Welcome to this afternoon's colloquium. It's a great pleasure today to welcome Professor Tom Mccreesh to be our speaker. I first got to know Tom when he was in Cambridge, but his career subsequently has taken on roles in Sheffield and Leeds and now in Durham. He's a professor of physics there. He's also been to vice chancellors research and his area of speciality is all about the reality of fluids.
But he's not talking about that today. He has many side interests, but one of them, far too much, has come about through his interaction with some people in Oxford because he also did principally some medieval historians. That's not who we normally collaborate with. It's just to suggest that some medieval historians have been working in Durham and together they've uncovered some rather interesting things that connects physics with a 13th century history.
So I think it's going to be a very interesting book by colloquium. Thank you very much. Oh, thank you so much. It's great to be back in Oxford. And as you can see, this is going to be a talk which involves Oxford, an Oxford Durham collaboration. So for many reasons, it's it's very, very suitable. As you may know, the Oxford Durham is a picture of a now the medieval University of the North up there. It goes back many centuries. A couple of Durham colleges were actually funded from Oxford, sorry.
All the way round of Oxford Colleges were funded from Durham when, when Durham was a parliamentary forbidden from funding a university itself. So we just helped you. The other link here is that we will meet a character I've become fascinated with, namely the 13th century polymath Robert Ross Teste, who's become a personal hero of mine, an English mind of extraordinary capacity. There ought to be far better known. He might well have been this university's first chancellor.
But your records, to be frank, are are little ropey back in the 13th century. And I don't think we'll ever quite, quite know. I think I probably hurled enough insults from the Durham verse to Oxford. William Barford is looking at me askance so well. We'll press on so upset, he said.
Giles Gospel. This is a very large collaboration. Other names will pop up is my colleague, historian, medieval historian how Smithson was a Dom she's experimental psychologist now in your department of Experimental Psychology, if of course, no longer in your building of experimental psychology here in Oxford. But she's currently on sabbatical with us in Durham. Sigg is Norwegian. He's a Latinised Richard is a cosmologist. Neil Lewis is a Georgetown.
He's a he's a medieval philosopher. My constable is an English from Durham. Expert on middle or middle English to the Pantheon is a talking after it. Rome is probably the leading cross test physics scholar currently, and Ron Tan is another physicist at Durham. So you can see that this is a very interdisciplinary team and I hope to explain to you why that is the case.
Many thanks to both our universities funding this from time to time and currently the Arts and Humanities Research Research Council. So let me just jump straight with no further ado into the business. And here is Manuscript and Annexe 12 three in Durham's medieval library. It's our growth test manuscript. And you can see straightaway why a physicist might have a little activation barrier before she or he gets very far with this material. This is our principal reference.
It's a collection, of course, test dicta, although I have to say we don't some we don't possess any of his scientific corpus. They are mostly held in Oxford College libraries these days. The Cathedral Library catalogue at Durham says that we should possess a copy of cross tests scientific treatise. But someone checked it out in 1349 and doesn't seem to have checked it back in again.
Never mind. But you see, the point is that medieval paleo graffiti or wine tasting for manuscripts ability to read this highly abbreviated medieval Latin to understand its its philosophical background is the gateway set of disciplines to getting anywhere with this material. So let's just jump in and say what does a medieval natural philosopher say when he's writing a document about light? So this is the first treatise that I read across the state UK on Light about 1224.
Now I thought, actually, this is Oxford, so that should work fine. So I'll just leave you to translate that as we go. I, when I was moving from Leeds to I should say I was first found out about this extraordinary 13th century mind through the history philosophy of science department at Leeds, for whom at that point there was a ghost scholar, Jim Ginter, who was more interested in his philosophy and theology than his his science.
But I always. To read his side. So this was the document I read this summer. I went to Durham and the first principle form which which is called the form of karate, I declare to be light. What's going on here? For light diffuses in every direction from a point of light into a sphere, however large it might be, might be generated. Unless, of course, something gets in the way and causes a shadow. For true, cooperative and extension of materials into three dimensions.
Follow. Now. Okay. This is rather interesting. I expected when I first came across this guy, something rather mystical, rather theological. What I did not expect was a discussion of what we now call material stability. This is an essay, an extended essay in the mid the early 13th century, written by Christian natural philosopher, pointing out the classical atomism does not explain this, the three dimensional extension and solidity of matter.
Well, this is a really interesting observation, because the point is it doesn't. And because this is saying that the point is that classical atoms are atoms, they are that which cannot be divided. They are point like a points, Michael, which of course, has by definition no extension. And what you're saying is, however large, a number of point like objects I have, I still have no extension.
I still have zero volume because zero multiplied by however a larger number I choose be that number finite still gives me no value. Now, I'm really enjoying myself by now because of course we know classical is indeed, it doesn't explain this unless because I mean you can always declared your atoms if a billion balls but it hasn't got you anywhere because you you require stuff with extension and you don't know what that is yet.
