Space Time And Shakespeare Paul Glendinning

TITLE: Space, time and Shakespeare - Paul Glendinning CHANNEL: Oxford Mathematics DATE: 2026-05-27 ---TRANSCRIPT--- [music] [applause]

So, I’m going to start somewhere completely separate from Shakespeare because it sort of explains that what my motivation for thinking about Shakespeare is. I’m an applied mathematician. Okay, I’m not a Shakespeare specialist. Um I’m not a historian. And I see something like that. This is um spider’s web after rain looking through towards my front garden. And it’s just beautiful. But because I’m a mathematician, I start thinking about it. And look, the droplets you’ve got separate droplets. Why aren’t they all falling down to the bottom? Why are they the sort of size that they are? Surface tension’s obviously important. But I sort of think, well, this they’re on Spider’s webs are sticky, so they not fall down because they’re sticky the stickiness. But then some of them might go into each other. Why is the regular spacing or apparently regular spacing of a lot of them? Maybe spiders put little dots of And so that’s stopping things going in. I don’t know. It’s not my area. But it illustrates the sort of thing a mathematician starts looking at the world. And all these things go woo woo woo woo. Maybe this, maybe that. And maybe somebody knows the answer to that question. I haven’t bothered to get the detail. Um but I find it that I can’t stop thinking about these things. And this is what I sort of think of it as sort of mathematical eye. You look at something and you see something through a mathematical lens. Now, my contention would be everyone has that. It’s not particular to mathematicians. It’s just I have a certain type of vocabulary that allows me to talk about it in a way that sounds very impressive. And for a lot of people, they just say, “Oh, look.” But it is interesting and I don’t really understand why that happens. It’s See, clearly there’s something going on. So, this is sort of universal thing that we have in trying to order, to make sense of and make order in the world around us. And so, this has been something I’ve been thinking about for a while. I’m trying to work out ways of articulating it. And so, after several false starts, really trying to think about things now, I realized that a lot of what I wanted to say, a lot of what I wanted to think about could be done through Shakespeare. And it’s really an intersection of two things. What do people think they know and how do they think they know it? And how do people use those ideas and express them, play with them, particularly for me, through a mathematical lens. And that’s about technology, it’s about knowledge, beliefs. And that’s just pervades drama, poetry, the arts. And so, I think this it’s an interesting way to look at things and having said what it is, I should say a bit about what it’s not. Okay. I don’t want a description of, you know, I’m not going to do a reductionist thing of Shakespeare as um a scientist, he wasn’t. But he was living at a particular time with particular technologies and evolving technologies. and scientific ideas, popular scientific ideas were around and I’ll talk a bit about that a bit later. The other thing that it’s definitely not is a narrative about how we’re getting clever and clever and clever at doing science. Okay, I’m sort of not really interested in that “Ooh, and we understood that. Ooh, and we understood that.” Okay, I’m much more interested in just the way that people sort of play with ideas and so on. So, the specifics then of why Shakespeare first and foremost it’s just fantastic. What an excuse to sort of have to have to? I don’t have to. I want to read Shakespeare, look at Shakespeare’s plays, think about them, reflect on them. You’ve got characters from a broad set backgrounds um social backgrounds, genders being articulated. And obviously, you know, if there are issues about how much Shakespeare knew about the different groups of people and I don’t want to get into that. My idea is that Shakespeare’s work basically gives me a world in which to play. Okay, so it’s it’s a selection of words. He’s chosen them in various ways. He’s depicting people in various ways. And that gives me something that is a sufficiently large body, I think, for me to actually get quite a lot of different things going on. And sufficiently finite that I don’t get completely lost. So, that’s one of the reasons for Shakespeare. The other reason is I actually think the historical distance gives me exactly the sort of thing I’m trying to get at when I’m thinking about how people think about things. Because the historical dis- distance means that there’s a lot of stuff that is alien when talking about stuff which is completely familiar. Okay, because their experience, their knowledge system was sufficiently different that you you come up and get and think, “Ooh, you know, what was going on there? Why why was why was why would somebody say that?” And so you have to work a little bit to try to see what’s going on. So I think