planetary motions, based on the assumption that the earth is at the centre and does not move. Almagest is considered to be one of the most influential scientific works in history.

The epicycle system of planetary motion, used extensively by Ptolemy in the Almagest in the second century CE, was first introduced by Apollonius of Perga in the third century BCE and used extensively by Hipparchus of Rhodes in the second century BCE.

1543, Nicholaus Copernicus

Just before his death, Copernicus publishes the book De Revolutionibus Orbium Coelestium (On the Revolutions of the Heavenly Spheres) in which he places the sun rather than the earth at the centre of the universe. This book is the beginning of the Copernican Revolution.

In English it’s Nicolaus (no ‘h’) Copernicus and in De revolutionibus the sun is not at the centre of the universe but somewhat off centre. Viewed strictly Copernicus’s system is heliostatic but not heliocentric.

1572, Tycho Brahe

Tyco Brahe observes a star being born and publishes his observation in De nova stella. Brahe’s observation refutes the commonly held view at the time, a view which dates back to Aristotle, that the stars are fix and never changing at the outskirts of the universe. Since Brahe couldn’t observe a stellar parallax, he concluded that the earth did not move. He proposed a model where the planets move around the sun, and the sun moves around the earth. (It was later shown that it wasn’t a star being born Brahe had observed, but the supernova SN 1572, i.e. a star exploding.)

In the first half of this paragraph we have an oft-repeated semi-myth. Although Tycho did indeed observe the nova of 1572 and it did contradict Aristotle’s cosmological theory of an immutable heaven this story is a myth for three different reasons. Firstly Aristotle’s concept of a an immutable heaven had already been seriously challenged in the sixteenth century by several leading astronomers based on their observations of several comets in the 1530s, so the nova of 1572 was not the first problem for Aristotle’s cosmology. Secondly Tycho was by no means the only astronomer to observe and comment on the 1572 nova and Michael Maestlin’s and Christoph Clavius’ acceptance that the nova was supralunar had more impact than Tycho’s. The attribution of this impact to Tycho alone is a version of the lone genius myth and historically false. Thirdly the refutation of Aristotle’s theory of the immutability of heaven actually has no real relevance for the geocentricity/heliocentricity discussion.

1609, Johannes Kepler

Using the observational data collected by Tycho Brahe, Johannes Kepler introduces his first two laws of planetary motion in Astronomia nova. The first law: the planets move in elliptical orbits with the sun at one focus.

Given that it was actually Kepler’s work that led to the acceptance of heliocentricity our author gives him rather short shrift in his chronology. What about the other two laws of planetary motion or the Rudolphine Tables?

 1616, Roman Inquisition

On 24 February 1616 a team of eleven consultants for the Roman Inquisition condemns the Copernican System, stating that the heliocentric system is “foolish and absurd in philosophy and “formally heretical”.

It should be pointed out that the Pope never confirmed the heretical status of heliocentricity thus it never was heretical.

 1633, Galileo Galilei

Galileo Galilei stands trial on suspicion of heresy “ for holding as true the false doctrine taught by some that the sun is the centre of the world”. At the trial he is found guilty and sentenced to formal imprisonment. Galileo spends the rest of his life under house arrest.

 1687, Isaac Newton

Sir Isaac Newton publishes Philosophiæ Naturalis Principia Mathematica (Principia). In Principia, Newton explains Kepler’s laws of planetary motion in terms of universal gravitation. Newton doesn’t consider the sun to be at rest, instead he uses the center of gravity of the solar system.

A small point, but one that irritates me. The man who published the Principia in 1687 was not ‘Sir’ Isaac Newton but just plain Isaac Newton who didn’t get knighted until 1705.

1838, Friedrich Bessel

Friedrich Bessel is the first to accurately measure a stellar parallax. In 1838 he announces that the star 61 Cygni has a parallax of 0.314 arcseconds.

Friedrich Bessel was not the first to accurately measure stellar parallax that honour goes to the Scottish astronomer Thomas Henderson, who measured the parallax of Alpha Centauri. Friedrich Bessel, however, was the first to publish.

1992, Roman Catholic Church

Pope John Paul II closes a 13-year investigation into the church’s condemnation of Galileo in 1633 by declaring that Galileo was right:

 Thanks to his intuition as a brilliant physicist and by relying on different arguments, Galileo, who practically invented the experimental method, understood why only the sun could function as the centre of the world, as it was then known, that is to say, as a planetary system. The error of the theologians of the time, when they maintained the centrality of the earth, was to think that our understanding of the physical world’s structure was, in some way, imposed by the literal sense of Sacred Scripture.

This final paragraph is just a horrible mess. Galileo did not practically invent the experiment method. Also the claim that he “understood why only the sun could function as the centre of the world” is simply bizarre. As I have pointed out in a number of different posts, in Galileo’s time the scientific evidence actually favoured a geocentric system. This also applies to the comment about the theologians, whose belief in a geocentric system was strongly supported by the available scientific evidence and was not just based on Sacred Scripture. It is also interesting to note how a chronology of the geocentric/heliocentric astronomical systems suddenly veers off into an account of Galileo’s troubles with the Catholic Church, which in real terms in the history of astronomy and cosmology is just a small side show.



