Christopher Wren’s Cosmos

(dramatic music)- Good evening everybody. I'm Katherine Blundell, Gresham Professor of Astronomy number 38. The focus of tonight's lecture is number nine, Sir Christopher Wren. Christopher Wren was born in 1632, which was 150 years before the United States of America was a thing. It was 12 years after the Mayflower set sail across the Atlantic that he was born, and the Copernican Principle hadn't fully taken hold. So enter Christopher Wren. But before we get too much into his life story, I want to pose the following question. What does it mean to be an influencer? Indeed, can you be an influencer if you don't care about likes, and if you don't indulge in self-aggrandizement? We'll see tonight that despite a remarkable lack of the use of first person pronouns on the part of Christopher Wren, he was a tremendous influencer. Yet his childhood, though not without many blessings, was pretty traumatic in a number of ways. Five of his siblings died. His mother died when he was a young little boy. War broke out when he was a 10 year old, and that lasted for nine years. Prior to that, the family had been on friendly terms with the Royal Family. Christopher Wren Senior, our Christopher Wren's father was Dean of Windsor. They were favored by the kings and indeed they were staunch royalists. But war broke out, as I said, when Wren was a mere 10 year old, and some pretty ghastly things happened to him as a child. Yet he was not defined by any of those bad things. It must have been heart rendering though to see what happened to Charles I, who must surely have attended his father's services in St. George's Chapel in Windsor Castle. This is Charles I with his head and without. Sorry for anyone who's squeamish. So this took place on the 30th of January, 1649. We'll be seeing tonight that Sir Christopher Wren was the most remarkable polymath, and a lot of his work concerned mathematics and architecture as well as mathematics and astronomy. Mathematics and architecture is going to be covered by my colleague, the Gresham Professor of Geometry, Sarah Hart, in a lecture in a couple of weeks' time. So I'll be leaving her to address aspects of his brilliance as they applied to architecture. I'll also draw to your attention that this Saturday, there is a special service at St. Paul's Cathedral, all dedicated to Sir Christopher Wren. So let's turn our attention now to what Christopher Wren focused on in the cosmos and how he went about it. How do you begin to understand the cosmos? It's a very hard thing to do in any case, but telescopes of the time were very poor quality. Wren's Cosmos, however, spanned all different length scales, from the microscopic, that which you could see through a microscope, to the macroscopic, that which you could sort of see through the not great telescopes of the day. It's a great challenge in any case, even with modern instrumentation from the vantage point of this rocky planet, to think that we might be able to explain and elucidate the universe and the way that it evolves. But it was especially hard with the limited optics that were available at the time, and the limitations of the worldviews and paradigms that couldn't be anything else given what was known and understandable at the time. Telescopes were truly poor quality then. Single elements of glass were involved in the very simple telescopes they had, hence all sorts of aberrations abounded, spherical aberration, chromatic aberration, all of them serving to degrade the quality of any images that were obtainable. In order to provide a very high focal length lens, you would need really, really accurate surfaces, and it was very hard to grind surfaces to be, to have a very accurate curvature in those days. Microscopes on the other hand, were much easier. They had abundant light, you could illuminate them with nearby light sources, and to be honest, you only needed to magnify by about 20 times in order to learn more about what was going on. So even with relatively poor lenses, microscopy was superior to telescopy at the time. Christopher Wren fully understood that innovation in instrumentation was crucial to lead to advance an understanding and in discovery. Christopher Wren was no mere hypothesizer in an ivory tower. Rather, he rolled up his sleeves and invented devices, and instruments, and new ways to make instruments to overcome the limitations of the time. Here is one such device, he called it an engine, that he developed to help with the problem of grinding the surfaces of lenses very, very accurately. He used a hyperboloid shape running over the glass lens that he was trying to shape to grind it very, very accurately. Of course, this was a labor of love and would've taken many, many, many months to build, but this was the kind of device that was needed to get an even halfway decent lens to get a good window on the universe. The problem is that big bits of glass that you need for high curvature and short focal lengths were very hard to obtain without impurities and defects. Whereas if you wanted long focal lengths to see fine detail, for example, to delineate the shape or the surface features of a planet, then you needed very, very shallow surfaces of immense accuracy. Immense accuracy here meaning to better than a micron, that is better to, better than 1000th of one millimeter. Making it smooth and correct was really tricky. But nonetheless, Christopher Wren's perseverance and ingenuity got him a very long way. He built a lot of these as a child, and then as a student, he was a student at Oxford. His connections with Oxford preceded him arriving