that’s sort of alien and um familiar to me is really quite an important thing. So I think there’s another thing that really irritates me um but which isn’t really part of this, which is I get very fed up with the way that science and technology and the arts are treated as completely different. And so I wanted to do something that is at least an attempt to put those things together. Right. Bit of what I call intellectual housekeeping. Um the version of Shakespeare that I’ve used most most is the Oxford um Shakespeare, complete works. Um the film clips are thanks to the um ERA, which is the Educational Recording um Agency, which is something that University of Oxford is part of, University of Manchester is part of um for educational purposes, except for one because the very first example is from the English Shakespeare Company um taken from YouTube. Again, they they have um they allow education purposes. And that’s because none of the BBC versions have the clip that I wanted. Which is really frustrating. And it’s actually true that almost [clears throat] all my clips come from the 1970s and 1980s. That’s not because those are the only ones available, it’s because they’re the only ones available that have the scenes that I wanted. Okay, so I went through a really frustrating and rather long process of saying, “Oh, that’s a really good I love this version. Hang on. Where are the lines I want? And they jump. Um there are a number of um books that I should mention. Um there’s a recent book by Jessica Mary um Otis on called By the Numbers, which is really looking at early modern England and number systems and how um ideas about number were were changing at that period. It’s very recent. I haven’t read it all yet. Um but I’ve taken some little bits from it. Um the book that I’m closest in spirit to, I think, is Adam Cohen’s Shakespeare and Technology, where he looks at the different technologies um that that are being developed, technology industry um in the um 16th, 17th centuries, and ties that in with um Shakespeare. And then there are two books that in some ways look much closer to what I’m doing, but I don’t think they are. Um Dan Falk’s The Science of Shakespeare is very much that that idea that there are these big scientific changes. There’s Copernicus, there’s this, uh that and the other. And he’s trying to map those changes on Shakespeare. And I sort of think that it’s not my style, okay? Um not what I want to do. And Rob Eastaway’s recent book, Much Ado About Numbers, where he’s really interested in the manipulative what games people were playing with numbers in particular. Um we have a little bit of um overlap, but that’s about it. Okay. So, what am I going to do? I’m going to start with two examples. Um just see how what what sort of how people were talking about doing things and what they were doing with mathematics um and so on. The bit on almanacs and the phases of the moon, there is going to be some maths. And that maths is the maths that you were expected to do if you were using that almanac. Okay? So, anyone It wasn’t aimed at mathematicians. It was aimed at It’s a bit like the manual. You know, if you in when you we first had home computers, you couldn’t just put a click a button and everything worked. You actually have to connect to things and you have to do things and things like that. So, it’s a bit like that. I won’t say very briefly a thing about three um mathematicians um just so that you can sort of see that people were mathematicians. Then I’m going to look at mirrors and sunrise. And then And so that that that first part is really about how maths and technology and understanding of the world around us gets into Shakespeare’s plays. But they don’t really illuminate Shakespeare’s plays. Okay? So, it’s just occurrences and what were people What were people thinking about? What were people able to do? And I want to do two things um Sonnet 77 and King Lear, which I hope are sort of more interesting and really about Shakespeare’s awareness of some of the technology and mathematical ideas around him, which is not weren’t, you know, the big technical things. It’s just the things that you would you would come across in everyday life. And then we’ve got um Act 5 there, which we will see whether we have time for. It can It can get curtailed if we need it. So, two introductory examples, counting the enemy and fine moon shine. So, the first clip is from the English Shakespeare Company from 1990, directed by Michael Bogdanov. Um and effectively, what we have here, I mean, Henry V Part 2 is really about the father-son relationships and Prince Harry learning to what responsibility might be. He’s a difficult teenager. He’s got under the influence of Falstaff. You’ve got a sort of change um going on for him, but at the same time in England things are not going well and you get a rebel faction that is really quite fed up with um the conditions and what how the king um King Henry the Fourth is behaving and the governance. [snorts] So, they’ve assembled in a Yorkshire forest hoping that a