M.C. Escher

Misha Glenny and guests discuss the work of Maurits Cornelis Escher (1898-1972), the graphic artist and printmaker best known for his impossible buildings, paradoxical perspectives, and repeating geometric patterns. Born in Leeuwarden and trained as a printmaker, Escher visited the Alhambra in Granada and found inspiration in the tessellating shapes of Islamic art. Through his career he went on to create some of the most famous images of the twentieth century and has been called a one-man art movement. After his work was exhibited in a 1954 conference, Escher’s work also caught the eye of mathematicians who appreciated his intuitive geometric precision. Escher was influenced by their work, and they were influenced by his – despite Escher never thinking he was actually very good at maths himself. With Marcus du Sautoy Simonyi Professor for the Public Understanding of Science, Professor of Mathematics and Fellow of New College, University of Oxford Sarah Hart Professor Emerita of Mathematics and Fellow of Birkbeck, University of London, and Fellow of Gresham College And Judith Kadee Exhibitions project manager and public programme curator at Hague Historical Museum Producer: Martha Owen Reading list: Marcus du Sautoy, Blueprints: How Mathematics Shapes Creativity (Fourth Estate, 2025) Marcus du Sautoy, Finding Moonshine: A Mathematician’s Journey Into Symmetry (Harper Perennial, 2009) Bruno Ernst, The Magic Mirror of M. C. Escher (Taschen, 2007) M. C. Escher, M. C. Escher: The Graphic Work (Taschen America Llc, 1992) Miranda Fellows, The Life and Works of Escher (Siena,1996) Frederico Giudiceandrea, Escher op reis or Escher’s Journey (Publisher Wbooks, 2018, in Dutch) Sarah Hart, Once Upon a Prime: The Wondrous Connections Between Mathematics and Literature (Flatiron Books, 2023) Douglas Hofstadter, Gödel, Escher, Bach: An Eternal Golden Braid (first published 1979; Basic Books, 1999) Siobhan Roberts, King of Infinite Space: Donald Coxeter, The Man Who Saved Geometry (Profile Books, 2007) Claudio Salsi, Paolo Branca and Claudio Bartocci (eds.), M. C. Escher. Tra arte e scienza. Catalogo della mostra (24 Ore Cultura, 2025, in Italian) Doris Schattschneider, “The Mathematical Side of M. C. Escher” (Notices of the American Mathematical Society, Vol. 57, 6, 2010) Doris Schattschneider, M. C. Escher: Visions of Symmetry (Thames and Hudson Ltd, 2004) Wouter van Reek, Nadir & Zenith in the World of Escher (Leopold, 2019) In Our Time is a BBC Studios production Spanning history, religion, culture, science and philosophy, In Our Time from BBC Radio 4 is essential listening for the intellectually curious. In each episode, host Misha Glenny and expert guests explore the characters, events and discoveries that have shaped our world.

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  This is In Our Time from BBC Radio 4, and this is one of more than a thousand episodes you can find in the In Our Time archive. A reading list for this edition can be found in the episode description wherever you're listening. I hope you enjoy the programme. Hello. Never-ending staircases, dizzying twists of perspectives and illusions that seem to defy the laws of physics. That's the world of the Dutch graphic artist and printmaker Maurits Cornelis Escher, known by us as MC Escher. Born in 1898, Escher was inspired by the geometric shapes of Islamic art and went on to create some of the most

• 3:08Speaker 04

  famous images of the 20th century. He's been called a one-man art movement. But Escher has also been celebrated by generations of mathematicians for his technical geometric precision, despite never actually thinking he was very good at maths himself. Well, with me to discuss MC Escher are Marcus du Sotoy, Simony Professor for the Public Understanding of Science, Professor of Mathematics and Fellow of New College, University of Oxford; Sarah Hart, Professor Emerita of Mathematics and Fellow of Birkbeck College, University of London, and Fellow of Gresham College; and Judith Kadee, Exhibitions Project Manager and Public Programme Curator at Haag Historical Museum.

• 3:54Speaker 04

  And I'll start with you, Judith Kadee. You've been curator of the Escher in the Palace Museum in the Haag. So tell us a bit about Escher. What was his early life like? And was he always interested in maths?

• 4:07Speaker 05

  Absolutely not. Escher grew up in the north of the Netherlands. That's where he was born, in Leewarde, and grew up in Arnhem, the region in the east. And what was special about Escher, I think he had quite a nice upbringing. His father had a very good job. He was one of the first hydraulic engineers to go to Japan. And he had a wealthy upbringing in that sense, loving family. But at the same time, he was also struggling sometimes a bit, because he was quite poor. As a as a kid, I had a lot of illnesses. And also, he was not good at maths. Especially, well, he was not a great student, to be honest. So he didn't pass his final exams, he didn't pass some courses, and he struggled.

• 4:50Speaker 05

  And I think that's something good and good to take away from this.

• 4:54Speaker 04

  So if he was struggling, did he end up studying anything? And if so, what?

• 5:00Speaker 05

  Well, at first he dabbled a bit in architecture. That's where his parents wanted him to go into, because that would give him a nice and proper job. But that didn't really work out. So he went to a school for both architecture and arts. And actually, he switched directions. So he got scouted by his teacher, Samuel Yeserunemaskita, who said, "You shouldn't be making buildings, you should be making prints." So he talked his parents into making Escher switch as a as a young man.

• 5:29Speaker 04

  And and what was his artwork like in this period in the nineteen twenties when he was studying?

• 5:34Speaker 05

  Hmm, I think it's fairly traditional, I would say. It was printmaking in the early twenties, so he was making still lifes, portraits, cityscapes, um, biblical studies also. And it was a few years for Escher just to figure out, how does printmaking work? How how does do you go about it? And what kind of subjects am I interested in? So it was interesting, it was, those were formative moments, but probably not the work that he would have become famous with nowadays.

• 6:03Speaker 04

  So, Sarah Hart, Escher travelled to Spain, and this was very formative for him. What did Escher see when he visited Alhambra, the famous Moorish palace in Granada? How did that inspire him?

• 6:18Speaker 06

  So he, yes, he travelled a lot in Italy and Spain, and in the twenties, he was perhaps more focused on making landscapes. But his visits to the Alhambra Palace gave him this profound love of symmetrical tiling patterns, which are typical of Moorish art. One of the reasons for that is that there's traditionally a prohibition against representing living things. So if you want something to decorate your walls with, a Beautiful geometric pattern is a good, a good option. So in the Alhambra Palace, there are these wonderful tile work patterns that just have beautiful symmetries, lots of different kinds of symmetries. And Escher was really inspired by these.

