In Our Time - Ptolemy and Ancient Astronomy

Episode Date: November 17, 2011

Melvyn Bragg and his guests discuss the ancient Greek astronomer and mathematician Ptolemy, and consider how and why his geocentric theory of the universe held sway for so many centuries. In his seminal astronomical work, the Almagest, written in the 2nd century AD, Ptolemy proposed that the Earth was at the centre of the universe and explained all the observed motions of the Sun, Moon, planets and stars with a system of uniform circular motions which he referred to as 'epicycles'. But Ptolemy was a polymath and did not confine his study of the stars to mathematical equations. He was also interested in astrology and his book on this topic, the Tetrabiblos, tackled the spiritual aspects of the cosmos and its influence on individual lives and personalities.Ptolemy's model of the universe remained the dominant one for over a thousand years. It was not until 1543, and Copernicus's heliocentric theory of the world, that the Ptolemaic model was finally challenged, and not until 1609 that Johannes Kepler's New Astronomy put an end to his ideas for good. But how and why did Ptolemy's system survive for so long?With:Liba TaubProfessor of History and Philosophy of Science at Cambridge UniversityJim BennettDirector of the Museum of the History of Science at the University of OxfordCharles BurnettProfessor of the History of Islamic Influences on Europe at the Warburg Institute, University of LondonProducer: Natalia Fernandez.

This BBC podcast is supported by ads outside the UK. Thanks for downloading the In Our Time podcast. For more details about In Our Time and for our terms of use, please go to BBC.co.com.uk forward slash radio 4. I hope you enjoy the program. Hello. Mortal as I am, I know that I'm born for a day, but when I follow the serried multitude of the stars in their circular course, my feet no longer touch the Earth.

These are the words of one of the most influential astronomers and mathematicians of all time. Claudius Ptolemy, writing in Alexandria in the 2nd century AD. Ptolemy's model of the universe may have been based on mathematics, but his motivation to map the solar system came not just from a thirst for knowledge, but also from his desire to touch the divine. Ptolemy presented his astronomical vision in his great work, the Almagest, and his view of the solar system with the Earth at its centre held sway for nearly one and a half thousand years.

But why was Ptolemy's universal model so convincing and how to be it? did it survive for so long? With me to discuss Ptolemy and the ancient astronomy. Lieber Tobe, Leibet Taub, Professor of History and Philosophy of Cambridge University. Jim Bennett, Director of the Museum of the History of Science at the University of Oxford, and Charles Burnett, Professor of the History of Islamic Influences in Europe at the Warburg Institute, University of London. Leibatab, who was Ptolemy?

Can you give us some background? Yes, I can. I'd just like to say, though, I'm very pleased that you've started by reading out that epigram, because I think it does give us a very nice. nice glimpse as to his own aspiration. Ptolemy, as you said, was working in Alexandria and what's now Egypt in the second century. We don't have very much information about him from a biographical standpoint. We know little about him except that he wrote quite a bit, and it's his writings that give

us information about him. So, for instance, we know that he was making observations in Alexandria. We do have some dates, 127 to 141. We know that he dedicated some of his works to someone called Xeros. We have no idea who that was, if that person was a patron or not. He wrote quite a bit on astronomy, not only in the work known as the Almagest. Its Greek name was closer to the English translation of mathematical syntaxes. He also wrote what we consider to be an astrological work.

He described it as another type of astronomy. That work today is known as the Tetra Biblos. He wrote works on instruments as well. He wrote a work that's a very elaborate sort of weather calendar, the phases of the fixed stars. He also wrote a geography. So his work was very far-ranging, not only on astronomy. He wrote an important work on the harmonics as well. We must assume that he worked in the great library at Alexandria.

