In Our Time - Johannes Kepler

Episode Date: December 29, 2016

Melvyn Bragg and guests discuss the German astronomer Johannes Kepler (1571 - 1630). Although he is overshadowed today by Isaac Newton and Galileo, he is considered by many to be one of the greatest scientists in history. The three laws of planetary motion Kepler developed transformed people's understanding of the Solar System and laid the foundations for the revolutionary ideas Isaac Newton produced later. Kepler is also thought to have written one of the first works of science fiction. However, he faced a number of challenges. He had to defend his mother from charges of witchcraft, he had few financial resources and his career suffered as a result of his Lutheran faith. With David Wootton Professor of History at the University of YorkUlinka Rublack Professor of Early Modern European History at the University of Cambridge and Fellow of St John's CollegeAdam Mosley Associate Professor in the Department of History at Swansea University Producer: Victoria Brignell.

Thanks for downloading this episode of In Our Time. There's a reading list to go with it on our website, and you can get news about our programs if you follow us on Twitter at BBC In Our Time. I hope you enjoy the programs. Hello, the German astronomer Johannes Kepler is widely regarded as one of the greatest scientists of all time. Born in 1571, his work laid the foundations for the breakthrough that Isaac Newton made a century later. Kepler conducted research in the field of optics and made important advances in mathematics. He became imperial mathematician of the Holy Roman Emperor,

but his most significant achievement was his development of his three pioneering laws of planetary motion, which revolutionized our understanding of the solar system. He accomplished all this despite the fact that he had little money, his personal life was hit by tragedy, his mother was accused of witchcraft, and he was a Lutheran at a time when an increasingly Catholic Germany often persecuted Lutherans.

He's also thought to have written one of the first works of science fiction. with me to discuss Johannes Kepler's life and science are David Wooden, Professor of History at the University of York Eulinka Rubelak, Professor of Early Modern European History at the University of Cambridge and fellow of St. John's College and Adam Mosley, Associate Professor in the Department of History at Swansea University. Adam Mosley, religion played a major role in Kepler's life

in the lives of many people at that time. What was the religious situation in Germany when Kepler was growing up? So what we think of as Germany was at that point of the Holy Roman Empire, which was a network of principalities and little states and Prince Bishoprics that was normally ruled over by the Habsburg Emperor. And it had been ridden by the Reformation. So that had generated religious conflict and it generated military conflict, which had come to an uneasy truce in the peace of Augsburg in 1555. One of the principles of that settlement was the cuius regio ais religio,

principle, whose region his religion. In other words, the territorial prince for particular principality could say whether that principality was going to be Catholic or Lutheran. There were also free imperial cities. Kepa was born in one of those imperial cities of Woldershtadt, so that was, in theory, that was mixed Catholic and Lutheran. But Waldershtat was embedded within the Duchy of Wittenberg, which was a Lutheran duchy. And Kepler was Lusuf. Lutheran, he was brought up in a largely Lutheran environment. Kepler had opportunities, actually, because he was bright. He was a good candidate for a scholarship, which was set up in order to train Lutheran pastors,

who in turn could educate the populace as to what it meant to be a good Lutheran. So you're saying he got a scholarship, weren't you, what did it do for him? So he got a scholarship which was ultimately going to train him. in theology at the University of Tübingen. What was his family background? He was born into a family that was in a sense on its way down. So in its heyday in the 15th century, his paternal ancestors had been minor nobles. They had been knighted through Imperial Service.

But the family had moved into the crafts and trades. His grandfather was quite well respected in Vandestadt. he was mayor. But his father was perhaps a little more restless, a little more feckless, and he became a mercenary and was absent for a lot of Kepler's childhood, in fact. So the mother kept the place going?

The mother was very important, and the grandfather too, in keeping the family together. Eulinger, what was the difference? Can you just give us some idea of differences between Catholicism, Lutheranism, and Calvinism? For this programme, Calvinism, isn't particularly, important, but Catholicism certainly is and Lutheranism. What are the differences, what

opportunities would be, could you have? Well, you tell us what the differences are and what opportunities were given and denied. So Lutherans think that the papacy should not be the head of the church. They think that Christ alone should be the head of the church. They don't believe in good works either. And Kepler certainly supported that. They think that believers are empty head handed before God. That means they affirm, and so do Calvinists, the notion that after the fall and the expulsion from paradise, humanity is fundamentally depraved. In fact, human nature is so depraved that there's nothing that you can do in your own life to right yourself. And that's why you're completely dependent on the grace of God. And he's granted that through the death of his

son, Christ, and if you believe in that, then you can believe in your own salvation. And alongside that, so this denial that there are good works is also, of course, the idea that celibacy is not a way of life. Human nature is sexual and therefore am mild by that sin, but you have to affirm it in a firm family life. And there are other beliefs about the Eucharist, so the idea that it's not the priest who consumptumptuards the matter of the Eucharist. It's there in the material. I mean, Luther says the Bible insists that this is my body and so I must believe it. And that at the time is so important because the Eucharist is the ritual of salvation.