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56 responses to “A misleading illustration.

  1. Great post Thony, a treasure trove of little-known facts.
    The only bit I (a non-expert) don’t entirely agree with is the statement “in Galileo’s time the scientific evidence actually favoured a geocentric system”. It’s a legitimate point of view of course, but my understanding is that different historians take different views on this…a fascinating debate….

    • “different historians take different views on this”

      They do? I can’t think of any historians of science who would disagree with what Thony said. Which historians are you thinking of, exactly?

  2. C M Graney

    I love the animation, especially the higher-resolution version on MalinC web page that you linked to. But the “an easy model and a complicated one” heading is certainly bogus. They are the exact same model — just, as you’ve mentioned, seen from the point of view of the sun on the left, and from the point of view of the earth on the right. One cannot be “easy” and the other “complicated” if they are the same. This seems pretty obvious, and I do not know why the maker of the animation mucked up this nice work with that heading. Were it not for that heading, I would use the animation in class as a nice illustration of planetary motions as seen from the sun on one hand, and the earth on the other.

    • Geometrically the same model, but not dynamically.

      And perhaps the canonical example of how unreliable a guide “simplicity” is. Kepler remarked, concerning the (non-gif) version of the right-hand diagram: “These motions, continued farther, would become unintelligibly intricate…”

      Donahue (in his translation of the Astronomia Nova) writes about Kepler’s diagram:

      [This figure] is a momentous diagram. Nothing like it had ever before been published. Astronomers had become so accustomed to thinking of celestial motions as compounded circular motions that it had apparently not occurred to anyone to consider the actual path traversed by a planet…

      But of course, Ptolemy & Co. had no reason to believe that the actual paths of the planets should be simple.

  3. Anyone who claims Aristotle was a student of Plato is extraordinarily I’ll informed at best.

  4. Hello Tim,
    A good example would be the highly respected Harvard historian Owen Gingerich. As Owen has pointed out in many articles and books, one has to be careful of demanding (as the Catholic Church did!) ‘proof’ of the heliocentric model. This would be an impossible ask of science (at any time, not just in Galileo’s era). As I’m sure you know, science can never prove something is definitely true (because we don’t know what new evidence will come to light that shows the current model is incomplete). Instead science works by inference to the best explanation for currently available data. Professor Gingerich points out that Galileo’s argument was not that one particular phenomenon ‘proved’ that the earth revolves around the sun, but that the totality of contemporary observations (the moons of Jupiter, the phases of Venus, the relativity of motion etc) made it more reasonable to postulate that the earth revolves around the sun rather than vice versa.
    A nice summary of the Gingerich argument can be found on page 180 of his article ‘Kepler, Galileo and the Birth of Modern Astronomy’ http://journals.cambridge.org/download.php?file=%2FIAU%2FIAU5_S260%2FS1743921311002250a.pdf&code=1c349b9062f1b288a52396b9fb4b0cce

    I should say it is by no means a minority view on this topic, I’ll dig out a few other favourites this evening if I can think of them
    Kind regards, Cormac

    • Baerista

      I don’t read Gingerich as claiming that the Copernican hypothesis had more evidentiary support than the Tychonic one. In fact, he acknowledges, like everybody else in the field, that Galileo’s observations jibed with either system. As a matter of fact, Owen Gingerich praised Christopher Graney’s book “Setting Aside All Authority”, which very stringently argues for the very point Thony made.

      • Quite right Baerista. Owen, like many scholars, has noted that, in his discussion of the Copernican vs Ptolemaic models, Galileo routinely ignored the Tychonic model. Different scholars have suggested different reasons for this omission. One reason seems to be that the main (only?) argument against Tycho’s model concerned an argument by Kepler on the pleasing, natural sequence of the orbital periods of the planets in the Copernican model. Certainly, Kepler considered this issue in detail, and thus the question falls within the larger question of Galileo’s consistent failure to invoke Kepler’s findings. As Fantoli has pointed out, there were probably good reasons for this behaviour – explicitly citing the work of a well-known Lutheran would have exposed Galileo to his enemies within the Church. On the other hand,using Kepler’s work without naming him would have exposed Galileo to censure from colleagues and philosophers etc etc.
        I seem to recall Gingerich has a substantial discussion of this point somwhere, it might be in his article ‘The Galileo Affair’

  5. Walter Hehl

    First, yes and thanks, the comparison of the two graphics can easily be unfair by insinuating that the former scientists were just stupid not to see the simplicity of heliocentrism. Instead those modern interpreters might not know the strangeness of the real observed planetary motions with loops and retro movements which make the right side graphics very natural.