• 6:59Speaker 06

  And in fact, after spending a few days at the Alhambra, drawing designs, copying the pictures that he was seeing, his work really took a new direction in nineteen thirty six.

• 7:09Speaker 04

  And the Alhambra Palace was built largely in the fourteenth century. So did the creators of this extraordinary tessellation, this tiling, did they understand mathematics or do we think this is instinctive?

• 7:23Speaker 06

  They absolutely understood mathematics. They would create very precise diagrams using kind of, you know, geometrical tools, compasses, and you can construct things by circle constructions, hexagons, twelve sided figures, geometrically that, you know, within the limits of what can be produced in the real world are as perfect as they can be. And the only perhaps thing that cannot be done in that sense is that if you are trying to create a pattern that could go on forever, you know, you've only got the finite extent of the wall or the floor that you're making it on. So you can hint at infinity, but you can't say all of infinity in this picture.

• 8:00Speaker 04

  Now, as I said, this is called tessellation.

• 8:03Speaker 06

  Yeah.

• 8:03Speaker 04

  Can you, can you explain that concept in geometry?

• 8:06Speaker 06

  Yeah, so tessellation or tiling, imagine a tiled floor that's just, for example, got different colored squares, so black and white squares tiling a floor. Now, if you've got any sense, you're not going to want to leave gaps and you're not going to want the tiles to overlap each other. So a tiling mathematically is a pattern of shapes. And if we're talking about, you know, a plane, a flat plane, a pattern of shapes that will exactly fit together with no gaps, no overlaps, and could be extended, theoretically could be extended forever. So squares fit together just perfectly. They don't overlap, no gaps, and they could carry on forever. And that would be a square tiling.

• 8:47Speaker 04

  So we all know this from our, our bathroom floor.

• 8:50Speaker 06

  Exactly.

• 8:50Speaker 04

  What have we got apart from squares?

• 8:52Speaker 06

  Well, so if you boil it down to the basic possibilities, um, you can think of having one kind of tile which you then use throughout your design. Those tiles, and our favourite kinds of ones as mathematicians, are regular ones. So like a square, all the sides are the same length, all the angles are the same. Another example would be the regular hexagon that, that, you know, bees love to make their honeycombs out of. So it's got six sides and all the sides are the same length and all of the angles are the same, 120 degrees. Another example is an equilateral triangle. So those are regular polygons. They are shapes made of straight lines where all the angles and all the sides are equal.

• 9:33Speaker 06

  And you can't make these kind of tiling subtilations with every single possibility because the angles don't work. So you can take four squares and put them round a point because squares have an angle of 90 degrees and four 90s are 360, right? So it works. But if you try and do it with something like a pentagon, a regular pentagon, the angle there is 108 and 308s are less than 360 and four of them are more. And so you'd either get a gap or an overlap. So you cannot make one of these lovely regular tiling patterns with regular pentagons.

• 10:08Speaker 04

  Okay, so Marcus de Sotoy, what Sarah is hinting at there, if I understand it correctly, is that symmetry here is a key. What do we need to know about the mathematics of symmetry?

• 10:21Speaker 07

  Well, it's very interesting because, I mean, Sarah is right that the artists in the Al-Humbur were very mathematically adept, but what they didn't have was a language to understand what symmetry really is. And that only came at the beginning of the 19th century with a French mathematician, Everest Galois, who began to understand, you know, how do you articulate what's happening on these walls, the symmetry of these walls? And I think most people listening will probably think, oh, symmetry, that's about reflection or symmetry. And you certainly see that in the the square and the hexagon. But there are other sorts of symmetries as well, rotational symmetries. But what Galois got to was to think about these walls and what makes them symmetrical. It's about the

• 11:04Speaker 07

  way that you can move the tiles, if you lifted them up off the wall, move them around en bloc and then put them back down again and they would sit perfectly. Inside the outline that's been left there. So what you're looking for is what are all the different ways that I can move the tiles? Such that they sit back down again on top of each other. And those are the symmetries of the wall. Now, I think the artists in the Alhambra were exploring, well, what's possible with all of these different designs? You know, you can take a triangle, but you can put a lovely little wave on the side of the triangle and that destroys the reflections, but you can still rotate it. And you can really see the artists there just exploring what's possible, but what are the limitations?

• 11:46Speaker 07

  So I think Escher as well was quite excited by, maybe I can make some some new designs. But but then he gets a letter from his brother. Who says, you know what, there's actually a mathematics behind all of this. And he was a geologist and a crystalographer. And crystals are somewhere where you see a lot of symmetry. And he said, there's actually a limit to the number of possible symmetrical games you can play. And there are actually only seventeen underlying symmetrical games you can play. And he sent a paper with these to Escher and Escher began to understand, ah, okay. So did the artists in the Alhambra discover them all? Can I do different realizations of these seventeen?

• 12:28Speaker 07

  And it set him off on this kind of journey of the mix of mathematics and art.

• 12:32Speaker 04

  So Escher began to understand that mathematics was key to the structure of some, if not all of his art. Is that something that you can generalize? Is mathematics underlying most art that we see, whether visual art or or other types of art?

• 12:50Speaker 07

  I would say yes, because if I was going to define mathematics, I would say it's the study of structure. And for an artist, structure is absolutely crucial for their creativity, for their framing of what they're doing. And so I think that what's interesting, you see a huge dialogue across the centuries between mathematicians and artists. I mean, take the Renaissance and Leonardo, he absolutely captures the fusion of of mathematics and art. But I think that what's exciting is an artist seeing new mathematical structures and being inspired. Inspiration for new framing. So I think Escher, beginning with his kind of tiling, chose quite classic sort of symmetries.

• 13:32Speaker 07

  But when he saw the other, you know, possibilities with these seventeen different designs, he then, it pushed him in new directions to try out, oh, how can I realize this rather exotic kind of symmetries with my, my tiling. And so I think it became an inspiration for him to try new things. And for me, I think that's where you see a lot of artists being inspired by seeing what, what's in the mathematician's cabinet of wonders that I might be able to use to, to frame what I'm doing.

• 14:03Speaker 04

  But Judith, before we get to the mathematics of it, let's go back to nature. He, he lived in Italy for a while. But he leaves in nineteen thirty five. Why did he leave in nineteen thirty five? But also, what did he pick up in Italy? Why was Italy so important to him?