there as an undergraduate. In fact, his father attended St. John's College, which happens to be my college. And there, Christopher Wren Senior, our Christopher Wren's father, left his mark in the old library in these stained glass windows. Just below that central dagger in this window, I don't know whether you are quite able to make it out. He's etched his autograph. For some reason, I have no idea why, he's altered the font between the penultimate E of Christopher, and the penultimate E of Wren. I also have no idea how you go about etching a stained glass window. Maybe you use a diamond or something. But anyway, Christopher Wren Senior left his mark at my college at St. John's, but our Christopher Wren went to Wadham College where he was an undergraduate. He was later a fellow at All Souls College. But at Wadham, his curiosity and his voracious appetite for knowledge were well fed. Wren contributed enthusiastically to discussions with many fellows, and formed a key part of the group of people that were the proto Royal Society. That all had its origins at Wadham College. And what they discussed there wasn't just the universe, they went beyond astronomy, to botany, to zoology, to mathematics. Truly, they had an intellectually rich diet. At Wadham, Christopher Wren invented all sorts of crazy things, not the least of which was the transparent beehive. I think it shows a remarkable creativity and zest for knowledge, to think of being sufficiently inquisitive that you should build a beehive that gives bees no privacy, yet you can see what's going on and how they breed and so on. But of course, tonight's focus is about Christopher Wen's astronomy, not merely his botany, about which you probably could fill a lecture by the way, but I'm not a botanist, so I'm going to stop there. Christopher Wren followed the patterns of our nearest star, and he designed and loved many sundials. There's a particularly famous one that's attributed to him in All Souls College. There are actually two sundials in this picture. This one is nothing to do with Christopher Wren, but this one is attributed to him. He was bursar of All Souls at the time. If you're the bursar of an Oxford College, you hold a lot of power and you get to oversee projects in all their details. And so I'm sure he had a huge involvement in this sundial. Sundials are absolutely lovely things because they reflect, if you've properly designed them for their latitude and their position, they enable you to calculate the time just from the shadow of the sun, given the way the sundial is set up. Of course, it doesn't always work in Oxford because the sky's are pretty cloudy in Oxford, but it's a beautiful thing, and it's a great idea, and it speaks of Christopher hen's interests in the patterns, and mathematics, and rhythms of the rising of the sun and the setting of the sun. But I want to turn now to our next, our nearest celestial body, which is the moon. Christopher Wren took great interest in the moon, which is of course our nearest natural satellite. Of course, the moon has inspired poetry, and art, and music through the centuries. But what Christopher Wren did was something pretty special. He didn't just look at the moon, he didn't just think of it as a piece of art, though it is in some ways, but scientifically it's pretty important. Christopher Wren was really the first person to seriously map the moon. He developed an eye piece micrometer so that he could accurately track across, and relay that into a drawing. He made a model of the moon, a 3D model out of pasteboard, which I believe is some kind of old-fashioned paper mache, sort of glued together cardboard stuff. He made a model for the king after the restoration of the monarchy, Charles II, to have a model of the moon. And that was something very, very special for the king, and apparently he showed it off to all his friends. Sadly, being made of pasteboard, it didn't survive. But there is photograph, sorry, not photographic, pictorial evidence of this model of the moon. In this portrait of Christopher Wren, which about a month ago, I suddenly realized I was sitting opposite when I was in the Sheldonian Theater in Oxford, which was built and designed by Sir Christopher Wren. I was in the Sheldonian Theater for the occasion of the admission of our new Vice Chancellor, Irene Tracy. And while we were waiting for the ceremony to begin, I suddenly realized I was sitting opposite this portrait, and I gazed at it intently, trying to take in as much detail as I could. So this was painted in 1708, and it gives lots of different evidence of various different domes and steeples of churches that Christopher Wren built. It's signed by no fewer than three artists. So clearly it's a labor of love, again, lots of people contributing to it and collaborating on it. They were Verio, and Nella, and Thornhill who all contributed to this painting. But what's of interest to us tonight is that in the bottom corner, there are two globes. And the one on the left is a celestial globe, the sort of thing that has the plow on it, the constellations of the stars as they could be understood. So there were quite a few of those around. But this on the left, on the right rather, is a picture of the 3D model pasteboard model of the moon given to the king. Now, you may be thinking, why is the moon such a big deal? Why were people excited about the moon? It's our nearest celestial neighbor. It rocks through the sky the whole time. Why is it exciting? Why is it special? Why did the king show off this beautiful first model of the moon to all his friends? Well, the moon