Can you give listeners a brisk view of that library at that time? Very difficult to do, actually. Not clear. And it's also not clear what his relationship was to other people working in Alexandria. He does mention, for instance, some astronomical instruments that were set up in public places but are in disrepair. He doesn't really mention very many people at all of his own time. In fact, it's quite striking. He talks about using observations made centuries earlier by Hipparchus. another Greek astronomer. And I should probably also add that he's working in Alexandria. He has a Roman name, Claudius, but he was writing in Greek. So linguistically, intellectually, he's coming from a Greek background. Was there a prevailing view of the universe at that time? And if so, what was it in the first, second century AD?

In terms of prevailing view, it's a little bit difficult to say what someone in the center of Alexandria might have been thinking. but it's very clear that Ptolemy's conception of the universe was widely held by others who thought about such things. So the idea that the Earth is in the center of the universe was not a new idea, and that's very clear. He doesn't seem to have thought that it was mathematically the center of the universe, and that's interesting, and we might come back to that later. He also believes that the universe itself is spherical. That was not a new idea. that was a fairly commonly held view. On the other hand, not everyone thought that.

But certainly most people who were educated and thought about such things would have shared similar ideas. Jim Bennett, how far was he influenced by the great Greeks who preceded him? Let's start with Aristotle and Euclid. Yes. Well, as far as Aristotle and Euclid concerned, that's a very different kind of influence.

For Euclid, Euclid, Euclid establishes the parameters of Greek geometry. and that the inheritance, the general inheritance that Ptolemy has from that Greek mathematical tradition is that astronomy is a mathematical science. That's fundamental to Ptolemy's project. So the idea is that the heavens, despite the confusion in some respects of their appearance, derived from an underlying systematic geometry. There's a rationale, and that rationale that lies behind the appearances is fundamentally geometrical.

So there's an intellectual inheritance at a general sense about the project of what astronomy and what astronomers are meant to do. But then at a more detailed level, it's not so much a direct inheritance from Euclid, but from other Greek geometers. For instance, Apollonius of Perga, who's perhaps four centuries earlier than Ptolemy, develops a form of geometry, particular methods within the geometrical practice to do with circular motions and motions of circles, moving on circles and so on, that can then be applied to discovering this underlying geometrical rationale

behind the appearances. The other Greek predecessor, geometration and astronomer, whom you'd have to mention in the context of Ptolemy is Hipparchus, who's working in Rhodes. He's about four centuries, two, three centuries before. Yes, about three centuries or so before. so a century after Apollonius.

And he applies the Apollonian geometry in the first instance. He takes the first steps in trying to make that fit the appearances of the heavens, particularly in relation to the moon and the sun, and develops those moving circles as a technique for dealing with the confusing appearances of the heavens. Ptolemy then expands that and rolls it out, as we might say, to cover all of the planets.

We hear about or we know about the Babylonians in astronomy and we know that Aristotle had a very strong view of what was happening as you were up there. Can you just bring those two into the argument? Yes. Aristotle's account of the heavens is much more that of a physical approach to the heavens. I mean, a natural philosophical approach is what we would say. He's interested in the nature of the heavens materially

on how they move and on how their motions are connected mechanically and so on. So it's much more of a physical explanation rather than a mathematical account. So that's where Aristotle fits in. And the other person you... Was Babylonians? Oh, yeah. Well, the Babylonians are crucial, of course, to the appearances. They come in really through Hipparchus.

So his observations start with, not start with, but we know that... Indeed. The Babylonian corpus of observations and of astronomical parameters is crucial to Ptolemy. to Ptolemy makes observations, they're maybe a little fudged. He uses them in

rather a flexible way. I mean, it's surprising the extent to which Ptolemy's theory predicts his observations, even though we know they don't match very, very well the positions of the heavens. So Ptolemy clearly has quite a fluid

view of the nature of observations, but the observations that he does, use are largely Babylonian through Hipparchus. But Ptolemy uses or at least describes instruments a great deal. Well come to the instruments in a moment if you don't mind Jim but

at the time or a few hundred years after the time we're talking about a man who was in the ascendant for 1,500 years. He seems to be better known as a geographer than as an astronomer. Could you just give us some insight into that? Well it's a very nice instance of that I think which we'll all probably be familiar

with, the fresco in the by Raphael in the Vatican, known as the School of Athens. We're down in the bottom right-hand corner, there are two chaps in a little group, including Raphael, holding spheres. And one's holding a celestial sphere and one's holding a terrestrial sphere. And sometimes people have been confused and thought that Ptolemy's holding the celestial sphere because he's such a famous astronomer. That's not the case.