• 14:24Speaker 05

  Escher loved Italy. He lived in Rome for, for over a decade. He met his wife in Italy. He had two beautiful kids there. And he loved going, well, what we probably nowadays would call backpacking. So he would sometimes bring a donkey also on like this off the beaten track. And he made a lot of prints and photographs, drawings on those journeys. And with what he loved in Italy was you have the high mountains, the low valleys. There's perspective everywhere and there's contrasts everywhere, dark and light, high and low. And that ended up in his work too. So in nineteen thirty five, Escher decided to leave with his family because fascism was on the rise and he really didn't like that.

• 15:07Speaker 05

  And also, one of his kids had early signs of tuberculosis. So in that period of time, mountain air was, was very well recommended. So the, the family moved to Switzerland. But he missed it tremendously, Italy. And it, it sort of stuck with him for, for decades.

• 15:23Speaker 04

  And you can see that, can't you, in, in the buildings that he uses when he's creating those strange images of stairs ascending and descending and that sort of thing. There's still that Italianate sense.

• 15:37Speaker 05

  Absolutely. Yeah, sometimes it's in the background. So you see a mountain ridge that comes back to, I think, sometimes a prince thirty years later. But also indeed archways or particular kinds of roofs that are very, very recognizable from the Amalfi Coast. So it stays with him throughout his life.

• 15:56Speaker 04

  And nature as well is very important because for all of his sort of weird shapes and symmetries and so on, he's got a lot of animals there as well.

• 16:07Speaker 05

  Yeah, animals, but but just nature in general too. So he's always focused on trees and mountains and whatnot. And he would love to go on hikes also in the Netherlands too. So that's always a theme in his work as well.

• 16:18Speaker 04

  So Marcus, on that issue of nature, what sort of things was he exploring? How does that turn up in his work?

• 16:29Speaker 07

  Well, I think you see that we've got this connection between mathematics and art. And I think nature is the thing which binds them together because I think we're all responding to structures that we're seeing in the natural world. I mean, Sarah's already referred to the idea of the hexagon. Well, that's we recognize as the beehive. So so I think that this actually is a very important component of his work, that he's looking at these connections between artistic expression, the underlying mathematics. But actually, these are all structures that we're seeing in the natural world. But I think this, coming just back to his time in Italy and the Amalfi Coast, I think there's something really interesting about the move in his art, because you see it going from very three dimensional, you

• 17:13Speaker 07

  know, he does these lovely cascading villages down the side of cliffs. It's very three dimensional. Yet when he then goes, when he then goes to the Alhambra, which is very two dimensional, you really see this shift in his art. And there's a, there's a wonderful piece of art called metamorphosis, which he's almost expresses in that piece on the left hand side of the, the piece. It's quite a long sort of horizontal piece. You see the Amalfi Coast, but it gradually changes until you've just got these two dimensional. Kind of Chinese boy figures which are interlocked with each other. He's almost expressing in that piece, I'm moving from my three dimensional world into just working in two dimensions.

• 17:55Speaker 04

  Yes, it's kind of a narrative of his own artistic trajectory.

• 17:59Speaker 07

  Yes, it's very knowing in a way. It's kind of interesting.

• 18:02Speaker 04

  Extraordinary piece of work. Sarah Hart, you've told us about tiling and tessellation. I think I managed to grasp it. But he also dabbled in something called spherical geometry. Now, I want you to be gentle in explaining this because if the listeners are anything like me, we're beginning to stretch my understanding of mathematics, yeah.

• 18:24Speaker 06

  Yeah, so Escher actually himself, as has already been said, he did not think he was any good at mathematics. And I'm sure Marcus would agree and all mathematicians that that is only because it's a misunderstanding of what mathematics is. Because he was very good at pattern and he was very good at structure and he loved those things and was brilliant at working with them intuitively. That for me makes him a great mathematician. So it's not just all about equations and formulas. And what Escher was doing, you know, as Metamorphosis shows, and he said he was moving from landscapes to mindscapes, which is a lovely little phrase, is exploring what is possible in this kind of geometry. So his work where he was making tiling patterns that are on a flat surface, like, you know,

• 19:07Speaker 06

  the tiled floors or walls, there are some limitations, the seventeen collections of symmetries that Marcus mentioned. And at some point, he'd explored these at length and he was sort of thinking, well, what else might there be? And there's another kind of geometry that in fact is all around us and that is the geometry of the surface of a sphere. We all live on the surface of a sphere. And the geometry on a sphere is a bit different. Example, when you're going on a long haul flight and you go from A to B, you don't go in a straight line as marked on a map, you go in a curved path because that's the shortest path. So those shortest paths, geodesics, they're like the lines on a sphere. And if you use those lines to make shapes, you can get triangles whose angles add up to more than 180 degrees, for example.

• 19:52Speaker 06

  So if you have different rules of your geometry like we have on the sphere, then you can have different patterns and possibilities. And so Escher explored, for example, in 1942, he makes a spherical version of the angels and devils image.

• 20:06Speaker 06

  That he'd originally made on a plane. Now he makes it in three dimensions on a sphere. And there's a third version that we'll come to later in another kind of geometry. So he's exploring again what you can do if you change your situation.

• 20:19Speaker 07

  There's a wonderful example of that, which I've I've got to mention because it's one of my favourite examples, which is a chocolate box that Escher made. And it's an icosahedron, so it's a platonic solid. Anyone plays Dungeons and Dragons, it'll be one of the dice in your box. It's made out of 20 equilateral triangles, so it's almost spherical. It's trying to be spherical. But he made this on this tin box, which is celebrating the 75th anniversary of a chocolate manufacturer. He put these wonderful examples of starfish and shells. And it's just a beautiful. When I retire, I'm hoping that somebody is going to give me one of these little tin boxes. I think there were about 7,000 made, so they're out there.

• 21:03Speaker 07

  But it's just a thing of beauty, but a beautiful example of, oh yeah, what if I put these shells and starfish on a three dimensional shape?

• 21:12Speaker 04

  And Judith, can you tell us a bit about another famous spherical object? And that's the hand with reflecting sphere. Can you describe that to us? It really is one of the weirdest, most remarkable pieces of art I've ever seen.

• 21:27Speaker 05

  Yeah, it's a lithograph Escher made in 1935. We see Escher in the middle of the of the print and he's sitting in his apartment in Rome. So feels very lifelike, right? And you see him holding the sphere that he is reflecting in. And if you look at Escher's hand in the in the sphere itself, you see him holding it with his right hand. Still makes sense, right? And then you look at the hands below that's holding the sphere. That's his left hand. So it's already a mirror image of a mirror image. And then also there's another layer. This is a lithograph and a lithograph is a is a print. So it's always printed a mirror image anyway. So it's a mirror image of the mirror image of the mirror image. So it's one of my favourites to point out also.

