Ptolemy and The Almagest

By the beginning of the 1st century A.D. the great age of astronomy in ancient Greece was coming to an end.  However, before it did, there was one last noteworthy figure, who would take ancient astronomy to its pinnacle.  Ptolemy wrote arguably the most important work of science in the ancient world.  Known as The Almagest, it would collect all early knowledge of astronomy into a single work, and set the course of science for the next 1000 year.  

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Transcript

More so than any other culture, the ancient Greeks were responsible making astronomy a science.  Astronomy in ancient Greece had started around the 5th century B.C, and had over the course of around 500 years become a highly sophisticated field.  While observations of the night sky had been common in Egypt, Babylon and many other early cultures, advanced geometrical theories of the solar system, underlined by observations, were a Greek invention.  

One interesting historical question to ask is why it should have happened here. And why at this time?  Of the many advanced cultures which have existed around the Mediterranean and the fertile crescent, why did it happen to be the Greeks who developed astronomy into a science.

Further, what is curious, is why, after several centuries of steady progress, did astronomy in ancient Greece stall.   By the end of the 2nd century A.D., there would be no more great advances and it would be over 1000 years before astronomy as a science remerged in Europe and the achievements of the ancient Greeks would finally be surpassed.

On the first point, we can’t say definitively why astronomy should have developed in ancient Greece, but I think at least part of the reason must be their intellectual culture.  The Greek city states had expanded around the Mediterranean, and The Greeks brought their scholarly interests with them. Initially these were Philosophy and Geometry, however, Astronomy proved to be a natural development of these fields.  In addition, the Greek language provided a lingua franca, allowing for the free exchange of ideas between peoples separated by vast distances, creating a vibrant intellectual life around the Mediterranean Sea.

However, by the beginning of the first century A.D., the world had changed irrevocably.  One by one, the Greek city states lost their independence and were slowly subsumed into the ever-expanding Roman Empire.  The Romans, despite their role as conquerors, had immense respect for Greek culture.  The ability to speak Greek for example, was a status symbol amongst the Roman elite, and Greek learning was appropriated by the Romans.  Nevertheless, the Roman’s were never as successful in the realm of science as the Greeks.  The exciting developments which had characterised Greek astronomy over the previous centuries began to slow down, and it wouldn’t be until the fall of the Roman Empire, that Astronomy once again began to advance as a science.  

The last great triumph of Greek astronomy, however, did take place inside the Roman Empire, in the city of Alexandria, then a part of Roman Egypt. And the man responsible was Claudius Ptolemaeus, also known as Ptolemy.  Ptolemy was born at the beginning of the 2nd century A.D, and while he may have been a Roman citizen, culturally, Ptolemy was a Greek, following in Greek intellectual traditions.

As well as an astronomer, Ptolemy, was a geographer, music theorist and mathematician.  He wrote on many scientific topics, and its likely we will return to Ptolemy, as we follow the development of early optics.  However, it is undoubtedly in astronomy that Ptolemy would have the greatest impact.  And the primary reason for this is the Book which would become known as The Almagest.

Originally known as Mathematical Syntaxis, The Almagest, comes from a corruption of the Arabic title, and means ‘The Greatest’.  And this seems fitting as it is difficult to overstate the importance of The Almagest in the development of astronomy and the history of science.  Virtually all astronomy which would take place over the next thousand years would be in its shadow, and there is no other scientific work of antiquity which provides such a holistic and definitive treatment of its subject matter. Even when Copernicus started to question some of its assumptions, it would be generations before it would finally become obsolete. 