It's just formed. You have recursion, which is something he points out. And so he set himself a problem. And it's a it's a seriously scientific problem. One of the delights of science I know about you, I'm often finding like pointing this out in the yeah. Whenever I have a cultural, half halfway cultural discussion, I try and sell science with, with this that science differentiates between the familiar and the understood.
Yeah. I mean, just because we're familiar with the fact we sit on our chairs, we don't fall through does not mean we understand them fall through. Here is two galaxies in collision, and a classical view of matter, as you know, is still more or less classical. It's a cloud of points, a mostly empty space, two galaxies. When they collide, they look like clouds. You know, when you jump out of an aeroplane onto a cloud, you expect you're going to.
But it looks as if you can bounce up and down the cotton wool, but you can't because it's mostly empty space. Galaxies pass straight through each other. Processes say the same thing would have would be the case with three dimensional matter. So where does this property of stability and extension come from? Now, you know, this is a problem which is not really solved until the advent of quantum mechanics. Goodness sake. Some of you work on this stuff, right?
So what he says is there is a property that is a phenomenon I know that has this property of filling space. It is light in that first sentence is encapsulated.
This is later informed by my Arabist colleagues. We have an important Arabist on the project, you know, just prior to the 13th centuries, this extraordinary century of the translation movement, when thanks to the Muslim tradition, Islamic tradition of North Africa and Spain, particularly Aristotle was being reintroduced in Arabic and then Latin translation from the Greek into Northern Europe.
And that's really what got all natural philosophy going again. Avicenna, who pointed out the need for this sort of first form, not a need something like first form to give you an extension, but just as is the first to say, I think it's light. So for him, he makes this hypothesis that not a sort of amalgam of atoms and light, and that infinitely multiplying light provides this thing called stability.
Or even says here, if it's not light, it could be something that has the same properties of light. So this one really falling off my chair. Okay, what else does he do? He then starts to mathematics, his his physics. He puts this argument about infinities and infinite into into a finite form. He starts saying, well, actually the there are greater and lesser infinities. Now, he's not being Cantor here. He's not, of course, identifying a proper classified hierarchy of infinities.
What he's saying is, I know I can't get extension if I multiply these infinitesimal atoms by a finite number, but suppose I could multiply by them infinite number. Then the mathematical description of my physics would be. An infinite divide by inferential input, multiplied by infinitesimal. And I think I can explain not only finite volumes, but all possible finite numbers of volumes by by comparing by taking the ratio of different infinities.
So we discuss is the ratio of the natural numbers to the even numbers. And of course, you know, he's you can feel him groping at limits here and that proper analysis but not getting at it but you know goodness, this is 1224. He thinks this is greater than one. Of course, we can easily imagine that by changing limits, it could be less than one. But you feel you know what he's getting at.
He actually does states that the powers of some of the powers are two divided by the halves, must still be two, must be two. Because each term is twice the the the the term it can be compared to. So that there are some interesting things going on here. But the point is that he's he's also deciding that physics needs to be mathematical physics. And as you said, this is the translation.
Like you said, whatever sustained extension matches either like or participates in some part in the properties of rights, I thought I would gratuitously, gratuitously put up pictures of the Hodgkin wave function to point out just what we are not saying. What is, of course, awfully easy to do at this point is and you know, if I were writing an article for New Scientist or something, it would be so easy to say, oh, you know, a quantum mechanism in eight centuries before his time.
No, of course not. Of course not. This is a medieval thinker with a medieval mind thinking of his own, his own period. However, what is extraordinary is that whenever we've added a new scientist to our team and we started to engage with this and his contemporaries writing We We are scientists don't find themselves in alien company. It's strange, it's very different. But there is an intellectual fellow feeling. I hope I can. I've been able to persuade you why that is. But first.
So let me see. So what has happened? When I got to Durham, I was kind of to point out it was in order to have the provost chancellor for research. So I was spending my first few weeks knocking around the university, different faculties, different departments asking, you know, what's good, what's going on, what little sign on can I do to help people join up?
And, and I found that the Institute for Medieval Studies being of course yeah thoroughly humanities and doing things things properly had this charming Tuesday evening seminar with a glass of wine at 5:00 where they talked about medieval authors. And I said, looking at, Would you like me to come? I love to find out what you're doing and would you like me to come?
We just talk very naively about what a contemporary scientist how with with, without more than a smattering of cognisance of the history of the medieval history of science, how he reacts to reading some of this stuff. So I've told them what I've just told you, and we had a conversation afterwards. Is it worth is it worth taking this methodology a little further? Of getting humanities scholars and scientists together, reading these these texts?