We know that Ptolemy, who in the fresco, is wearing a crown, because he was often confused, it was a confused idea that he was part of the Royal House of Egypt. Well, who are the Ptolemy's? But of course that's not true. That's just a renaissance confusion. But he is holding the geographical sphere because in the 15th and 16th century, he's much better known as a geographer. And although we think the recovery of Almagest and the printing of Almejus in 1515 is a crucial moment for the history of astronomy, by that time there are at least a dozen editions of the geography. Is that a tetra biblos?

No, the geographia. Oh, the geography, yes. known often as the cosmographia in the Renaissance. But that has astronomy in it as well, because the cosmography links the heavens and position on the earth. So the cosmography deals with the stars and the sun, but not, of course, the planets. They're all in Almagest.

Charles Bennett, Tomé's famous Astronomenex, as Jim said, and I think Leibre referred to it, is the Almagest, which is a mixture of Arabic and Roman as I understand, the greatest. Can you give us an introduction to what it's about? Yes, it's interesting that we should be calling it by its Arabic name. I mean, it is an indication that at least in the Middle Ages and the Renaissance it was through a translation from Arabic into Latin, that it became known and was read. So, Aramogest, as you say, comes from originally from the Megiste, Megistae,

the biggest systematic treatise. and it consists of 13 books. The first book gives preliminaries in regard to cosmology and geometry. It is in this first book that he establishes the importance of studying astronomy. That astronomy as being one of the mathematical sciences is the one science that enables you to get close to God. it is a therapeutic kind of exercise. Why did you think that it was the one science that got you closest to go? What is anything to do with, I'm sorry to Harper at Euclid,

but that Euclid seemed to have established the idea that mathematics could be true, and you had a truth there, and so other truths could be measured against it. It is anything to do with that? Well, absolutely, because he picks up on Aristotle, who divides science into three, into physics, mathematics, and theology, and he says that everything to do with physics is so, vague and uncertain and changeable

that you can't really have true knowledge of it. And theology, again, is too much beyond our ken, beyond reason for us to really grasp it. The only science that we can grasp is mathematics. And the highest part of

mathematics, of course, is the mathematics of the heavens. So if we're wanting to get an inkling of what God is like, of the divine, then we can approach it through mathematics. So this alma just sweeps through his view. So can you give us some summary of them?

Well, having started with this very lofty aim, as it were, he then goes on to describe how basic cosmological details like whether the Earth is moving or the heavens are moving. Of course, he established that the Earth is, is, is, is static at the center of the universe. And then he has to deal with the geometry, the spherical geometry, picking up, as Jim has said, on his predecessors, Apollonius, Euclid, and others in establishing the geometrical framework, the geometrical theorems that he's going to be using.

Then he describes the movement of the sun in one book. and then the more complicated movements of the moon in two books. Then he has this enormous and very detailed star catalogue which describes the positions and the sizes, the brightness of 1,022 stars in heavens, the fixed stars, as we call them, which are thought of as being on a single sphere, the outside of the universe.

And then he returns, of the planets, the other planets. Of course, the sun and the moon are regarded as much as planets as the other five planets, Mercury, Venus, Mars, Jupiter and Saturn. And the final book deals with the latitude of the planets, and that's the 13th book. And by then, he's really run out, well, completed what he wanted to say. And indeed he's said a great deal and a very comprehensive treatise. Could another book called the Handy tables be called a companion book,

a sort of more artisan effort? Well, the Handy book was written after the Amherst and in fact it brings together all the tables which are scattered throughout the What tables are we talking about? Let's be absolutely The tables which give

the movements of the planet so you can predict where any planet will be at any time. And this is very useful for farmers for instance. Well, perhaps the greatest use that was made of these tables actually was for astrology because you really had to be able to tell where the planets were in the horoscope at the time, when you were taking a horoscope of a newborn child, for example. Farmers had a more rough and ready way of observing the...