And it's given in both kinds to all believers. And he took this completely seriously? Well, he takes it seriously, but the key to understand Kepler is to look at the complexity of his personality. So he tells us that already as a teenager, so very early on, just as he gets that scholarship makes his way into that Lutheran boarding school in Wittenberg, he is very interested in the most complicated riddles, in the most complicated programs, And of course, he thinks about the differences in Protestantism. So apparently he tells us he writes to the University of tubing, age 13, to ask about predestinations to the idea that you might be elect by God and might be already decided whether you're amongst the elect or not that go into heaven. And he is also always very troubled by that idea of the Eucharist, of the communion,

the ubiquity of Christ, because if you think that really materially Christ is present, well, then he would have to be everywhere. And Kepler has to find for himself a different answer to that question. What was his, how did he, what was his original name? He was sent to this place to become a pastor, a Lutheran pastor. He came out as a mathematician. How did he go from there to becoming a man who went into science? Yeah, in many ways. That is a, somewhat an accident and a surprise. So just before he finishes his degree,

he receives a letter with an invitation to become a math teacher in Graz, in Austria, and that is a mass teacher at a Protestant school for aristocratic sons. And he hums and halls about this, and he's really been set up to be a pastor and talks to his family, talks to his teachers, and then decides to go for it for two reasons. The first reason is that he always felt that he didn't have the right body to be a pastor. As a pastor, he meant to be bulky and bearded, and he's inherited his mother's body. He's very slight.

He's short at a student play in tubing on the Market Square once he's cast as Mary Maudlin. And on top of everything, he catches a cold. So, you know, he hasn't got, he always feels he's got a scholar's body, not a pastor's body. But also more fundamentally, he's already aware of the fact that to be a pastor means to engage in this. endless confessional polemics between Lutherans and Calvinists. And he's heard that in sermons ever since he's a child. And he's really offended by it. And he doesn't want to become that man. So becoming a scientist means that he can become a theologian in a way, a think about natural philosophy, about the book of nature. And for him, that's a much more satisfying

career. How does moving Austria to teach maths helping on that? Well, I mean, you might think at first it actually might not. It doesn't start very successfully. So we know that he's quite hardly anyone sitting in his lessons. It's a complete disaster. What he does and spends time doing is making calendars, astrological calendars that are more successful. But meanwhile, and that's an enormous leap.

He becomes tremendously ambitious. So he enters Graz, age 23. Within a few years, he's put together this book that claims to explain the mystery of the universe. And from then on, he sees himself as a prophet who is the first one eventually, he claims, to understand fully God's buildings plants. Through geometry?

In part through geometry, yes. David Wooden, can you give us an outline of the general view of what people thought of the universe at the time that Kepler was growing up and then... Growing up and then going to do you. Yeah. For 2,500 years, everyone has assumed that the Earth is stationary at the center of the universe. The heavens turn around the universe, around the Earth, the Sun goes around the Earth, the planets go around the Earth.

Indeed, the Sun and the Moon are planets that go around the Earth. Copernicus changes that in that Copernicus argues that the Earth and the moon going around the Earth go around the Sun. But Copernicus shares the assumption that have been there for 2,500. years, that movement in the heavens is circular, it's mathematically regular, it's constant, it's unchanging. And he certainly doesn't question the view that these great bodies moving through the sky are carried in transparent orbs. There's a physical solidity to the heavens and that it's all driven from the outside. It's a mechanical system driven from the outside. What happens in 1572 is Taekobrahi sees a new star where there shouldn't be a new star

because change in the heavens according to Aristotle and according to the whole tradition of astronomy is impossible. The heavens carry on doing the same thing over and over again. And then Taekobrahi also sees in 1577, a comet which he argues is cutting through the mechanism, the orbs, the transparent structure of the universe, in which case there isn't a mechanism there. space becomes in some sense empty for the first time. So that Kepler inherits a question about what is out there within this structure of the universe. What was the key motivation? You've almost said it that he thinks he the first person to understand God's purpose in the universe.