And does this add anything or is it does it just risk anachronistically modernising these people? And the answer was no. We'd like to take this further. And the reason we took this further is because you have asked us questions about this text that we've not asked ourselves, and we don't think they're silly questions. They're quite interesting questions. They might we might phrase them in different ways, but let's that's set up.
So the Old Universe Project was born and it now consists of historians, panellists, scientists, all sorts. We are producing new translation editions of the texts. So what we hoped is that by by working together collaboratively on these documents, we would be able to identify more of the intellectual contribution they were making.
A crude I would say, you know, the way I put it is if you're good enough at Latin to translate this stuff and read it, you probably gave up science when you about 13 years old. And so when it gets serious, the mathematical and physical, you know, you just you sort of miss it. And that's what the humanities scholars kind enough, enough to say as well.
So we've produced these new editions and then what we've called functional analysis of the texts through modern eyes, not modernising the writer, but using the inheritors of the subsequent centuries to to re-evaluate and analyse what step it was logically and mathematically he was taking a we've also had fun inventing and this is a radical in this very project and actually getting medieval Latin artists and physicists,
psychologists into a room talking with each other. It doesn't happen easily, just like. That and this Hannah Smithson who's here notes I said before, puts it When we first got together around the table, all the humanities scholars sat on one side of the table and all the scientists sat down the other side of the table. And it was all a little bit delicate. But as we got to know each other and have meals with each other and go on conferences together and so on, it got rather easier.
And we do have a publication series actually. This is now changed. It's not the Pontifical Institute, it's Oxford University Press are now publishing. We are pushing with them a series of of commentaries and reappraising appraisals of this extraordinary polymath science. But there's a little bit more to that. This is what we didn't expect, and this has been the unexpected delight. Our great hope was that we could produce rather finer editions countries.
What we did not expect was that at some point in the reading of every one of these 13th century treaties, one of the scientists will say, Well, that's an interesting question. It's a strange hypothesis. Does anyone ever revisit that? Did they want to do that calculation or this experiment? And because science is so redefined and rich, some of these questions have not been followed up.
So as well as the humanity's series of papers, we've also managed to to spin out some papers that have been published in journals like the Journal of the Optical Society of America, Proceedings of the Royal Society, Nature and Nature Physics. You may have heard of some of these journals of science, which is contemporary science, which has been stimulated methodologically, all substantially by this medieval encounter.
So that's been a real delight. So here's one the actual court space from the 13th century, we'll be visiting that before the end, if we're lucky and precocious, makes extraordinary insight into rainbows. The History of the Rainbow. Yeah, I think you could probably write the history of science around the Rainbow alone, actually. Michael Brooks, science writer, has taken this project, his fall in love.
With this, he writes for New Scientist. He's had a number of articles from him and others, and there's now lots of YouTube clips and things. So let's just go briefly into cross test and then we'll look at some of the some of the science that he is he became after his period writing science, he became a bishop of Lincoln. And as you know, the 13th century, the Diocese of Lincoln was huge. Oxford was in it. Some of you might might know this, but one of very humble origins.
So as typical for the time, I don't really know quite when he was born somewhere in East Anglia. We know that by the end of the 12th century, he was a deacon for William de Vere, bishop of Hereford. Hereford, a very important centre of scholarly learning. Then we really didn't know. We know he was Oxford and the scholarly community are divided to the point of being at loggerheads about whether he was ever in Paris or not,
which is southern. So some of you will have heard that that name very now, now deceased. But an established English medievalist has a personal crusade to make cross test the great medieval English philosopher and wouldn't have it that he was in Paris. I think, frankly, he probably was. But it's some of our textual analysis helping to solve that problem. He was actually obviously here he was tutor to the brand new early Franciscan movement, and that's when it got intellectually interesting.
It was during the 1220s that he was writing most of his science and as I said, 1235 Bishop Lincoln He takes several missions to the Pope. Leo And not quite sure why Leo has become plural, but so he's often recruited as of early reformer. He stands up for good pastoral behaviour in the church and, and, and, and good editions of Scripture. So you, you read, you go back to the, the Hebrew and the Greek and he dies in 1253.
So he was extraordinary scholar. And here there's the there are two pictures of him. No idea whether they're like this or not. This is this is the other one. He he writes about the whole curriculum, the medieval curriculum, the liberal arts. He writes about many science. You write you, of course, write theology. And it's not the same thing. He's perfect. You can tell he's he knows when he's doing science and he knows when he's doing theology.
It's different. As I said before, he's interested in going back to original languages to improve the quality of a text. He's passionate for proper pastoral care. He writes for agriculture, he's interested in farming practices, and he spent some time as a bishop and a politician. So very rich, medieval career. What's going on at the time contextually to say in this is very important to understand and I don't know about you.