But I understand it, I'm probably completely wrong, so do correct me, that actually people, I use the word artisans, which was just to cover up, that they had a greater knowledge. They relied a lot on knowing work. the stars were, knowing where the constellations were for things like sowing and reaping. Oh, they did. Yeah. No, no, they did very much. But we have a whole branch of what we call folk astronomy, astrology, which records all the observations made by farms. That's actually written down. And in the Arabic world, in fact, this was mainly based on constellations

through which the moon was moving. So Ptolemy was not the main source for this. In fact, I think one might say that Ptolemy, and Ptolemy's work was always appealing rather to mathematical elite than to the common people. Thank you. Lebo, we've had an introduction to Ptolemy's to the Amherjus, but can you explain in more detail how his model of the universe worked?

Just to tell the listeners, when he set up his model, what did he think it looked like? He drew it on a bit of paper. What would it be like? Well, I don't think that the model is presented in any one place. So we've mentioned several works already, the Almagest, the planetary hypotheses, the Tetra Biblos. To have a full conception of what he thought was going on, I think we have to look at all three works. Having said that, we've used the word system a few times.

And in the Almagest, he does describe the motions of the heavenly bodies, And he's doing them, as Jim has already explained, geometrically. And he's relying on certain principles of geometrical astronomy that were established centuries earlier. The most basic principle being the idea that the heavenly bodies are moving in uniform, circular motion. They're moving in circles, and the speed and direction of their movement remains the same. He doesn't treat them all in the Almagest altogether, and that's what's in a certain way interesting. Charles, I think, alluded to this, that he treats the sun, the moon, and each of the planet separately. So actually, if we were going to draw the motion of each of these bodies,

we'd have a whole series of drawings. It wouldn't be one. But if we turned to the planetary hypotheses, there we would see a picture of nested spheres where he's putting together all of the motions to give us a sense of what, for lack of a better word, the architecture of the universe would look like. He has nested spheres. What do you mean by nested spheres? One inside of the other. Concentric circles?

Yes, concentric. And one fitting very closely inside of the other with no empty space in between. And he does this. He accomplishes this using 41 spheres, but he also says you don't need full spheres. You can just have a band of a sphere. You don't need the whole thing.

and he contrasts this with others' conception, including Aristotle. Aristotle needed 56 spheres. Ptolemy is quite pleased that he can bring the number down. He thinks that that's a simpler and better solution to the problem of trying to account for all of the motions together. So we are talking about concentric circles. We're talking about spheres, some further away, some nearer, moving, but not evenly. I'd like to come back to that in a moment. but talk about the measurement system going on, Jim Bennett. You made a sally towards it in your introductory remarks, and I said, later please, and now it's later. Well, in Almogest, despite the fact that Ptolemy's not remembered, particularly as an observer,

he does describe a suite of instruments that you would use for making the kinds of observations that his system would require. Some of those, the basic ones, are very straightforward instruments that make a single observation. instance, there's an instrument, a thing called an equatorial ring, which just determines the time of the equinox, either the spring equinox or the autumn equinox. That's all it does. It's a circle set in the plane of the equator. And when the sun's motion coincides with that plane, then you know it's the equinox. So that's a very precise instrument, very, very singular instrument. Then there are others that, again, make singular observations,

concentric rings in the meridian, a quadrant for measuring the altitude of the sun, as it crosses your meridian, as it's due south, and a zenith instrument for measuring the zenith distance, the distance, the angular distance between the point directly overhead and the target position of the moon. So these are very particular instruments. And then he expands that out to a single extraordinarily complicated instrument,

which makes all the observations you could possibly want a thing called an armillary sphere. And that's amazingly complicated. There are about seven interlocking rings. If we think that the planetary space, system is complicated. Here it's kind of realized in a physical context

