Non-Fiction Reviews
Ptolemy, The Book of Astronomy in Antiquity
A New Introduction(2024) edited by Christian C. Carman, Flame Tree Press,
£9.99 / Can$16.99 / US$12.99, pbk, 253pp, ISBN 978-1-804-17791-4.
This is an abridged edition of the earlier Ptolemy’s Almagest (‘The Greatest’), by C.J. Toomer (1998). In her new Introduction to it, Prof. Carman describes Claudius Ptolemy (c.100-c.165 CE) as “the greatest astronomer of antiquity and one of the greatest scientists in history”. So great was his influence, for so long, that in 1989 I praised a history of astronomy in India for its ‘breathtaking leap’ which dismissed the entire 2000-year dead end of Western geocentric theory, ‘not even in a sentence but following a semi-colon’. Ptolemy’s intellectual achievement was so great that it was almost impossible to challenge, or later to omit from any history of astronomy, and yet it was entirely wrong.
Such modern histories make a point of saying that Aristarchus of Samos correctly deduced that the Earth rotated on its axis and orbited the Sun, yet Ptolemy’s views prevailed. Almost all of us could quote that, but only those who’ve read the Almagest could say why they prevailed, and that’s probably the most valuable part of this book. At the beginning Ptolemy sets out his reasons for believing what he believes, and they’re all perfectly logical, as long as you accept the basic concept: that everything in existence, out to the stars, is confined within a space which is larger than the Earth, but not that much larger.
Then it becomes obvious that the stars are all fixed to a sphere surrounding us, all at the same distance. Otherwise, the shapes of the constellations and the distances between the stars in them would appear to distort as they cross from the eastern horizon to the west. Clearly the constellation shapes are unchanged, so they must all be fixed to a rigid surface which is perfectly spherical. The Earth cannot be in motion within that sphere, otherwise the constellation shapes would expand as we approach them, and contract as we draw away. The Earth cannot be rotating on its axis, otherwise the constellation shapes would again distort near the horizons. He notes that the Moon does appear larger nearer the horizon, and at first ascribes that to atmospheric refraction, then realises that it is purely an illusion. (Patrick Moore proved that live on camera, in an episode of The Sky at Night on Selsey Beach.) The Sun and the Moon must be spherical, because otherwise their shapes would distort as they move around us. They must be moving in almost perfect circles, because there’s little variation in their size during the month and the year, but there is some variation (though never by much), and they always return to the same average sizes, so they must be moving on smaller circles (epicycles) whose centres are mounted on the larger ones. The movements of the planets are harder to understand, but they must be accountable in the same way. And once Ptolemy has reasoned all that out, he’s ready to undertake the great intellectual achievement of accounting for it all, by geometry alone, so close to perfectly that it took 1,700 years for the discrepancies to be tabulated in sufficient detail to mount a challenge to it.
I have to confess that after following the first few proofs, I left Christian Carman to it with the rest. The calculations are extremely long and complicated, and if there were any faults in them they would have been discovered long since. (One of the very rare examples, apparently a transcription error on Ptolemy’s own part, is highlighted on p.222.) When they lead to checkable results, such as the calculated distance to the Moon, they are correct within the limits of accuracy which he could achieve – limits which led him to greatly underestimate the size and distance of the Sun: had he known it, the best he could do was to establish minimum values which were much too low. His ranking of the planets in order, from first principles, verifies the findings of his predecessors; his confirmation of the Precession of the Equinoxes was similarly correct. But when he was working out the fine details of his theory, such as the ratios of the sizes of the epicycles, how many have to be superimposed, and how long it takes to circulate round each to account for the observed results, when he got to the acronym ‘Q.E.D.’ all he had done was to determine what would be the case if the theory was correct, and from our superior position, we know that it’s not. It doesn’t diminish the magnitude of the achievement, misguided though it was.