• 22:12Speaker 04

  But also I gather very accurate in terms of the scale. Tale of the object in the in the sphere.

• 22:18Speaker 05

  Absolutely. When I just started working at Escher in the Palace as a curator, we got an email of someone who rebuilt Escher's apartment and they said it was completely accurate. Only the table on the right, it was tailored just a little bit to fit the image, but everything else was perfectly fine.

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• 25:57Speaker 04

  So, most of Escher's work wasn't these kind of 3D objects. What kind of techniques and mediums was Escher using at this time?

• 26:06Speaker 05

  So, Escher was mostly a printmaker. So, always two-dimensional, so on paper. And I like that, Marcus, that you just mentioned sort of this mixture of 3D and 2D because Escher loved playing with, making something like a piece of paper, just a two or a three-dimensional image also. And Escher was really a craftsman. So, he loved the woodcut, he loves lithographs, and especially the woodcut, I always enjoy explaining because it's so difficult and technical. Escher would have a block of wood, he would... Uh draw an image on it and he would gouge the whole block of wood. So he would cut the image out and then he would put some ink over the top layer. Only the top layer

• 26:47Speaker 05

  would end up on a piece of paper. And it it was a procedure that could last days, if not months, for his bigger works like Metamorphosis II. That took him five months to make, uh all the twenty different wood blocks. And it's also an unforgiving material, wood. So if you cut a little bit too much out, you can't get it back. So uh that was really a struggle. But he really enjoyed that. And there was also a lithograph of which I gave the example of hand with reflecting sphere, which is more like a drawing. So it's a drawing on a a lithographic stone and with a chemical procedure, it's uh put on paper as well. Uh and it's really Escher loved the printmaking and he loved the craft of it. And sometimes

• 27:29Speaker 05

  indeed he dabbled and he made a very interesting chocolate tin uh or some or something like a tiling pattern, but his basis was really on paper.

• 27:39Speaker 04

  Sarah, can you tell us why nineteen fifty four was a turning point for Escher? Because he's he's well into his fifties now. He's he's established to a degree, but he he hasn't reached anything like the fame that that he has now. So what happens in nineteen fifty four?

• 27:56Speaker 06

  Well, there was a big mathematics conference in Amsterdam in nineteen fifty four.

• 28:01Speaker 04

  This is the International Congress of Mathematics, which is held every four years and and still is, as I understand.

• 28:07Speaker 06

  Yes, every four years. And it's at that conference that the Fields Medal is awarded. Uh so, you know, everybody who's everybody, anybody in mathematics comes along to this conference. And it's kind of a jamboree. You all get together. Thousands of people are there. To go along with this, there are often cultural activities. And that year, the organizers thought, well, we've got this local artist, Escher, who's, you know, mathematicians seem to like his stuff. So why don't we do an exhibition of his work? So many people, many mathematicians come from all around the world, heard of his work and saw it for the first time. And you get people like Coxeter, Donald Coxeter, another mathematician, um we might talk about more presently, but but he made connections in the mathematical world and word spread.

• 28:52Speaker 06

  And so he becomes this this figure and he talks with mathematicians and they have these conversations and back and forth, which is a lovely thing to see. It's not just one-sided. He's not just learning from them, they're learning from him too. And it all starts in nineteen fifty four.

• 29:06Speaker 04

  And so he's corresponding with these mathematicians.

• 29:09Speaker 06

  Yeah, so for me, I think favorite relationship that he has with a mathematician is the conversation with Donald Coxeter that goes on for many years. Because Donald Coxeter is a, I guess, is it fair to say is the best geometry of the 20th century? We can argue about.

• 29:27Speaker 07

  I'm not sure, yeah.

• 29:30Speaker 06

  You're on the spot there.

• 29:31Speaker 07

  Geometry warfare.

• 29:32Speaker 04

  Got it, I'm gonna hold the ring here. I have no dog in this particular fight.

• 29:39Speaker 06

  But yeah, so Donald Coxeter was.

• 29:42Speaker 04

  One of the best geometrists of the 20th century.

• 29:44Speaker 06

  One of the best geometrists of the 20th century. And he was absolutely fascinated by symmetry and a lot of his work is on symmetry. And he bought actually a couple of Escher's prints in this 1954 exhibition. His wife was Dutch, so could talk with Escher in his own language. And a couple of years afterwards, after 1954 exhibition, Coxeter was writing a mathematical paper about symmetry. And he wanted a couple of illustrations. He wrote to Escher to say, please may I use two of your tiling designs as illustrations of symmetry in this paper? So Escher says, yes, very nice, very flattered. Start of 1958, Coxeter sends the finished paper to Escher, just as, you know, thank you very much, here's the paper.

• 30:29Speaker 06

  And Escher has a flick through it, he's not really understanding much of the mathematics, but he sees this amazing picture. And it's a tiling that Escher has never seen before, which is drawn within a circle. And it's got triangles that tile together, but they they get smaller and smaller as they get closer to the edge of the circle. And because of that, it means you could fit kind of infinite design within this circle on one piece of paper, but it's a tiling Escher's never seen. So he gets super excited by this, he writes to Coxeter and says, tell me all about this. And they had this conversation. And as a result, Escher produces many beautiful works, including his famous Circle Limit series.

• 31:10Speaker 04

  Marcus Soto, we've, we've already heard about Euclidean geometry, spherical geometry. Now there's-

• 31:18Speaker 07

  Brace yourself.

• 31:19Speaker 04

  Yes, exactly. Hyperbolic geometry as well. Explain, explain, you know, in ten easy sentences, explain what that is and-

• 31:28Speaker 07

  Yeah, well, these were discoveries of new geometries in the 19th century where strange things happen that don't happen in Euclidean geometry. We've already heard from Sarah about triangles on, on spheres whose angles add up to more than 180. But these hyperbolic geometries, which are a bit like, if you think of a Pringle crisp, for example, it curves up one way and down the other. Or if you've gone to the Olympic Park in London and seen Zaha Hadid's, the aquatic centre, that's another example of a kind of curved geometry which curves up one way and down the other. And if you draw triangles on the sides of these shapes, the angles add up to less than 180.