third another collabor- collabor- collab- yeah. Another um conspiracy, let’s say, Northumberland will come and join them, a rebel um and this is is where they learn you that I have received new dated letters from Northumberland. Their cold intense tenor and substance thus He is retired to ripe his growing fortunes to Scotland. And concludes in hearty prayers that your attempts may overlive the hazard and fearful meeting of their opposite. Thus, do the hopes we have in him touch ground and dash themselves to pieces. Now, what news? West of this forest, scarce a foot and goodly form comes on the enemy. And by the ground they hide, I judge their number upon on either rate of 30,000. The just proportion that we gave them out. Let us sway on and face them in the field. What what Well, it might be the just proportion, but um they don’t have North- Northumberland, so it’s not going to end well. Um The point about this, two things we learn that Northumberland’s going to sort of do a little side um hustle. And the messenger comes in and it’s not an easy part to play a messenger. Um And he says, “West of the forest scarcely off a mile in goodly form comes on the enemy by the ground they hide. I judge their number to upon or near the rate of 30,000.” And so this is just just small little example in Shakespeare of how people manage things. So for a mathematician, this is easy. Amount of stuff is density times the area. Okay? So this is the sort of thing a not a messenger. He’s not carrying a message. He’s actually done some scouting. He’s gone out. He’s looked. So he’s experienced in this sort of thing. He will know they are in goodly order. So that means uniform density. And he’s a very good judge of area. So he either has a little book which says density you know, are they in goodly order? Oh, yes, they are. And um what ground do they cover? Or he’s he’s good at judging that. But the basic idea is that you have some simple mathematical way of looking at things that says I I’ve got I know roughly speaking for that sort of army army um marching in this sort of way how dense they are, I know how much ground they cover, I multiply the two. Okay? You could also there are other variants on this where you could count the number of sub-units if they’re marching in groups. Um or how camps pitched. You could count the number of fires or the number of tents. And actually um Julius Caesar used this in Germany. Um so this is an old technique. Okay? This isn’t new. Okay? Julius Caesar used it. He what he did was he got his army so the Roman armies were very disciplined. You know, they knew how to pitch tents. So he got his lot to pitch them rather close together. So they covered less ground. So that the um German sort of looked at this and just looked at the ground they covered. Assumed it was standard Roman procedure. And assumed that there were rather less people soldiers than there actually were. And that didn’t end well either. The same technique was used in the 19th century counting buffalo herds in the USA. Um Trump’s inaugural ceremony 2017 there was a little controversy. And the same technique effectively was used again. In fact, it’s so prevalent it’s got a name. It’s called Jacob’s technique after a an engineer or mathematician from the 1960s. So these things get used over and over and over again. Um and then now actually it’s interesting um despite the fact they’ve sort of 2,000 years that this has been used now it’s changing because we use AI. So people put drones up and AI captures it. So um So that’s the first little example. It’s just a little example of something where something comes on and you’ve got these words that you’re not quite sure what they mean. They’re actually just very simple techniques that people had to understand the world around them to make make decisions. The next clip I want to do is Midsummer Night’s Dream and I’m going to show you two clips. Going to show you two clips because both of them neither of them neither of them have the lines I want and they do it slightly differently. The thing about these from the 70s and 80s was they at least they have some of the lines. The things from the 90s and 20s 2000s um don’t even have the lines. They cut. They jump. So, this is really the thing I want you to concentrate on is the almanacs which come in the middle. We will have such a problem. But there is two hard things. That is to bring moonshine into a chamber. For you know Pyramus and Thisbe did meet by moonlight. Doth the moonshine that night we play our play? A calendar, a calendar. Look in the almanac. Find that moonshine. What else? One must come in with a bush of thorns and a lantern and say he comes to disfigure or to present the person of moonshine. [laughter] Then there’s another thing. There’s always another thing. Um so I was going to try to give you the plot of A Midsummer Night’s Dream but I can’t work it out. I mean it’s very complicated, involves um drugs, fairies um what’s happening here is a group of what we’ll call rude mechanicals are planning to stage a play led