One of the drivers for me in this project is I've never really quite bought the sort of coffee table history of science story, which told me when I was a teenager that, you know, signed the origin of proper science was around 1600. It was in the Enlightenment. And that nothing before that. Really counted. It was. It was, you know, mysticism and alchemy and still magic and stuff. And and because I'm a kind of gradualist at heart, I don't really think everything comes from nothing.
Really believe that. And, well, you shouldn't believe it because it's not true. And there's all sorts of mathematical fuss and physical and scientific development. To me, this is what's going on for me. The blue touch paper for the scientific revolution was lit in the 12th century when I said most of Aristotle and Plato was rediscovered by the scholarly communities of North Europe. Thank you. Thanks to the Arab transmission and and people started reading it.
So people like other easy Arabic named Ibn Rushd of Cordoba, just as Aristotle at the time is, tends to be called as the philosopher.
If you saw the was the philosopher, it's almost always means Aristotle in 13th century, if you ever saw the words of the commentator fundament averroes who commentated and developed Aristotle science going on all over the the Middle East and Constantinople of course Sicily but particularly said before Spain, talking about Toledo and Cordoba, great performance of intellectual interdisciplinary awakening in the 12th and then the 13th century.
So girls just inherits all this ancient science, this then the 12th intellectual revival, this reconquest of Aristotle, this a copy of Aristotle's Opera Logic. I think it's in a library in Oxford, actually, that one that and he develops a rather nuanced natural science and scientific method get in talking in his commentary and as to Aristotle's posterior analytics about how we induce knowledge of the universe in an opposite way from how we did use mathematics from its axioms.
It's a very advanced and subtle philosophy of a scientific methodology. But of course he is in a Christian theological world and he knows. So these are the the the the era as well. When once we when he's asking questions about science, what might we know about the way the material universe works? We don't know. Now, this is where the intellectual connection for theology comes from, because it's clear that it's because of the audience of God's creation.
That's where the universe or universe label comes from. That one can therefore logically hope to do something about only entangling creation with reason and rationality and and all of us. And if we're not experimenting, we are most certainly observing. And that's a rather subtle issue.
Some of you will know that there's an historian of science who first wrote about Columbia, S.C. Crombie wrote about ghost science in the 1560s, had a very strong opinion that it was just to establish the beginnings of experimental science tradition in in England. That's probably overthinking the pudding. But you'll see he gets pretty close to it. Observation, however, is certainly important.
And for those of you interested in the background philosophy, there's a theological transition going on here from Augustine to acquires mean by that from from a theology that some based on divine light. You know we are inspired to know things from Aquinas who would say no we by our own hard work,
we can do science and we can work things out that we didn't know before. So from a doctrine of, well, we're just fallen beings, so we can't hope to do anything from a sense of actually we might recover a sort of knowledge of creation that a divine creator might contain this to to have. We're going on. Of course, Aristotle was being adopted into the philosophical question that the physics of of of of the time. And of course that creates some very delicate questions.
You know, how far does a Christian philosopher take on arrest and arrest? Aristotle, a pagans, is thinking, where do you go? Where do you stop when you see some interesting points in the science there? And he's clearly motivated by his biblical theology to look at science as well. And we've got to now get to a European transmission. So this is not a sort of static, intellectual time. It's a fervent of you. Thoughts? What does he write about in science?
He writes about sounds. His early, early, early text is about how sound is made and how we perceive it. And he writes about the heavenly spheres. It's a sort of undergraduate text of the Aristotelian heavens and how to calculate eclipses. And someone talks about comets and how elements work in the universe, how this sky moves on light colour.
He comments out in Aristotle's physics. He writes a sort of spatial geometry of the nature of lines and place, and he finishes with a treatise on the rainbow before he he himself, which will visit bye bye bye by the end. So I think I'll just skip over the sources actually, and we'll. Just wanted you to just look at this little bit because he's he's.
There are echoes that the sort of reflection that Einstein had on the almost miraculous way we can do science is he has these these these thoughts as well. And I rather loved this description of of what he's trying to do. He's trying to use sense perception in the world to re create an imaginative grasp of the inner structure of matter of the sky and of the incorruptible, universal fast essences. The first causes effects. Okay, I said before. So we've got authorities.
We've got these ideas to explain nature, rationality and text on the rainbow and the introduction of mathematics into into science. So there's a lot going on. He does something extraordinary with the treatise on on on Light. So we'll go back to that. It's the next thing we do. He he's established this I explained that his observation that light has the property of space can might explain the solidity of matter. He then does this a second extraordinary thing he says, well, actually does it.
If this explains matter on the scales around us, might it also explain the largest objects we can conceive of? They move the universe as a whole. This is another one that I think he's almost a medieval version of what Newton does when he looks at the app of Apple Fall or imagines the Apple fall and says, I wonder if there's a connection between that force by that tendency and the orbit of the moon. So I was just saying, look, we've got a theory of the activity of light in ordinary matter.