Was that the great motivating force? The crucial thing to see here, I think, is that for Kepler, God is the architect of the universe. Nothing can be random. God doesn't play dice. God doesn't throw things out randomly. Everything has to have a design structure, and that structure has to be beautiful. And beautiful for him means mathematical. So underlying the universe, there has to be a mathematical structure which nobody has understood. And what he claims in his first book, the mystery of the universe, is that he has grasped the mathematical structure of the universe for the first time.

And what he's understood is why there are only six planets in the Copernican system, the Earth's stopping a planet, why the spaces between the planets are what they are. And that's because God, when he constructed the universe, built into it the spaces that you would have if you put between each planetary orbit, orbit is a new word that Kepler and events, between each planetary orbit,

a what's called a platonic regular solid. There are five platonic solids, and they, in God's mind, feel up the space between the heavens. You can't tell us what those five platonic solids are there. You can't get away with it. The simplest platonic solid consists of four isosceles triangles fitted together to make a sort of pyramid. The next one is the cube with six sides. Then there's one with eight sides.

There's one with 12 sides. And there's one with 20 sides. And those are the five platonic solids. Kepler's working within the notion that the orbits of the planets are spherical and he wants to place these, he wants to nest these solids into the orbits. And that explains what the spacing of the orbits is. So he's seen into the mind of God. Geometry enables you to understand how God sees the universe.

Adam, Hanam Mosley, can you bring in the influence that the Danish astronomer Taka Brahe had on Kepler? Sure. This is before the invention of the telescope and its application to the heavens in astronomy. Tika Brahe is the preeminent observational astronomer of the 16th century, and he, with the support of the Danish crown, builds an observatory and construct. a range of instruments that allow him to observe the heavens with great unprecedented accuracy. That's partly because Tico in common with other Lutheran astronomers sees the study of the heavens as important, sees astrology as an important tool for understanding God's providential governance of the universe,

and is therefore committed to an observational reform of astronomy and astrology in order to be able to understand God's plan for the universe better. Tika Brahe is not a Copanican. Tika Brahe elaborates his own system for the world, which is a geo-hilo-centric system. So he believes the planets circle the sun, the sun circles the earth. So he keeps the earth at the center of the universe. Towards the end of his career, Ticabrahi falls out with the Danish crown,

and he migrates. And he migrates from Denmark, eventually, to Prague where he's appointed imperial mathematician by Emperor Rudolph II. Kepler knows a little bit about Ticabrahe at the point in his life when he's producing his first book on The Secret of the Universe. He knows about that because his mathematical mentor on Tubingan, Michael Messlin, is one of Ticabrahe's correspondence. So they've been exchanging letters.

Messlin's also seen some of Ticca Braghe's publications that have not yet made it generally into the open market. So Kepler includes a mention of Tikabrii in his first book. He's very keen to know what Tikabrahe makes of that work, and so he initiates a correspondence with him. Eulinka, when he's in contact with these people and his teaching, is he still held back in any way by being a Lutheran? The Catholics are gaining force in Germany at that time.

Does he have problems with that? Well, he never has a university position. Because he's not a loud one. That is right. So he's in Graz very quickly in a terrible situation. As a 27-year-old, he's married by then. And in Austria, there's militant counter-reformation. So books are burned, Catholic. Yeah, absolutely. And he writes desperate letters back to Tubing to his teacher, Michael Maslin, who just mentioned. And it's clear that Maslin just doesn't respond. He's not helping him at all. So Tico Bray really, the move to Prague, I mean, by then they've collaborated, is fundamental for him and he's so lucky to be appointed there. He tries nonetheless all his life. We associate him very much with Prague. He all his life.

He tries to get back to Wittenberg, to his home territory in Germany, that is Lutheran. But it's decided very quickly by theologians there that this is an unreliable, man who can confuse the young with his doubts about, in particular this question of the Eucharist, where he's leaning more towards a Calvinist stance. And that ruins his prospects to ever have the security of a university position and the salary that comes with it. David Wooden, you've mentioned this, you've talked about this, and you've given us the five platonic solids, which none of us will ever forget, and the reference for a reference. And you've talked about his first major work, The Secret of the Universe.

Can you talk more about it? What Kepler is trying to do is construct a universe in which bodies move through space. And so he asks the question that nobody has asked before, which is what's moving them. Now, in the old system, there are these transparent orbs, which are mechanically driven, as it were, by some divine force.

