When you're school, we often get asked to make a choice.
Is it Shakespeare or the second law of thermodynamics or DNA rulings?
Or relativity? Or you all? Or only science?
When I was at school, I was deeply frustrated being asked to make such a choice when I was in school.
I started learning the trumpet and I really enjoyed doing that orchestra as I sang
in the choir here in Los Angeles to come up to Boyd employees to do concerts.
I didn't go to theatre, enjoyed doing theatre at school, and so I really enjoyed the artistic side.
But around the same time as I was starting to learn the trumpet, that was amazing.
I also fell in love with the world of science.
I loved the idea of mathematics being this amazing language, destroying the world around us, where we come from, where we need to go next.
The world of science was very exciting and I find it very difficult to decide which route to go.
And I got frustrated by this kind of request that I should make some sort of choice.
Now, I said I was waiting for my malkani tables and my sales and my trumpet, so I chose the mathematical reasons.
And so here I am, a professor of mathematics at university offices.
But I've always kept the contact with the artistic world.
And, and actually as time has gone on I realised is really this is a false dichotomy,
but actually there's much more in common between the two disciplines of art and science.
And in a way, I think mathematics forms a sort of bridge between the two.
So what I want to do in this lecture is to explore some of my favourite artists and some of the things that they love creating.
And I want to show you that actually the structures that they are drawn to
are often very similar to the structures and I'm fascinated in a soft tissue.
So I called my answers on caves and actually secrets, mathematicians and those.
In a sense, I think they're doing mathematics in disguise.
So my name starts with one of the arts, which traditionally has a big connection with mathematics, and that's the arts of music.
I think a lot of people have thought about connections between music and mathematics,
and probably here in the department we probably could gather an orchestra from the professor's because there seems
to be such an idea that trumpets that there are other instruments here that we could have in our orchestra.
But as the secret mathematician I Chazen from the World of Music is actually a 20th century composer and one of my favourite composers.
Olivier Messiaen and Olivier Messiaen was obsessed in mathematics and put a lot of mathematical structures in science.
He's use sometimes consciously, but at other times actually subconsciously.
That that's one of my favourite pieces of the late game ideas.
He very deliberately uses Mass to create a very interesting effect.
It's called the cortex at the end of time. It was a piece that he wrote swans.
He was a prisoner of war during the Second World War and in a prisoner of war camp there he made pianos a rickety upright piano.
There was a violinist, Vanessa Specialist in the camp as well.
And so each composer's quartette for but the form it was at a very desperate time.
And so the piece really captures a sense of unease.
And also in the first movement, it's listen to a crystal mason.
I wanted to capture a sense of never ending time, of things, never quite finishing.
And what's amazing is that to use a mathematical trick in order to create this effect and only is a never ending time.
So the piece starts actually with the clarinets and the advantage, says Birds.
Messiaen was very obsessed with things used to collect these and put them into his music,
but the piano was where the amazing mathematical structure begins to appear.
So this kind of balance actually has a huge lack of passages.
So the catalogue starts as a rhythm sequence, which is 17 notes, a rhythm which then just repeats itself again and again.
So the 17 notes of rhythm get repeated again and again.
But the harmonic sequence, he's got 29 chords, which again repeat themselves through a whole piece.
You get to 29 chords and then you hit 29 chords again and again.
But the for these numbers, 17 and 29, these are examples, the primal, indivisible numbers.
And this choice is very deliberate because the.
1729. Short. The rhythm and the harmony just came out of sync.
Inadequate all back into place until you've heard 17 times 29.
Cause what are we talking the pieces that sound so impressive?
Very challenging on fundamentals he would have had this effect.
So 70 notes of the rhythm sequence.
They start with crotchet, crotchet crunches. And then he goes, It's nice, syncopated rhythm ending with a man.
And then after the red line you sing it properly. Crunchy crotchet of his syncopation, exactly the same rhythm.
The passages exist throughout the whole piece by volume sequence.
The 29 holes go all the way out to here, and then you see the same cool sampling again.
And this destroys of the primes. It gives you the sense of unease.
I mean, it's very difficult to balance the message using these lines as you listen to the piece,
but you certainly get the effect of the unease that he's trying to create and the sense of times that are going on.
So he's good at the end of time, the opening.
So let's listen to these crimes, 17 and 29 taking effect.
That's 17 minutes. Mm.
No. Cause I'm still working their way through the 29.
The civil rights. And I was on the line cause they said they started it in by the rhythm, the place.
And so they say we go on and on is gone somewhere else.
And I've had these twice on time on the same read the same for the previous.
As intriguing as very often. I think what happens here is that the crimes, crimes,
the things that we're obsessed with here in this department, we don't really understand these numbers at all.
But it is a composer using these appliances and things in his piece of music.
Almost intriguing.
I think the connection between the mathematician and the artist is very often we're responding to ideas that are already there in the natural world.
So you can actually find the same train of the primes in the world.
So it's a very curious cicada which lives in the fires in North America,
which uses violence in a very similar way to the way the machine use them in the cortex at the end of the time.
So here we have the rhythm sequence. 17 notes is the the alpha 17 years.
The second rate is again and again.
So we believe that it has a 17 year life cycle because it it's trying to avoid a predator which has a different periodicity.
So, for example, if the predator appears every six years and the calendar appears every nine years, actually is a bad choice of numbers.
Shows these because things get into sync too quickly, six and nine.
So repeating themselves all the 18 years. So that's a.
Was it a bad choice for the for the cicada? Because they get wiped out very quickly.
But anything else changes in order to survive. Now, explain the sanctuary, because the mission seven and six don't have any common devices.
And you didn't hear this in your piece until you're 42.
And that same pattern amazed so many as pieces of equipment like the rhythm is called,
and that the harmonic sequence is that the predator is using these growing 17 and 29.
He manages to keep them out of sync. And so you get the same effect as is happening in the forests in North America with the cicada avoiding predator.
That's interesting, that's very often mentioned was kind of interesting in mathematics.
It was already known and is sort of pandering in my mind to mathematicians, cabinets of wonders to produce effects in his music.
But interestingly, it isn't always one way traffic. Sometimes it's the artists and musicians who are discovering things before the mathematicians.
