Somebody recently linked to one of my earlier posts on Galileo and as I flew over the contents I was reminded of a promise that I had made there that I would discuss Galileo’s failure to acknowledge Tycho Brahe’s geo-heliocentric model of the universe in his Dialogo. This post also has a second purpose and that is to at least partially explain why I don’t accept Thomas Kuhn’s concept of the paradigm shift in the history of science.
In his most notorious book, Dialogue Concerning the Two Chief World Systems, Galileo Galilei presents what could best be described in terms of modern dramatics as a cosmological Celebrity Death Match featuring in the red corner the aging reigning champion the geocentric system of Ptolemaeus weighed down by a 1400 hundred year old Greek gravitas, seconded by the Aristotelian Scholastic philosophy and in the blue corner the sprightly young challenger the heliocentric system of Copernicus buoyed up by the scintillating new telescopic discoveries and seconded by the new philosophy of GG in person. Although presented with far less polemic and showmanship this is the same story that was told by Thomas Kuhn in his The Copernican Revolution, the historical study that led him to develop his concept of the paradigm and the paradigm shift. According to Kuhn a scientific discipline is defined by its paradigm under which the participants in that discipline work, doing normal science, until enough unsolved problems within the discipline have accumulated, which leads to a crisis and in a revolution the old paradigm is replaced by a new one. This description ignores the very major problem that Kuhn never really succeeded in clearly defining what a paradigm is and assumes for the sake of argument that it is clear. Kuhn’s prime example for a real paradigm shift in the history of science was the Copernican Revolution, according to him the Ptolemaic astronomy found itself in a deep crisis in the High Middle Ages and was overthrown in a revolution by the Copernican model, like Galileo he saw this as a two way competition between the systems. However both Galileo’s and Kuhn’s presentations fail on the fact that the astronomical and cosmological transition in the 17th century more resembled a Royal Rumble than a straight one on one fight. As Galileo and the other early telescopic astronomers first made their discoveries at the end of the first decade of the 17th century there were not two competitors in the ring but a whole handful weighing in for the honour of explaining the mysteries of the universe.
Before returning to my cosmological Royal Rumble and presenting the individual participants I want first to deal with another of Kuhn’s false claims, namely that the Ptolemaic system was in crisis. The Ptolemaic system relied on a sophisticated geometric model of deferent circles, epicycles, eccentrics and equant points to describe the motion of the planets and to be able to predict their positions for any given time. Kuhn claimed that this system was highly inadequate and that over the years Islamic and mediaeval European astronomers had added epicycles on epicycles to the system in an attempt to make it work and that by the 16th century it had become hopelessly confused and in danger of collapsing under its own complexity. This is the crisis that according to him called the Copernican model in to existence and led to the revolution in which the new paradigm replaced the old. Unfortunately for Kuhn this is simply not true. The Ptolemaic model had been, over the centuries, actually improved and simplified and was actually surprisingly good at doing what it should do that is predicting the positions of the heavenly bodies for use in astrology, cartography and navigation. Having said that one does have to admit that those predictions were far from perfect, a product of the limitations of accurate observations in antiquity when the raw data for the model was accumulated and secondly the errors that had crept into that data over the centuries in the process of copying and translation astronomical manuscripts. The problems caused by these inaccuracies were well known the members of the first and second Viennese Schools of mathematics who set out to renew and reform mathematical astronomy beginning in the middle of the 16th century. Peuerbach and Regiomontanus produced new astronomical textbooks that were among the earliest printed science books, which served to educate a new generation of mathematical astronomers, including Copernicus, who set out to improve the accuracy of their discipline. It was in the pull of this general movement that Copernicus produced his new model and we don’t actually know why he did so. At first his book was greeted very favourably, not for the cosmology but for the mathematical astronomy, in the hope that it would provide more accurate figures for the planetary positions. Unfortunately as it was largely based on the same raw data this hope soon proved an illusion with in some cases the figures calculated using Copernicus’ model being even more inaccurate than those generated by the Ptolemaic model. It should also be pointed out that the Copernican system was more complex and contained more circles than the then prevailing geocentric model.
Inspired by Copernicus’ work and disgusted by the inaccuracies of both models Tycho Brahe set out to collect a new set of raw data on which to base astronomical calculations. Rejecting Copernicus’ cosmology on both astronomical and religious grounds he also developed a third model his geo-heliocentric model in which the planets except for the earth and the moon all revolved around the sun, which revolved around a stationary earth. This model retained all of the new explanatory power of the Copernican model without the very real problems generated by a moving earth. This model was actually preceded by the almost identical model of Nicholas Reymers Bär, known as Ursus, which although it had the earth in the centre gave it a daily or diurnal rotation instead of having the sphere of the fixed stars rotate daily.
As you can see we already have the first four contestants for our Royal Rumble and if we proceed to 1609 and the eve of telescopic astronomy we see that they did not enter the ring alone. For some reason, that as far as I know nobody has really researched, the astronomers at the end of the 16th century were more prepared to accept a daily rotation of the earth around its own axis than an annual rotation of the earth around the sun. In 1600, with the publication of his De magnete, William Gilbert proposed a Ptolemaic geocentric system with diurnal rotation, which was very popular and was responsible for many people adopting the Ursus system rather than the pure Tychonic system when they finally abandoned a geocentric model. Also available and although not wildly popular was the Egyptian or Heracleidian model from antiquity in which only the two inner planets, Mercury and Venus, circled the sun which along with the other planets, Moon, Mars, Saturn and Jupiter, circled the earth. This model could, like the Tychonic model that was modelled on it, explain the phases of Venus discovered with the telescope that proved fatal for the geocentric models of Ptolemaeus and Gilbert. The last contestant to enter the ring was the fledgling of the group, and the eventual victor, Kepler’s world system as first proposed in his Astronomia nova from 1609. Galileo, for reasons that to this day remain unknown although much speculated upon by historian of science, completely ignored Kepler’s work although it offered better arguments for heliocentrism than anything he had produced himself. Kuhn like many historian treats Kepler as if he were just a minor amender of Copernicus and therefore not relevant however a survey of the astronomical and cosmological discussions in Europe in the first half of the 17th century show that Kepler’s system, the elliptical astronomy, was regarded as a separate system and a competitor to Copernicus’ system.