where there are axes that allow the instrument to track the equatorial motion of the whole of the heavens. And another axis set within that that is parallel to the set the fundamental circle parallel to a thing called the ecliptic which is the

apparent path of the path for Ptolemy of the sun through the celestial sphere. That's amazingly complicated. It doesn't really work. People try to make it work. Sorry? Do any of the instruments really work? Yes. Oh yes. The simple ones would certainly work. The meridian instruments that Ptolemy explains in Almejest become the foundation for all fundamental astronomy thereafter. So that's, those certainly would work. But when he's ambitious and goes for the, as astronomers devising instruments always are, they always go for an instrument that will do everything, then that falls flat, I'm afraid. But becomes a kind of symbol. Astronomers are often shown holding our military spheres, even.

if they don't use them, because they represent the project of astronomy in a material form. So this is the armory for astronomers pre-t telescope. Exactly, yeah. Charles Bennett is often associated with Aristotle. Now, that again has been a couple of references. Can you tell us how their views compare and how they diverge? Well, first of all, when autonomy was writing, because there were various different philosophical schools, Aristotle was just one of them.

But after Ptolemy, Aristotle's physics became the main philosophical view in the West and in the Arabic world. And there was always regarded to a contrast between, or even a contradiction between what Aristotle and what Ptolemy said, because Ptolemy's geometrical model was taken to be real. and this idea of having epicycles mounted on eccentric spheres and so on did not tally at all with an Aristotelian physical universe in which all movements had to be circular round the centre of the earth. Can I ask why, given the authority of Aristotle, people prefer Ptolemy's view. Well, it depended who those people were.

Well, I'm we told that Ptolemy's... views obtain and predominated over the next 1,500 years, not those of ours, I'm just... Well, the Ptolemae system... Yes, I mean, the Ptolemaic system was accepted in astronomy

and as Lieber has already hinted, Ptolemy attempted to fit his system into a physical universe in his planetary hypothesis, which was a later work of his, which was his final word, as it were. And... But even so, there were many criticisms of this system by Aristotelians or within the peripatetic tradition,

which was the tradition that followed Aristotle, saying that this just didn't, this system just didn't make sense from a physical point of view. And so there were attempts by, for example, the Arabic Albitrugi, whose work was translated in Latin as the work of Al-Petragius, to make another system, astronomical system, which would, in fact, fit the Aristotelian model more closely. Can I come back to you now, Lee, but so far I've talked about Ptolemy as a mathematician and an astronomer,

but in his introduction of the Amidus, there's also a sense of philosophy there, isn't that? Can you, even an ethical, even a moral dimension to Israel, can you bring that into the conversation? Absolutely, and Charles has already mentioned this, and I'll just try and expand a little bit. Charles mentioned Aristotle's division of theoretical philosophy into physics, mathematics, and theology. Aristotle thought theology was the most important type of science of theoretical knowledge to pursue. Ptolemy thinks not. He thinks it's mathematics. And he's very clear that if we're going to proceed as mathematicians, we should try to set our sights on explaining the most divine, the most eternal. the most everlasting thing in the world, the heavenly bodies.

If we do that, we will be spending our time, studying the most important thing in the universe. That will be a very good way to spend our time. There's an ethical and moral dimension to that. He's also very clear that the mathematics that explains the universe explains the entire universe. So I mentioned the harmonics earlier. He sees the harmonics, the way that we hear sound as human beings, That is a type of mathematical proportion and ratio that pervades the entire universe. It's present in terms of structuring the universe.

It also helps structure our own souls in the way that we understand the world. For him, it's very much connected. Harmonics is for him also a mathematical study. It's not geometrical. It's arithmetical. Jim's mentioned his work on observation and instruments. He also uses observation and instruments. to study harmonics as well.

For him it's all of a piece. He's going to be a better person for doing this and for teaching us how to do it as well. When he says he's going to be a better person just for a little longer, does that mean, is there any sense? Because the word divine has cropped up in notes. And is he a better person here?