is pretty special, and its structure is remarkable. And I'm going to tell you now a very, very brief story about something that happened to me once when I was working at my observatory in rural southern India. This is one of my domes. I don't have as many domes as Christopher Wren. This is the observatory in the heart of the school in India where I was working just last week in fact. Now, when you commission a telescope, the very first image that you take is called your first light image. And it's really special, because it is. You've got light through the telescope, you see an astronomical object. Everyone's very happy, all good. Now, shortly after that, I was asked to give a talk to school teachers who were visiting the school where my observatory in India is. And I didn't have a whole lot of notice before giving this talk, so I pulled together some astronomical images taken from this telescope, of which the first one was the moon. And I explained it was our first light image from the telescope, and how excited we were to be able to see in detail the craters on the moon. And as I was infusing about these craters on the moon, I suddenly got a sense that two thirds of my audience were in tears. I truly hope that isn't happening tonight. But let me tell you why it was such a moving experience for those teachers from rural southern India. In that part of the world, retina screen iPads aren't a thing, glossy magazines aren't a thing. Televisions aren't a thing. They hadn't ever seen a picture of the surface of the moon before. And so to actually see it, to be able to connect the sort of slightly dark patches you can see on a very clear night with an actual image that tells you about genuine structure on the moon was moving for those teachers. If we haven't been exposed to the moon in earlier parts of our life, when we suddenly see it as became possible for people in Christopher Wren's time, it's really pretty special. So this is all the more, this is the only pictorial record that we have, it's only a 2D record that we have of this model of the moon. But I want to emphasize Christopher Wren wanted to map it. He didn't just want to do a piece of art, he wanted to map it, he wanted to measure it. And I feel sure that this fed into his enthusiasm and commitment to the Longitude Project to which he contributed in later life. The whole business of seeing these craters on the moon is quite eye-opening for inhabitants of Earth because they remind us that one of the very special things about living on this planet is that we have an atmosphere. And this atmosphere, which the moon does not have, protects Earth from being splatted with meteorites, which give rise to these craters than is the case on the moon. The moon has no atmosphere. So if a meteorite rocks up and goes splat, there you go, you have a crater. So it's a reminder, I mean the atmosphere is, of course, super useful for breathing, but the atmosphere is very useful for protecting us from meteorites, because under frictional heating, most of them burn up. That's not always the case. And it's the subject of my next lecture, which will be how life on Earth might be wiped out, that I'll be addressing that. But let's stay on cheery matters today. Earth's gravity is sufficiently strong so that we have an atmosphere and life can be sustained, not so for the moon. So in seeing the moon, we get a sense of the reality of the brutal existence that is out of space when there is no atmosphere to protect us. Let's now move on to Wren and Saturn's rings. So at the time there wasn't a clear picture or a clear acceptance that all the planets in the solar system orbited around the moon. Heliocentrism was becoming a thing thanks to Galileo and Copernicus, but it hadn't fully clicked in with all the modern thinkers of the time. So we've all had the picture in our minds of the planets orbiting around the sun very happily for a couple of centuries now. But the picture then was far from clear. And one of the most mysterious was planet Saturn. That perplexed and fascinated Galileo, and Wren, and Huygens amongst others. We have a fairly good understanding of Saturn today. We now know that there are rings in a pretty similar plane to moons, which also orbit around it. It's almost like Saturn is its own little solar system orbiting within the solar system around the sun. They had none of that, of course. They couldn't do computational calculations that we could do and they certainly couldn't produce images of this quality. This is another image taken at my telescope in India that I referred to a few moments ago. I took this image on the 20th of December, 2020, the first Christmas of lockdown. Jupiter and Saturn were doing an unusually close encounter. These images are taken 24 hours apart and they're unusually close in the sky. They hadn't been this close in the sky for about eight centuries. But you get a a little bit of, you can see Jupiter's Galliean moons there, and a couple of the satellites also in Saturn. It's an absolute joy to be able to image these beautiful planets in such detail now, but that absolutely was not possible at the time. It was much harder to interpret what was going on as far as Saturn was concerned because of the aforementioned poor quality optics that they had. Sure it was possible to see distinct points of light that orbited around Jupiter. But in terms of image quality, in terms of revealing stripes on Jupiter, that wasn't possible. In terms of deconstructing what was the shape, the underlying physical structure of Saturn, that wasn't possible. It was partly because of the image