And an interesting example of this is this very famous sequence of numbers.
So tell me what the next number is in the sequence. 112358 1321, 34.
This is a very famous sequence where you have to put these numbers together and get the next one in the sequence.
Sequence numbers. One of the lot of birds and these are a very famous sequence which you probably all heard about at some point,
if you read the debate code, you will come across in large numbers.
The Golden Girls. You know this because she is 12th century Italian mathematician, realise these numbers and very important things in nature.
They explain spirals in pinecones or pineapples, the way a snail grows or flowers, for example.
The number of patterns in a flower and invariably is one of these Fibonacci sequence is the one with description.
How he shows how he said off cheesy numbers also tell you how rabbits grow one generation to the next.
So he has this very well sort of mathematical model of how they saw us in a pair of rabbits.
And a pair of rabbits requires one generation, a old one one month in order to mature, in order to be our children, all for that one month.
Then they have another pair of rabbits. So after the third month you go to the rabbits.
The one they just gave birth to requires another month before it matures, before it can have another pan, but the one is already generating dies.
And all of these these problems never die. I mean, this is a classic mathematician's model in rabbits.
This is how you are going to have these incredible patterns.
But, ah, what criminology was interesting. Okay, it's quite complicated.
It sort of sets off. But then you quickly realise what capacity is the work?
How many rabbits are one generation to the next? You just add it to previous generations together and that is the answer.
But actually these numbers should not be called the given option on this because they were discovered by technology first.
In fact, they were discovered slightly involved in Archie by artists, musicians and poets in India.
And they were aggressive in trying to understand what sort of rhythms they could create with a mixture of long and short beats.
So the poets was interested in long short beats and musician as well.
And so pretty well how many rhythms he might say, you go for beats in a bar, you can have a long beat,
which is an unknown to beats, or so that is one of the typical possibilities, but it will even be for short.
Or you could do short or long, short or long.
So they were falling into different rhythms that they could mine. But what if I had eight beats in the ball?
How many different rhythms can I make out of these long and short beats?
So even can all these. But I quickly realised that there's a consequence of this, and the pattern is exactly the same sequence.
Because you know what? If I want five pieces. What do I do?
I take all of the rhythms for beats in the bar and I sure beats or I'm going to take 1 to 3 listenable and am only those.
So you see great. A little bit of rhythms with volume. So I take the ones before me and assured me of three weeks and I will repeat, you know,
the two numbers before give me how many different rhythms there will be with points.
And so these Indian mathematicians,
musicians and poets actually have understood that these numbers are very powerfully working out all the different possibilities of rhythms.
And so, as is the magic already in the work. Sandra Before the dance, you have a roadmap.
So, so as you may think, the Alexandra number is not numbers, but I think it's intriguing that his analysis is interesting.
What are the possibilities in that particular art and arriving at some numbers, which are some of the most famous numbers in the whole of mathematics?
So the connection that I talk about so far is about rhythm and counting.
And actually one of the famous quotes about connection between mathematics and music relations.
LYDEN It's one of the inventors of calculus once famously said music is the pleasure of the human mind,
experiences and counting without the wind discounts thing.
Actually, the trumpeter and an orchestra spent a long time counting balls.
We all have. But I think there's much more connection between the two.
And it's about the idea of saying Who decides?
When you listen to music, you'll find you're looking out for the patterns that connect a sequence you just said the one that's,
you know, how has it changed? What's the connection with what you just said and how that changed into something else?
And actually, if you talk to a composer, they will say that what is very helpful is that language in mathematics.
So employing interesting structures, interesting ways of changing things.
Here's Stravinsky writing about his composition.
The musicians you find in mathematics a study as useful and as a learning or
another language is complex mathematics seductively just below the surface.
Certainly he was writing at a time when there was a very mathematical approach to transforming music which is still going on,
should make sure that it was really trying to disrupt this idea of tonal music.
And he wanted an idea breaking away from the idea of major, minor scales.
And he said, Well, why don't we consider the 12 notes that make up the chromatic scale and all equipment as equally valued?
And then he said, Well, it is going to throw this structure away. You need to put new structure in.
And that new structure came very much from mathematics.
So we'll go on to show what the date was to say, Hey, will you do one sort of a permutation of these 12 notes?
You arrange them in some interesting order, which makes some choose some some theme which is appealing to you.
But then you use mathematics to transform that theme and make variations.
And so what he does is to apply, first of all, a sort of translation.
So you take a well-known theme and you just push all of the next up by one note.
And over the top, one of the top is important. And also you keep on pushing these, knowing something anyway, all come down to the bottom.
You get 12 different new themes which are connected to each other because of this mathematical operation.
But you can do other things as well. You can adjust reflected in two lines instead of just playing the theme backwards in some sense.
Or you can write inverses. So you turn this sort of theme upside down by natural things like that.
For example, Bach used a lot in his music,
but this is a very systematic approach to these 1210 rows using these mathematical operations which generate the power to create difference 1210 rows.
We could all have some interconnection with each other.
A brain and a composer would be intrigued by finding some particular 1210 row where when you make these operations,
there seems to be some interesting connections and patterns that emerge.
And then this would be your product, which in songs composing I see as an acquisition, you know, this is a symmetrical operation being wrong.
I guess I would say this was the deal revealed itself across the site through order to acting on this musical scene.
Well, not only composers say, but interestingly enough,
Maximus actually was somebody who loves this mathematical approach to to generating interesting ideas.
And there's a beautiful example of Messiah actually rediscovering a mathematical structure,
but not realising he was drawn to this structure for extended reasons.
What he did was to take to 1210 rows, and he found rather useful in a structure that he uses to generate this piece.
It's funny to say that kind of in the film too, but if you consider these objects mathematically, they had to pay attention to all 12 things.
And actually if you generate, you can think of them as kind of shuffles as well, of course.
And we then combine these suppose to see what all the different combinations are like.
Actually, an object is symmetrical objects, which is only discovered at the end of the 19th century.
And it's a very interesting design, one where essentially the mathematicians include the massive group of order out.
We have a periodic table of symmetry, a lot of the symmetry falling passes,
but there are 26 what we call sporadic groups of symmetry, which are very strange anomalies.
