What did Hypatia really know? The Science of Agora

With almost no cinema distribution and with the sales of the DVD virtually non-existent, Agora will probably vanish almost without a trace, not unlike its main character. The life of an historical figure few have heard of seems not to be a commercial proposition even when it gets generally good reviews on film buff blogs.  But there have been some heated debates online. Although any film where religion is a key part of the plot could upset someone somewhere, most of the discussion I have seen has been about how accurate a portrayal it was.  The historical background is one thing, but the question I find most interesting is what Hypatia actually did or didn’t do.  Where does Hypatia fit in the history of science?

The film proposes that she was working on the problem of whether the Earth or the Sun was the centre of the Universe, and this quest is central to the character as she is portrayed.  It is a bold assertion, because we have none of her actual works to refer to.  We only have refences to what she wrote.  But it really makes all the difference.  If she was simply an upper class pagan woman who got caught on the wrong side of politics, then her death is just one of many tragedies.  But if she was the first person to work out that the orbits of the planets are elliptical, then her death potentially set back science for centuries.

So how likely is it that the film’s central premise is correct?  Lets look at the context.

What did the ancients know about the world?  If you aren’t familiar with this period it might come as quite a surprise just how much they had worked out.  For a start, it was not believed that the Earth was flat.  Everyone knew the world was round. This is so trivially easy to prove that nobody in particular deserves the credit for pointing it out.  I could have worked it out myself as a child.  Growing up besides the English Channel I could see that only the tops of ships out at sea were visible.  There is a song that goes they all laughed at Columbus when he said the world was round.  In reality he would have been laughed at for saying the world was flat.

All ancient civilisations were well aware that the world was spherical.  The Greeks went one step further.  Eratosthenes managed to work out how large it was.  He did this by a beautifully simple experiment.  He measured the angle of the shadows cast by sticks placed in the ground at two different places at exactly the same time. The difference in the angles was equal to how much of the circle of the earth lay between the two sticks.  Once you know that you can very easily work out the size of the whole circle.  Eratosthenes’ estimate was only 85 miles out and was not bettered until the British started mapping the globe centuries later.  He must have been a really good at measuring very small angles.

The method used by Eratosthenes is both simple and valid.  But the geometry only works if you assume that the Sun is extremely distant.  We know this to be true, but how could Eratosthenes?  Well, he worked that out too.  How he did so isn’t known in detail, but he was right within 1%.  Whatever the precise details he would have needed very precise measurements to get anywhere near the right answer.  Tiny measuring errors would multiply into a very large error in the final answer.  As a hands on scientist myself, I am in awe of his precision, this in the third century BC.

A later astronomer, Ptolemy,  seems to have lacked the almost superhuman skill of Eratosthenes.  His estimates of the distance of the Sun and Moon were much smaller than the real values.  In fact, Ptolemy managed to get just about everything wrong, but he got it wrong in such a brilliant way that his work still commands enormous respect.  Working in the second century in Alexandria, he came up with a working mathematical model of the Universe with the Earth positioned at its centre.  The seven planets – which include the Sun and Moon according to this way of looking at it  – all revolve around the Earth in perfect circles.

A simple circle isn’t enough to fully explain what we see in the sky.  For example the planets vary considerably in brightness and sometimes appear to double back on their tracks.  These glitches are removed by introducing epicycles. These are simply further circles added on top of the main circle which modifies the orbit somewhat.  If you select the right epicycles you can come up with a model that is a pretty good approximation to what is observed in the skies.  The trick is to continually refine the model by making observations and checking them against the model.  To produce anything worthwhile requires a great many observations.

Illustration of Ptolemy’s Epicycles (Thanks to Wikipedia)

Ptolomey’s published work on cosmology was called the Almagest. The name is of Arabic origin because it is one of the many texts that were lost in the west, and only got back there via the Arabs.  The achievement of Ptolemy was both impressive in its ability to foresee the future, and for the demonstration of raw calculating power.  It also required a huge amount of data.  In the film we see Hypatia and her students trying to rescue scrolls before the Christians get their hands on them. If they had had time, I imagine that the priority would have been given to the raw data of astronomical observations.  And if I had been there, I would have been panicking too.  Anyone who has lost data from an experiment will know how gutting the feeling is.  Astronomical data can only be recorded once, and if the only copy of it is lost, it is lost forever.

(Incidentally, people who know me are often surprised that I am somewhat skeptical of climate change models. It doesn’t seem to fit with my generally liberal, green and pro-science views. It is Ptolemy’s highly sophisticated, very predictive and totally wrong model that was accepted by everyone for centuries that makes me suspicious.)

Another facet of the ancient world that is surprising is the sophistication of its instruments. The naked eye measurements were done with a precision that would not be matched again until the seventeenth century.  The skill of ancient craftsmen still has the power to amaze.  The Antikythera mechanism for instance was so intricate that it has taken decades to work out what it even was.  This dated from about 400 years before the time of Hypatia and was a device for predicting  lunar and solar eclipses, and probably the movement of the planets.  The ability to make something so intricate was not regained until at least the fourteenth century, probably later.