I mean, there's no, as it were, post-death better person. You're shaking your head. I must interpret this, but you're nodding and shaking your head. Better if you talk. Yes, I will talk. What the afterlife might be, you hinted at your reading out of the epigram at the beginning of the broadcast, and that's why I was so pleased that you did.

He does have a sense that he may, if he's fortunate, live on. He'll live on. Here we are having a special program today talking about him. I think this is what he aspired to. He wanted to make progress. He knew that he was building on the work of others. He mentions Aristotle. He mentions Haparchus, who he refers to as a love. of truth. He wants to do more work, and he wants it to leave a lasting legacy. In terms of divine, it's not clear that he has any sort of idea of a god in a way that we might think of in the Judeo-Christian world. He doesn't seem to be referring to traditional Greek gods like Zeus. For him, divine means eternal. Can I come, Jim Bennett, can I come back to something Charles Burnett said, if you could develop it. And There were problems with Ptolemis system, which as Charles has pointed out, people kept bringing to the attention of his followers for the next 1,500 years.

Can you just give us some idea of the problems that were big problems and that kept challenging, though not overthrowing this system? Well, I'd like to say that there were problems also with Aristotle's system in the sense that Aristotle's system would be completely hopeless at predicting any of these astronomical phenomena, particularly in relation to the planets. So in answer to your previous question, one could say that people got good at dividing the labour up. There were people who thought, my business is prediction and I'm a mathematician. There are people who thought my business is physical explanation and I'm a natural philosopher.

And keeping those two things reasonably separate, the wind discussion was something that was a convenient device. But to think about the problems with Ptolemy, we haven't said very much yet about the technical content of the planetary, and we're going to have to do a wee tiny bit of that just to... Why don't we start now? Yes, well, we haven't said, for instance, much about the deference circle, which is the large circle, which moves around the central Earth, and carries on it a little circle, an epicycle, which is rotating in the same direction as the deference circle,

and creates the looping motion that explains, or attempts to explain what we see in the heavens that the planets, although they're moving against the background of the surface, stars in the opposite direction to the daily motion occasionally turn around and move retrograde and so on and then turn back again and they behave in this erratic manner

which the combination of different and epicyclic circle in the Ptolemy Talomec planetary theory can deal with that's fine Hipparchus had that Ptolemy takes that over but Ptolemy adds another geometrical device that we'll

just have to mention briefly which is a thing called the equant point remember that we began with the principle of uniform circular motion. The motion doesn't have just to be on a circle, it has to be evenly, it has to be equal, it has to be uniform. The heavens aren't really like that. We sort of know that

from Kepler's second law and so on. So it's going to be hard to fit that on to the appearances. Ptolemy deals with that with a little trick where he says that well the uniform motion is not about, not only is the earth not at the center of the circle, but the uniform motion

is not about the center either. Now, it is about the position of the earth. It's about, it moves around this other point. And if we were standing at that point, we would observe uniform motion. But that point's not at the center of the circle. And that means, you think about it geometrically, that the motion on the circle isn't uniform. Now, that little trick is kind of hidden in Almejest. You do see it. If you really get into the maths. And once you see it, you think, oh no, he has broken the cardinal rule there. And that was, there was an unhappiness about the equine point. So that's one of the things that troubled, not just the physical, the physicist, the natural philosophers, but also the mathematicians themselves.

What's the card in the rule has broken? Uniform circular motion. Silt circular, but it was no longer uniform. The speed of the planet moving around its deference circle was uneven. Can I come Charles Bennett to Ptolemy? is spiritual, so if we can use that word. The tetrabiblos. What is happening in there?

And we're moving towards astrology, aren't we? Well, this indeed was regarded as a textbook for astrology. And Ptolemy described it as a second systematic treatise. And he starts off by saying that the science of the stars is divided into two parts.

The first part is what he deals with in the Almagest, which is the mathematical part, for which there are certain dependable arguments, and nobody can gainsay those arguments. The second part is the part which studies the effects of the stars on the sub-lunar world, the world around us. And that is what we would call astrology. And it's what Ptolemy calls a physical science.