• 32:11Speaker 07

  So, so these are what we call negatively curved, in contrast to the sphere which is positively curved. So very often these geometries are kind of infinite and we think maybe our universe is perhaps an example of hyperbolic geometry. But what was beautiful was this picture that Escher saw is a realisation of this geometry that Poincaré, a mathematician, French mathematician, came up with, which is actually, you can capture this infinite geometry within the confines of just a circle. And Sarah already hinted at the idea that triangles kind of get smaller and smaller to the edge of this circle. Actually, what happens if you take a ruler and you move it

• 32:53Speaker 07

  towards the, the edge, the ruler gets shorter and shorter and shorter and shorter. Not if you're in the geometry, it's still a metre-length ruler. But if you're outside the geometry, you see that you can fit actually infinitely many metre rulers. They're just getting smaller and smaller and smaller and they never quite reach the edge. So for Escher, and you know, the, the artist in the Alhambra would have just been blown away by this because they're all excited by the way that Thailand- Can capture infinity, yet suddenly he's got infinity captured in a finite circle. And that just sends him on these just wonderful images that he makes with angels and devils being, instead of just triangles, being tiled to the edges. And he knows, you know, how far can he go?

• 33:36Speaker 07

  I mean, that's a real kind of challenge, but he wants to try and fit as many in as possible to to give that illusion.

• 33:43Speaker 04

  I think I understand what you're getting at. But let me ask you, Dikantay, relativity is probably one of the most famous of Asher's images. Can you describe it for us and why it's so special?

• 34:00Speaker 05

  Yes, relativity is one of those impossible buildings that you can't really get your mind around. What you see on the image, it's an impossible building with a lot of staircases. And at first glance, it seems okay, you know, can exist. We see some doors, some archways, seems fitting. And then all of a sudden, the penny drops. There is no gravity in this print.

• 34:22Speaker 07

  Or it doesn't drop.

• 34:25Speaker 07

  That's very good, yeah, I like that.

• 34:27Speaker 05

  That is a very.

• 34:28Speaker 07

  Or it drops in three different ways.

• 34:31Speaker 05

  Yeah, exactly. If you turn the turn the print around also, it really doesn't go anywhere, to be honest. No, it's a really, it's a really funny print in that sense because people are walking in that print and living in that print like nothing is going on, nothing is happening. That's a very normal reality to them. People are going on a romantic walk, they're reading a book and just walking the staircase sideways as if that's just a normal reality. And I think a lot of people really love this image and it's everywhere in popular culture. From like Squint Game, the Netflix series to Harry Potter. I think it took inspiration from those staircases, so it's still a very well loved print.

• 35:11Speaker 04

  And also the people he has in relativity and in other prints as well. They're kind of weirdly robotic, human, they're odd.

• 35:22Speaker 05

  Yeah.

• 35:24Speaker 04

  What are they? Who are they?

• 35:26Speaker 05

  Well, I quite like that about those prints, actually. I think sometimes it was a bit of a cheat code for Escher too, because he struggled with human anatomy sometimes. But I think Escher liked them to be anonymous, not to have very clear facial expressions. They are just cohabiting in this space that he created, and that is just very normal. And sometimes he has someone that is maybe looking towards something that he created. So for instance, in relativity, you see someone looking over the ledge and just, but he's just casually looking, you know, it's just, it's just another day at the office.

• 36:05Speaker 04

  Marcus, relativity also caught the eye of Roger Penrose. What happened with that?

• 36:13Speaker 07

  Yes, Roger, a colleague of mine in Oxford, I mean, he was just a student at that time, went to the International Congress and, I mean, he saw a cattle and he was just like, what is that going on there? And he suddenly sees these kind of paradoxical worlds and it's what inspires him to create other versions of these kind of visual paradoxes. And he comes up with this impossible triangle, which is a, it looks like you should be able to build it. He draws it on a piece of paper. It seems to have kind of joins at right angles, but if you follow the whole thing around, you know, locally it makes sense in little parts, but globally, it just, you can't build it. And, and it sent Penrose off on this kind of idea of just creating

• 36:57Speaker 07

  these kind of weird things that sort of you can draw in two dimensions, but could never exist in three dimensions. He sends this to Escher and there starts to be a really good conversation going between them. And Escher thinks, oh, that's really beautiful, but it's, it's kind of rather abstract and mathematical. And he creates out of that the idea of the ascending, descending staircase, which I think is another of the images which is very famous of Escher's, which is this staircase, which seems to be climbing up and up and up. And there are people walking up. They look a bit like monks. I'm not sure whether they are monks, but, but then you look and you see, well, actually, but the staircase comes back around to the beginning again, but they've been going up all the time. So shouldn't they be on the floor above? And, and they're not. And there are some people

• 37:42Speaker 07

  going down. They're descending. And so using this illusion, you can create this incredible prints where it seems to be the staircase is ascending, but it never gets anywhere.

• 37:53Speaker 04

  Sarah, one of the extraordinary things about this, I mean, you've talked about his relationship with Coxeter, and Marcus has talked about his relationship with Roger Penrose, and yet he didn't really have the language of mathematics. So how did this artist and these mathematicians communicate with each other? Was it entirely visual?

• 38:16Speaker 06

  It was heavily visual, I will say. And there's another mathematician he corresponded with called Polya, who was one of the first people to classify these seventeen symmetry groups. And yes, Escher absolutely was all about the diagrams, and he would try and work out how things were put together using his intuitive geometry, you know, geometrical constructions with compass and straight edge. He always said, I don't understand equations, I don't understand formulas, and therefore thought he wasn't a mathematician. Of course, I disagree with him. But yeah, he would ask and have communications with these mathematicians. Sometimes they would tell him the equations, but he wouldn't really pay attention, but

• 38:57Speaker 06

  he loved the pictures. So he had a picture that came from a paper by Polya with each of these seventeen patterns. And I think what the glorious thing is, you know, as Marcus has hinted to already, that, you know, what Escher is doing, he's taking the mathematical idea, the bare bones of a structure, and then he is adding his artistic interpretation to it, you know, and you take a symmetry design that Polya has sketched, which has, I don't know, parallelograms or something, and then Escher creates from it this amazing design with lizards crawling around a piece of paper that's just charming and beautiful, but still incredibly symmetrical. And he does this with the inspiration he gets from Penrose, he does it with the inspiration from Coxeter. You know, Coxeter's picture

• 39:41Speaker 06

  just has black and white triangles, but then Escher's got fish swimming along beautiful arc lines in hyperbolic space.

• 39:48Speaker 04

  And Judith, he was, seems to have this very...

• 39:53Speaker 04

  Warm and intense relationship with mathematicians, but he didn't have that relationship with everyone. Can you tell us the story about Mick Jagger and M C Escher?

• 40:03Speaker 05

  Yes, Mick Jagger. Well, Mick Jagger wanted to use one of Escher's images, Färben from the Second World War, and he wanted to use that image on one of his LPs for The Rolling Stones. So you will kind of think, okay, that's quite an honour, right? Not for Escher. We didn't really like that popular kind of music. And he received a letter saying, Dear Maurits, can we please use one of these images? And Escher thought it was an inappropriate question to ask that way. So he didn't allow The Rolling Stones for the image to be used.