If you have been keeping count you will know that we have seven contestant in the ring squaring off for the cosmic championship, Copernican heliocentricity, Ptolemaic geocentricity, Gilbertian geocentricity with diurnal rotation, Tychonic geo-heliocentricity, Ursian geo- heliocentricity with diurnal rotation, the Heracleidian model and last but anything but least Kepler’s elliptical heliocentricity. All of these model or systems had their supporters and detractors in the early decades of the 17th century a fact that gives a very different picture to the one presented by Galileo or Kuhn in their works. We don’t have Galileo’s two way fight with the scales stacked in favour of Copernicus or Kuhn’s Copernican paradigm ousting the Ptolemaic one in a clean revolution what we have is a plethora of astronomical models all jostling for centre stage.
Found too lightweight to really compete the Heracleidian model was the first to fly over the top rope and out of the contest. Crippled by the telescopic discovery of the phases of Venus the two geocentric models, with and without diurnal rotation, soon followed but both went out fighting as illustrated by the famous frontispiece in Riccioli’s Almagestum novum from 1651 that shows Ptolemaeus lying on the floor and seemingly out for the count but defiantly claiming, “I will arise again”.
Riccioli’s book, which lists and discusses six different models of the universe, is a strong piece of evidence for the competition described here. The Copernican system sort of just faded away in the face of the superiority of Kepler’s elliptical system. By the early 1630s there were only three serious contenders still battling it out for the cosmic championship, Kepler’s and the Tychonic systems with and without diurnal rotation. At this point in the contest the Tychonic system with diurnal rotation was well ahead on points. This is the point at which Galileo published his Dialogo in which he presents a contest between the Copernican and Ptolemaic systems blithely ignoring the fact that both were effectively already out of the running. His book proved popular amongst literati who were not astronomers who enjoyed his very obvious polemic writing skills but contrary to popular opinion it didn’t play a significant role in the contemporary scientific discussion.
By around 1660 Kepler finally carried the laurels in the contest for two different reasons. As already mentioned astronomical models were judged on their ability to predict the position of heavenly bodies at any given time for various applications. In 1627 Kepler published his Rudolphine Tables based on Tycho’s data and on his own system. These tables of planetary positions proved so superior to anything and everything that had existed previously that it convinced the vast majority of astronomers of the superiority of Kepler’s system. Also as Fontanelle explained in his Conversation on the Plurality of Worlds from 1686, a popular presentation of a Cartesian, elliptical heliocentric model, the Tychonic systems had been abandoned around 1660 because of their complexity in comparison to the Keplerian one, an application of Occam’s razor.
It should be pointed out that the transition to Kepler’s system was not all plain sailing. His replacement of the perfect Platonic circles with ellipses was accepted without any major resistance and his third law connecting the radii of orbits to their periods in a fairly simple mathematical formula was also accepted with joy by an astronomical community convinced of a mathematical regularity in the laws of nature. However his second, the area law, was almost universally rejected as ungainly and ugly, as was his highly dubious mathematical proof of the same. A strong debate raged through the mathematical community throughout the 17th century with various participants, most notably Ismael Boulliau and Seth Ward, offering simpler and more elegant alternatives, which unfortunately didn’t work. This problem was first solved in 1672 when Nicolas Mercator provided a new correct mathematical derivation of the area law. Shortly thereafter Newton subsumed the Keplerian system in his much wider ranging Principia and the show was seemingly over.
Defenders of Kuhn might argue that with Newton the paradigm shift had taken place. Two things speak against this hypothesis firstly that which I have described resembles that which Kuhn describes as the pre-paradigmatic phase of a science that is the phase before a discipline has developed its own paradigm and is therefore not yet a scientific discipline, however he claims that astronomy was a discipline with the Ptolemaic geocentric astronomy as its paradigm. Secondly even following the publication of Newton’s Principia we still don’t have a single, dominating. unchallenged model. Both the Cartesians and the Leibnizians challenged Newton’s model because it was not mechanical with its action at a distance concept of gravity and the Cartesians fought a rearguard action supporting Descartes’ vortex system against Newton’s gravity until deep into the 18th century. Leibniz also challenged Newton’s assumption of absolute time and space, proposing a relative system instead; a challenge that would with time lead to the refutation of Newton’s system but that as they say is another story.
Proof of the contest between a multiplicity of astronomical systems in the 17th century can be found not only in Riccioloi’s Almagustum, as already mentioned, but also in the astronomical section of Robert Burton’s The Anatomy of Melancholy first published in 1621 and then in many expanded edition over the next ten years and in the work of Athanasius Kircher as well as in numerous books and pamphlets published by the participants. In my opinion this evolution of the astronomical and cosmological systems in the 17th century gets ignored largely because it’s too messy to be pressed into a neat philosophy of science model of scientific progress. Why sacrifice academic elegance for the messy reality that is real history?