quality, but also Saturn changes with time. Now Wren was very much on the right lines with his thinking, although in fact he favored elliptical rings being around Saturn. He was very much on the right lines, but in fact, really the person who nailed it was Huygens. But Wren was utterly gracious and utterly admiring of Huygens' model and said the following,"I confesse I was so fond of the neatness"of Huygens' idea and the simplicity of it,"agreeing so well with the physical causes"of the heavenly bodies that I loved his invention"beyond my own." That's a beautifully gracious thing to say, even though Wren himself was very, very close. Not for him going after the credit, much more taking joy in what was out there and what had been understood. Of course, we have it easy today with the Hubble Space telescope launched by NASA and ISSA, which has made some really beautiful images of Saturn. The Hubble Space Telescope, by the way, has the mass of two adult African telescopes. It's obviously orbiting the Earth, orbiting above us right now. And this telescope gave rise to these even sharper images. This is December, 1994, and this image is May, 1995. And you'll notice that Saturn's rings are presenting a very different inclination towards us. So what's going on here? In fact, it's because Saturn's obliquity, its tilt with respect to its orbit around the sun is quite significant. It's about 27 degrees. And so as we orbit around the sun, and as Saturn orbits around the sun, it's a subtly different angle from time to time, we go slightly above and slightly below Saturn's planes. And at these times it's possible to see the rings at different angles. The Saturnian year is about 27 years. And so roughly speaking, these crossings, when Earth's orbit crosses Saturn's orbit, it's about twice per Saturnian year. It's the details of the orbit mean that it varies between about 13 years, sometimes up to 15 years. But these are the different shapes that Saturn's rings are present to us on Earth over the course of a decade or more. So imagine what it must be like with a very low resolution, blurry, imperfect telescope to see bulges on either side of Saturn's main body on one occasion, and then suddenly to realize that they're all disappearing. This must have compounded the development of models by all sorts of people, Huygens and Wren at the time. There's no doubt that Saturn's rings, the obliquity of Saturn with respect to its orbit caused serious confusion. But as I say, twice per Saturnian year, we are exactly in plane with the rings, and so we see them just as a line, and that is what Wren and Huygens would've seen as rings disappeared. They would just have seen something that resembled all the other planets or the larger ones. The mass of Saturn's rings is relatively slender depending on your definition of slender. It's about half the mass of the ice shelf in Antarctica on planet Earth, but it's distributed over really thin surface area. That area being about 80 times the surface area of the Earth. They're really thin, so that's why when you see Saturn's rings edge on, they seemingly disappear. And we certainly know that that caused serious confusion to Galileo back in the day when he was observing. Moving further afield now, now out to about 444 light years from Earth, we're now looking at Wren and the Pleiades. The Pleiades are fairly well known in the night sky. If you start with Orion, which is a very well known constellation, produce the line that form his belt, go via the bright star, which is Aldebaran, and then you see a collection of stars and that's the Pleiades. That's how you find it. Wren made some of the most accurate images of this star cluster that persisted for quite a long time. Again, his emphasis on measurement, on quantitative observation, not just an arty feel-good image, if you like, was extraordinarily impressive. If you have good eyesight, and you're at a dark site and there are no clouds, chances are you may be able to see six stars with the naked eye in the Pleiades cluster, seven if you've got really sharp eyesight. With the limited telescopes of the day, but with Wren's micrometer eye pieces, he was able to actually measure the positions of 40 stars in the Pleiades using the technique of measuring and mapping. This is a modern day image taken by my friend and colleague, Steve Lee, in Australia of the Pleiades star cluster. And with such modern images, you can see that in fact there are about 3,000 stars in this little cluster. It's like a mini galaxy on its own embedded within the Milky Way. One of the many other things that is impressive about Christopher Wren is that he built friendships even with people who were hard to make friends with. Robert Hooke, the Oxford Polymath was famously disputatious. He was pretty cranky, more of that later. But these two built an extraordinary bond that lasted for decades, and was enormously fruitful. There were quite a few opinions differ on which things should be attributed and credited to Hook, and which should be attributed and credited to Wren. It seems to me that a whole lot of dialogue and stimulation went on in both directions. This is what Hooke has to say about Wren in the context of microscopy, talking about some drawings, which Hooke did on the using again, this clever micrometer that Wren had developed."As the hazard of coming after Dr. Wren did afright me,"for of him I must affirm that since the time of Archimedes,"there scarce ever met in one man in so great a perfection,"such a mechanical mind"so good at inventing things and building things,"and so philosophical a mind, so