And this what?
12 is one of the first this out and I got some interesting connections with Kobe Gary but here we find missing reselling for purely aesthetic reasons.
He found these 1210 rose interesting in a way that they combined and that was his motivation for the choice
and grace is beautiful piece but actually what he's created is a match but all didn't know what was in it.
We can see in three dimensions. It's a sexual object that lives in very high dimensional space.
We need a language or mathematics to be able to articulate it.
But weirdly, his message in articulating it, not using mathematics, but using music.
So I can't show you this natural object. You can listen to it.
I think my title is one of these things.
And does this look like frantic? So it takes a little bit of time to get accustomed to.
But I think Siri is an intriguing example of a musician being drawn to a mathematical structure purely for aesthetic reasons.
There's a number of my favourite 20th century composers that used some actual structures in his composition.
This is actually symmetrical structure that you can see.
The composer is, yes, the monkeys. He's a great composer.
He is using these for cello. And the variations are done by using a particular central project, which you can see.
So I want you to listen to this piece of music and see what some actual object is conjured up.
Any lines? You.
Anywhere. You get a smattering of objects on the pairing and.
When I was in my cube all the time, all pushed to do that, but I did a little bit on there.
I probably need to buy you more because the ways in I'll just use the symmetries of the
cube is that only eight corners of the cube he puts musical in is the child playing.
So for example, you heard a second. So with less and the music, I was just like, turns the bow upside down and slaps the strings with the woods.
And that's an empty slide is put on. The pawn is the cube.
There's actually a second to controlling the amount of time spent on each of these ideas and each new variation.
He does a symmetry of the cube which tells him a new sort of constraints in order to compose the next variation.
So you probably cheats the guy.
You had one of the variations because you only start to hear the symmetries of the key once you get more of these things.
But it is. Szymanski used to write, actually, that I could only be created under huge constraints.
And so he used to like this idea as a matter of putting some constraints.
I'm going on, I'm putting this right. And then you let your imagination loose within those constraints.
Symmetries of the cube. I mean, there are eight different possibilities.
There's a lot of different ways to rearrange space.
But any constraint on the signatories of the cube constraints a what a connection between the different.
It's music from one variations to the next as that as an office as well as being a composer.
He was also an architect. He works with my second choice.
I'm secret mathematician, a little bit easier on a committee that was made in Brussels.
And it's interesting that if you look at these designs,
they're actually very similar to some of the manuscripts that he wrote for some of the music that he composed for for the show.
So my second choice for mathematician, as I say, is, look, appreciate and and we're moving out of world architecture,
which again, is one of those arts which by its very nature has had some connection with mathematics.
I mean, you can be as creative as you want, but these buildings have got to stand up.
So you have to have some connection with the world of engineering.
I mean, we put lots of wonderful artistic ideas into the mathematics building here at the University of Oxford,
but we also need to be able to make sure that they actually the piece of doors and say,
I'll put in the place if I look to be a sort of loves using mathematics space,
just the buildings I want to build, but also to supply new ideas and new structures in these buildings.
Back to you. You find lots of architects have had an ideal framing in their background.
Zaha Hadid, for example, she was saying ideas in Iraq before she moved to London and would have they have become an architect.
And you see, for example, if you go to the Olympic Park, it's really a piece of mathematics sitting there.
It's not just a piece of architecture.
Local museum is very fascinating is anywhere near the technology numbers and golden ratio and actually a way to tax forces
rhythms inside a building and he writes rhythms apparent to the point and clear in their relations with one another.
And these rhythms are the vagaries of human activities. They resound in man by a mechanical inevitability, the same volume inevitability,
which of course, is very similar to the golden section children, old men, savages and alertness.
And so he loves put in this idea of something that we've all been drawn to as a thing,
which we find is that it can be pleasing when she sees the idea of something
called the golden ratio as you build golden ratio out of these Fibonacci models.
And so as you look at what they did was not to use the numbers that we see already in the rhythms, but as a sequence of numbers.
And these are the kind of ratios he used in the buildings that he produced.
He called them Simple Solutions in his book. And you can see that often while there's the same rule applies to 0.03 plus 0.70 is 1.13.
This same rule generates the numbers in the sequence and essentially the same with what you call multiply.
Now he believe that these ratios and something that goes back to Leonardo the auto also believe
that the these the ratios inside the body were connected with these seven arching numbers.
And so he uses ratios inside of body the single one to an answer to construct these buildings.
And if I asked you if you use these ratios, you very quickly get this thing that he referred to,
the golden ratio, because, for example, if I make a building, I use it in all this.
I have a little one by one room and I want to build in that room.
So I go when I got home, I was looking to add another one by one room onto that.
Well, now I will add to it so I can add it to. To answer this one out of the like three because one side is like three.
So I had a 3.3 ones that 5.1 and as we build up the rooms, they get bigger and bigger generator for the previous room.
So you get this rectangle which is closer and closer to this rectangle, which we call this perfect rectangle, the rectangle with golden ratio.
You have a lovely spiral, which is, which is why the Fibonacci numbers tend to lead to natural structures with side rows inside.
And so the golden ratio is a rectangle. If you do this, then it's a rectangle which has this particular relationship between the sides.
So it's a short distance, the ratio of the longest side to the shortest size,
if that is just the same as the ratio of the sum of the two sides the longest.
Then for some reason we find that the most aesthetically pleasing rectangle is called the golden ratio has a lot of arbitrary properties,
especially when you use it in buildings. So already the ancient Greeks knew about the golden ratio and its kind of special properties,
and it's believed that, for example, the construction of some of the great buildings,
the Parthenon in Athens, it's believed that hidden inside there are a lot of uses of this idea of the golden ratio,
but luckily they use these movies and series to do the same thing.
So you would try and generate all the out of these smaller numbers which would somehow have these aesthetically pleasing ratios.
So one of the most famous examples is actually in Marseille.
This is a city you have years where if you look at the ground plan for all of the rooms, they have this kind of similar spiral rings inside.
Although I actually you a place that unfortunately was a was an aesthetically pleasing building.
But actually residents say it's actually going to set a very nice sense of growth inside.
It's not as intriguing, you know, how much is this culturally specific?