Might that account for the structure of the cosmos as we see it? And he come, he says he says, I think it might, because we know, of course, what is the cosmos he's thinking about? He's thinking of the Aristotelian cosmos. The geocentric cosmos, of course. You know, we can't blame him for that. He didn't have a telescope. But without a telescope, there is really insufficient evidence to establish anything but the geocentric theory and.
So this is the universe that he wants to account for. Why does he think he needs to account for us at all? After all, for Aristotle, the question of how the universe got there doesn't arise because there can be no first, cause there's no first. Aristotle was the first city state cosmologist.
But GROSS says although he embraces Aristotle, science in almost its entirety, says that actually because Aristotle, because he's a pagan, you know, he doesn't know everything as he thinks the universe always was. Of course, within the Christian metaphysics there is a creative moment, so one has to account for that. But what he does not do, and I think there are some people in churches today who would who would do well to listen to him.
He doesn't say answers in Genesis. He doesn't. Of course he doesn't. No one has ever for the centuries taken taken the first chapter of Genesis as being anything other than metaphorical, these great, great thinkers. If it was metaphorical, he does the same thing. But he does. No, it talks about a creative moment. So he says no. What we need to do is to take the science we've inherited from Aristotle.
With Aristotle, but against him. You need to account for the the cosmology that we see is fascinating. What he's saying is the structures we see in the sky when we look into the night sky are patterns and consequences of the dynamic moments of the early stages of the universe. So remarkable insight, because that's more or less what cosmologists do today, right? That's the microwave background, the pattern of the early movements.
And he uses this light idea to do it, you know, light at the beginning of time, extended matter, which you could not believe, drawing out along with itself into a mass the size of the world machine, the universe itself, he says, who's a kind of medieval big. And it has extraordinary consequences. He has a density feel. This is where this is where the scientists sort of start resonating with this text, because he describes this expanding sphere.
And he says this will be more dense in the middle than the outside. And he then starts and starts imagining simple axioms, a set of simple axioms that can that would would result in the universe of nested celestial spheres that he thinks he observes. So if this expansion is great, as you probably know, the idea was that these were perfected matter out of the orbit of the moon. Everything was perfect. He is, he says, look, suppose because nature never abhors a vacuum.
If I'm never going to get to a vacuum, there must be a minimum density. Look at that minimum density. I can't verify further. Therefore, there must be a minimum density which the universe somehow crystallises and freezes. Okay. Point. So far it's quite intricate. So this expanding sphere has its lowest density at the outside. So it's at the outside points where this minimum crystallisation density must be reached.
And when it's reached, of course, the expansion stops and that's the fun that surfaces this thing ferment is purified matter. Pure matter also radiates. So we now have an inward light pressure, if you like, that then starts exciting matter from the outside in.
If we have a sort of luminous centric cosmology, uh, that, that the light starts radiating from the outward spheres inwards, and there's this excessive compression and the series of moments at which, which this critical density is, is retained actually is a series of multiples of the integers. And that is his theory for how the forces were formed. And actually, there's even something rather more remarkable than that.
If you know anything about this medieval cosmos, you'll know that, as I said before, above the orbit of the moon was this perfected crystalline matter. Below the orbit of the moon was this impure matter above the sun when everything was in circles, below the moon is where the elements are vertical motion precipitation of wind and fire. Goodness knows what. And the earth is in the middle.
Until this point, this this phase transition or the symmetry breaking, if you like, had never been explained, his body language never been explained. But think about gross hysteria. He has a ability to explain it because at some point nature is getting more and more compressed. The light filtering down through these spheres is getting weaker and weaker. At some points. There's no more compression to do. You can't reach that purification crystallisation position anymore.
That's what the orbit moves. So he has a unified theory for the the the very that's a two phase structure of the apparent medieval cosmos. Now, I hope with me so far the point is. Not that this is complete baloney. Obviously, it's wrong. We know this is wrong, but that he's going about it in that sort of constructive, theoretical, physical way that we do things today. And here are his laws.
You know, this like expansive states tend to think we have multiple multiplication that is conserved is a minimum density and perfection. It's like for those six, it turns out you construct a cosmology. Well, that's what we did. So this is a bit of fun. But it turns out we did all the fun. So Richard Dyer from the Institute of Cosmological Computing, I went to say, Would you like to join this project? We've discovered something that looks rather cosmological, both up your street.
Would you like to. Would you like to discover what the cosmological cosmologists competition cosmologist was thinking eight centuries ago? Actually, I am. I think there's a him. I went to the whole seminar, to the whole institute. And all but one were looking at me with the same with expressions that number of you are now asking What on earth is this supposed to be about? But Richard was absolutely either fixed.