The reason for this was due to the fact that The Almagest was a hugely ambitious work, collating all Greek astronomical knowledge of the previous centuries into a single cohesive treatise. It’s likely that Ptolemy had in mind that other great technical work of antiquity, Euclid’s elements, when writing the Almagest.  Like The Elements, The Almagest sets out to derive its theorems from a set of basic assumptions. Of course, being a work on Astronomy, these assumptions aren’t as self-evident as Euclid’s axioms, but instead comprise a series of arguments, such as, for example, an argument for the sphericity of the Earth, or that the Earth is very small compared to the celestial sphere.  Ptolemy presented this knowledge methodically, setting out his assumptions, before demonstrating his theories with rigorous geometric proofs.  

These two works, The Almagest and The Elements, in fact make for an interesting comparison and we can see many parallels between them. For example, they both collated the whole of Greek knowledge in their respective fields; they were each highly regarded works, becoming essential reading for all educated people; and they both maintained this revered position for over a thousand years, continually copied and commented upon throughout the Islamic golden age and the European renaissance.    

Its arguable that the Elements may have stood the test of time better than The Almagest.  However,  its also true that The Elements was primarily a book which collated and organised the Theorems of earlier thinkers.  By contrast The Almagest is split between work which derives from earlier Greek astronomers, and that which is original to Ptolemy.

In terms of his working methods Ptolemy clearly derived much from his predecessor Hipparchus.  Hipparchus had demonstrated the essential role of empirical data in Astronomy, and Ptolemy set out to take his own observations.  The Almagest for example contains a huge catalogue of the fixed stars, over 1000 in all, which were probably an updated version of those left by Hipparchus.  More generally the observational data included in The Almagest is immense and in total gathers data taken over the previous 800 years.  

Ptolemy does in some parts also make direct use of models which were already well accepted. For example, Ptolemy doesn’t attempt his own Solar theory, but uses his greater body of observations to demonstrate the accuracy of Hipparchus’s, deriving the same values for the length of a tropical year, as well as the same lengths of the seasons.  He then goes further and computes a table which would allow the Sun’s position to be calculated at any given time.  This was a remarkable achievement, and demonstrates a high level of sophistication, as these positions were derived as a consequence of Hipparchus’s theory rather than from observation.  

However, The Almagest is more than an update on Hipparchus’s work, and its greatest original achievement is a theory of planetary motion. 

The motions of the planets are far more complex than Solar motion.  The Sun moves across the sky daily from East to West, with a slower motion along the ecliptic, corresponding to the seasonal variation in the Sun’s motion.  The planets however, are less predictable.  If we observe the planets nightly, we may see them move generally eastward along the Ecliptic.  But occasionally they will change directions westward, in which case we say they are undergoing retrograde motion.

Ptolemy’s predecessors knew about retrograde motion and also realised that it occurred under different conditions for different planets.  For example, Saturn, Jupiter and Mars seem to undergo retrograde motion when the Earth Sun and Planet are aligned with the Earth at the centre, known in astronomical terms as opposition.  In contrast, Mercury and Venus undergo retrograde motion when they are aligned with the Earth and Sun, with the Sun at the centre, which is called conjunction.  

To give a brief explanation for this in modern terms, Saturn, Jupiter and Mars, are the superior planets, further away the Sun than Earth.  Retrograde motion occurs as the Earth, on its quicker shorter orbit around the Sun catches up with the planet and overtakes it.  Think of a runner on the inside track of a 400m race.  To the runner, it appears that his slower opponents on the outside track are moving backwards as he overtakes them, a simple consequence of relative motion.  

However, to the ancients, still attached to geocentric theory, this phenomena was far more mysterious.  Apollonius of Perga had been the first to suggest a solution, in the form of an epicycle-deferent model.   We mentioned this in the last episode, but as a reminder the epicycle is a smaller secondary orbit which a celestial body follows, while also moving around a larger orbit known as the deferent. To use another analogy, you can think of epicycles as being like the spinning teacup ride at a fairground, where the whole ride rotates around a central axis, while each of the teacups also rotates separately.  