creative in his thinking." And this from Hooke who was, you know, better known for being pretty cantankerous, to be so gracious about Wren, I think is a tribute to Wren's character himself. Let me just show you this book then, which is attributed to Hooke, but has such these gracious words in the acknowledgements. Slightly grandiose title of, Some Physiological Descriptions of Minute Bodies Made by Magnifying Glasses with Observations and Inquiries Thereupon. We are not allowed such flowery titles these days. But actually they're slightly justified when you see the beauty of these images, drawn from what was seen under a microscope by Hooke. But Hooke foolsomely attributes this technique and similar drawings to Wren. The detail is absolutely exquisite if that is you like fleas. I'm not so keen on them myself. This is a fly with its compound eyes. The detail is absolutely beautiful. Microscopy in the 17th century was really very remarkable. Not matched by commensurate prowess in telescopy, but nonetheless still enough to enrich and enlarge the cosmos at the time. Talking of things that enlarge the cosmos, let's now turn to Christopher Wren and the comet of 1664. This is even mentioned in Samuel Pepys's diary entry on Thursday the 15th of December over coffee, much like the modern day, a lot of scientific thinking takes place over discussions over coffee. So in the coffee shops of the day, there was great talk of the comet. It was a big deal. More people noticed it and saw it, because of course, light pollution was much lower in London three and a half centuries ago than it is today. So these are some of the depictions that we have, this is a German one of that particular comet in 1664. Now as a drawing, it's obviously somewhat stylized. The actual halo is possibly not very authentic, but one can appreciate what the artist is trying to draw. There's a resemblance with modern day comets. This is Comet NEOWISE photographed from my back garden during July of lockdown. And as you can see, there's actually a little meteor that's rocked up there on the left. But as you can see qualitatively, this comet matches the drawings of 1664, especially if I zoom in. So a number of people at the time in Europe drew this comet. It was one of the brightest ones that had been known at the time. But Wren's interest was in measuring it. Wren's interest was in mapping its trajectory. And so what he did was to start to think, well, what could its trajectory be? What could its orbital path be? If I fold that back, if I reverse engineer it to reconstruct what was the trajectory given that we're on an Earth, which is moving through space in orbit around the sun, because we believe that the Earth goes around the sun, don't we? This was his attempt at interpreting the passage of that comet. Now, aspects of it are not correct. It was predicated on the notion that was prevalent at the time that comets move in rectilinear motion, they move in straight lines. Now we now know that they follow orbits that we collectively refer to as conic sections. I'll come back to that later in my talk, which obey Kepler's laws. But actually small segments of comet trajectories can sometimes be treated as straight lines. And this gives an interesting insight into what Christopher Wren thirsted for. For him, measuring things and taking a quantitative observation were really what mattered. Not everything in Christopher Wren's adult life was as happy as the joyful observation of a comet. Three of his four children died. Two, he married twice and was widowed twice a few years after the marriage and the birth of children in each case. He lived through a pandemic, he lived through the dreadful Fire of London, which we'll come to now. Again, terrible things to endure, but he was not defined by them. And his activities show that he thrived despite these terrible things. Christopher Wren, like a certain other Gresham Professor of Astronomy, developed a real taste for eclipses. I love eclipses. By remarkable coincidence, our nearest satellite, the moon, although it's physically got a much smaller diameter than the sun, its distance from us is such that it subtends the same solid angle as the sun. It's a remarkable coincidence. And this means there are times when everything aligns appropriately that it can exactly block out the sun. And this is what happened in 2019 just before our pandemic, when the moon moved across the disk of the sun. It's truly a thrilling thing to watch a solar eclipse. It's not just geometry. You get a strong sense of being in outer space, which we are all of the time, of course. But to have this sense of celestial bodies moving is just remarkable. And I really recommend if you get the opportunity to witness an eclipse that you take it up. Christopher Wren watched the solar eclipse in 1654 in Oxford assisting Richard Rawlinson and others. And this is the path that the eclipse took. I'll just zoom in on the United Kingdom. So it didn't actually go through Oxford, it went through the north of Scotland. But nonetheless, just seeing a partial solar eclipse would've been a pretty exciting phenomenon. Again, feeding his thirst for geometry, and understanding orbits, and quantitative observation. This is a calculation of just how much of the eclipsed sun Christopher Wren would've been able to see from Oxford in that eclipse. So definitely an appreciator of the finer things in life, by which I mean eclipses. Now let's turn to something else a bit quantitative, stellar parallax. So in order to understand the nature of the cosmos and remember how small their cosmos was at the time, they