I have the first question. So he actually translated we translated together cross tests. Six axioms. I mean, this is clear. They're actually quite easy to turn into differential equations, and it turns out that you can you can solve them. And so, you know, we can now this is now the point is this may sound anachronistic, but if we if we promise ourselves to translate the Latin into English. I mean, translating the texts into mathematics is just one more step.
So we're making a mathematical translation of this medieval model. It's you know, this is the this is the light field. It's generated by matter. It's absorbed by matter. And this says that the like the velocity of the matter follows the radiation field. And so this is a continuity equation. So you will know these things. It's great to talk about this in the physics department more often. This is just more paper. But, you know, this this is these are the critical, critical ratios.
So let me give you some idea what we've done. This layer here is the Latin behind the English. And we've sort of layered this with with with mathematics and started to compute with it. So you can compute with it what that is going for, be we at the outset. Oh yeah. Yes. He says there is. Okay. There are parameters we have to allow ourselves. He says there is a minimum density. So the boundary condition is that there is a minimum density.
And when you hit that medium density, that's the boundary condition. And there's nothing beyond that. No, there's nothing. There's nothing. There's nothing. Nothing beyond that. Yes. If you like. Yes. How do the shells and lies of the Group of Eight come out? Okay. So actually they come up. Very good question.
He what's interesting is that he in the text, he's aware that although he's thought through carefully this minimum set of principles, he kind of feels that though he can't prove that that hasn't specified the number of shells. So he the text finishes with this weird Pythagorean argument that there must be ten, because ten is the fourth triangular number. Um, there is this kind of cute, but, but, but he kind of knows that something else sets the number of shells.
And I'm going to show you, but I'm just trying to run this through. This is a. Moving his calculations. I think this will probably run. Should run. Yes. So this is the the computation of the incoming lumen from the outer sphere.
It turns out that if if he doesn't ostensibly mention anything through his opacity and absorption, when you don't have any absorption of the light coming in from the outside, as you can see, the light pressure actually increases and increases because you get concentrated in this one overall squared way. And when ends up actually with an infinite cascade of integer shells. So what we liked, what we wanted to do was to put in the absorption term.
That actually the very process of doing this through as back into the text and it got got everyone looking at the text a lot harder. It turns out that we had overlooked the point at which he explicitly writes that this light cascade is being weakened as it descends through the shell.
Obviously, he didn't have access to this computation, but but that does illustrate some of the textual and humanities advantage of doing this crazy stuff that by asking these apparently anachronistic questions, one is actually forced to look at the texts in different, different ways, and they like that. So this was the solar system solution. So in fact, it turns out that there's a whole phase space of of different shell numbers.
So perfect. You set me up for this one sort of loop that there are three there are three parameters to this. Um, the opacity that the, the original strength of light and the, and the transparency of the purified material and if you want, it is a number of shells. If you want ten shells, which is our solar system or know what he thinks is you're living in this this red shell there in terms of the parameter space.
So great. Great question. So there are parameters which which is no, I mean, just reception. As you probably know, the first attempts to attempt to solve Einstein's gravitation gravitation general relativity field equations in in spherical symmetry for the entire cosmos was performed simultaneously by Friedman in Soviet Union and and George Schmidt Belgian Catholic priest.
And when he was actually working in Cambridge with Eddington and what later was called the Big Bang, but not by these people, the expanding universe was was, was the result. Now, we don't know for sure that gross test was aware of that. The that was aware of gross yes. We do actually know that a that an Oxford humanities scholar of gross test who loved this text gave a lecture at the British Academy in April of 1922, at which course we still have the transcript.
He said that he believes that were a contemporary physicist who had mathematics beyond his own capabilities to look at this text and be inspired from it that it might have something to say about the cosmos. Today we know that a party of academics from Cambridge, including people who work with Eddington, went on to London by train to attend the lecture. We do not know whether Lavarch was was one of them, but it would kind of make a go just to.
I'm still hoping that St Edmunds College might serve up a diary where he he comments this would not be it would be lovely. And I think we should look briefly at colour before we put before we stop because this is important and gave us another of our lives onto the rainbow and other things I like to tell you about. This lecture needs to be transportable across the Atlantic so that when he writes a jewel of a treatise after The Theory of Light,
he writes about colour. It's 400 Latin words is the first one we actually looked at in detail and produced an edition of Because it was so short. And for him the colour is important because it's the validation of his theory that matter is atoms with light amalgamated with it. So the consequence that is common. So when he sees colours, he sees his idea of light upholding and giving space to matter.
So short takes 11 manuscripts. There's one in the British library, rather damaged by the fire of London. This one, it fits between the look which you've just looked at and the Rainbow text written at 1255. And so let's set off and see what the gallery is all about. I could almost put the text up on one one slide. It's very, very short and it's very precise and condensed. He starts saying like colour is like embodied in the. That's okay.