Because certainly the waste tends to like the golden ratio.
But actually in the east, especially in Japan, it's found that they see responds to a rectangle with slightly different portions.
So it's a rectangle which is secondly a similar ratio.
So racism is a similar issue. What do you think?
Actually a rectangle which is in the relationship of one square root of two as your piece of A4 paper.
For example, in this ratio it has a nice property, an able piece of paper and I would be able to for in to that has exactly the same proportions.
So this is a very nice rectangle.
That's why you have 83, 80 to a one, they're all the same ratio but before one in hall and you guys still had one two square root of two.
This isn't a similar ratio. The same ratio is you need to add another one by one room on the site.
So this is a rectangle which is a one or two plus one.
And other cultures like these are very aesthetically pleasing ratio.
For example, buildings in Japan, this sort of pagoda is slightly sited in many different places.
This particular ratio kind of more elongated rectangle.
I got to be very busy design to rank them up for you.
Now let's do a little survey of the audience just to see.
And you look at these two rectangles, which one do you find aesthetically pleasing?
So you can put your hand up if you find that the top rectangle aesthetically pleasing of these two.
That's why it's quite a large proportion of you got your hands out and.
Okay, what about the lower ones? I actually oh my gosh, that's a kind of 5050 split, I would say.
That's very intriguing and sort of a mixture of cultures here.
And I don't think there was any particular bias on one side or the other.
So maybe we should do more research into this and exploring whether the old ratio this is the first
place on this idea of ratio is actually a use in architecture is not used in the 20th century like it.
In fact, if you go to Canada, one of the great architects of the past, he loved using the idea of ratios and important ratios.
And so I think it's actually why you get a sense of this amazing equation.
You know, whenever I go to Bologna dinner and there's a kind of feeling of perfection about the space that your your visit
and all this is because what Bologna loved doing was using ratios which are called operation relationships.
And in fact, so this relates very much to the musical harmony, the notes that we find all are also in a whole number ratio.
So you've got strings on the sides of the roof and.
So if you take the strings, the length of the rooms inside of a longer villa because they're in a whole generation to each other,
you pop them, you get actually notes, which we find very harmonious.
So a 1 to 2 relationship is two notes which are in an octave.
Oh 2 to 3 relationship is two notes which are imperfect things.
So as you apply this thing sort of phrasing this musical harmony, all the reforms through across cultures in India,
in Far East or in the West, this perfect faith is very often the key, which all music is great.
Here we go to the and music is architecture is often called phrase music because
it's got these lovely alterations it's a dreamy both melody and look blues.
Yeah. I mean it needs to be very similar so mathematicians have work and it wasn't attribution is interesting
and seeing what all the different possibilities are to make out this particular structure.
So love is taking the whole number ratios and arranging them and seeing what different possibilities are.
Luca You like something a little bit less symmetrical?
So he's trying to use his series Lose and see what he's learned.
I might kind a slightly asymmetrical here to the bird's eye view was natural variant
of feather but argues that it's a more modern better look at these days which
uses these different ratios and it's interesting actually want to amend that
look I used we tried all of these ratios inside them as an intuitive resonance,
kind of asymmetrical version of Vitruvian Man.
Leonardo's picture, I think you see this Vitruvian Man is a very, very well known image, beautiful image.
But actually this is a solution to an architecture problem.
Vitruvius was a Roman who wrote about architecture.
Andrew St James A lot of relationship between ratios in the body and the ratios inside a building.
A building works and it somehow reflects the humans that are inside and occupying that building.
And so he believed there was a nice way that you could reduce that.
It was a nice way to either arrange a circle and a swing such the human body.
But inside both of them and for generations, people were trying to solve this puzzle.
You could see images before Leonardo's where they find a sort of belly button is a common centre, both set on the square.
You get really strangely proportioned humans and it was in a this idea actually to shift the centre so the centre of the circle
is pretty much on value but that's where it should be down its centre is sort of the idea is that you could use these ratios.
They actually create a building which resonated with these images.
Now I get to move in ways in which these individual, individual moments and place.
Where you going to see lots of geometry works.
I could easily have chosen Leonardo as a secret mathematician, but is he really somebody who bridges the arts and sciences?
But I think modern art is something that only Salvador Dali thinks of his paintings.
It is full of lots of different ideas, both for mathematics and science.
There are elements of DNA appearing in there. You are very obsessed with the ideas of relatively in time.
It's not easy. There's not a clock sawing off the size of melting away.
And you reference outline of a container fish swimming in sea waters, the cold water bones and hot water science.
And as is the much more enjoyed by his scientists adaptations round to his house rather than the artist to try and find interesting ideas.
But if any basic sound and actually in his paintings you see a lot of different mathematical ideas being exploited.
So this is the image I'm going to show you.
Okay. Which are not matching all the things. I just called that one and on the next slide.
So there's a one who painting who went to the Last Supper.
I see somebody inspired by one of the paintings of The Last Supper.
But actually, he wants the audiences to stage the dinner inside alone.
Though he's an aesthetic, he is interesting because if you go back to the ancient Greeks and they old man is shaping the shape of the universe.
So the idea is this last supper is taking place inside the shape, which is, in a sense, the shape of the universe.
And again, I wanted to bring you that. And it's not just all this flowering.
The mathematicians can be very interesting shapes. Actually, the mathematicians benefited from all this theoretical watching all these things.
If we go back to the Renaissance, we find a huge number of paintings where these symmetrical shapes that he drew.
This is a painting of mathematician Lucy Lucia, actually, as you see on his desk at the Hedren, which he used in the last segment.
But there are other things as well. It's really this strange glass floating of these hall filled with water as well.
And this is an example of a road in Rome. Meet you all together.
So this the mathematicians have discovered it already.
And you can see elements. There are five symmetrical shapes you can make where the faces are all the same shape and arrange the central map.
So they're like even being one of them, the cube and three others then all completely.
So what about if you use different shapes as well?
Okay. So if you think about the classical world that one gets around when the sun is made out of of goods and hexagons,
so they all have the same edge so they can fit together.
But there is an asymmetrical shape made out of pentagons, of hexagons.
So all of to. Okay, how many more than all of these?