So the world that Hypatia was born into was one where there was a considerable background of theoretical and practical knowledge.  She would be very well aware of the works of Eratosthenes and Ptolemy.  She would no doubt know that Aristarchus of Samos had proposed that it was in fact the Sun that was central and that the Earth moved around it.

We will never know what Hypatia actually wrote as her works have been lost, but we do have some idea of what she worked on.  Two of her projects stand out.  She reviewed the work of Appolonius on conics.  This is the area of mathematics that deals with mathematical properties of circles and ellipses.  And she also edited a new edition of Ptolomey’s Algemist.  She was also an adept at instrument manufacture.  She is credited by many with inventing the hydrometer.  This turns out to be a myth, but as is often the case with myths the truth is more interesting.  Her association with the hydrometer is known from a letter written to her by a former student asking her to make one for him.  He gives her some details of what it should look like and what it should do, but obviously is happy to take it for granted that she will understand the science well enough to be able to work out exactly how it should work from first principles.

(Incidentally one of the people who has spread this myth about her inventing the hydrometer is me.  I sometimes give tours of the lab and a story about the hydrometer being invented by a woman whose name we know in the third century is one way I have used to try and humanise a subject that many people find boring.  I don’t know where I picked the story up but I have been misleading people for years about it.  Labs have a folklore and it’s no more reliable than any other kind, and were it not for researching this article I would have carried on believing it.)

She did work on astrolabes, precisely what is used to take astronomical readings.

So all the information needed to come up with the notion of ellipitical orbits would have been available to Hypatia.  She was also quite likely to be in a position to look at data generated over time in Alexandria.  And it’s likely she would have been good at  generating new data herself.  We don’t have a copy of the Almagest from that period.  It would be great if we did, because it is quite likely that by the time of Hypatia discrepancies between predictions and observations would have started to accumulate.  If a new edition was being prepared, isn’t that just the time to look at  the model again?  And given that the calculations using ellipses are both easier and give better predictions, is it so far fetched to suppose that someone in the position of Hypatia might have joined the dots as she is shown in Agora?

And the view of the world that the ellipitcal orbits of planets around a central sun is very different to what you get from Ptolemy.   In the Ptolemaic universe, the rules governing behaviour in the heavens are different to those here on Earth.  The Earth is central and different. Ellipses are much more like the way things we are familiar with behave. Going back to the work on conics, an ellipse is just one of the geometries that can be derived from a cone.  So can a parabola, which is the path a ball describes when you throw it.  Put the Sun at the centre of the Solar System and suddenly you can use the same basic ideas to describe motion anywhere in it.  Once elliptical orbits had been proposed in the Seventeenth century, progress in studying motion followed quickly afterwards.  In the film, this revolutionary possibility is represented by having Hypatia doing experiments dropping a sack from the mast of a moving ship.

But the fact is we don’t have the documents so we just don’t know.  We don’t even know if there was still a library in Alexandria at all for sure.  I find it hard to believe that there wasn’t.  If work was being done on the Algemist, then there must have been astronomical data to work on – lots of it. And that means lots of papyrus.  If they had room to store the data, and more importantly cash to pay for the papyrus, they probably had the full compliment of reference works and earlier authors.  Hypatia attracted students from all over the empire and they must have signed up for more than just the power of her personality.   We don’t have a positive sighting of a library from the time that Hypatia was working there, but it has to be more likely that there was one there than there wasn’t.

We will never know exactly what she was doing in the years up to 391, but we do know that this was a watershed year. The Emperor Theodosius issued a decree making paganism illegal. The Christians were now in power and in a position to destroy paganism.  Bishop Theophilus in Alexandria moved against the pagan temples.  The central one in Alexandria was completely destroyed and a church built instead.

Was Hypatia’s academy caught up in this?  It is not hard to imagine.  The burning of parchments in the film is not corroborated in the surviving literature but it seems plausible to me. If there was a library, it would have been destroyed.  Christianity was still at this time a religion that appealed to the poor and underprivileged.  These are not people who would be the first to appreciate the arcane matters of astronomy.   In any case, if you believe the world is about to end the centuries long accumulation of knowledge must seem like a particularly pointless activity. Why would they not destroy the words that were not the words of their God?  And they were hitting out at the people who had used to persecute them.

Whatever was going on in Alexandria at the time of Hypatia, it has not survived.  We know a tantalising amount about the events and personality of the woman herself, but not enough to get to really know her.  This makes her a glass into which you can pour whatever you wish.  The known facts are compatible with her being a spoilt upper class airhead who only gained her position with the help of her well known Dad and did nothing of note once she got it.  You can see her as a scheming politician who pushed her luck just a bit too far.  I am probably simply betraying my own prejudices by seeing her as a scientific pioneer who saw things that were to remain hidden to everyone else for another 1100 years.