Take that away, and bodies are traveling things. through space. And the question then is, when we're putting the question is, how do they know where to go? Supposing there are the planets have souls driving them, how does the soul know when to turn, how to turn? And particularly what Kepler does is he does a drawing which shows how under the Ptolemaic system the very complicated spirals that planets have to move to the heavens. And the question is, how do you know to turn here when there's no marker there? And Kepler's answer to that is there has to be a physical interpretation of this process and it has to be one that's as it were realistic it has to either be that they can navigate they have markers that enable them

to navigate or there has to be some comprehensible force driving them and from very early on capela's convinced that this force emanates from the sun and that this force must be thought of as being something like magnetism which can operate over a distance so he's trying to build a model of the universe where the sun is driving the planets through the heavens, and the force that's emanating from the sun is a bit like a magnetic force, and that this is acting on the planets and pushing them along. He's got no concept of inertia. Galileo begins to get a concept of inertia. Inertia enables you think the planets will just float along through space.

On the contrary for Kepler, they have to be pushed all the time. Some force has to be constantly preventing them from coming to a halt. Can we move on to these laws of planetary motion? And can you tell us about the first two, first and second Adam? So what we think of as Kepler's first two laws of planetary motion are expressed in his new astronomy of 1609. And his what? His new astronomy, a publication of his of 1609, which has a longer title which invokes physical causes, celestial causes, which is something relatively new in astronomical works of this period because of a traditional distinction between doing astronomy, mathematical modeling the heavens, and things. thinking about physical forces.

So what we think of is his first law, was actually the second one he arrived at, but that's the law that says that planets move in ellipses, not circles, and that the sun is at one of the two foci of the ellipse. You're looking as if you might want me to explain that. I'm just looking inquiringly, and you read it as you want to.

If you want to explain, explain it why. So an ellipse is an, we can think of as an oval with two axes of symmetry. So it's an elongated circuit line, so it has a long axis and a short axis. It's symmetrical about both of those. And the two foci on the long axis, and they're part of how a mathematician would define a particular ellipse. And if you take any point on the ellipse, you know, and you draw a line from that point to these two points, the sum of those two lines is always the same length,

and it's always the long axis of the ellipse. So what's important here for Kepler is that, I mean, he has a long struggle. He arrives at this discovery through his work on the planet of Mars, which is the task, calculating the planetary motion of Mars, is the task that Dikabaraj set him when he first arrives in Prague. And through a long struggle, Kepler arrives at, an ellipse for the orbit of Mars because he works with circles, he works with ovals, and none of them agree with Tico Brahe's observations to the degree of accuracy that Kappa has

convinced those observations and relate to. Can we take that on the planet's emotion? And also talk about the circumstances, which is quite important in which he's finding himself at this time. He's having, he's got very little money, his first wife's dying, living with a lot of children, some have died, managed again more children, more poverty and so on, and doing this work. Can you give us some idea of how planet's emotion is going on with a frantic, as it were, in terms of getting some money in family life? Yeah, it's one of the astonishing and really

inspiring features of Kepler's life, how he manages to keep doing breakthrough research, as we would call it nowadays, while his circumstances are so problematic. So meanwhile, he's had to leave Prague in 1612 when the counter Reformation progresses there. His wife, as you say, has died. He's got these children. He's got to park somewhere and then finds a position in Linson brings them back there. He hasn't even got access to a printing press

very easily. He's got to buy himself paper to get all this organized. We think often that print made everything possible. It was actually incredibly hard for someone even like Kepler to put his ideas into print and find money for it. When he writes the harmony of the world, which is published in 1619, we move into the period where his mother is accused of witchcraft, and he actually has to shelter her at home for some time. So you couldn't really imagine more difficult circumstances.

But another feature of Kepler's personality, which we haven't touched on so far, is that he's tremendously optimistic. He's inspired and kind of fired on by the sense that he's living in an amazing time of the new signs in a way of new constellations, new heavenly constellations, of God also who still creates. And that makes him very different from much of the tone of the time. So he's very offended by Lutherans who endlessly think in apocalyptic terms, who think the world is coming to an end.

You know, the stones look less brilliant than they did. The light is dimming. Everything becomes more dark before the world ends. And he finds himself arguing from a completely different position. And I think that gave him the energy to carry on despite his financial problems. But, you know, he gets in 1610 a letter from Galileo, which must have done. just enraged him. Galileus says, look, I just,

you must have worked with quite a mediocre observational instrument. I've got amazing ones. I've just got a huge gift from the Duke of Tuscany. He gave me a lot of money as a salary and I've got all the time in the world to carry on

with my work. So really this territorial behavior and his life is completely different. He hasn't got money for instruments. and he can't even travel to other place to make observations. Can we conclude the laws of planetary motion, David? We can.