by Quince the carpenter and they’re trying to think through how they’re going to um work it out. That’s a 1971 version and it jumps a line or two and you could see the almanac which is the thing I’m interested in was presented and then just thrown down. Okay, this is at least they got it in there. The 1981 of things. And that is to bring the moonlight into a chamber. But Pyramus and Thisbe we need to meet by moonlight. Does the moon shine that night we play our play? Ooh, calendar. A calendar? Look in the almanac find out. Why is it down right that night? Why then may you leave a casement of the great chamber window where we play open? And the moon may shine in at the casement. Ah. Or else one must come in with a bush of thorns and a lantern and say he comes to disfigure or to present the person of moonshine. And there’s another thing. So, um those of us of a certain age will recognize quite a lot of those actors. Um one of the great things about the BBC is its ability to bring sort of people who aren’t always regular theatrical actors into their productions. But um Bottom, Brian Glover there, um is trying that I mean that and Quince, who is the the thoughtful Geoffrey Palmer um character there, they’re trying to work out how to get the moon into their production. And there are two ways. Either you could have the moon, and that’s the almanac. Is there going to be a moon um on that night? Or you could have a something that sort of stands in for the moon. Okay. And so that’s a nice bit of problem solving. But let’s just think I because the almanac is one of those things that was really developing at that stage. It was going from it was I mean the way I like to think about it is it’s almost like your smartphone. Suddenly you had access to information. Um So, they want somehow to use this almanac to find out moonshine. And if you look a bit later than Shakespeare’s period, 1641 for example, this is an almanac um by Jonathan Dove. And you can see in I I hope you can see May have 31 days. First quarter um 7 days 45 minutes past 11 at night. Full moon 14th day 48 minutes past 7 at night. It’s quite exact. It’s telling you pretty much where the the phases of the moon. And you can see that below that actually there’s a list of um you know, on the first there’s some um information about the astrology, the position of the stars, and then it says pleasant weather. So, this is the sort of thing that you get from your almanac. In fact, you get lots more. I’ll talk about that in a minute. Um and almanacs appear several times in Shakespeare. Another example here is um Saturn in from Henry IV Part 2 again. Um Saturn and Venus this year in conjunction. What says the almanac to that? So, that that would be looking to say what’s the consequences? And so, what’s in an almanac? An almanac contains just lots of information. It told you about the weather. Told you the best time to sow and crop. It gave you medical information. It gave you the phases of the moon, tides, astronomical conjunctions with their astrological consequences, current knowledge, consequential history, date It’s sort of a compendium of stuff that is meant to sort of entertain and educate. And you know, there’s some of them have you know, important dates from the past. Some of them have the sizes, the relative sizes of planet. Some of them have, um, and then just lots and lots of whatever hit, you know, whatever they think is interesting and I’ll actually come back to that in a minute. And so, um, Leonard Digges in the mid, um, 16th century, so a bit before, um, Shakespeare’s time had an almanac where the idea, and he wasn’t the only one doing this. So, the idea with an almanac is it tells you about things that you need to know. Every year those things are slightly different. So, by the mid 17th century you had around 300,000 of these things being printed each year. Okay, that’s a lot. And they were printed each year because they updated the information. The Some of the early almanacs and, um, Leonard Digges’ example is a is a good one. From he actually set things up so that you calculated, he gave you a little recipe to calculate in the year that you were interested in how to do things. Okay. But that meant he had to explain the calculation a bit. So, Dove just gives you the information. But Digges has to tell you how to do things. And they’re all based around some very nice arithmetic connections which are actually related Most of them are related to the sun, moon, and earth, um, dynamics which I’m not going to go into. So, we’re interested in the phase of the moon, so I’ll talk about lunar months. Strictly speaking, it’s not a lunar It’s it’s a It’s got a posh name. It’s But the phase of the moon going from no moon, half moon, full moon, half moon, no moon. Okay, so the average month is a bit less than 30 days. That’s a bit lower than our most of our months. The solar year is 6 365.24. That 24 is really important. That’s That’s your leap years. That’s dealt with by leap years. And the Julian calendar managed that. But 25 would be managed