So it's linked to his like hypothesis. He's like metaphysics. Then he says something extraordinary. Identifies three bi polar qualities of colour. Colour, he says, can either be the last, is pure and impure, or somewhere in between or obscure, perhaps bright and then or somewhere in between or copious gifts. Not all great or little or somewhere in between.
And he then goes on to insist that the purity, impurity that's dominated by the material and these two other dimensions, if I may call it, are properties of light themselves and a particular oddly for trees on colour. No colours are mentioned in the ecology apart from black and white, but it's, it's a theatre for colour. And he starts doing combinatorics with these three different axes. What can you see.
What kind of Smithson or experimental psychologist who's one of the world's colour experts actually might have been rather intrigued by this, which is, of course, because I'm sure you know that our perception of colour is three dimensional. And that's because in the rest of our eyes there are three different physiological types of cone cells. They have different three different pigments in them. Imagine he called the short, medium and long wavelength cones.
And so an arbitrary, high dimensional spectral content is filtered by our perceptive apparatus by three numbers. And the neural fine rates from these three different cones into what's called the confocal and captures and it starts it's neurologically processed by the brain. So that's why this is an LGB field, because with a red and green and blue light, you can construct any colour scheme you want.
And there it is on the retina. And here is a retina imaged by Hannah and her team and here they've coloured in the if one can identify now where the short to the medium and the longer cones are. It's a rather interesting random array with excitable bits from time to time. So you can what you do mathematically. You would think about colour today in a sort of kind of cute.
One way of doing it is project this this mathematical structure, this vector space structure into colour cubes and plot the long way, medium and short with, you know, a comb. And when they're all turned off, 000 is black. And when they're all turned on, the opposite corner is the white colour. Okay, so this is the normal, normal human human vision and I can fill that coat, that space in with all the colours that we can expect, as we can see.
So. No, this is excluded because what's beginning to emerge is something that looks like a description of the three dimensional mathematical space in which colour results. Is this really what's going on or is the three there because of the Trinity or something like that? And we're just projecting a sort of wistfulness back onto on the cross test. Well, Moore is true. He then starts doing combinatorics with this text and it becomes a highly mathematical text.
So there's no algebra in it because algebra was being invented at the time, was being adopted here in Europe at the time. He starts counting colours and he says that there are seven colours exactly from these three quantities and that seven turns out to be too cute on this one because he says that from white there are seven colours close to what is known. No more, no fewer. What's he doing?
Turns out he describes this by saying these three quantities, which are 111 white one can now reduce them either by reducing one at a time, which is equivalent to moving down the edges of the key or two at a time, holding one fixed, which is equivalent to moving across the diagonals of the phases or three all at once, which is moving down the diagonal. So that's. Seven different colour directions in this colour states. There they are with Cartesian coordinates, as we call them today.
Now note that this is most definitely not, as some of the current literature was saying, just a recapitulation of Aristotle. Aristotle has that colour does. The colours are between black and white, but they're on a linear line. This is a ladder of descent from colours of white towards toward towards black. In his descent, Switzerland since R2. So it looks as though we're really onto something.
There was one little flaw, however, and I told you that because this is white is Malta chloro Puram not all three together. So given that he also knows about Black, you'd expect him to discuss Black as being the opposite of those three. That would be polka interior and obscure, wasn't it? But the sentence we get to at that point reads looks impure. Negrito is thus black. The word obscura is not there.
It's in the current position. It's a pity because everything was looking so mathematically tight. Of course, there's no grammatical problems with this. With this text, it didn't look problematic, but the scientists were beginning to be convinced that he was thinking highly, mathematically and abstractly about this thing with some surprised.
This one flaw is that. Now, this is where we learned about the history of of scholarship about this manuscript, because the last edition of this we're working on from Bauer edited German scholar. And it is all across the songs at about 1910. He only had access to rather late manuscripts. Um. Here is his the family tree of manuscripts. You can do this just as you just the biologists do phylogeny, by the way, because it was always nice. Kids get copied by scribes one from another.
So if any scribe introduces an error, any subsequent copying will typically copy the error and not reverse it. So one can reconstruct all the family tree. Just this one reconstructs mutations in several features. And so the point is that that that was editing from this one down here, he didn't have access, which just cascades in cascades of error. Charles pointed out this manuscript here in Madrid was unknown to him, but that he happened to be going to Madrid that July.
Would he like us to check on that early manuscript from a different branch to see whether perhaps our hypothesis that the original full three dimensions of blackness had been written down? You know where this story is going now? I don't think so. He came this is actually what he did. And and the PDF winged its way back there where we said we expect it to be as the word you put it very obscure.
Yeah. So this is our Da Vinci Code moment where, you know, by doing by doing some mathematical physics on this. This is the manuscript we were somehow able to predict. Were you to enter the vaults of a museum in Madrid you would find in Latin on a 13th century document the word obscura at this point there. But but. But it kind of does validate what validates the project. So why isn't that? Yes, there are other other textual problems emerge of some interest.