I mean, just to go back to this, I mean, Kepler is a man of principle. He has endless opportunities to sell out. He could have become an Orthodox Lutheran and got a nice job in university. He could have converted to Catholicism and been showered with rewards. He insists on holding to his lonely, isolated position, unlike someone like Galileo who's prepared to sell out any time you ask him to almost. Kepler accepts the consecrated. of refusing to fit in.

He's a very exceptional, determined individual. Back to the laws of planetary motion. We did the first one, which is the ellipse. The second one is that the area swept, if you imagine a line from the sun to a planet and the planet is going around the sun, the area swept out by the line as it moves around, as a planet goes around the sun,

in any period of time will be the same area. where you've got an ellipse, the planet is sometimes closer to the sun and sometimes further away from the sun. As it comes closer to the sun, it speeds up. As it moves further away from the sun, it slows down. And the law that governs the way in which it speeds up and slows down is Kepler's second law,

which is that the area swept out between it and the sun will be the same in any period of time. And that gives you a way of calculating the speed of the planet around the sun. And the third law? The third law. The third law is the most difficult. The third law... Do you want to skip it?

No, no, no. I'm determined to do it. You may get cut out of the program later. The third law is one which established... If you think of a planet going around the sun, in modern terms, if it goes too fast, it'll fly off into space. If it goes too slowly, it'll fall down into the sun. There's a right speed for every orbit. The third law is about that right speed.

It says that if you take the diameter of the... orbit of the planet around the sun and you cube it and you take the time the planet goes around the sun and you square it and you divide one into the other you will get a constant very simple terms if you take the diameter of the earth's orbit around the sun and call that one you take the period that the earth takes to go around the sun and call that one one year you cube one square the other they divide them into each other and you'll get one. Now, if you take those same units for all the orbits and do the same calculation, you'll always come up with one.

And will you? Yeah, it's right. Adam, he was Kepler's most celebrated during his life for his rudolphine tables. Right. So when Kepler, first Mr. Prague, as Ticoabra's assistant, Tico has been commissioned to produce these astronomical tables. And they take a long time to finish, and Kepler is the one who finishes them.

when they're eventually published in 1627. Tiga Bri is still listed as the main author, and Kepler is the one who's completed the work. So, astronomical tables are the tables that are expressions of the mathematical models that you use for modelling the behaviour of the planet, and they're tables that allow you then to determine the positions of the bodies in the heavens

at any given moment in the future or indeed in the past. So there have been previous sets of tables. The tables that were used through the Middle Ages were mostly the Alphonseen tables, named after King Alfonso the 10th of Castile. Then there are the Prutanic tables or Prussian tables produced in the mid-16th century. Kepler produces the ridrofen tables that are much more accurate than these earlier tables, because they're based on his laws of motion, which are based on the mid-enoughlin more accurate observations of Tico Brahe.

These tables allow predictions for the first time. So predictions of the transit of Mercury. So Mercury passing across the face of the sun, Kepp was able to predict that for 1631. He doesn't live to see that transit and therefore live to see this prediction come true, but it is observed by some other astronomers after his death. And it's remarkable how close the tables are.

the predictions are in the time of this event? Ulinka, in another world which is coexisting, his mother is accused of witchcraft, which is a very serious offence at that time. And he defends in depth. He takes it very seriously, he examines all the evidence. He conducts a very long different.

Must have been curious, wasn't it? I mean, one minute he's talking about planetary motion and cubes and squares and whatnot, and then he's got to go back to his village or a small town and defend his mother against accusations from another woman in the village, being a witch. What did he think of having to do that? Well, he, of course, when he gets a letter from his sister in 1615 telling him that the mother is accused of witchcraft, he knows immediately that this is something he has to take so seriously because his whole reputation is at stake.

Why is his reputation is like? Well, if you were brought up by a witch, that meant that you were brought up by someone who was infused with. a devil. And that meant that you yourself were tainted by that. So he takes it very seriously from a start, turns into a six-year-long process, and he decides to take over the legal defense. Now, what's important is that there are actually real links between his scientific work and the way he conducts that defense. The scientific world at the time is full of enmity. And Kepler has perfected a way to deal with that. It's very factored. orientated. So he's trained himself to not throw insults at other natural philosophers,

as we would think of them, and many of them do throw insults at each other. He's perfected a very fact-orientated mode of unpicking his opponent's arguments. And that's exactly why he insists that he must get all the trial documents on paper in writing, and he dissects it brilliantly in just the same way. He says this is inconsistent. This witness says, my mother did this 15 years ago, and that's also far too long. And the other one says it was seven years ago. So he treats it like a text, and that makes possible that she's not burnt.