Apollonius was able to demonstrate that the epicycle could account for retrograde motion, but didn’t apply this to any specific orbits.  Ptolemy however, working with his vast body of astronomical data tried to work out this epicycle hypothesis in detail.  Unfortunately, he found that it was insufficient to fully predict all of the planet’s motion.  So he introduced a further modification by assuming that the deferent, or the larger orbit, was no longer centred on Earth.  He called this new point the ‘equant’, and it gave him a marked improvement when comparing to observations. 

However, Ptolemy’s theory was actually even more complex than I have described.  In the first instance the superior planets, and the inferior planets, needed to be treated separately, since the inferior planets seem to follow the Sun in a way the superior planets do not.  Mercury was also especially difficult, which we now know is due to its orbit being especially elongated.  Further Ptolemy also needed to introduce corrections, to account for the fact that the planets do not quite orbit in the same plane as the Sun.  He treated these corrections separately and they were successful in allowing reasonably accurate predictions of the planets positions.

This was a notable achievement, as even Hipparchus had failed to give a full account of planetary motion.  

Unfortunately while Ptolemy’s models worked reasonably for the planets it worked less well elsewhere. Ptolemy’s lunar theory was largely derived from Hipparchus, and as we discussed last week it was essentially an epicycle-deferent model, placed off centre from the Earth.  However, Ptolemy also observed that there was an additional anomaly in the Moon’s motion which Hipparchus had not detected.  While the Moon’s position was well predicted at a syzygy, that is when the Sun, Moon and Earth are aligned, there was a discrepancy when they were in other configurations, such as when we have a half moon.  His solution was to adapt the epicycle-deferent model of Hipparchus by having the centre rotate at some constant speed.  But even this modification couldn’t reproduce the observed values and so he went even further by introducing non-uniform rotational speed for the epicycle.  

By this point however, as you’ve probably noticed, the Almagest’s lunar theory had become head spinningly complex.  Ever since Eudoxus, astronomical models had been going down a path of ever-increasing sophistication, and Ptolemy’s work was in many ways the pinnacle of this.  However, its also true that these models were becoming more complicated and elaborate. In attempting to achieve greater accuracy, more and more adjustments were added, and the models had become increasingly unwieldy.  

The irony was that in seeking more accurate observations, The Almagest had at times introduced new, even larger, problems.  For example, the lunar model implies that the moon, orbiting in its epicycle-deferent configuration, should vary significantly in its distance from Earth.  By the parameters of Ptolemy’s model this means that the moon should sometimes look double the diameter at certain points compared to others.   

Ultimately the problem faced by Greek astronomy was that it would never give up two basic assumptions which had been laid down by Eudoxus and Aristotle.  The first of these was that the Earth lies at the centre of the solar system and is unmoving, with all the heavenly bodies rotating around it, that is the famous geocentric model.  The second, which is less appreciated but arguably just as important, is that all motion was assumed to be circular.  The epicycle-deferent, was actually an attempt to keep the assumption of circular motion while making the necessary corrections for the various inconsistencies in the observations.  

These two assumptions would be amongst the most enduring ideas in astronomy.  Eventually the first assumption would be dropped by Copernicus who devised the heliocentric model and the second by Kepler when he demonstrated that the planets orbit in ellipses.  These advances would in turn lead Newton to develop his universal law of gravitation, setting the scientific revolution in motion.  

However, at least for the time being, astronomy was not ready to question these underlying notions, and at this point we should give Ptolemy his due. Despite their complexity, the theories in The Almagest were far from arbitrary and actually the simplest models which would describe the celestial motions while retaining these assumptions.  Ptolemy’s achievement was to collect all of the astronomical knowledge in the ancient world and create a definitive treatment which would remain the most important astronomical text for centuries after its publication.

Unfortunately, this was largely the end of the line for ancient Greek astronomy.  One of the reasons for this was, as mentioned, that it really had no place to go if it wouldn’t give up the assumptions of Eudoxus.  Ptolemy’s treatment was, in its own way, complete.  