The text goes on to say that the seven colours from whiteness, as I said before. Similarly, he says, there are seven colours. Augmenting from blackness. And then so he says there are nine altogether. Now, those who know me will know that getting Matt's right is not my strong point, which is kind of unfortunate for a theoretical physicist. But even I know that seven plus seven doesn't usually equal nine.
So we run this. We had all sorts. It turns out this is a rather simple explanation if you can go through the manuscript tradition. Cross Test was looking at Arab manuscripts the first time. He was one of the first to adopt what we now call known of as Arabic numerals rather than Roman numerals. So he wrote his 14 as we would but but was rather open for the medieval four is a is a modern meaning of X of this scribe who doesn't know numerals sees a written 14.
He thinks he sees a one and then across. And then of course, the next one translate that says no. Then because he thinks he's looking at the latter nine and that's that's that's that's how it happens. So the translation issues as well. We'll just finish with the Rango because we still haven't answered the question. Does cross test's three dimensional colour scheme map onto our RGV colour scheme any way at all? Don't forget, the problem was he didn't mention any colours.
Oh, for a TARDIS to go back with a colour deluxe colour chart, you know, do not sell the charts back to the 13th century. Bishop Robert, would you mind telling us which of these colours you refer to as Flora Obscura? Whatever. Then we come across to everything on the rainbow, most of which is about the geometric optics of lines and clouds forming an arc and so forth.
Actually, he's the first to identify refraction as the source of the rainbow, but right at the end he talks of the rainbow in that same colour space language of glory. Aha. Because rainbows in the 13th century is very much like the rainbows here. He talks about greatness and less, but not our Parker as being strangely not bright or dim colours, but the different colours in the rainbow. Oh, that's a bit of a surprise. But he then says, Consider the space, not a one rainbow.
Consider all possible rainbows in all different clouds, sophisticated for itself. Consider all possible rainbows. And if you have a if you see rainbows made by different droplet sizes, the only difference so his artificial rainbows created by this golden spray large droplets give intense colours, smaller droplets because there's more diffraction from them cause more desaturated, more hazy colours. And this is what he says is pure, impure, irritating.
And then so we could have done, of course is to use the HLC money to send this all around the world and take photographs and colour measurements, all different types of rainbows, which would be very nice. But actually now we're in a position to do a quick job on that and that's do the full theory of the rainbow, uh, is the rainbow colours are not prismatic colours. Of course they're not at all.
They of course caused by refraction but it's a caustic effect is a subtle, subtle effect of of rays of different coming into a droplet, different points bouncing out at different times, but forming a maximum and the angle at which they emerge causing the caustic. So you have to do some other subtle calculations of what colours you get for different droplet radii in rainbows and then project those rainbow coordinates onto the colour space.
So this is this plane across that colour cube and in which this is the red green axis and this is the blue yellow one. Turns out that the colours of the rainbow, when projected onto the three triple cone, captures form a spiral coordinate system and different rainbows cause different spirals. And indeed this conjecture, that's the space of all possible rainbows map or net colour space is more or less true. It's related to a coordinate system, which is a generalisation of the Polar Gordon system.
But no, actually the political system is only one extreme of a set of polar transformation, of conformal transformations of a of the Euclidean grids. Under each of these are the Z, and there are a whole set of orthogonal transformations which provide coordinate systems like this openness of which the rainbow is a sort of distorted rainbow, Cohen says, sort of distorted example.
So his third coordinate was was the different types of spectrum from the sun, so that the sun also can give different, different lights. And those are his three different colours of the rainbow, different clouds, different sunlight. So the third coordinate we had to do by calculating the absorption of light, by the sunlight, by the atmospheres, quite a lot of data on that.
And this is the this is the, the net of that spiral coordinate system for one rainbow taken through as the sun gets redder and the original illumination hits, it gets red. So here's the rainbow in colour space and his that linguistic the linguistic space it turns out that therefore this is this is one of the clues we've taken for a serious piece of experimental psychology on on how rainbows also span most of the important area of perceptual colour space. So we've. Created.
I hope you see the link between as a fundamental link between matter and light in this extraordinary man. He has a combinatorial three dimensional space of of colour. A theatre in which colour can be manipulated. And the very end of that colour, treatise says, leaves a fascinating point hanging, which will which will leave him.
He says, Look, if you don't believe what I'm saying, then you yourselves can do this by manipulating different kinds of light in darkness, materials of different kinds, and see if you can't make all the colours that there are. So with with that, we'll leave this tantalising idea that the beginnings of an experimental series of science might have begun right here in Oxford around 1320. Wouldn't that be a nice thought? Thanks very much.