One thing which I have noticed, and I’m not sufficiently versed in the theory to assess, is that the cited observations of the inner planets, Mercury and Venus, were all taken at times when they were at greatest elongation from the Sun, and all of the outer planet observations were at times of conjunctions or oppositions with the Mean Sun, which (we now know) corrects for the variation of the daily solar motion due to the eccentricity of the Earth’s orbit. Ptolemy does remark that the different basis for the calculations is necessary because for the outer planets the elongation from the true Sun can have any value, whereas the inner planets have a limited range of movement. He also makes some remarks about the difficulty of reconciling Mesopotamian observations, tabulated by Hipparchus, due to uncertainty about the ‘stations and phases’ (p.183), and at first Ptolemy seems to be referring to ‘stationary points’, when the outer planets appear to come to rest against the stars as the Earth begins to overtake them, again when they recede, and the inner planets do the same, as they overtake us and recede; but later it seems as if he is referring to the effect of local conditions on observed rising and setting times. The note in brackets saying that stations and phases are ‘first and last visibilities’ is too vague to be helpful, and this is the only criticism I have of the translation.
What occurs to me is that by limiting his planetary calculations to those particular times, Ptolemy may have unwittingly been setting some of his hypothetical epicyclic motions to zero, so cancelling out the further discrepancies in the motion of the planets which were eventually to prove him wrong. Another of his simplifications was to reduce all planetary motions to movement in ecliptic longitude, along the Ecliptic plane. That would be fine if they were all moving in combinations of regular circular motion, as he assumes; but not when they’re actually in elliptical orbits, travelling with varying speeds.
Warning note: in these chapters on the movements of the planets, Ptolemy assumes a thorough familiarity with the workings and uses of an astrolabe, for instance in transferring those motions to the Ecliptic plane. I used to have a leaflet on Chaucer’s treatise on the instrument, which I acquired at the London Planetarium, in its very early days when you could still get such things there. I lent it decades ago to the author of a book on Chaucer which never appeared, and I’ve never missed it till now – but to get thoroughly into the accounts of planetary observations by Ptolemy and his predecessors, something like it would be essential.
As it happens, I’ve already mentioned one of the events which began the questioning of Ptolemaic theory, in my review of Florian Freistgetter, A History of the Universe in 100 Stars. On September 3rd, 1457, a lunar eclipse was observed at Melk, Lower Austria, by George von Peuerbach (first dedicated astronomy professor at University of Vienna) and Regiomontanus (Johannes Müller of Königsberg). Existing clocks were not accurate enough for the purpose, but of course the motions of the stars were known precisely, so they timed the phases of the eclipse by observations of Alcyone, the brightest star in the Pleiades. Another reason for doing so was that the town clock (assuming there was one) would be running on local Mean Solar Time, and even that was suspect – doubly so, when compared to the stellar timing. The results revealed the inadequacy of the classical tables, based on Ptolemaic Theory, which von Peuerbach was already working on. After his death in 1461 the work was completed by Regiomontanus, and later taken up by Copernicus, leading to the heliocentric theory which bears his name.
Observations of the planets were causing still more trouble. Before the invention of the telescope, very large, very precise wall-mounted instruments were used, and they were the province of very rich men like Tycho Brahe, whose huge compilation of observations allowed Johannes Kepler to come to the realisation that all the epicycles could be done away with, and the wholly unnecessary celestial spheres could be discarded, just by recognising that the planets moved not in circles at all but in ellipses, and in a much larger volume of space than Ptolemy had ever imagined. To get past Ptolemy’s huge intellectual achievement and reputation took a giant mental leap, but with it came the rearrangement of the Solar System, the recognition that the planets were worlds in their own right, and the possibility of space travel – as Kepler himself was first to recognise, in a letter to Galileo, and in the first science fiction novel to be written since Lucian of Samos (see review, The Astronomer and the Witch, Johannes Kepler's Fight for His Mother). But that is, literally, another story.
Duncan Lunan
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