    Thony, I am alarmed by your comment “Galileo did not practically invent the experiment method”. What about the experiment with the inclined plane? Isn’t he the first to have had this (brilliant) idea to make the time measurements (almost) feasible by slowing down the motion? If not, i would really not see much of his scientific fame left. His explanation of the tides is a shame!

    • Joseph O'Leary

      The fact that Galileo performed a given experiment does not demonstrate that he invented the experimental method. In order to demonstrate such a radical and wide-ranging claim you would have to engage in extensive historical research that safely established that nobody had done experiments prior to Galileo’s experimentation.

    • You can find the experimental method both theoretical and practical in the works of Archimedes, Ptolemy, Ibn al-Haytham, Roger Bacon, Grosseteste, to name but a few, long before Galileo

      • Walter Hehl

        Thanks Joseph and Thony for your clarifications, but:

        Dear historians,
        you bring me in the precarious position to defend Galilei (presumably).
        You might be right from a principal point of view that the experimental method was even prehistoric,
        but as a physicist I see the „Inclined Plane Experiment“ as a real first in practice:
        1. It measures (quantitatively) a full function, here an f(t),
        2. does this by a repetitive series of experiments,
        3. has a non-trivial and ingenious gimmick (the introduction of an
        inclination angle) bringing the range of values to be measured
        (approximately) in the range of the precision of the measurement
        This makes the experiment to a (simple but) genuine and valuable textbook example repeated 1000-fold even today.
        Which earlier experiment of this kind of methodical severity do you see? Bullet No 3 is really the sticking point to make it to a real experiment:
        Who had this idea? Was it Galilei?
        Or do you know any precursor to Galilei?
        Independent of the discussion on the real accuracy of the Galilean experiments.

      • I wouldn’t argue against the fact that Galileo took empirical experimentation to a new level but he didn’ invent it, as he, being abundantly informed on his predecessors, was well aware.

      • Yes of course for Ptolemy etc., but I’m curious what you had in mind for Archimedes. “On the Method”? (Thought experiments, not actual experiments, but maybe that’s why you wrote “the experimental method both theoretical and practical”?) The famous Eureka! story? His engineering feats for the King of Syracuse?

      • The famous Eureka! story is a textbook example of the application of scientific methodology

      • To Hehl: well, “the experimental method” has been evolving from the ancient Greeks to the LHC experiments with thousands of collaborators. At every stage new aspects have appeared. I don’t think it makes sense to pick out one feature as the defining criterion.

        Buchwald’s The Rise of the Wave Theory of Light provides an interesting illustration in sections 1.3-1.4, a propos your point 3. In the period from 1690 to 1810, experimental standards changed dramatically. Newton, La Hire, and Haüy gave refraction formulas (for the extraordinary ray in double refraction), None of them were particularly good, and simple experiments, quite doable at the time, would have revealed the inadequacies. As Buchwald writes, “there were no commonly accepted standards of experimental reporting demanding that formulas be pushed as far as technique permitted.” So, Newton (apparently) checked his formula only for small incidences.

        By 1810, it was accepted that a proposed formula should be (a) checked over as large a range as feasible, and (b) independent estimates of the “error bars” should be given, rather than just looking at the results and declaring the agreement good enough.

  6. For Tim O’Neill, other historians in the published literature who take the view that, in their totality, Galileo’s observations and arguments tended to favour a heliocentric model rather than a geocentric one (or indeed a Tychonic one) are: Stillman Drake, Annibale Fantoli, Michael Sharatt and Anthony Millevolte .
    Like many such debates, it is far from obvious what the ‘right’ answer is – what is at issue involves quite a few technical points in observational science (astronomy and mechanics), in the philosophy of science, and in historical accuracy. Long may the debate continue…

    • Well, looks like Baerista beat me to it, both by noting that Gingerich does not say there was better evidence supporting the heliocentrism in 1632, let alone 1616, and by noting Graney’s excellent book on Riccioli and why versions of Tycho’s model carried the most scientific weight in the seventeenth century and did so long after Galileo’s time. Expecting Galileo to “prove” heliocentrism absoutely may have been unreasonable, but he couldn’t even show that his model was most likely. This was because (i) there were still outstanding objections against any heliocentric model that he could not adequately answer and (ii) his model – that of Copernicus – was actually wrong, as were some of his own arguments for it. There were solid reasons the overwhelming majority of scientists of the time rejected his thesis and they were substantially scientific, not religious. And Graney’s book is also interesting in showing that it was people like Riccioli who tended to use mostly scientific arguments against heliocentrism while the minority heliocentists resorted to (rather bad) theological arguments in a great many instances, i.e. the opposite of the common perception of the seventeenth century debate.