by a leap year. 24 is a bit less. So actually the Gregorian calendar, when it came in, dealt with that. Which we will come back to. But the point is that a multiple, it doesn’t really matter what it is, it happens to be 235, of the lunar month is almost exactly the same as a multiple of the solar year. And that means that and it’s actually the the number of solar years is 19. So it means every 19 solar years you sort of reset the phases because you come back to the beginning. Okay. And um there are there’s also a shortfall of 11 days in the lunar year compared to the solar year. And this is what So I’m not going to go through this in detail, but this is basically what Diggs gets you to do. There is a thing called the prime, which is not a prime number, it’s the prime. It’s sometimes called golden number, which tells you where you are in that 19-year cycle. Okay, so you know that the first So you’ve got um you should have some starting cycle, and you know that that’s going to repeat every 19 years, which means you have to sort out those where you are in that cycle. You also then have to got this 11-day shorter, so roughly speaking, if if you’re in the you know, third time if your cycle starts um 1st of March, say, and you’re 5 years later, there are 5 * 11 days which um shorter, so you’re 55 days on than you you thought you were. And you divide by 30, so you multiply by 11 to get the number of days, divide by 30 to get um the roughly speaking that the the number is 29.53. Um roughly speaking, the um way the remainder gives you where you are in the um on the 1st of March, where you are in the in the um cycle. Then you have a thing called epact, which basically counts you on to get um something I’m not going to go into this, but basically you have a calculation that you can do it. You can do you Sorry, the epact is is what Sorry, it’s what I just said. It’s It’s prime * 11 modulo 30. So, and you have a table helps you sort of orientate yourself. It goes from 1 to 19. Now, so where What’s your start date? Cuz if your prime is 1, then you multiply by 11, so you’re 11 days on. So, it must have been the previous one that was your start date. That was 19. They’ve avoided using zero. They’re using zero in the numbers, 1560 has a zero in it. But they’re not using zero in the calculation or the indexing of the calculation. I hate indexing. This is All the mathematicians will know indexing is a complete pain. Whether you go from 1 to n or naught to n minus one really matters when you’re trying to write something down clearly. And there often is a better way of doing things. Anyway, that’s a side issue with mathematicians. Um no, so but 19 is sort of zero, so so 19 has to be What do I do? I do 19 * 11 and divide by 30. Well, if I do 19 by 11 and divide by 30, I’ve got almost almost seven. So, I’ve got seven remainder almost nothing. So, the remainder is nothing. Okay, up to the accuracy that we’re doing these things. But it wasn’t written down. It wasn’t They didn’t give a it a zero. They gave it a 19. 19 is playing the role of zero here. But you have to calculate that. So, let’s go on. So, you can now think of this scene where they bring out the almanac and they scratch their heads a bit and they’ve got to work out what it is that they’re trying to do. Um but that takes too long and it’s not a very important part of the story. Right, three mathematicians. I want to do this very, very quickly. This is the Wiki version of So, John Dee is wonderful. And you should go beyond Wiki. I encourage anyone to find out anything or one of the fictionalized versions. There’s lots of things about John Dee. Possibly um modeled Prospero in The Tempest. But he was he was a really flamboyant mathematician. Um he I mean, I said that he’s an early celebrity scientist. Okay, he went round impressing people. You can see him Here he’s impressing um Elizabeth first with some amazing light show. Um and he was a an appropriator, he was interested in everything, he had an amazing library. Um he died a pauper because well, he would got on the wrong side of too many people. Um and but he also wrote a preface to the first translation into English of Euclid’s Elements. And that even now is an absolutely fantastic manifesto for applied mathematics. And so I’m going to come back to that in a minute. Leonard and Thomas Digges, they’re father and son. Leonard was um possibly the inventor of the theodolite, possibly the inventor of a telescope because he was a surveyor. So he would wanted to be able to um find things. He also um didn’t end well um although it wasn’t really his fault. Um Thomas Digges, his son, early adopter of I’m going to mention Copernicus twice. That’s the first Well, it’s not it’s really strictly speaking the second, but that was in the introduction, so that doesn’t count. Um he was an early adopter of Copernican theory, which we’ll come back to possibly. Taught by Dee, there’s a close relationship with him. Interesting, his wife Anne um remarried after his death to a man who became um an overseer of Shakespeare’s