There's no doubt that if he hadn't taken over the defence, he would have been burned as a witch. So what effect did it have an effect on him? It must have an effect on him. It must have an effect on him. So let's forget that. That would be terrible. In fact, if any, did it happen in his work? Well, we can notice he literally, first of all,

he has to put his whole work on hold for more than a year. He moves from Lins with his family back to Wittenberg, to Germany, and can do, of course, much less work than he would have done. He returns then to Lins, has to unpack his boxes. And you can see that this otherwise optimistic person is really quite traumatized. It takes them a while to start writing letters to people again to take up his work. He's still troubled by that question.

Why, of all people, did this happen to us and to our family? Now we're in the last third of the program, and there's an awful lot more he did, so astronomy. So David, what about the mathematics? You described him as a brilliant mathematician. He's a great mathematician. He's a great mathematician, and astronomy is a major professional enterprise, primarily in his world because it's linked to astrology.

He's hired as the imperial mathematician so that he will do horoscopes for the emperor. Pure math hardly exists in Kepler's world, but Kepler has the capacity to be a great pure mathematician, and he identifies mathematical problems that continue to puzzle mathematicians. He, for example, he makes a little study of the shapes which it is possible to cover a flaw with,

which are always repeated and leave no spaces. And there are only three of them, the triangle, the square and the hexagon. And the hexagon, he shows how this runs through nature in the shapes of beehives and so on, the cells of... And in that sense, what he's doing is showing

how you can read patterns into nature. He does an analysis of the question of what's the most efficient way of stacking cannon balls. This is asked by Sir Walter Raleigh of the great English mathematician Harriet. and Harriet knows how to stack cannonballs the same as stacking oranges, but he says to Kepler, why is this the right way? Actually, there are several different right ways that all work out roughly the same. Why is there no better way?

And Kepler produces what's called Kepler's conjecture, which isn't proved to be true for 400 years. It was only proved to be true a couple of decades ago, explaining what the limits are on the right ways of stacking cannonballs in order to maximize it. So they couldn't crack it for 400 years? They knew how to do it, but the mathematicians were worried about why was this the case? pure mathematical problem.

Kepler also, when he goes to Linz, I think it is, he sees these great barrels with wine in it and people measure how big the barrel is simply by taking the diagonal. And he says, but that can't be reliable. That can't be the right. So he does an analysis of the curve of the barrel and how you work out with the barrel,

the size of the barrel, the volume of the barrel is. And this, of course, is related to the fact that he's working with ellipses in astronomy and he's got to do analyses of the areas within the ellipse in order to do his second law. So what he then does is work out the mathematics of this curve, and this leads on to complicated mathematical questions about infinitesimals,

which is the sort of problem that Newton works on later. Kind of now his study of optics. Yes. And he inherited a great body of work from the Arab world at this stage. Yes. So optics is a subject of a longstanding mathematical tradition, treating light geometrically. Kepler publishes two important works on optics. And the first of these, one of its, part of its style is the optical part of astronomy,

because optics is very important for astronomy because you're observing the heavens, you're seeing visible objects, you need to understand how optical phenomena can affect your observations, particularly the accuracy that Kepler is working with following Tika Brahe. In that work, that first work, published in in 604, Kepler's really interested in a range of optical phenomena. but the beginnings, though, really to do with what happens in eclipses and how you observe them. You can't observe the sun directly with the eyes, so you project it through an aperture. How does the aperture affect what you see?

Why is it that in eclipses, the diameter of the moon appears to be different than at other points in its cycle? And from working on those problems or related problems, Kepler moves on to actually study the human eye. And he works out for the first time that the in-the-euvreau. the human eye, light projects an image onto the retina. He is the one who establishes that. And he does that through his study, geometrical study of light, but also through drawing on the works of contemporary anatomists and thinking about the structure of the eye. There's a second important work in optics, the diatrix of 1611, which is partly in response to learning about the task was used by Galileo, and in that Kepler is studying to...

to a lens systems such as you get in the telescope. He devises a new combination of lenses to lenses to produce a telescope that generates an inverted image, unlike the telescope of Galileo, but astronomers don't care that the image is inverted. If the image is better, then they don't mind if it's upside down because that's not important to their studies. And so Kepler invents this new kind of astronomical telescope. And this is a major move forward to the object.