  7. In the book ‘The Case of Galileo – A Closed Question?’ , the historian Annibale Fantoli comments (p245) that Galileo never claimed to have proof of Copernican hypothesis, and notes that he is unaware of any Galilean scholars who have made his claim. That certainly chimes with my own reading. As Owen Gingerich has pointed out in his well-known article ’The Galileo Affair’, if one sets religion aside for a moment, the debate between helio-centrism and geo-centrism can be viewed as a debate about the nature of scientific discovery and the interpretation of science, with Galileo’s pioneering use of the hyothetico-deductive method under fire (as you know, the hyothetico-deductive method is the repeated testing of a hypothetical model as it passes ever more stringent observational tests). I very much like Gingerich’s point that “it is an irony of history that Galileo’s methods of scientific argument were instrumental in showing that what passes for truth in science is only the likely or the probable; truth can never be final and never absolute”.

    It’s quite a serious point with ramifications for science and society up to this day. To give a grim example, a motion recognizing the scientific hypothesis that human activity is contributing to changes in the earth’s climate was recently defeated by the US congress. I was struck how closely the arguments advanced by several Republican senators mirrored the arguments of some of many of Galileo’s opponents all those years ago: the mantra of ‘case not proven’ seems reasonable but is easy to abuse.

    • That’s all fine, but the fact remains that Galileo did not have enough of a persusaive case in 1632 and it was the Tychonian model (or versions of it) that had the greatest weight of evidence in its favour well into the seventeenth century. And opponents of the Copernican model like Riccioli did not claim to have definitive proof either way. He weighed up the arguments on all sides very even-handedly and was actually quite generous in his assessment of the Copernicans. But he, and the majority of scientists of the time, came down against Galileo and Copernicus.

  8. Bob Lince


    Thony, do you have an comments on Stephan Wolfram’s blog post re: Ada Lovelace?

    Found at: http://blog.stephenwolfram.com/2015/12/untangling-the-tale-of-ada-lovelace/#comments

  9. Hi Tim, the timeline of my comments seems a bit mixed up, apologies if I seems to be talking past your argument. I don’t agree at all that it is a matter of fact that the Gal did not have sufficient evidence to argue for the Copernican model against the Ptolemaic model. I think this is, and has been, a matter of great debate amongst a great many historians, now and in the past. It involves a consideration of many areas of science, the philosophy of science and history and one should be wary of sweeping certainties. (certainly, Gingerich comes down overall in favour of Galileo, despite many shortcomings, in the articles I have to hand.)

    As regards Galileo’s attitude to Tycho’s model, that is a very different question. Indeed, many historians seem to slide rather quickly over this issue, with the honourable exception of Thony. I suspect one reason is that, from the point of view of the philosophy of science, it’s always quite difficult to say why a particular actor didn’t invoke a particular theory. As Galileo wrote very little on Tyco’s model, we can only speculate.

    For what its worth, my own speculation is that for Galileo, the main target was the reigning Ptolemaic model – the lesser known Tycho model was probably a side issue. Indeed, a physicist might argue Galileo didn’t invoke Tycho’s model because he didn’t need it. With the discovery of the moons of Jupiter, it was clear that gravity was a universal phenomenon – there was no longer any pressing reason (from the point of view of science) to assume that the earth was special. Given the huge size of the sun, it was relatively straightforward to construct a primitive orbital model based on the relative size of the planets and the period of their respective orbits. Why suggest a more convoluted scheme, with the huge sun orbiting the earth, any more than suggest that Jupiter orbit a Medici moon ? But that’s just a speculation from a physicist….

    • C M Graney

      I recently translated J. G. Locher’s Disquisitiones Mathematicae of 1614 (book is well through the process with a publisher, but not set yet), the “Booklet of Theses” that Galileo makes much sport of in the Dialogue, and Locher has things to say which might shed light here. He says the telescope clearly proves Ptolemy wrong in certain key ways. The phases of Venus do that, he says.

      But, he does not see the moons of Jupiter as favoring Copernicus. He sees the moons as … drum roll … proof that Ptolemy was right about epicyclic motion! Yes. He says Ptolemy assumed epicycles exist in order to explain the observed planetary motions. But thanks to the telescope, Locher says, we now see that epicyclic motion is REAL. That stunned me, to read an astronomer seeing support for Ptolemy in the moons of Jupiter. But he is right. The moons of Jupiter are epicyclic.

      Locher says the Tychonic system, which he sees as being in the spirit of Ptolemy, is probably the way to go. The jury is still out, he says. But he says Copernicus is weak because of physics, and because of the star size problem and the Copernican tendency to invoke God to solve it (thanks to the shout-outs above on my book, speaking of star size stuff).

      The geocentric model shown in the animation is not Ptolemaic. Mercury and Venus are circling the sun as it circles the Earth (its easier to see on the MalinC web site, and I think the outer planets are, too. I think it is just the same model seen from the sun and the Earth. I would not call it Copernican and Tychonic, even, because these animations don’t show the stars.

    • Baerista

      “With the discovery of the moons of Jupiter, it was clear that gravity was a universal phenomenon – there was no longer any pressing reason (from the point of view of science) to assume that the earth was special. Given the huge size of the sun, it was relatively straightforward to construct a primitive orbital model based on the relative size of the planets and the period of their respective orbits. Why suggest a more convoluted scheme, with the huge sun orbiting the earth, any more than suggest that Jupiter orbit a Medici moon?”