How many different ways to put together these objects? And so you use another example is Romeo all together.
It's made out of triangles and swings. I mean, all these triangles this ways together.
In many ways, it's unusual. The challenge was how many more?
So it just over there are 14 different ways that you can piece these flat shapes together to create these shapes.
But actually, for my antiquity, it was kind of lost what these 14 were.
There was some documentation that all these had indeed discovered.
14, But nobody knew about the Renaissance, really, what a small team were.
And I sort of took the skill of the artist who was able to actually represent these shapes on
a canvas over on a page for us to actually go through it and sort of rediscover those motifs.
So, you know,
the mathematicians really had the artists to thank would suddenly try to show how good they were expected to be able to draw these shapes.
And we have a great challenge that from the keyhole to even really show the artist's perspective.
And finally, although it is raising a book quite actually illustrating all of these examples of the way we see symmetrical objects.
Yeah. And so I really wanted some perspective.
And actually Leonardo was used a lot of ideas in his paintings.
I could have easily chose him as my secret mathematician. This is the painting which Dani kind of based his idea on The Last Supper.
And it's there's lots of mysticism about this know secret messages hidden inside.
And there's certainly, I think,
no secret of the fact that being able to use mathematical relationships in order to place design in the placement of something.
So you find lots of golden braziers hidden inside the way this painting is constructed.
And again, probably nowadays, most famous painting by Lisa is believed to have a lot of Fibonacci numbers and ratios in the relation that,
in fact, you see all the Mona Lisa is perhaps hidden in mathematical beauty.
And then sometimes it just means that there are a lot of drawings of Leonardo's
or he looks at face and constructs the face based on these Fibonacci ratios.
And but Dani was interested to see these very classical shapes, but also in a much more modern 20th century shapes.
Image. This is the image that I'm going to talk about.
So don't actually use the same fractals.
Fractals were discovered in the 20th century.
Somehow the shape of chaos is in some words, these shapes recognise these shapes as they have some infinite complexity as you zoom in.
They don't get simpler. So one of the classic examples is a space suit where you have a triangle and then you invite a smaller triangle on that one,
and smaller and smaller and smaller,
as she only uses in a painting, is on the wall where he you think he looks a bit like a face because your two eyes and a nose there.
And he uses like I'm taking a sculpture which looked like this love triangle.
And any side is the eyes and the mouth he puts on another skull.
And then it's like those you can see another skull.
And so it's kind of is the sense of infinite complexity is produced by using this structure, mathematical structure and only this painting.
Actually, fractals were also used, but I'm sort of subconsciously by another famous 20th century painter,
Jackson Pollock, if you remember his paintings, the lovely paintings with all of this paint just dreadful over.
But it maybe would criticise all of this. That's come on my mind.
I got 210 year old girls, tweens and teenage sports fans know something like this, but get these paintings available, you know, £75 million, so.
Sure. Well, it must be doing something wrong, especially with my ten year old girls.
Can't do so. So what is it? It seems that there's a very special quality that these paintings have,
which they had is perhaps a quality that only they have a complexity to examine.
This is very difficult to tell what scale you're looking at this painting.
Here are four different pictures which I zoomed in all over to take up all of this.
I think it's very difficult. I think by the top right hand corner, you can tell that's probably the closest one, but only on the three.
I, I think it's quite hard to tell which is after painting, which is a zoomed in version.
And so pull up is creating this, these trips which had very special quality, they had this fractal quality to it.
And in fact there are people trying to fight. So when you think of a painter and a huge one, but actually it's quite hard to do what it's doing.
And so quite a few tend to be fakes because they don't have this fractal pointing to you can even measures and fractal connections.
And so in different periods it follows crazy prices have different fractal mathematical quality too.
Now the reason Pollock was doing something well, the special grading is this is you have rice specific style raising.
It's kind of very about a balance. So it wasn't very steady.
You you'll see sprinkles and when he was making these paintings he would often be pretty drunk.
I thought it was it's when he's playing his hands, he's actually acting.
You know, if I feel better, I would do this. I'm actually a bit like a pendulum on a very simple pattern and I'm crazy about it.
But if I actually start moving where the pendulum is so caught up to what I was creating something called the chaotic pendulum,
and then the shape is made is actually this flat.
So there is a way to make trying I do this.
It seems to me that's important, which is to set up a positive page on the page about and to move where the actual pages attached to.
And he did decide if this was the only way to get it.
But that is the principle of the book. But it's no use what is coming back suddenly and his obsession with new sites.
He also is fascinated in shapes and applications of creating beyond the three dimensional world that is so visual.
Here's the image since 2000. So it's one incredible painting where he takes a full directional cue.
Now, you know, I don't want to use the idea that in three dimensions,
but what you can do is sit on a ramp or dimensional cue into a three dimensional universe in the same way that Y is a three dimensional cube.
I mean, how do you make a three dimensional cube out of a piece of paper?
What do you agree is what's called the net. So you have four sways, two on the side, you have a cross shape.
And then you can sort of fold this on out and you can create all cube when you do the same thing from three dimensions into order.
So you can have a net of a quarter cube. This is what you're looking at here.
So if we lived in a four dimensional university, a way to connect all of these to the ends in order to be able to create what we want.
I think this we can't do. We can at least have this knit downstairs in three dimensions.
And what would I think she was doing? Don't you find this totally fascinating?
He was a very religious man as as being interested in science.
And the idea of these two intersecting crosses was too much for him and the idea of a fourth dimension, something spiritual beyond our physical world.
So as you choose this shape as the shaped, cruciform, Feustel says amazing painting,
which shows Christ being spied on what's cool this tesseract unwrapped for you.
You can actually see other. There's an architect in Paris who use another way of seeing one dimensional cube.
You can take a shadow of it. And if I think of the small cube inside a larger cube and hear the object in Paris,
use the idea of a shadow, for instance, to create a three dimensional object it's made of yet again.
These are some extraordinary effects.
A We kind of sucks through the whole there.
I mean, it's very weak. It's going to be got to be steel everywhere else.
But it's actually the reason they put this kind of we paint sculpture is to try to sort this wind down.
But I always have to ask, does something weird like opening up a wormhole into the 1970s four dimensional shape?