but it isn't enough on radio to know. No, but it's an improvement on all previous telescopes. And crucially, when Galileo produces his first telescopic observations, people say they must be wrong. This is completely false. Somehow the telescope is creating this illusion. And what Kepler does is explain how the telescope works and therefore explain how it comes about

that telescopic observations are reliable. And Kepler also has the extraordinary credit of when Galileo reports his discoveries with the telescope, of immediately saying, I believe you, he's the first person to believe Galileo and to publish in Galileo's defense, even before he's seen it for himself, before he can get a telescope himself, which is good enough to see the things Galileo has seen. He wrote something called Somnium or The Dream. How does that fit into the pattern of his thinking?

People have said it's the first science fiction work, but can you tell us what he was trying to do there? The Somnium brings out a crucial aspect of his thinking, which we haven't taught. on so far. So we've emphasized how he is interested in regularity and explaining causes that way. But another part of his thinking is very

much attached to the notion of playfulness. Because he thinks of God is still creating, as a playful creator, he thinks that God also speculates and tries things out and that parts of the creation are still unfinished. And in his

own mind, I mean, part of him is a bit interest in regularity, but he can also become a bit bored by it because he's such a hyper-intelligent thinker. So, and that means, for instance, clocks that are very elaborate at the time, they bore him because they're too regular. And therefore, his own mind is interested in science fiction. What would the earth look like if seen from the moon? That is what the somnium, the dream is about.

And that's why it's one of first pieces of science fiction. And he wants to show how the people on the moon, say what happens on the moon, think that everything is fixed, just as many people on Earth think everything is fixed. But in fact, everything is in motion. And that is the point of the exercise. But it links to the witchcraft trial in very intriguing ways because the science fiction part about the moon has a little prologue. And that is a story about a mother and the sun. and the mother is a witch and the son is a scientist. And when he goes back to Linz, he unpacks his boxes and he finds his manuscript.

And actually what he does for the next years is to annotate it to say that none of this is autobiographical. But he sort of convinces himself in this very traumatized way that it was because his manuscript circulated that the people first started to think that his own mother could be a witch. That comes round and so forth to kick him in. that he does not, really. That he was responsible. Well, that is, I mean, it's a guilt syndrome, a traumatized guilt syndrome.

You think he does have a suspicion of it circulating, but I don't think he's right at all. Can we come to you finally, David, and please all join in. But you say in your notes that Kepler laid the foundation for Newton's work and not this his greatest legacy. Could you develop that? Yes. I think first of all, we've been talking about Kepler's three laws.

They're not laws for Kepler. He doesn't use that word. That's a word that is introduced in the 18th century. They're not laws for Newton. What Kepler's rudolphine tables show, because he's baked the laws into the rudolphine tables, is that this is how the universe appears to work, that if you use these laws, you get the right results. And in that sense, Newton inherits this, and he inherits that these are the principles on which, mathematically you can explain, you can predict what's going to happen. What Newton then

asks himself is if these laws shape what's going to happen, what sort of force could be generating this sort of behaviour? Kepler thought it was some sort of mathematical force being driven out by the sun. Newton introduces the concept of gravity to produce the results that Kepler has described. And what Newton does is show that if gravity works the way Newton claims, gravity works, then Kepler's laws follow necessarily. The universe has to be Kepler's universe. Did Newton know about Kepler's work? Absolutely.

I mean, Newton's a wicked man, a monster. He does not refer to Kepler in book one of the Principia. But when the Procipia is given to the Royal Society, they enter in their log books. This is a book demonstrating the truth of what Kepler has done. Everybody understands that what Newton has done is take Kepler and turn him from a description of the world into an explanation of the world.

Olinca said earlier that Kepler wants to produce explanations, well, in a sense, what Newton has done is complete Kepler's work by producing a superior explanation out of Kepler's work. It's a good place to finish. Thank you very much, David, David Wood, Adam Mosley and Eulinko Rubik. Next week, in our time, we'll be off the air. But we'll be back on January the 12th with Nietzsche's Genealogy of Morality. Thank you for listening.

And the In Our Time podcast gets some extra time now with a few minutes of bonus material from Melvin and his guests. Well, go on, then what did we miss out? Rinker pointed to something that I had not understood before until I was reading up for this programme. And it sort of thrilled me, though it's also complicated to talk about. When in the Somnium, he asks, what does the earth look like from the moon?