      To me, it sounds like you are projecting post-Newtonian convictions back into an early-seventeenth century discussion, where issues such as gravity were still up for grabs. I don’t see why a large object orbiting a smaller one is any more “convoluted” than the opposite. The number of circles one has to draw does not change. Historians of astronomy nowadays agree that Copernicus’s system – which is the one Galilei defended – was, if anything, more complicated than the old Ptolemaic one. More generally, whether Galilei successfully defeated the Ptolemaic system is not really the issue here, notwithstanding the fact that Galilei and his latter-day propagandists have worked hard to convince us otherwise. The real issue is whether Galilei had decisive arguments against the notion that the Earth is stationary. As long as the Tychonic system was still an option, simply demolishing Ptolemy was never going to be enough.

    • “For what its worth, my own speculation is that for Galileo, the main target was the reigning Ptolemaic model – the lesser known Tycho model was probably a side issue.”

      By 1620 at the very latest the Ptolemaic model was no longer the reigning model, having been refuted by the discovery of the phases of venus in 1613 by Galileo, Harriot, Lembo and Marius all independently. The reigning model was very definitely the Tychonic one, which makes Galileo’s decision to ignore it all the more extraordinary.

    • Unlike both Copernicus and Kepler Galileo has no real concept of ‘gravity’ in the modern sense.

      • And even this understates things a little: Galileo explicitly rejects gravity as one of those occult scholastic qualities. He wonders, what do you gain by saying that gravity causes a stone to fall, rather than just describing the fall? In some ways a rather modern viewpoint, yet not one that (in its historical context) proved helpful.

  10. By the way I love the debate ;))

  11. Hi, really like this page. Excellent article, I shall be endulging in more. I wrote an short article about how the Arabs sewed the seeds for the renaissance, you seem to be quite an expert! Any feedback welcomed.


    • Baerista

      Yikes! Propaganda!

      • Please point out the propaganda….

      • Baerista, I don’t quite understand what your issue is. You have commented on two of my posts, both of which have been arrogant, unhelpful and rude. Firstly, you still haven’t pointed out the “propaganda”, secondly, your propaganda claim would have been relevant if I happened to hold a biased disposition. However, I write from a secular perspective with no inclination towards any particular world view. It appears to me that you have a personal qualm with my perspective, perhaps you feel insulted by the facts that I have presented. I think it is important to be objective, if you feel I haven’t been, there is an etiquette to delivering positive feedback and criticism, to which I will respond by making the necaccary adjustments. Until you do so, your comments are unhelpful and serve no purpose. I’m on here for educational purposes, not to be a recipient of your impolite comments. Everybody is free to write as they see fit, we won’t all agree, but that doesn’t give you the right to be malicious. If you can’t be polite and respectful, perhaps you shouldn’t pontificate on my posts.

  12. Baerista

    1) Not sure this belongs in Thony’s comments section; 2) Your tone trolling is of absolutely no concern to me; 3) If you’re here for educational purposes (isn’t that what propagandists like to claim?), why are your blogposts replete with egregious errors like “Pre 16th Century, the consensus was that the earth was both flat and at the centre of the universe” or that Adelard of Bath travelled to the “House of Wisdom”.

  13. Hi all, I too find this a most helpful debate. If nothing else, it provokes me to re-read what few books I have on Galileo and Copernicus (I usually find I have mis-remembered the relevant passage).

    I think Thony is really onto something when he continually asks the question “why did Galileo favour the Copernican model over Tycho’s scheme?” . I have found relatively little on this point in the various Galileo biographies I have to hand. I see my own little speculation concerning the moons of Jupiter was rightly trashed. As regards projection I should say I wasn’t thinking in terms of the force of gravity but simply in terms of the earth-not-so-special-after-all argument. As regards Thony’s point on the reigning model in Galileo’s day, I would have thought that it took quite some time for wide acceptance that the observations of the phases on Venus posed a genuine difficulty for the Ptolemaic model, but I’ve no idea really).

    I’ve been doing a little reading on the motivations behind Tycho’s model. Of course, there is the advantage of a scheme with all the benefits of a Copernican model without the hypothetical motion of the earth (a motion that had never been observed), plus the business of the comet of 1577, but I hadn’t realised that there was also a serendipitous aspect to the model. Some research by Gingerich and Dreyer suggests that at least part of the motivation for Tycho’s model arose from incorrect estimates of the distance to Mars, and then incorrect estimates of its speed. It seems Kepler was aware of these problems, so perhaps Galileo too?