Now, did he, people who want to know, did he think that we are influenced by our stars? Oh, absolutely. But he had a very interesting qualification, didn't he? Well, he... You could be wrong. Well, he was saying that you can't be sure, we can't be so sure, of the conclusions that we come to in astrology as in astronomy,

because astronomy is mathematics, which is based on demonstration, demonstrative arguments, which are irrefutable. In regard to astrology, because we're dealing with things around us, which are always changing, which have an infinite number of differences, it's very difficult to be absolutely sure of anything that is going on.

One can only, I mean, he says at one stage in their tetra biblos, that one must use natural science, but also conjecture, intelligent conjecture. So there is a certain amount of guessing. He also uses a word which is the same word as is used for, archers when they're trying to hit the point with an arrow. So it's a stochastic art where you might hit the point or you might not hit the point. But because, well, he gives the examples indeed

of agriculturists, of shepherds and so on, who are always observing the stars in order to know when to plant their crops, when to set sail and that sort of thing. And they're usually right. So there must be something in it. Can I just move on? I must get to Kepler and Copernicus and so on, but just before we do it, leave it,

can you just briefly bring these two together, the astrological and the astronomical are so far apart now, but to him they weren't. To him they were two types of astronomy, as Charles has suggested, that the mathematical, geometrical astronomy in the Almagest is more precise and it's more dependable, where as the astronomy in the tetrapyplos

deals with the 50s, physical influences on our realm, on the terrestrial realm, and there are different factors that make it not exact, and it is a stochastic science. We're aiming to do something. He says that even though we may not be able to predict things completely accurately, some things we know generally, like how climate changes in different places and people may have different illnesses or dispositions in different parts of the world, almost a sort of ethno-geography that he brings up there, He says that doing astrology is good because even if we don't know for certain something will happen, if we have some foreknowledge that it might happen, we'll be able to prepare ourselves for it.

He says it's something like putting ourselves in the hands of a physician. A physician isn't always going to be correct, but they will be able to make the best effort at healing us from disease. They're not as reliable as a sandal maker. If we want to have a pair of sandals made, normally we'll go to someone like a mathematical astronomer. He'll be able to do the job properly. Physicians aren't always able to do their work without any interference by different factors in the same way. Jim Bennett, this holds for 1,500 years. They're widely translated, Arabic, which Charles might want to come in on, Iter and Sanskrit.

Yet, can you just briefly, because I really do want to get around to time it was ever, say, why it held on for so long. It's an immense amount of time. There are scholars, especially in the Arabic world, there are scholars in Europe, there are scholars still in Greece. Why did it hold on for so long? Well, it works very well. It produces good results. And it's a very challenging problem dealing with particularly the motions of the planets. Once you, it takes, there's a lot of work required to get into Alma jest and to understand it.

And then you become more and more impressed by the geometry. So you become sort of inculturated into being a Ptolemaic astronomer. So it's like any discipline. You invest a lot in getting there and really being part of it. You're impressed by how well it works. And there is no real alternative as far as making those kind of precise predictions concerned. Ptolemy is really the only show in time for that. Until 1543, I met Copernicus with his book on the revolutions of the heavenly bodies,

and the change began. It was post-Potlolemaic after that. Yes, there are problems, of course, and the passage of time makes them more obvious. We dealt with one or two problems earlier, but one of the most obvious problems is the lack of the slip, slippage between what the model predicts and what you observe in the heavens. And that particularly applies to the vernal equinox, to the spring equinox. That's important because the date of Easter depends on the spring equinoxy.