The whole of his astronomy is really based upon asking, how does it... The problem in the Copernican system is, The sun is stationary, but the Earth is moving. You're observing the universe from a moving platform. The question is, how do you eliminate that movement? How do you observe the universe from a fixed point? One place to look at it from is from the sun.

Kepler devices, extraordinary techniques for making measurements as if they were taken from the sun. When he was looking on the orbit of Mars, he has to somehow discount for the movement of the Earth. He does this brilliant thing, where Mars goes around in an orbit every 635 or 643, days, whatever it is. He takes observation 643 days

apart and says from these we can see how the Earth would look from Mars. And so he calculates the Earth's orbit by placing himself on Mars and saying every 643 days, Mars is in exactly the same place. How does the Earth look

from there? And in that sense, this capacity to move himself somewhere else and carry out a measurement that says if it's from somewhere else is the very foundation of his astronomy. And this has to be about in. Sorry, you're a link. The Kepler's ability to think outside the box is really astonishing. So the ellipse, if one thinks that the circle was this quiet, perfect, beautiful form.

To think the ellipse before anyone has thawed in an airs this very dynamic space is one of the greatest achievements in the history of science. I think I'm not qualified to say something like that, but it did seem extraordinary looking at how he got from there. that. And anybody else had any notion that it might be an ellipse? Well, I think the thing to bear mind is that for technical astronomers, mathematicians, they've been working with combinations of circles. So you can't get a circle just by itself to work to model the planetary motion. So you have to build circles on circles. You have to have circles that are off-center. And so actually, some of the constructions that were already in use, if you instead of, if you take the resultant position of an epicenter,

cycle on other circles, a circle moving on a circle, and you draw out that curve. Then you end up with a shape that is not circular. So in a sense, mathematicians have been working with different kinds of curves, but they hadn't, because Kepler was so motivated by the idea that there had to be an underlying geometry, and there had to be a related physical explanation. So he didn't want to produce motions just from combinations of circles, because there's no, there's no, there's no natural underpinning to that. He wanted to understand what was really physically going on. At the same time, this is a man who believes that the earth is alive, that it is like a body, really, that is anima, that it's belching and has winds. And that is what Galileo just finds

ridiculous when he comments on it. He truly believes that in that form as that potential for ongoing creation is also a man who collects horoscopes and cast horoscopes. It's intensely interested in astrology, but moves away from some of the given scholarly opinions about astrology. He learns how to cast horoscopes as a student in tubing. It's part of the regular university education at the time. Yeah, he really lends a new form of astrology because he dispenses with some of the old things such as the zodiac, and he emphasizes the geometric relationship between plants. He comes up with new kinds of relationship that he thinks are significant new aspects.

And then he offers an explanation of how these relative planetary positions can have an effect on the earth, which and on people on the earth, which relates to the ability of the soul to recognize geometry. And one of the effects of the witchcraft trial is that he assumes that children are born under the same constellations as their parents, and therefore share a lot with their parents. So he moves to something I would call social psychology because it pushes him to think so much harder about how he's different from his mother. Because he's got to argue that they're different.

So in the harmony of the world, he actually has a whole paragraph on how his mother is different. And he explains that, for instance, by saying, well, she's a woman, she doesn't have access to school education, as I had. And that is revolutionary. I mean, it's obvious to us today, but at the time, nobody has said that. I mean, in a way, he is an end of this man's curiosity and ability. He made investigations into snowflakes, Adam.

That's right. So he produced, in 1611 a little tract on the snowflake as a New Year's gift. And the question for him really was, why are snowflakes hexagonal? So he investigated that. He didn't have a very good answer, it turns out, in the end, but he explored packing crystal structures. And so this work is seen very much as a kind of early work in crystallography. But it brings out his ingenuity as a writer.

He's in Prague. It's snowing. He looks at them and he thinks, why are they so regular? And he says, okay, I'm going to write this little pamphlet trying to explain it for one of my best friends. I mean, he's the first person to see that they're regular. You'd think there have been snowflakes forever. He's the first person to recognize that they're regular. But also it's a beautiful little thing because he's wearing, he's got nothing to give to his friend.

And then he gets this pun where in German the word for snow and the word for nothing are very similar. So he says, I'm going to give him snow. And snow will melt away and it'll be nothing. And in that sense, he turns a non-gift into a gift, this beautiful little gift. But as usual, there's a serious point to his very playful side because the friend that he gives this work to is an atomist. And Kepler isn't an atomist. and so Kepler, part of the point therefore, is that atomism, which is about, you know, ultimately reducing things to their smallest point, that this is not correct. And so his treatise is part of his rebuke to his atomist friend.

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