didn't really know about other galaxies. They knew about nebulosity and patches of fuzz in the night sky, but they didn't know about the extra galactic universe. But in order to advance that knowledge and that understanding, and deepen their picture of the nature of the cosmos, it was necessary to understand how far things were away from Earth. Only then when you know how distant things are, can you work sizes and energies, and only then can you calculate the scale of cosmos. So for all sorts of reasons, being able to measure distances was really important. Christopher Wren was interested in parallax all his life. So what is parallax and how does it connect with what Christopher Wren measured? So a key prediction of Copernican theory is that if you've got the Earth moving around the sun, then when the Earth is here, it will see nearby stars aligned with distant stars over there. But when the Earth is here, you'll see the nearby star aligned with distant stars over here. I hope this diagram illustrates what happens. So when the Earth is on the opposite side of its orbital path around the sun six months later, you will see any nearby star to be shifted by a parallatic angle, an angle of parallax, alpha here, given by how much it's moved as a function of Earth's annual motion. So this is quite a well-posed problem. You look at the positions of stars and you say, how much do they move apart by when you measure them at six month intervals against the background of very distant stars, which you are hardly going to see any movement in. It's relatively simply posed, but in practice, the change in angle is different to measure for all sorts of natural reasons like something, a phenomenon that was understood some decades later called stellar aberration, which is to do with the fact that the stars themselves are moving with respect to Earth and the solar system. It's also hard to measure stellar parallax, and these small angles due to the mutation and wobble of Earth's axis, and perhaps principally due to the proper motions of stars themselves. Stars are shooting through our galaxy the whole time with a non-zero motion with respect to the solar system. And so that rather stuffs up what you think might be going on. But more prosaically, there are difficulties with telescopes and the technology of the day. Flex in telescopes was a major, major hindrance. You couldn't point telescopes in any meaningful way. There was no such thing as tracking. Modern telescopes absolutely rely on good gear boxes, precision engineered, we call them mounts, but they're basically gear boxes to take account of the pointing and the tracking. No such thing then. So the strategy that was employed by Wren and by Hooke was to try and build what are called zenith telescopes. A zenith telescope is a telescope that only looks at the zenith. The zenith is the bit of sky that's directly over our heads. And of course, as the sky rotates above us, I mean it's really the Earth spinning, but as the sky, as the stars move through the sky, that telescope will only be able to observe the stars that move through that particular path. But that's a zenith telescope for you. But the strategy was that if you built a very, very rigid zenith telescope, then maybe for the stars that you did, it would be rigid so you didn't have to worry about pointing and tracking, you'd just build it rigidly, then maybe you could hope to see movements of stars. What you'd need was a really, really tall telescope so that you could get the kind of precision that you needed. And I think there were various early attempts. Hooke was involved with building, I think a 35 foot telescope. He cut a hole in the roof of Gresham College. Gresham College has never let me do any telescope building through their roof. Not sure what that's all about, but actually it was completely insufficient. But when the monument came along, that amazing monument to the Great Fire of London, the apocalypse that happened in September of 1666, Wren and Hooke seized the opportunity to turn this monument into not only something which recognized the truly awful experience that London had been through, the fire lasted for four days, two thirds of the city was destroyed, 13,200 houses were destroyed, and 87 churches were destroyed. Not only was it marking that dreadful thing that had happened, but it was turning it into an opportunity to say, let's learn more about our cosmos. Christopher Wren didn't get rich after the Great Fire of London, but he and the then professor of Gresham, Professor of Astronomy, Hooke, took it upon themselves to design lots of churches, St. Paul's Cathedral and other buildings to rebuild London, to rebuild the society. And the monument is the most striking example of that. This is Wren's initial design. So it had a lot going for it, it's over 200 feet tall. And they planned it quite carefully, Hooke and Wren, using this monument or rather this monument, to actually, there wasn't, you could remove the lid at the time so you could see out, always important for telescopes. So what they planned was to study a particular star, which goes by the name of Gamma Draconis. It's the bright star in the middle. So crucially, it's bright enough to be able to see from London skies, so long as there isn't a cloud. I'm going to show you a little bit of a data sheet now, it's a little bit busy, but let me show you the crucial point of information, which is why this star, Gamma Draconis, was important for Wren and for Hooke. It's declination, and you can think of declination as being celestial latitude, is plus 51 and a half degrees. So