• 40:33Speaker 04

  And he didn't like having his first name, is that right?

• 40:36Speaker 05

  Exactly. It was Dear Mr. Escher to him, so.

• 40:39Speaker 07

  That's brilliant. Yeah.

• 40:43Speaker 04

  Okay, and now we're moving on to the really weird bit, Marcus, and that is strange loops and consciousness.

• 40:50Speaker 07

  Yes.

• 40:51Speaker 04

  How does Escher come into the picture of strange loops and consciousness?

• 40:55Speaker 07

  Well, people might know of a very sort of iconic book called Gödel, Escher, Bach by Douglas Hofstadter. This is a book actually about consciousness. And people probably know who Bach is. And interestingly, Escher loved listening to Bach when he did his work. So already a connection there. But Gödel is the mathematician here, a logician who proves a theorem about the limitations of what mathematics can prove. But the point is, he uses self-reference to make that proof. And Hofstadter got very excited by the idea of mathematics being able to talk about itself. And he coined this phrase, a strange loop, something that somehow is a hierarchy. When you get to the top of the hierarchy, you're actually got

• 41:38Speaker 07

  back to the beginning again. And he wrote this book, which is about Gödel and consciousness. And his dad said, oh, but you've not got any pictures. And so he suddenly thought, oh, yeah, what's a good picture of a strange loop? And he knew about Escher's work. And Escher's paradoxical images are wonderful examples of strange loops. We've already heard the staircase, which you don't quite know, you think you're ascending and then you come back to the beginning. But I think the one. Image for me, which really captures the idea of a strange loop, is the hand drawing the hand drawing the hand. There are two images of hands and you you look and one seems to be drawing the other, but then you look and it's actually drawing the first one. So this is a very good example of a strange loop where you don't know where the bottom

• 42:22Speaker 07

  and the top of the hierarchy is. It sort of goes around in a circle. And Hofstadter thought that this is what the brain does. This is how we achieve consciousness, that we are able to think about our thoughts. It seems to be a great example of self-reference. So Hofstadter thought, all right, this idea of mathematics being able to talk about itself might be the right language to understand how consciousness works. And the illustrations of that were these wonderful pictures of Escher.

• 42:55Speaker 04

  So I think Marcus has gone some way, Sarah, to explain why mathematicians like Escher so much. What do you think? Like, he still remains incredibly popular amongst scientists and mathematicians. Why is that, more so than any other artist, I'd say?

• 43:12Speaker 06

  So I think there are there's a couple of reasons. One is, it's so great when, you know, you have an artist that has this interaction with mathematicians and we all we all love those stories. And in fact, when Escher was creating these beautiful circle limit pictures, he used to say, I'm just going to do some coxetering now, which is maybe the only the only verbing of a mathematician's name in the service of art that I know of. So we love that, talking to artists. And we believe mathematicians that what we do is itself a creative art. We have some of the same motivations, making and exploring beautiful things and ideas. It might be more abstract than some concrete kinds of art, but it's it's all the pursuit of the same kind of thing. And our love and joy in structure and pattern.

• 43:57Speaker 06

  Shared by, actually, I think, all human beings. We all love patterns and structures. That's why we like the music of Bach and we like beautiful tilings in our homes. You know, it's not just Escher. We all have tiled patterns probably somewhere in our homes. You know, but we are perhaps mathematicians maybe more acutely aware of seeing these patterns and structures everywhere around us. And so we identify with Escher and, you know, his aesthetic joys are the same as ours.

• 44:25Speaker 04

  But Judith, is there a danger here that he's so engaged with structures and patterns that he's missing the emotional aspect of art? Because when you see an Escher, you don't immediately think, oh my god, that's beautiful. You think that's fascinating. What about that emotional impact? Is it there?

• 44:45Speaker 05

  Well, does it need to be emotional? I think that's also a question that Escher would ask himself too. I think Escher is portrayed as more rational. He has sort of a scientific approach to art that is maybe different from a lot of other artists. But he has something special in that, in my opinion, too. What I saw a lot in Escher in the palace is that people would just come and look at Escher's art with grandparents and their grandkids, people on their first dates, and they just look together and they talk about it. They tell you what they're seeing. And in that sense, they don't feel burdened by, oh, I need to have our historical background to understand it. I need to have read up on Escher. And I think that's actually a strength rather than a weakness.

• 45:27Speaker 04

  And why is it that he was so averse to being categorised?

• 45:34Speaker 05

  Well, I think he saw himself firstly as a printmaker and his craft was the most important and his ideas kind of came second to a degree. And I think he just didn't want to be in this box of, oh, I'm a part of this movement. He just did whatever he wanted to do. That's how he would phrase it himself.

• 45:53Speaker 04

  Sarah, you wanted to come in there.

• 45:54Speaker 06

  Well, yeah, you asked about why isn't there the emotion that's generated? And for me, there is an emotion that's generated and it's joy. Because it's the experience of the sublime that you get if you're listening to, you know, a beautiful piece of music by Mozart. It's just, this is exactly perfect. This is how. This is how nature is, this is how the world is, it's lovely perfection. And you look at an Escher picture and it's just absolutely brilliant, perfectly there. And that makes me very happy. So I think that's a valid emotion to feel when you're looking at art.

• 46:26Speaker 04

  Final question for all of you. What's his legacy today? Where do we see Escher?

• 46:32Speaker 07

  I think this idea that he didn't want to be put in a box is really important because I think we silo our subjects so much. And Escher is a beautiful example of the bridges that you can create between the sciences, mathematics, nature, art, music. I feel that's his legacy. He brought together subjects that traditionally have been seen to be very separate.

• 46:53Speaker 04

  Anyone else on Escher's legacy, the import?

• 46:56Speaker 05

  Well, I think his visual language is so recognisable and still decades later. So I think it will stay with us for many centuries to come. It's the black and white, it's the impossible staircases, it's the mathematics that are underlying his works. It's one of a kinds.

• 47:13Speaker 04

  Sarah?

• 47:14Speaker 06

  I think there are so many iconic images that are still pervasive in our culture decades and decades after he died. And they are going to stay with us. So Escher will always be a part of our legacy, I think.

• 47:26Speaker 04

  My thanks to Marcus Dusotoi, Sarah Hart and Judith Kadee. Next week, how a million and a half people from India were transported to sugar plantations from 1834 onwards to replace enslaved labourers. That's Indian indentured labour. Thank you for listening.