Easter occurs Sunday after the first full moon after the vernal equinox. That may not seem important to us now, but that was absolutely crucial to the church's management of the ecclesiastical calendar. It was great splits in the high, how the church fight. So that was a big problem, and Copernicus felt that very acutely as a canon of the church. But he also felt very acutely, some of the problems we mentioned earlier, earlier, the Equine point he really hated. And if I may just say very quickly, one of the things he hated was this idea which we began

with that there isn't an overall system. That's to say, in Ptolemy, you can put the planets really in any order you chose. Ptolemy puts them in a conventional order where the period is greater, they go further away. But actually, when you're sitting at the centre, you haven't got any parameters, any observations which impose that. And Copernicus didn't like the idea of the lack of an overall. called Cosmos. So just to go back to the school,

on precisely what did Copernicus do, which changed the game? Well, he sets the sun at the centre. He makes the Earth a planet. He gets rid of the equine point, but he keeps a great deal of the traditional geometry of Ptolemy, and that was very good,

because Copernicus, for his system, because he's doing something very radical in cosmological terms, and he knits together in the whole system because he can prove that the speeds of the planets are slower and slower until you get to the fixed stars of course which are stationary.

But if the system's the same, then people are familiar with the methodology of doing astronomy so they can continue doing a kind of Talmec astronomy in terms of the calculations and so on, even though the cosmological assumptions have radically changed. But the door to a new universe as it was open, Charles Bernard, and the next person quite quickly after which was the Danish astronomer Tico Brahe.

What did he bring? Well, he actually restored the idea that the Earth was stationary, perhaps because of the revolution in nature or saying that the Earth was going around the sun. It took a lot of time to get used to. And that all the planets, all the other planets, were going around the sun, which in turn was going around the Earth. But I think what was revolutionary about Taito Brahe

was first of all, his observations. He had some very, he invented on the island of Uranibur, some wonderful instruments which could measure with much more precision than ever before, the positions of the planets. And he had this idea that one could do away with the spheres. The idea that there were concentric spheres in which the planets moved

no longer seemed necessary for him. And so he had the planetary movements actually intersecting with each other. And the whole sort of Ptolemaic framework started to break down in this respect. Can I come, I'm sorry to rush on like this, but we, anyway, there go. Can you tell us about Kepler, then, because Kepler, as it were, nailed it, if I can be so crude? Well, Kepler broke away from the idea of uniform. circular motion. He adopted elliptical orbits instead. And this was not something that was easy for him to do emotionally. I mean, he despaired over this. He used Tico's observations. He was also a mathematician,

was committed to describing the motion the way it had been done before, uniform circular motion. But he had problems with Mars, as had had Ptolemy as well. And in the end made what was, I think we can say, revolutionary break away from this geometrical model to something very different, to ellipse instead of a circle. Though there's a way also of understanding the, I mean, the use of the equant sometimes is equated to what we end up with using the ellipse. So what did Kepler do then? This was, we're talking of a time of significant change. We're into post-telling.

Absolutely. We're in the beginning of the early 17th century. And what's really critically different about Kepler? is that he's the first person to concentrate simply on the path that the planet is following. And he finds that to be an ellipse. And he says, well, my path is actually very like Ptolemy's resultant path. He says it would be very much the same, but the concept of an orbit is different. Kepler says, Ptolemy's path is much the same, but he puts in all these other fictitious circles and so on.

And Kepler wants to say, God hasn't put any of those circles out. I'm only interested in what God has left so that we can learn. what the divine aesthetic is, and there's only the planet and the path that it follows, and that, of course, is an ellipse, and the motion is non-uniform. So the equine has a sort of reappearance in Kepler. But he's fundamentally overthrowing what Ptolemy thinks astronomy does.

But Lebo, what you hinted out very briefly is that this is an emotional pull for these men. They were committed to Ptolemy, the idea was so, oh, we're running out of time. I mean, it was a big emotional pull, wasn't it? Well, I think so. And it's very interesting that Kepler also ends up using geometry to portray the way the universe fits together. And so in that way, he is echoing Ptolemy as well.

Sorry about that, Lebertobe, Jim Bennett, Charles Burnett. Thank you very much indeed. Next week it's the second century BC revolutionary Jewish leader, Judas Maccabeyas. Thank you for listening. Thank you for listening to this Radio 4 podcast. If you've enjoyed it, you might like to try others like it, such as Start the Week or Thinking Aloud,

which are both available from the... Radio 4 website.