that's pretty much the latitude of London. So that means that it should pass overhead of this zenith telescope that couldn't track and point like normal telescopes or modern telescopes. This is its right ascension, right ascension maps to you can think of that as celestial longitude, and a right ascension of nearly 18 hours means that this particular star is up in the night sky over London in the northern summer. So it should work. It's, although the London skies, the UK skies never get truly technically astronomically dark in the northern summer, nonetheless with a brightness of about one magnitude in the red band, plenty bright enough to be able to see even in a twilight sky. Now the measurements didn't happen, didn't work, didn't lead to the results that were hoped for and longed for. Hooke claimed a parallax angle of, I think it was half a minute of arc or something, which would've been extraordinarily large, and had the implication that Gamma Draconis would've been remarkably close to Earth, which wouldn't have agreed with other things. There were a lot of problems. There were horses going clip clop on the roads outside, and all the vibrations from London traffic. The inherent flex in the building was just insufficient to be able to measure the true parallax of this star, which is actually just 21 milliarcseconds. So an arc second is one 3600th of a degree, and a milliarcsecond is one 1000th of that very small angle. There was no hope. It was a 200 foot building in noisy London with even the presumably relatively light traffic of the day going past that you had the slightest chances of being able to measure accurate positions. So it didn't happen, but it was a brave attempt. It was a brave attempt that really, you could interpret it as a null result. You didn't see systematic repeatable, parallactic angle, parallax angle changes. So this null result is actually the real reason why it wasn't possible for them with the technology that they had at the time to determine the size scale to the nearby stars, and hence to get a grasp on how big the cosmos was because it was bigger than they had thought. Probably they wouldn't have attempted the experiment had they had any instinct that the idea was only one, it was only 21000ths of one 3600th of one degree. So at least it gave them a sense, well, the stars have to be further away than this. The cosmos has to be bigger than this. Let me now talk about planetary orbits. Wren keenly used telescopes wherever he could in Wadham College. I believe in New College in Oxford, here in Gresham, and elsewhere. And planets were clearly something people studied a lot at the time because they moved through the sky relatively rapidly, at least compared with the distance stellar background. What we know now is that orbital paths, which I described in my Gresham lecture in my first year, entitled Shapes of Free Fall, orbital paths now followed by celestial objects orbiting around stars are given by this beautiful yet very simple equation that all of the different geometric shapes that you can get by putting in different values of the letter either, this entire equation describes all the different shapes you can get for all orbits, for comets, for planets, for stars orbiting around one another. It's truly beautiful. Now various people were already on the way to working out how, what the orbital paths must be, particularly as the decades went by. And telescopes did improve a little bit, although not in pointing and in tracking. Hooke's own 1670 Gresham lecture had certainly grasped that gravity, gravitational attraction applied to all celestial bodies. And he also discussed the fact that he thought, or some years later, he discussed the fact that he thought there was an inverse square dependence on that gravitational attraction, which he communicated in a letter to Isaac Newton. Isaac Newton is the person who gets all the credit for this particular law, which is very famous and used every day in physics, the inverse square law of gravity. It simply says that any acceleration that you feel goes as the square of the distance between the two bodies involved. And the graphical form takes that sort of shape. Now what Newton did was to make the link between this inverse square law and those orbital shapes known as the conic sections that I mentioned a couple of minutes ago. He had to invent new maths to do it, but he did it and it was a massive achievement. But one of the remarkable things is that Hooke actually wasn't the only person to discern the inverse square law of gravitational attraction. Wren himself did. Hooke also himself did independently of Newton. And Newton does actually acknowledge this. And I think the very fact that Wren's mind was so agile that in the face of all the tragedies that happened in his life, the pain and anguish of war on his doorstep in his homeland, losing close family members, yet he could look out of his horizons and build, think about building churches and building society, think about how planetary orbits worked in our solar system and beyond. Christopher Wren's mind could span the cosmos as it was known then with ease and with joyful curiosity. Christopher Wren didn't seek acknowledgement or credit for having come up with this foundational fundamental inverse square law of physics. And yet he was a joyful contributor to it. Isaac Newton was another of those somewhat cantankerous scientists of history. And yet Christopher Wren could acknowledge graciously and engage with all the discoveries and the inventions of Isaac Newton as well as Hooke and others. Christopher Wren's