There actually is, if I have to be careful, it's not the suburbs of Paris.
All right. I think you guys are. Exactly.
I'm going to say it's like all secret mathematician now who actually who's obsessed by the idea in four dimensions.
And he comes from the world of literature.
I think literature is slightly more of a challenge to find connections between literature and the world of mathematics.
Poetry? Yes, certainly the kind of patterns one sees in poetry.
Borges, an Argentinian writer. 20th century, is a choice of my favourite secretive mathematician in the world of literature.
His. He writes about short stories and short stories, a full narration of the ideas of paradox,
the ideas experiencing the nature of space and the beautiful stories and exploring also things on interesting in classical.
I was interested to hear what Wilson thinks. Was he reading?
And it seems that he was certainly interesting reading Bertrand Russell and maybe Von Grey as well.
There's one story in particular which is my favourite school is the Library of Babel,
and it describes a librarian who is trapped in his library, and he spends the short story trying to work out what the shape of his library is.
First of all, he just has his local knowledge of what's the room that he's in is like,
and that the short story opens with a description of what is going on in the universe,
which all the school library is composed of an indefinite and perhaps infinite number of hexagonal diamonds from any one of the hex.
So you can see it's only the upper and lower floors.
So the structure of his library is a little bit like honeycomb.
So each of the rooms is a hexagon and you can guess there are two doors.
So you just go in and out of these hexagons into another hexagon and you can see an upwards through staircase.
There's more axons out there lower down the sort of the libraries also speculates.
Okay, so what that means it's gone forever or is there somehow a wall in the house or something?
So it's an interesting mathematical challenge.
You only know local information. And so anything about clue or structure is something that we study by the ultimate practice.
Now, there are also books. This is a library. It's full of books and books that are in this library.
Kind of interesting because that equals analysis realises they all have parts and they all seem to be the same sort of structure.
Not only that, but it seems to me every single book possible he writes.
So this is a structured each book is a 410 pages, each page 40 lines, and each line is an 80 letters and all graphical numbers.
Nine 2525 The number is a speculate that's actually in his library.
There's every single book possible that ever could be written within this structure, and he believes there's only one.
So each book is unique. So they will be first 410 pages of the complete works of Shakespeare somewhere.
They're also the same axes. So when we actually calculate how many different books there are,
because for the first 25 voices the same amount over another 25 choices, it's either 25 or 35 choices.
For the first two letters of any of these books that you can count the number of letters and work out the different poses,
there always is another 25 choices for each different letter.
So as you remember, we had 80 characters on each line.
So you find the number of things that are possible 25 to the power 80.
But we've got 40 lines so great that some have 40 and there are 410 pages.
So that's we have raised the path for. So there are quite a lot of books in this line.
I think a sense of how many books that are in the observable universe are in fact only ten of the 18.
We believe atoms in the universe made every single atom one of these books ever near.
I can go through all the different possibilities of books. But on the other hand, there's numbers, points,
which means maybe the library means they may be libraries notes they must have an end, or does it have a name?
And here we didn't get into the challenge for the mathematician.
Yeah, okay. How can you have a shape made out of all of these hexagons layers?
And finally now we're getting into the question that many of us consider not our universe, which we know we call the universe.
What is the shape of all universe? If you think about all of us as kids look out into the night skies in these stars,
you guys want to solve random or what does it have all of you and Xena decided?
It's not. That's what the ancient Greeks believe, that they were somehow advanced.
All that we were sitting inside. But that's kind of weird because what's on the other side of that?
I mean, surely we're not living in The Truman Show. That's going to feel great.
Well, maybe we all there. But here is this kind of idea.
Okay, so what we do every year, at some point it is mind we find out what will happen to people together.
Either there's an end going to get out of it. I think the lover thinks that's true because this is all there is.
As the results come up with us,
it is one end of the short stories come up with the idea that we come up with the what possible shape all universe could be good,
as he mentions, to suggest a solution to this ancient problem.
The library is unlimited now has more in any secret and all power to cross into any action.
After centuries, you won't see the same volumes repeated in the same disorder.
I for you, we think the same structure is happening in all units.
So if you keep on going somehow you go back to where you started.
That would be a solution. So some of you might remember playing this game here.
We will be following that. It says, I don't have anything on my mind.
My son did the same last year. It's a beautiful example of the universe.
It's a finite universe on your computer screen. So the universe is just sitting here, but it has this rule.
And if you go to the top of the screen up at the bottom, and if you go off the side of the screen, you reappear on the other side.
So I'm sorry, this is unlimited. If you've ever hit a wall and bounced back, it feels like it just goes on forever.
But it is falling out. So what is the shape of this universe?
Well, we have the luxury of living in three dimensions, and we can actually explore what the shape of this is.
So we can use it that I mentioned to connect this thing up. So ask me what the shape of the universe is.
It's it's actually the shape of a force or a doughnut.
So when you go off the top of the screen about round background,
the bottom as you're going round the inside of the bangle or you go with one end in the other, you come out, the other side is wrapped up.
So the top of the bottom of the screen connected, joining them all and in the left and right hand side of the screen.
So that's drawing those up. And then you see the shape emerging for you.
It's the shape of the course. But we live in three of us with all my story.
So I mean, suppose that this lecture is a walk on you to the spine as we go up to this size.
So how would this work? I mean, this universe, this is not the three which we should be able to about tackle this wall.
It should somehow be our liberty. How do we make it work?
Well, here's trying to what, if anything, asteroids with this root.
So we got the left hand side of the room just magically appeared from the right.
Or what happens if you go through the seed? Well again you should come back is going.
As you can see, they were coming through the floor. So that's game to potential game as well.
And we've got to think we can go. When I go out, the back will actually be attacked.
But you won't find the massive all the angles something.
We had a pair back on stage here. And so this is a model of how our universe can be connected together.
I knew this could have a cyclical nature to it. And then the question is how to treat it?
What does this universe look like? Well, the lights that's coming from the back of my head is what's happening.
The light is going out through the screen here. Would it be appearing as my collected data?
So actually, I can see the back of my head out there and I can see it again and again.
So this is the image, what your unit has and maybe some of those cells we're seeing in the right size.