However, this is not the only reason, because The Greeks also had larger problems.  Around this time they were becoming subsumed into the Roman Empire, which itself fell in the west in the 5th century A.D..  The Christian Byzantine Empire in the East, while Greek speaking, were never scientists in the same way as their predecessors. At least in scientific terms Europe was entering a dark age.

However, through The Almagest, astronomy as a science would live on, thanks to rise of the next great scientific culture, The Arabs.  The early Arabic empires valued knowledge and a great translation program brought all of the great Greek scientific work to the east.  More so, while the early Arabic world used to be thought as simply incubators of Greek work, they actually did much to nurture and develop Greek knowledge in the following centuries.  Eventually when astronomy resurfaced in Europe, it was at least partially due to The Arabs.   

We will follow these developments in detail in future, however, for now that concludes our tour of ancient astronomy and ends this first season of the show.  I hope that you have enjoyed it.  If you have, please leave us a review, or maybe even recommend the show to like-minded friends.  This is a small independent production, in a podcasting world that’s becoming increasingly commercialised.  My goal with the show is to build a small appreciative audience who want to come on this journey with me through the history of science.  For my part I promise to return with the next season as soon as possible where I plan on investigating the other scientific developments in the ancient world, specifically in Medicine, in Optics and, the part I am most excited, exploring the life and work of one of the greatest scientists of all time, Archimedes.

So goodbye for now, and keep watching the Skies!

Outline

·         More of a question to start?  How did astronomy begin? End?

·         Ptolemy and Almagest intro

·         Ptolemy’s debt to Hipparchus

·         Ptolemy’s original theory – planets – success – introduce epicycles again

·         Lunar theory – failure

·         Why?  Wouldn’t give up assumptions

·         Legacy/failures/geocentrism/non-uniform speed

So far when discussing Greek astronomy, we’ve primarily discussed the motion of the Moon, the Sun and the fixed stars.  However, one element of astronomy we’ve neglected has been the planets. To ancient astronomers the existence of Mercury, Venus, Mars, Jupiter and Saturn was well known.  When observed from the Earth they, to a good approximation, orbit in the same plane as the Sun, along what the Greeks called the ecliptic. Indeed on a night where the Moon and several planets are visible they all lie on roughly a straight line across the night sky.

However, the key difference when observed over the course of a year, the Sun and the Moon will consistently move in the same direction eastwards, with respect to the fixed stars.  But the planets; especially Mars, Jupiter and Saturn, will change direction from time to time, beginning to move westward over the course of several nights. Saturn does this most frequently, travelling westward roughly 138 days in every year.  Because of this the Greeks called them ‘wandering stars’ or ‘wanderers’, which is the derivation of our word ‘planet’.

Greek astronomy had attempted to become more accurate and quantitative it had also failed to fully describe the celestial motions.  One of the ironies was that in attempting to correct for the anomalies he had observed, Ptolemy ended up

What is slightly curious is that Ptolemy and Hipparchus did happily drop some of the other assumptions Greek astronomy, such as the assumption of uniform speed, which they essentially accounted for with their off-centre rotation.   As we discussed however, this was necessary to account for the non-uniform seasons, an so when the evidence was overwhelming its clear that they were adaptable.

In real terms the deferent describes the annual the motion of the planet around the Sun, while the epicycle allows for the retrograde motion to be considered.  The equant then, is necessary because these orbits are also elliptical, rather than circular, and their speed is non-uniform.  Ptolemy’s theory of a off centre epicycle-deferent model then, is a reasonable approximation then, to what we now know is a heliocentric solar system, with elliptical orbits.

This is generally true of all of the Almagest’s models, which even to a modern, mathematically adept reader, can be difficult to follow. In fact later copies of the Almagest often greatly simplified its mathematics, leaving only the outlines of Ptolemy’s theories.  In the Greek world, geometry was a central intellectual pastime, however removed from this context, readers in the following centuries often lacked the mathematical background to follow its arguments.