will. So the connection to Shakespeare. His son, Leonard Leonard Jr. I don’t think they called him Jr. in those days. Um actually was a poet and probably I mean there’s a lot of scholarly stuff that sort of seemed to say that there there were quite strong connections between Shakespeare, so so certainly moved in the same social circles as um Thomas’ son, Leonard. So there there’s connection to Shakespeare. They lived relatively close by in London, so that’s good. And so here we have the preface. So, Billingsley, who had been a mayor of London, did this English translation of um the Almac, and it says um this is a fruitful preface made by D, specifying the chief mathematical sciences, what they are and where unto commodious, where also disclosed certain new secrets mathematical and mechanical until these days greatly missed. So, um what did D do? Well, he basically laid out he had this ground plan um for mathematics, which starts with what we would now call pure mathematics. Actually, probably wouldn’t. I’d much prefer not calling it pure mathematics, but fundamental mathematics. Um arithmetic, geometry, and mixed, where you put arithmetic and geometry together. And then he has a list of what you use this stuff for, and and to some extent how you use it. So, perspective, astronomy, music, cosmography, astrology, statics, uh arthro- arthro- arthro- pography, uh measurement of human body, and a whole lot more, which are really interesting. This is what he he was interested in. He has examples of them. And the last one was meant to be the highest form of mathematical art is archimastry, which was linking basically mathematical theory to experiment. So, it’s making that connection to the theoretical view of life to the the view. But it’s really worth having a little It’s very easy to find on the web. Um really worth having a little look at that if you’re a mathematician just to see how the pure applied divide to some extent was even happening here. But that the highest form of mathematical art was putting the two together to some extent. So, anyway. I want now to move swiftly to two examples. Mirrors and sunrise. So, I want to do this very quickly cuz we’re running out of time and I want to show some things. Um so, mirrors, this is part of the revolution in technology that was going on at the time. So, the Romans had been very good at making mirrors. That had been lost and in the uh 14th, 15th centuries, um certainly by the early 15th cent- early certainly by the early 16th century, um glass mirrors had started being produced on on in quite a large scale in Venice in Venice. And they could be made quite small. So, actually the early ones were quite convex because they they were very good at blowing um bottles. So, you blow a bottle, you stick some um mercury and I think it was tin um into it, swish it around a bit, cut it open, and you’ve got a mirror. Ish. Okay, it’s a bit more complicated than that, but but the the the thing of applying it to a sheet was was harder and that took a bit more time to do, but by the 16th century, these hand mirrors were pretty much everywhere. And if you think about this this I mean, I think of this as a selfie. This is the equivalent of a selfie because suddenly you’re able to see yourself in real time. So, rather than having a I mean, before it would have been some um burnished um metal or something like that, obsidian, or, you know, uh static, you might have been if you’re rich enough, a static mirror, large mirror. But, now you can carry this thing around. You can be in church and just check your makeup, whether your hair’s looking good, and actually see yourself really quite well defined. I mean, my mother in her book Electricity has a line um about when the first electric lights were put on in rooms. And suddenly you were able this harsh light went into all the dark corners, and you could see things that you’d never thought about what was actually happening in that corner. Well, it’s the same thing here. You can suddenly see things. And there was quite a lot of moral outrage. I mean, in France in 1575, this quote comes from, “Alas, what an age we live in to see such depravity as we see that induces them, I women, even to bring to church these scandalous mirrors hanging about their waists.” So, that the the worry was that people would spend the whole time looking at themselves. But, it does revolutionize the way that you see yourself and the timing that you can do that. And that you can actually compare good versions of your versions that you can see with what you can see on other people. And you can see that that that’s that’s got that’s a really, you know, they they really really took off around this time. And Dee, of course, was not immune to being interested in mirrors. But, he liked the idea of a cylindrical mirror. A mirror that create deforms things and and actually part of the thing about this was um sending messages that nobody else could read because you could only read them through with a cylindrical mirror. And so um that’s another thing. Now, I’m