It's our own sun, but we're seeing it's sort of looped round again and again.
So it is. But this has a shape. Intriguingly, what is this showing?
This is actually well supported shape. I would have to join all of these together.
And what I look at is what's called a in.
For instance, I will get a very high dimensional way.
I, I see that so many times.
I wonder, I can't actually show you the same, but we can use I see this law, but this is actually what Ford has ended up constructing in his library.
By the shape of the library, the way you ended up is you created this void.
I will be right this through this narrative, not realising anything about mathematics of higher dimensional forces.
And actually one of the great breakthroughs in mathematics has happened in the last
few years was a solution with one great conjecture by a Russian mathematician,
Gregory Pope. And what he actually did was to solve the problem of, well,
what are the other ways that we can join up our universe by new this I give you a way of doing that turns into the point of dimensional language,
but there are other ways of doing it. Observe this finite part without any rules or boundaries and permanent solution for the point break.
And there's actually something even in that this is geometric transition conjecture is actually
a list of all the possible universe is that Borges could have used in his short story.
If I recently I used this idea of the library available.
This is a few years ago. I just love this story.
And I worked with the choreographer and composer today to try and explore as
creating an artistic work which combines mathematics and choreography in music.
And so this is actually I ended up dancing, which is kind of my first imaginary little clip of me dancing.
The construction of the hexagon using this router and.
Yeah. I think I ask you first, I am for Corey.
I believe in Babylon as you create another piece, which I please come home to say about the corner of your voice.
But I would have created a piece of theatre with another actress from this site.
And we're staging a play groups and one which I took this book as a short story as its inspiration.
But we sort of take it somewhere else that's going to go on in the science museum, from the temple type of thing.
That's all that can be easily accessible.
And I think it was doing that piece of choreography that I learned about my
fifth and final super mathematician who comes from the world of choreography.
And the choreography really is in some sense, geometry in motion.
And I think that a real common use of all the mathematical ideas and mathematical notation, he created his own notation,
which has a lot of mathematics, to sort of articulate what was happening in a piece of choreography.
He wrote this dance.
It should have a sense of the three dimensional geometry with which the massive set man is inclined to follow, to connect, to connect,
sometimes with the 12 on points to the animals eat or in his movements, travelling, as it were, on an invisible network of paths.
And he used to want to try and make that some that we tends to be a bit like a three man mixing two dimensional,
but nobody wanted the dancers to really feel the space around them.
I would ask the dancers to actually really feel like all their movements must be
at all knees the size of Michael's Adrian or maybe dodecahedron around them.
And they have a connection to the world of mathematics, because I'm showing them also,
and I think all artists have a little bit of maths going on inside them, but I think it works the other way around as well as mathematics,
although the maths I think is really driven by an artistic sensibility, I think that a lot of the things we do,
the choices we make, the structures we like choosing, aren't chosen because they're useful in the real world.
We actually choose them because we find them surprising, useful or something exciting, which I think is the same thing, which is motivating.
So one of the books that really inspired me to become an acquisition was a book by a jihadi who had mathematicians topology.
And this Cambridge mathematician writes about what it's like to be a mathematician.
And I was working on this book about that time when I had this crisis about whether I don't get your dreams or the science.
And I really something that's a bridge between the two because HONY really
describes the mathematical world and creates all these sort of American attention.
Y. Kapadia Okay, so our I'm interested in mathematics only as a creative thought he was writing down on anything applied his subject.
So I think he'd be quite surprised to see the ways that even some of his mathematics he's now used the Internet cryptography.
But you know, I think if I was going to choose a beautiful theorem in my mind and I love this one,
it's one of the and so we sort of choose the element of surprise that we kind of find exciting in a piece of what Fermat proved.
But if you take a prime and finally you divide it by four, has a major one, then you can always write that five numbers to square was added together.
That is a kind of weird I mean, why should a prime member have anything to do with sequence?
And so, for example, 41, you might have like four yet remain one.
So 41 can be written as 12, which is squared plus minus one.
Now all for the primes out there, anything, any bronze or anything, any primes which I remain to one one.
The reason why for our secret one every time you get one Fermat's proof guarantees that you'll always be able to write it is to swim.
Yeah, and I wouldn't say that that's particularly useful.
I've never seen it used in any piece of technology, but for me, this is this is a beautiful gem, you know.
And if you read the proof, there's a magnetic excitement, subjectivity out of you guys in its prime.
And so as to swaying numbers and its moments, it's a bit like reading the story with somebody character turns into somebody you didn't expect,
or a musical theme which can take some patience somewhere else.
For me, I had a pleasure in reading proofs of this.
There are many different proofs and it's a sense of pleasure I think I get when I read a piece of literature or listen to a piece of music,
and suddenly somebody surprised me. I think that's what we're all fighting for.
And a piece of mathematics is a piece of mathematics that I created is less complicated than that.
So what about the idea of is this is a symmetrical object that I found in my own.
But I decided to dismantle all day. Had something to do with solving equations in the curve because it's a very different area as well as symmetry.
It's an area that we still find very mysterious trying to find solutions.
These two guys rather like myself here. But the reason for all this I discovered action and encoded in them questions about solving these equations.
Now, for me, it was a creative act to focus on these things.
I could add a computer just to generate endless symmetrical objects, which you have no interest at all,
just like a library Bible is full of all alone, boring books and everything.
Do that. And all the acts of the creative acts of a writer is to say, You know what?
This is the book you should be reading. This is the one, as you know, this is the choice I'm making out of all these possibilities.
And it's the same thing that this idea of creativity and discovery.
Well, there are all these different mediums in mathematics. We've got to choose, make.
But I make a choice. It's this one I want to tell you about and examine all that.
I'll give it to my fellow mathematicians because I can take you on this incredible journey.
Know, wow, how does it connect with that person that's going around with the quotes?
This is a quote.
So I want you to think this is a quote like an oasis or is it a place by a scientist to create precisely information, useless combinations?
Invention is its own choice. The central foundations do not present themselves in the moment.
And I lot of you think that that's an artist talking about so that their way of working.
Fusion using all these unique seats. Scientists working on their way.
These are not usual. Yes, it's something I would like you to all be putting your hands.