But whether Hypatia took advantage of them or not, the circumstances that were so favourable for the discovery of the Earth’s true place in the Solar System did not last. The Church was quick to take control of the production of documents,  education and the keeping of records.  It was to maintain this monopoly for centuries, and a great deal of what we know about the history of this time we only know from documents produced by scribes who were monks or under the control of monks.  Investigating the Universe was off the agenda.

The Dark Ages had arrived.


Thanks to John Collick on http://johncollick.com/2010/11/agora/ for encouraging me to watch the film.  I must also thank the posters at http://armariummagnus.blogspot.com/2010/05/hypatia-and-agora-redux.html for robustly correcting some misconceptions that I held and pointing me in the direction of some interesting literature.

If you haven’t seen it, here is  my review of Agora

To my mind, the best account – in the sense of being easy to read – of Ancient Astronomy is Isaac Asimov’s, even though I am not a great fan of his fiction.


Filed under History in Culture

12 Responses to What did Hypatia really know? The Science of Agora

  1. A wee bit tangential, but have you seen this video of a lego model of the Antikythera mechanism which has been causing a bit of a stir on FB and Twitter today?

  2. That is amazing isn't it, thanks for putting me onto it. I think going off at a tangent is mathematically appropriate to this post.

  3. Thanks for the analysis! I've posted a link to your piece on my “reel vs real” post about Agora and added your site to my blogroll. I just finished Hypatia of Alexandria: Mathematician and Martyr (Prometheus Books, 2007) by Professor Michael A. B. Deakin of Monash University who does a very good job of looking at Hypatia's mathematics. But this is the best I've seen so far on the science of the times.

    And RWMG…loved the video! Thanks for the link.

  4. So how likely is it that the film’s central premise is correct?

    I would give it a probability of < 0.5% and that is being extremely generous.

  5. You may be right Thony, but I remember that the hairs on the back of my neck stood up when I saw a list of what Hypatia had worked on. She definitely did have all the background information she would have needed. I’d still put the probability below 50%, but 0.5% seems very ungenerous.

  6. 1) Hypatia was a neo-Platonist, ancient cosmology was ruled by the so-called Platonic axioms which state very clearly that all celestial motion is circular and uniform.

    In fact Copernicus’ main motivation was the fact that Ptolemaic astronomy, in his opinion, broke the Platonic axioms.

    2) Hypatia did not have the astronomical data necessary to calculate elliptical orbits. It took Tycho 30 years with a large team of observers and some pretty impressive instruments to acquire the necessary data.

    3) There is no evidence what so ever that Hypatia possessed the necessary mathematical skills to perform the calculation of elliptical orbits.

    4) The arguments against a heliocentric cosmology, which she would have known both from Ptolemaeus and her father, Theon, are not easily disproved or ignored.


    You get the picture? 😉

    • 1) Neoplatonism wasn’t a religion, and epicycles already mess up the perfect circle notion. And neoplatonists often disagreed with each other. I don’t see any reason why Hypatia couldn’t have come up with a novel conception.

      2) Hypatia worked on astrolabes and the resources potentially available in Egypt in the fourth century would have been greater than those Tycho Brahe had at his disposal.

      3) Hypatia had a mathematician father. She might well have been a Mozart of mathematics brought up from an early age to work on that kind of thing. Other people’s skills often seem impossible to me.

      4) Agreed, particularly the parallax one, but someone had to overturn them. Why not Hypatia?

      I’ll agree it is a long shot, but it doesn’t seem completely impossible.

    • Lou

      You stated that: 3] There is no evidence that Hypatia possessed the necessary mathematical skills to perform the calculation of elliptical orbits !! This is your hypothesis!! Not necessarily
      a fact.

  7. Zo0tie

    I have a copy of Agora and watched it several times mourning the loss of so much knowledge. Yet I know the scholars did nothing to elevate the poor to their level of love of knowledge and so when the end came there was no one to stand with them to repel the darkness.

    Scientifically I had to doubt the idea that Hypatia could have discovered the elliptical nature of planetary orbits. A conic derived ellipse would have two apogees and two perigees with the sun at the center, not at one of the foci. Her assumption that the sun is at one of the foci seems to come from nowhere. Without the inverse square law of gravity to help clarify things she would have found an elliptical orbit just as unlikely at an epicycle. It made a good story though.

    • It’s a bit beyond my knowledge and skill to confirm this, but I would have thought that a model using ellipses with the Sun in the centre would be a lot closer approximation than circles and epicylces? And the idea of placing the Sun at one of the foci doesn’t seem particularly radical once you have hit on the ellipse idea in the first place? And again, I don’t know this for certain, but wasn’t the inverse square law from gravity derived from the data on planetary motion some time after Kepler proposed ellipses? Sadly it is all speculation anyway unless someone digs up some more evidence.

  8. based on the story, how does belief/religion affects science?

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