• 47:45Speaker 01

  And the In Our Time podcast gets some extra time now with a few minutes of bonus material from Misha and his guests.

• 47:52Speaker 04

  What did we miss out?

• 47:55Speaker 07

  There was one thing I was hoping to slip in, which is

• 47:59Speaker 04

  Now's your chance.

• 48:00Speaker 07

  Yeah, exactly. Which is, you know, very often it feels like a one-way traffic that mathematics inspiring artists. But what's so exciting is seeing when an artist asks a new question which stimulates mathematics in a new way. So, and Escher does this because he's absolutely fascinated in colour, not just the shapes, but the colours the shapes have. And he's asking, well, what if you want to preserve the color? So, you know, a black tile has to go to a black tile. And this question actually mathematicians hadn't thought about. I mean, I said there were seventeen different symmetrical games you can play with with no color. But if you introduce color, then there's a new theorem which gets proved, kind of inspired by Escher, which is there are, I think, sixty three

• 48:45Speaker 07

  symmetries if you're actually trying to preserve color as well. So so I think that's a beautiful example of it isn't one way traffic. The the artist can ask a new question, which are the mathematicians? I'd never thought of putting color on these things and keeping that invariant.

• 49:00Speaker 04

  Um, Sarah, is there anything that you'd like to highlight that we missed out?

• 49:04Speaker 06

  Well, I think there's a really curious little story about circle limit three, which is a one of these circle pictures which is drawn. It's kind of like a map of hyperbolic space. So if we drew a map of the world, we know that we're going to distort some things. And that's exactly what happens with this hyperbolic representation. It's a map, and so some things look distorted. But if we had our hyperbolic glasses on, everything would be fine. But Escher produces this picture, and it it looks like what you see in the image is a kind of fish swimming along along these curved white lines. There are arcs of circles. And it's beautiful design, very, very intricate, took months to make. And he complained to his son, George, about this, like, it's, oh, you've got these five different

• 49:49Speaker 06

  bits of wood, and they've got four different colors and all of this. It's a nightmare to make. But when Coxeter saw this picture, he saw these kind of lines that the fish were swimming along, these circle arcs, and he thought that Escher had got something wrong about the geometry, because there's a rule about the way that these lines have to behave in in the hyperbolic world, which they have to meet the edge of the circle at right angles. And these white lines don't do that. It's more like eighty degrees. So he kind of thought, artistic license, something's fine. Then it turned out, no, these particular lines, they're not kind of straight lines in the hyperbolic world, but they're, they're lines that are equidistant from each other.

• 50:31Speaker 06

  So it's a slightly different equation, but Escher had nailed it intuitively. He'd managed to make this, and what it does is it creates within the hyperbolic pattern, it sort of gives you the illusion of a Euclidean one. So it's this really clever way of kind of having a Euclidean thing happening inside this weird hyperbolic world that Coxeter said gave him an entirely new understanding of this kind of geometry. And he wrote several mathematical papers about Escher's work. And so it's just, it's such a marvelous thing that his first look at it thought, oh, well, it's just, he's, he hasn't quite got that right. And then he realised, no, he's got it, he's got it totally right, but it's, he's doing something different than I thought.

• 51:14Speaker 04

  Marcus, now, this is fascinating, the Murbius strip. I want you to tell us about the Murbius strip, exactly, Escher, the ants. Perhaps Judith, you can describe the ants first of all, and then Marcus, I want you to tell your amazing story about the Bach-Murbius strip, which just left me completely, it blew my mind. Judith, tell us about his Murbius strip phase.

• 51:41Speaker 05

  Yes, well, the Murbius strip, or there's one print that he's quite famous for, and the Murbius strip is such a simple mathematical concept. Even I, as a humanities student, can kind of grasp it, I feel. And it's just one sheet of paper that is turned, or it's twisted and is put together. So it creates this endless loop. And Escher made a very simple print with that, in which he has ants walking alongside them, both on the inside and on the outside, and on the inside, on the outside.

• 52:10Speaker 07

  In fact, there is no inside and outside. That's the extraordinary thing about... It's quite a good example of one of these strange loops, actually, because you think there's an outside and an inside, but when you go around it, you realise that if you tried to colour it, this shape, you know, if you didn't do the twist, you could have a red on the outside and blue on the inside, but if you tried to do it with a Mürbür strip, the red would go back and you'd find you'd covered the whole shape. So it's actually only got one side to it, which is, if you tried to cut it in half around the actual loop, it would not fall into two pieces, but would be just one, you know, your listeners have got to try this, because it's just such, it blew my mind when I first saw it. But yeah, as you say, okay, it's a physical thing, but how does it come up in music?

• 52:55Speaker 04

  And because Escher was so fond of Bach and you can see that, you can feel the connections between Escher and Bach. Tell us about the...

• 53:04Speaker 07

  This is a great example, again, of artists being drawn to structures that they don't even know are pieces of mathematics. And actually, the Mürbür strip hadn't even been discovered yet. Bach had already realised it in musical form. So he used to like to create these kind of puzzle canons. So he'd write just a single line of music and then there'd be kind of code. So you'd understand, okay, that's, the right hand is playing that piece of music, but the left hand is going to do something different. It's based on that little bit seed that he's written, but the kind of symbols around it say, I'm going to do something, maybe I'm going to start a little bit later, like a canon. So this, it's actually these puzzle canons that were discovered quite recently

• 53:45Speaker 07

  that were written after the Goldberg variations. And one of these canons, if you realise it, actually what Bach is asking you to do is to take this little seed, put it on a Mürbür strip, a transparent one, and basically you play with one hand going round the Mürbür strip, but on the other side, and everything's reversed because you're seeing it through transparent. And so...

• 54:09Speaker 04

  So the two melodies are going forwards and backwards, but they are perfectly aligned.

• 54:15Speaker 07

  And they're captured by the music on this Mürbür strip. Now, Bach didn't know that, but you know, we realise that what he was asking the pianist to do is actually realised by this kind of rather extraordinary geometry.

• 54:29Speaker 04

  So where do we go with Escher now? If you look at Al Hambler from the 14th century, and you don't get that much tessellation, tiling in art, until Escher comes along. Is he now part of every artist's education? Do you have to know about Escher if you want to be a serious artist?

• 54:55Speaker 07

  Well, I think most serious artists are really snobby about Escher.

• 54:58Speaker 05

  Exactly.