    But that wouldn’t in any case be a reason for Galileo to dismiss Tycho’s model entirely, if I understand correctly, Instead, a very different idea struck me yesterday, from a very different area of science (warning: warning: speculation to follow):

    I think most of us agree that the main motivation for the Tychonian system was to preserve the stationary earth (as no evidence of the earth’s motion had ever been been detected). Perhaps this is where Galileo’s other interests come to the fore, in particular his profound thought experiments in the relativity of motion. I re-read an excerpt from the Dialogo sopra thingy this week and was struck anew by Galileo’s detailed explanation how the ship (earth) could well be in motion without the passengers being aware of it. He wasn’t the only one thinking of such things of course, but it’s quite a profound exposition and it brings me back to the theme of the totality of Gaileo’s world vision…

    Kind regards, Cormac

    • The change from a purely, Ptolemaic, geocentric system to a, Tychonic or semi-Tychonic (there were several on offer) hello-geocentric system took place relatively rapidly following the discovery of the phases of venus in 1613. The empirical evidence, confirmed by at least four independent observers including those of the Vatican, was too strong to continue to support of pure geocentric system. However the complete lack of evidence of a moving earth plus the very strong arguments against it, known since antiquity, combined with the religious objection led to the acceptance of a Tychonic half-way house.

      As pointed out previously the so-called Galilean relativity arguments can already be found, although not so well or extensively argued, in Copernicus’ De revolutionibus. They also turn up somewhere fairly prominent in the classical literature of antiquity but I can’t at the moment remember where. Although we, with hindsight, regard Galileo’s arguments as very perceptive they lacked the power of persuasion for the majority of his contemporaries. It is very, very obvious to anybody, who considers the question, that the earth doesn’t move! ;))

    • ” As regards projection I should say I wasn’t thinking in terms of the force of gravity but simply in terms of the earth-not-so-special-after-all argument.”

      I doubt that the “earth-not-so-special-after-all argument” was actually an argument at all at the time. That argument (unless I misunderstand you) appears to be a later projection onto the whole Copernican V Geocentric debate.

      • IIRC, the Copernican humanists regarded humans as more special. In the geostationary models, the earth was at the bottom of the world, the bilge of the universe, as far from heaven as you could get except for hell (which was thought of as the center of the earth and very very hot. The Copernicans were pleased to elevate the earth into the third heaven, thus increasing its importance.

        The problem was that Copernicus would up with more epicycles than Ptolemy. His system was not simpler, because the system was a set of mathematical algorithms, not a hypothetical bird’s eye view of the solar system. This was because Copernicus a) made few astronomical observations of his own and relied on the standard Alphonsine Tables, corrupted by centuries of copyist errors; and b) insisted on perfect circles. The orbit of each planet was solved independently, and so each orbit had a slightly different center, none of which were actually the sun. Instead the center of the earth’s orbit was employed.

        His model could not explain the lack of parallax nor the lack of Coriolis effects. If the stars were moved Real Far Away so that parallax would be undetectable, then the observed diameters of the stellar discs indicated enormous sizes for the stars. It would not be for another couple centuries that Coriolis was observed in plummeting bodies and parallax in nearby stars, and the apparent stellar discs were found to be due to aberration.

    • laura

      Nick Jardine has some interesting work on the understanding of kinematic equivalence (an application of relativity) among 16th century astronomers, arguing essentially that by 1590 all serious astronomers (including Tycho, Clavius etc.) understood that models, in particular the Copernican and Tychonic models, were indistinguishable based on astronomical observations and therefore had to be settled on other grounds. They lacked modern language to get the point across and so their explanations (in translation) are often awkward and tedious. Kepler has a discussion of the issue in Harmony of the World, specifically to explain why his alleged celestial harmonies are still beautiful (although less so) if you accept a Tychonic version of his system, because viewed from earth they are the same either way. On the other hand, some of Galileo’s (who after all was not a mathematical astronomer) attempts to deal with kinematic equivalence in astronomy in Assayer and Diaologo, run him into problems, e.g. with his discussion of predicted planetary sizes under the different systems. Which isn’t to say his discussion of relativity in Dialogo isn’t evocative and brilliant, just that the ideas, or closely related ones, were very much in the air at the time and even Galileo’s understanding of its implications was imperfect.

  14. It’s fun to readjudicate the old controversy, and serves as a useful corrective against the bad old conventional wisdom: that the opponents of Galileo were all benighted religious reactionaries impeding Progress.

    For me though, Kuhn’s discussion in Chapter 12 of Structure illuminates the history better. Yes, I know that “paradigm” has been knocked down six ways past Sunday. Call it what you will: hypothesis, theory, worldview, perspective. Obviously we have a clash of some sort between the heliocentrists and the geoheliocentrists.

    I think Kuhn’s central point still holds: there is no objective “weighing up the evidence”, and declaring a winner. How to weight the evidence, what criteria to use, was itself in dispute. For one side, the absence of parallax, the stellar size problem, the absense of “Coriolis” type effects, were fatal objections. For the other side, they were problems to be resolved. For one side, the greater simplicity of heliocentrism was self-evident, for the other side, illusory.