Cosmos was smaller than ours as the non-success of the zenith telescope demonstrated. They knew about fewer planets than we know now. Obviously they only knew about the solar system, but Uranus and Neptune hadn't been discovered. That was to come later. The number of galaxies known at the time was pretty close to one. That didn't come until Herschel. But the expanse of Christopher Wen's mind, his polymath approach to life, showed that he was not in some narrow disciplinary silo. He was truly collaborative. He was not seizing credit, he was outward-looking, manifestly church building, society building after the dreadful apocalypse that hit London in 1666. I only learnt yesterday, Christopher Wren was an MP. How outward-looking is that? Truly Christopher Wren's Cosmos was larger than ours. So there is a memorial to Christopher Wren in St. Paul's Cathedral. I'm going to make sure I take a look at it at the service on Saturday. And I just want to draw your attention to this little bit at the end. Reader, if you require a monument, look around. Christopher Wren lived more than 90 years, and as his memorial says, not for himself but for the public good. Truly, Christopher Wren's Cosmos was enormous, and truly he was an influencer. And that's all, thank you.(audience applauding)- Do I see any hands up in the audience? I should just briefly warn you that we're in an educational establishment, which always means we have to finish precisely on the hour. I do have a couple of questions online which I will just pick up. The first one I think is just a sort of matter of fact question, which is, is there any evidence as to whether the far side of the moon in Wren's model had any features, or was it featureless, asked someone masquerading under the name of Meta Mathematics online.- Goodness, an interesting question from Meta Mathematics then. Christopher Wren couldn't have known anything about the far side of the moon. It's tightly locked with respect to Earth. The far side of the moon is always the far side of the moon. It has erroneously been called the dark side of the moon by the way, but it isn't dark when it's new moon on Earth. So that's not true. Christopher Wren had no means of knowing what was on the far side. It's only today with lunar reconnaissance missions that we have access to that information, and that feature of the lunar model in the bottom right corner of that portrait that I showed, that's in the Sheldonian Theater, we only see the front.- [Host] Yeah, okay, we only see one side. The gentleman here.- Thank you.- Can you give us a sense of the size and scale of the lenses that they were endeavoring to grind out in those days? And what quality of images would they have perhaps seen through them, if you could just give a sense of that that'd be great, thank you.- So I think the size scales of the lenses, there would be quite a bit of variety. In microscopes, of course, they would probably be very tiny. But for doing astronomy, you need lots of collecting area, which means big lenses. And getting uniformity and homogeneity in the glass was hard, nevermind, you know, in the density of the glass was hard, nevermind grinding the surface to a smoothness that depending on what focal length you are interested in, has to be better than a very small fraction of a millimeter. But the, I've not been in the monument in London, but I think my impression is it was a couple of feet or three or four feet, something like that. So non-trivial to make, very, very difficult to make in fact. Sorry, I think you had another question right at the end.- [Speaker 2] The quality of the images that they able to see, or the lack of quality of the image I should say.- Yeah, so I think our best handle on the quality of the images,'cause obviously that image of the comet that I showed you, comets are really big, and I'm sure people didn't use telescopes very much at all to, other than the sort of the actual measuring the path. That was a naked eye drawing. But the best handle we have on the quality of the images is the fact that they couldn't discern Saturn's rings as rings. I mean even with a relatively straightforward, very inexpensive telescope that could be, you know, a child's Christmas present or something. You can see the rings of Saturn as rings. I mean maybe it helps that you know the answer and you know what you're looking for. But the very fact that people referred to Saturn as being a three body planet. There was the main body and then there were these two bulges either side, which I think is what led to Wren's elliptical ring interpretation, and then understandably being very startled when the rings became edge on, and so invisible given the collecting area of the day. I think the best handle we have is just imagine the image quality that you would get if you had a sufficiently low-grade optics and blurred telescope that you could see it was elongated and a little bit bulgy here, but not so bulgy you couldn't tell the bigger bit was in the middle. I think that's what we're talking about. And yet he was transfixed by it, and committed to making lots and lots and lots of measurements.- Super answer. Yeah, I'm afraid time is going to press on us, I'm afraid. It's a rare treat listening to that lecture. I mean, I've never heard a lecture about Wren's astronomy before, so that was rare. To hear it from a professional astronomer is double rare. To hear it from a research active professional astronomer on the top of her career, I mean that is going some. So that was just an amazing evening, Katherine, thank you very much. Thank you.(audience applauding)