• 54:59Speaker 07

  I think, you know, the control and the predictability of Escher for some artists is actually too controlling and somehow the unexpected is not there. And that's somehow often disappointing for, I think, an artist. And you know, actually, you know, Bach loved pattern, but he loved disrupting patterns. So the Goldberg variations is a perfect example. There's so much structure until you get to the last variation, which is a quadrille bit, a musical joke, has nothing to do with anything before. But then you suddenly appreciate the structure because when it's broken. So and Escher, I'm not sure he break, he likes things, as Sarah said, the perfection is part of the charm. But sometimes it's too perfect and therefore

• 55:42Speaker 07

  doesn't perhaps connect with the messy side of our emotional world.

• 55:46Speaker 05

  I think the issue is in art history, Escher has been kind of avoided. When I started working for Escher in the Palace, I came from a museum about Piet Mondrian, the modern artist. And it's a very emotional painter to a lot of people. And I said, oh, I'm going to work with Escher. And people were like, OK, lovely. And they didn't get it. And maybe also myself, when I started, I was just curious to be surprised. And I was also a bit scared maybe about the mathematical or the scientific side of Escher. And I think that there are so many layers to Escher that is a bit unfortunate that it's just sort of pushed away from the mainstream art historical perspective. But also, I think, when you look at Escher exhibitions,

• 56:29Speaker 05

  they're always unbelievably successful.

• 56:32Speaker 07

  Yeah.

• 56:32Speaker 05

  So it shows how popular Escher is, but maybe not with a typical art historical group of people. But, you know, maybe we can sway them a bit more.

• 56:41Speaker 04

  Sarah, you've written a book about mathematics and Moby Dick. Um. Going on beyond Escher into other areas of art.

• 56:50Speaker 06

  Yes.

• 56:51Speaker 04

  What is it about mathematics and literature where, you know, I can see the relationship with music, but the relationship with literature, explain to me why you think maths and literature live together and.

• 57:04Speaker 06

  Yes.

• 57:04Speaker 04

  So. React together.

• 57:05Speaker 06

  So, um, the book is about the connections between mathematics and literature and really one of those connections is structure and pattern because that's present in all our forms of creative expression. Poetry, for example, there has, it's full of patterns and understanding those and exploring them is fascinating, but also it provides more structures for writers to work with and use. So if you understand the patterns of poetry, maybe you write different kinds of poetry. So poetry, but also novels. Um, one of my favourites is The Luminaries, has this wonderful mathematical pattern inside it. But then there's writers who use mathematical ideas in their work. So Herman Melville is one of them. Loads of mathematical ideas in Moby Dick. So this sort of symbolism comes into writing

• 57:50Speaker 06

  numbers in fairy tales. It's all pervades literature. And then, of course, you get the stories that involve mathematicians themselves, like Moriarty. Sherlock Holmes is, you know, is a mathematician. So, yeah.

• 58:05Speaker 04

  But as the author of six non-fiction books, I'm not necessarily engaged with mathematics in any way.

• 58:10Speaker 06

  You are, you are. Here's why, here's why, right? Here's why. It's all geometry, right? Okay. When you write anything, you will have letters that make up words, that make up sentences and paragraphs and chapters and volumes. And in geometry, you have points that make lines, that make planes, that make spaces. So there's this hierarchy of dimensions, which is exactly like what's happening in literature. And at every stage, you have a choice about, do I divide my book into chapters? How am I going to shape my paragraphs? How are my sentences fitting together? Mix of long and short words in a sentence, mix of long and short sentences, and those kinds of decisions. That is you doing mathematics without knowing it.

• 58:55Speaker 04

  Right. So basically it's two different languages, but they're both performing the same function.

• 59:01Speaker 06

  Yeah, yeah.

• 59:02Speaker 04

  And they're translatable, presumably at some, at some level.

• 59:05Speaker 06

  Yes, exactly. And, and even there's, there's another kind of link, which is. If you are writing something down, describing something about the world, fiction or non-fiction, you are simplifying to get at the greater truths.

• 59:17Speaker 04

  Tell me about it.

• 59:17Speaker 06

  Right, so that's exactly what mathematics does. Like, there's no such thing in the real world as a truly perfect circle. But by simplifying and saying, this is a circle, constant radius, so on, you can get at truths that tell you something about the world in the same way that a piece of factual writing can get at deeper truths by leaving out unimportant details. So it's, again, it's the sort of same methodology in mathematics and in writing that we're trying to uncover the truth.

• 59:42Speaker 04

  Well, just as I would recommend anyone to go to an M C Escher exhibition, I would also say that if listeners are anywhere near Alhambra in Granada in Spain, not to be missed, an absolutely magical experience. So, thank you very much, and here comes Martha.

• 1:00:02Speaker 06

  Tea, coffee.

• 1:00:03Speaker 04

  Yay, tea.

• 1:00:04Speaker 06

  Pecan tea.

• 1:00:05Speaker 04

  Tea, please.

• 1:00:06Speaker 07

  Can I have a peppermint tea, please?

• 1:00:07Speaker 06

  Tea, tea, peppermint tea, coffee.

• 1:00:09Speaker 04

  In Our Time with Misha Glenny was produced by Martha Owen. It's a BBC Studios production for Radio 4. The Moral Maze on BBC Radio 4.

• 1:00:19Speaker 05

  I've never been more concerned about the future of humanity than I am now.

• 1:00:23Speaker 04

  Examining one of the week's main news stories through an ethical lens.

• 1:00:27Speaker 05

  If we don't do something, millions will die, billions will die. That's the state of play here.

• 1:00:33Speaker 04

  Sometimes combative, sometimes provocative, always engaging. I'd like to go one level deeper and talk about your fundamental moral commitment. Do you have any?

• 1:00:45Speaker 04

  The new series of The Moral Maze with me, Michael Burke, from BBC Radio 4. Listen now on BBC Sounds.

• 1:00:56Speaker 04

  Sometimes we all need an extra helping hand, especially with a tricky business problem you've been putting off. Claude is the AI. For just that, it's the collaborator that understands your entire workflow and thinks with you, not for you. And Claude isn't just for quick questions. Hand it a whole task, like turning a folder of scattered notes into a report, and it does the work and hands back something finished that you can open and edit. Claude can now draft a doc or deck right in front of you, and Claude Design now lives right inside Claude. Describe the website or prototype you're picturing, attach your design system, and it comes back in your own design language, ready to edit right on the canvas. It works with your files and the tools you already use, like Gmail and Slack.

• 1:01:41Speaker 04

  And whether you're debugging code at midnight, building a financial model, or strategizing your next business move, Claude extends your thinking to tackle the problems that matter. For problems worth solving, get started with Claude at claude.ai/solve. That's claude.ai/solve. And check out Claude Pro, which includes access to all of the features mentioned in today's episode. claude.ai/solve.