    Three other Kuhn points also wear well. First: “Usually the opponents of a new paradigm can legitimately claim that even in the area of crisis it is little superior to its traditional rival.” Kuhn made this observation, explicitly with regard to the Copernican controversy, at a time when the bad old conventional wisdom still prevailed among many historians. I don’t think Kuhn was aware of the stellar size issue, but he gives full force to the other geostatic objections. Also, in both Structure and The Copernican Revolution, he notes the historical importance of the Tychonic system and its variants.

    Second: “the importance of aesthetic considerations can sometimes be decisive. Though they often attract only a few scientists to a new theory, it is upon those few that its ultimate triumph may depend.” True for Galileo and especially Kepler. The misleading “two diagram” argument that Thony objects to, is just an animated version of one of Kepler’s arguments.

    Kuhn also notes that other idiosyncratic factors often play a crucial role, despite lacking strict logical necessity. Thus, Kepler’s theological views. Or take the impact of Kepler’s Rudolphine tables: from a logical point of view, their unprededented accuracy has no bearing on the question of the earth’s physical motion. But Kepler was a well-known lheliocentrist. Surely his Copernican views acquired some increased credit by association.

    Finally: “Ordinarily, it is only much later, after the new paradigm has been developed, accepted, and exploited, that apparently decisive arguments … are developed.” Kuhn cites the Foucault pendulum. To this we can add the detection of stellar parallax, and Airy’s theoretical resolution of the stellar size problem.

  15. elteoremadecuales

    I cannot see the problem with the pictures. If one gets the left one staying stationary with respect to the Sun, one gets the right one being stationary with respect to the Earth. None is more real that the other.

    Great debate, by the way.

    • The two pictures are geometrically equivalent, but not dynamically. That is, the right hand picture requires additional so-called pseudo-forces (using Newtonian mechanics).

      If your goal is to find a “celestial physics” to explain the motion of the planets, you’re better off starting with the left-hand picture. This was indeed one of Kepler’s goals, and of course one of Newton’s achievements.

      On the other hand, few (if any) of Kepler’s contemporaries shared this goal. Most felt that mixing physics and astronomy this way was a Bad Idea. We may be inclined to give Kepler a big thumbs up, but this is an instance of the “fixed evidence fallacy”: judging in light of knowledge not available at the time.

  16. I agree entirely Michael, you have articulated the exact point I have been endeavouring to make , but couldn’t get clear. Of course I accept all of Thony’s points above, he knows the history in far more detail than I do.

    But I worry that, just as popular science writers often make the elementary error of claiming G.was ‘right’ because measurements in the centuries to come supported the Copernican model, I think there is danger in deciding that G. was ‘wrong’ because the evidence didn’t justify his assertions at the time. The latter statement is a very hard call to make, and involves all sorts of judgement calls on the nature of evidence and the nature of the scientific enquiry. About the only thing I do know is that historians do not have a uniform view on the matter, at least not as far as I can make out.

    A rough analogue from the 20th century strikes me: few in the physics community were convinced by Einstein’s special theory of relativity in the years 1905-1912 (although supporters included some very eminent figures who were struck by the internal logic of the theory,). There wasn’t a shred of direct evidence to support the theory when it was first postulated, and the first series of experiments to be done (on the velocity and mass electrons in 1908 and 1909) seemed to contradict the theory. Thus you might argue that supporters of the theory were wrong to argue for the theory in this time period – but that seems to me to take a very narrow view of the progress of science..

  17. By the way, I also agree with Michael’s point on the gifs at the top of the post. When I first saw the images, I had the opposite reaction to Thony!

    Of course, the point that one is not comparing like with like is perfectly valid. But for me, there is another sense in which that’s exactly the point of the diagrams – they neatly show how the Copernican model changed everything, simply by shifting the viewpoint away from the earth.

    Again, one could argue this point to and fro for ever. But as Michael points out, this is why Kuhn insists that there is no ‘right’ and ‘wrong’ – the two worldviews are incommensurate, because the observers are viewing the evidence in different ways….

  18. Walter Hehl

    “ the two worldviews are incommensurate, because the observers are viewing the evidence in different ways….”

    Kinematically, the world views are as already stated in principle equivalent. For the inner planets, they are “de facto really” equivalent because the center of the epicycles for Mercury and Venus is the sun. There it is splitting hairs. I learned from this blog to see the Jupiter moons as a proof for the reality of epicycles …
    But the kinematic view cannot be maintained against the dynamical perspective!

    Trying to bring the difference to the simplest physical situation in a Two-Body-situation:
    Physically speaking, this implies basically that a body of small mass is further away from the common center of gravity than a heavy body:
    this is objectively true and measurable. And easy to see (if measurable) for the Sun-Earth-System with a ratio of 332946 times. The symmetry of the two world pictures is definitely broken when you are able to measure this resp. the dynamic consequences.