going to show you I’m not going to show you the whole of this clip. This is Patrick Stewart um as Macbeth. Um I think I’m not going to show the whole thing for time. [sighs and snorts] Is this a dagger which I see before me? The handle toward my hand. Come. [clears throat] Let me clutch thee. I have thee not. But I’m not going to go through in all. But of course the new man, he would. And in the um preface, he talks about being able to go um to a friend in London where he will set you up and you will lunge with your sword and you will see a sword coming back into your face. All done with mirrors. Okay? And um so Ian Wright um in 2005 wrote a very nice little um piece suggesting that you know, what’s in the air. First of all, this preface the Euclid’s Elements was was that that version had quite a large circulation. The preface therefore would have had a large circulation. And so that the things being in the air so writers suggesting that the idea that you might see something that’s actually almost real. Um might have given Shakespeare some of the ideas. I think I think I mean certainly an interesting idea. It’s It’s but it’s it’s that thing of what’s in the air, not necessarily that it was the immediate thing that people but people had certain images um around them. And the the thing I like about this is of course is everybody knows this is Pepper’s Ghost. Which is a 19th century phenomenon. So it was um used in plays in um and it’s simplest version. I don’t know why the arrows are going this way. Should in a sense go the other way. But um you see you have a plate glass with which is dark enough on on the right hand side here that’s quite a lot of the light that that gets reflected or quite quite a lot of the light that is remains gets reflected and you see what’s on S as though it was on S primed. Okay, so you’re seeing your mind is interpreting it as S primed. And with my daughter Ursula we did this um a couple of days ago which we have a a large window onto the garden. And as it was becoming dusk we lit Ursula’s hand holding a knife with an iPhone. And the reflection off the window we could see with garden behind it. And it’s exactly the same principle. So it it’s a bit pre-Raphaelite I think rather than early modern but the principle is the same. Okay. So, Julius Caesar is all uh this is so much about atmospherics, comets, weather, um and so on. And Casca that so you have a conspiracy against Julius Caesar. Casca is one of the conspirators. He Someone said Cinna says, “O pardon sir.” Uh sorry. Decius says, “Here lies the east. Does not the day break here?” The important here thing is that Casca says, “No, you’re wrong.” Because here as I point the sword the sun arises, which is a great way growing on the south, weighing the useful season of the year some 2 months hence up higher towards the north he first presents his fire and the highest east stands as the capital directly here. It’s sort of meaningless to us. Can you imagine doing that, you know, asked as a 16-year-old to do that? You go, point point point point. Not quite sure what’s going on. But to someone who lives not in a city and where and or where buildings are much lower, you’d be really quite aware of where the sun rises. And you would know that it doesn’t rise in the east. Okay, it does twice a year. But it moves. The position of the sun moves. This picture shows um the position of the sun over the year at 12:00 noon. And it’s very famous analemma, but there’s a similar sort of thing with where it rises. So, it rises I’ll always get this the wrong way around. It It rises um in the southeast. Don’t know why I’m pointing that way. Um Yeah, in the winter solstice and the northeast in the summer solstice. It’s got really quite a large variation. So, what Casca is actually saying is you’ve got the timing wrong. Okay? It’s It’s This is where it’s This First of all, this is where it’s rising. And that’s not the east because of the time of year we’re at. Okay? So, you can unpick it that way. And um Christian Doll actually does quite a nice job on some of this. And he His His line is also that that you can equate the sun with Caesar. So, Casca is the one that sees Caesar first because he sees the sun first, so he strikes Caesar first. So, it’s sort of pre- pre-telling the story of of of the death of Caesar. But, there’s another side to this because when you really go into it and try to interpret this for March the the um 15th I Ides of March then the seasons aren’t right for what he’s saying. And there there’s a really nice thing both um Shapiro and Doll play about the role of the anxiety about the two calendars, the Gregorian and the Julian calendar. Julian being in the UK, Great Britain um Europe Well, Catholic Europe taking the Gregorian meant that there was a a change a difference in in days between them. And there was there was a difference in New Year. So, the New Year in Julian was I think the 25th of March, in the Gregorian was the 1st of January. And I have a note of it somewhere. Um the legal beginning of the year