    The cited view of Galilei that “gravitation is an esoteric concept” is, I apologize, ingenious and completely correct, at least up to the theory of General Relativity, and maybe even up to now. It is just that we (Isaac Newton) learned to calculate with these forces which attract everything with a, thank goodness, very simple law. This is “meat to the bone” but the bone is esoteric. You jump, and the whole earth acts together to bring you back – isn’t this magic? Not such a big philosophical difference to a Aristotelian natural motion, btw.

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  21. C M Graney

    This is in response to the comment from laura of January 31, 2016 at 11:38 pm, but also to other comments.

    I don’t think that the problem is so much that astronomers in this time didn’t have the language to get the point across and so their explanations are tedious in translation, but that there just has not been much translation, and very few people can read this stuff in Latin. I find it really hard to read, and I’ve made a project of doing it for some years now. It is not getting easier very quickly.

    But, when I do get through it the results are usually pretty clear. I find the same anti-Copernican arguments in the mouths of differing writers:

    *No parallax. Thus the stars have to be very far away in the Copernican system. Anti-Copernicans viewed this as an “ad-hoc” construction that served no purpose other than to solve a big problem with the Copernican system. And it also means absurdly giant stars — every last one far larger than the sun — since the stars were understood to have measurable apparent sizes comparable to the planets, and making them much farther away than the planets made them much larger, too.

    *Physics. Anti-Copernicans prior to Newton criticize the physics of Copernicus, not the physics of Newton (obviously). And if you read Copernicus, he postulates a double natural motion:
    “We must in fact avow that the motion of falling and rising bodies in the framework of the universe is twofold, being in every case a compound of straight and circular. For, things that sink of their own weight, being predominantly earthy, undoubtedly retain the same nature as the whole of which they are parts. Nor is the explanation different in the case of those things, which, being fiery, are driven forcibly upward…. rectilinear motion occurs only to things that are not in proper condition and are not in complete accord with their nature, when they are separated from their whole and forsake its unity.”
    The anti-Copernicans I’ve read do not see this in the context of Galileo’s ship and common motion. They see this in the context of a rotating spherical planet, where there is actually little common motion because every different point of latitude moves as a different speed, as does every point of altitude. What happens to that natural circular motion for a body at the pole? What happens as a body rises or falls, or moves over latitude, and thus has to have a different circular motion?

    And isn’t a fixed earth with natural motions up and down, and reasonably-sized stars just past Saturn, just a heck of a lot simpler? That’s the arguments I’ve been reading. In other words, contrary to the animated image above, they see the heliocentric model as complicated, and the geocentric model as simple.

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  23. Please move this one as well. (Or delete it; I mainly want to make sure that you read it. No email access at the moment.)

    Thanks, though I don’t see cormac’s question an my reply, though I guess they are moot now that this comment is in the correct place.

    I am posting from my WordPress.com account, so surely any spam filter should be based on that, not IP address.

    I’m not sure what you mean by my “website”.

    In any case, my comments are not spam by any sensible definition, and I’m pretty sure that any IP address they (appear to) come from is also not associated with spam. That, and the inconsistency (sometimes I get through at a given blog, sometimes notP), points to a bug at the WordPress end, along with the fact that there are blogs where I never have problems, blogs where I sometimes do, and blogs where I never do.

  24. This week, I received a copy of Stillman’s Drake’s OUP book on Galileo, an updated version of his 1978 biography.
    I must say I really enjoyed the book, particularly the way it is primarily focused on the opposition to Galileo’s writings from the philosophers (with the intervention of the Church as a side issue). Indeed, the book pitches the dispute as a battle between seeing the natural world by the method of traditional Aristotelian thought experiments and Galileo’s rising emphasis on measurement – this is pretty much as I see it too (what would today be called a dispute concerning the philosophy and epistemology of science).

    Drake marshals many of his published papers to present thorough and very convincing evidence that Galileo was not the blind, avid Copernican he is sometimes portrayed to be (in agreement with the broad finding of most biographies I have). As Drake puts it “Indeed , he (G.) refrained from asserting that he had incontrovertible evidence. What he did have was a preponderance of evidence that linked together such things such as the phases of Venus, satellite eclipses, planetary speeds and distances from the sun, and the existence of the tides: that made these compatible with his terrestrial physics, and that showed Aristotelian cosmology and physics could be mistaken on various matters. There were still a great many puzzles….but the preponderance of evidence known to Galileo indicated that the earth’s motions were actual, and Galileo’s belief in them was scientific, even though some of the evidence he relied on was later found to be inadequate”.

    As so often, there is very little on the Tychonian model, but Drake mentions two objections that were apparently raised by Galileo in his Letters on Sunspots. The first is the issue of contrived models ( – strange that the sun should set all planets into motion except the earth) while the second stemmed from Galileo’s own astronomical observations (the problem of the prediction of the eclipses of Jupiter’s satellites). Drake also points out that such writings are often overlooked because critics tend to focus on Galileo’s writings for the public audience, a point Gingerich has also raised.

    All in all, I think this book is well worth a read, and it reminded me that this interesting issue remains far from settled.

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