moved It wasn’t It was the legal 25th of March was the legal New Year until 1752 when England finally chose to join the Europeans. And so, I think that there’s a sort of very clear thing in Julius Caesar of anxiety about time. And I think this is another example of it, though I don’t have time to go through it. Right, I want to I’m going to do one of these. Which one am I going to do? Um Okay. Let’s do Sonnet 77. So, I told you already mirrors were the new techniques and they they were being used everywhere. Almanacs, huge increase in availability of knowledge, huge um increase in numbers printed and um availability. But also timepieces that there were um new portable watches, portable sundials were available. Spring mechanisms were starting to be introduced. So, watches were also really changing technologically. So, Shakespeare you just anyone who was there would know these things were happening. So, Sonnet

Thy glass will show thee how thy beauties wear. Thy dial how thy precious minutes waste. The vacant leaves thy mind’s imprint will bear and of this book this learning mayest thou taste. The wrinkles that thy glass will truly show of mounted graves will give thee memory. Thou by the dial’s shady stealth mayest know time’s thievish progress to eternity. Look what thy memory cannot contain. Commit to these waste blanks and thou shalt find those children nursed, delivered from thy brain and to take a new acquaintance of thy mind. These offices so oft as thou wilt look shall profit thee and much enrich thy book. So, three things there. The glass to see clearly, the looking glass. The dial to measure time. and the blanks. So, almanacs I told you you had to do calculations on some of these things and you might want to take notes. So, almanacs fairly rapidly developed the idea of leaving some pages blank so that you could write in them. And actually in in the English Civil War, people were using this to um People have analyzed the almost diaries. I mean they they it’s effectively diaries of things that they’ve done according to the almanac. And so this is the mirror the portable watch and the almanac all in one all great great new um new technologies. And what I really like about this I could go on for quite a long time and I don’t have time. This is compared to most of the sonnets this is really optimistic. Okay, a lot of the sonnets are oh no I’m getting old. I’ve got a wrinkle. You’ve got a wrinkle. Will you still love me? This is not that. It’s actually these offices so often so look shall profit thee and much enrich thy book not not make you feel rubbish. But actually enrich you. And so I would see this as really quite an a it’s first of all it’s the white heat of technology um sonnet for Shakespeare and it’s got it’s really I think quite positive. It’s saying yes things change. Yes, things are different. Yes, you forget things. But actually the stuff here which will help you help you age help you manage that change. So, um the thing that I’m not going to talk about, which is a shame cuz I like it, is King Lear, which has an awful lot of nothing. And um we could talk about naught quite a lot. We saw naught and um the point about the nothing is that that it was coming in and Roman numerals were on their way out. You saw in the Diggs 1555 that zero was being used, but not as a number. He was using 19 * 11, the remainder thereof, to um to talk about zero. And so we can think about King Lear, who makes a really bad life choice. He um sort of basically asks his daughters whether they want to take over the kingdom. Two of them say, “You’re wonderful. We love you lots. Yes, of course, give us all your money.” The other one says, “Well, I love you as my duty requires and that’s fine. And so he gets very fed up with her um and things go apart. But I I like the idea he he does hand over his kingdom, so he becomes a placeholder and that’s an early idea of um very early. I mean, going back to the Babylonians and Mesopotamia um idea of zeros, where it just tells you that there’s not a 10 or whatever. Um madness, you actually become go from a placeholder to being nothing. And then you can become something again through death, where he becomes a historical king. He becomes a number, you know, position. Um so just to conclude, I think this is Shakespeare’s just I’ve just so love looking at Shakespeare, so that’s nice. But also it gives you this slightly alien view of the way people are um managing information and mathematical ideas in their ordinary life. So, there was massive technological technological changes going on and that’s reflected in the writing. Um and I think I hope, you know, the last example gives you a sense that if you know a little bit about those technical changes, it does change the way that you see some of Shakespeare’s work. And I did realize when I got to the end, I didn’t told you when he lived. So, here’s some dates to finish. That Those are numbers and there’s not a zero amongst them. So, um I will stop there. Thank you.

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