I wasn't sure, because actually the message here is that, you know, how how much similarity are processes?
I mean, it was, in fact, a mathematician, a very famous mathematician, or maybe the inventor kind of gave it away.
But actually, Stravinsky always used to pull back himself as an event that he was inventing his music.
But he was a mathematician. And I think that is very often we make choices which have extraordinary impacts on the technological world,
and so help us describe the physical universe around us.
But I think it's driven mathematics is driven really by the same sort of aesthetic sensibility that drives all the secrets repetitions.
Artists like. Owe you.
Yeah, I know. You want me to ask them why they think golden ratio?
Yeah. Oh, my God. How can I see you guys every time you want to change your mind so that you don't screw up?
And so please remember what you're doing.
This would not do anything for me. Yeah. So I'm kind of intrigued, which, you know, systematically pleasing.
So I go to rectangle rectangles here, ones in the golden ratio of ones.
And so there is you find the first rectangle as you probably glance.
Quite a lot of you gave the golden ratio. Okay, what about the second rectangular selection?
Who likes that? The best? And she says had a 5050 split now and yet more simply doesn't deserve to be.
And that's what I feel. But now it's old John's last piece in Boston.
And I did see you press the Japanese open that you are a very erudite one is one of the really challenging questions so you say please be ready.
That is now more than 80%.
Do we have any questions going around? Yes. If we get more assertive, you can stand up when you ask a question that I don't want.
And that's people like rudeness and little things which are related.
I research the poll numbers and on the other hand is that people prefer the golden rectangle,
which is the least high school, which is a real contradiction.
And actually, I've never seen any research that confirms that people do prefer the golden ratio decisively, actually the field.
And he also mentioned some of these music many people find on this album, and it's the composer whose buildings many people find unliveable.
Now, perhaps there's not enough just by mathematics, and some mathematics can be quite strong.
We see. And so I love useful mathematics and I that's where the universe is.
And I think that's that beautiful. You says it's very jolly.
Yes. I mean, I think it is interesting that this kind of attention, because you're absolutely right,
that the gold ratio is an example of an irrational number which cannot be arranged.
Is there the ratio of two to Homer? So it seems to be almost polar opposite ends to those holding on to ratios appliances
using extremely model also like the ratio of ones in the square to doing readings,
partly because when you cut not really hall, you get to see four of the same ratio.
So so I think that's a, you know,
still that golden ratio is in some ways does have a connection cause to hold down the ratios
because the simplest way to generate it is by taking the simplest generating process,
which is to take one, one, two, three,
five and those ratios which very naturally arise from trying to grow something so you find grow out of whole numbers,
you find yourself arriving at that name. It will be so.
So I think that although this is an irrational number, it's still a number which probably had is the original number which is as close to one,
has a measure of that to something which is generated out of whole number ratios of fractions.
So that might be why we're finding both in the world of architecture and both in world of all natural growth.
And that gold ratio does crop up in terms.
And I think that's the what one would say is the reason why we responding to this ratio,
because it's something we're very we're seeing so much around our evolution program
to see it as something natural and and something that we can be at home with.
Interesting gave you come back to Pollock Pollock's fractal paintings he sort of started with some simplicity
then when creating a comparison in interactive and then settled down something that you can measure.
The dimension of these fractals is between one and two,
and what you discover is that the qualities that people find most is that you can please all those
pollocks that have a fractal dimension which is very close to the background you see in nature.
And you know, Pollock data, all of these paintings I went to studio is surrounded by fractal like trees.
And so actually what he's doing is recreating something that we can find we resonate with in the natural world.
Let me go to your second point, which I think is fair, which is, you know,
a lot of these people who are putting mathematics inside their offices are just
producing things which are not very easy to get to grips with when you first hear.
But I think that's true of mathematics as well.
Mathematics requires an investment of time and energy to be able to appreciate the beautiful things in our world.
And it doesn't have to be easy. You know, it's something which is great, shouldn't be just so easily accessible.
And I think that actually, if you listen to it for some time, I mean,
I have the same reaction that I found quite an angry world, but I spent more time in there.
I really came to appreciate and enjoy the complexity of structure that's there.
So I wouldn't necessarily say that just because something first site is not appealing to the masses that we should throw it out.
We did that when we set out with my master's. Lived in the building.
Have you ever. I haven't. No, no. I mean.
But I say I mean, I actually the words counter what you say.
I mean, because I think the resident residence in the city is really enjoying the space.
And I think visually from the outside, it's not perhaps so interesting.
But the inside structure, I think,
is much more appealing than something that might look very similar but doesn't have that incredible mathematical logic to it.
But I think it's great the question marks. More research needs to be done to know how a lot of the duplicate buildings are going after this time.
There's an amazing structure of the chapel, which is kind of a piece of my body geometry that he's made up.
And I find that very. There's a question down here.
We got my hair. And then there's the second question, which just.
So you pass along the facts and you have to stand up to that.
Hello? Another minute. I'm not a mathematician, but I know there's a pattern in when you multiply the number nine,
does the sum of the result always be nine when you add it up?
I was curious if know if it's been applied to me in any way that when.
Well, yes. This is how I apply it to my kids actually, because it is a very useful way when I teach my kids the nine times they will,
you know, it is basically if you want to do so, let me do this search.
You see the ability for design. It has to be 36.
So this is the right easy way. So eight times 972.
And in fact, you know, that's an interesting pattern. And then you say, well, does it always work?
And I think that's the power of mathematics and especially the mathematics of algebra.
The algebra. When I try to explain to people what algebra is, I think it's it's it's finding those kind of the logic behind those patterns in numbers.
You keep on seeing this structure happening. You want to why I was always then you need a world of algebra to represent one discipline every.
I mean another example that I quite like and I'm doing teaching multiplication tables is
my skills is if you take a number and swear it so five times five then and I say five.
And I said, okay, what's more times six? And you go, That's 24.
And then I do. And with another number, the seven nine, 749 six, Sunday 48.
After a while they fall. But what I do is when I take the square and I say the numbers on either side, it's always one less the ones on the sides.
So and that's why I always look at anything.
That's the power of algebra, this language that was introduced by by the Arabs.
And so coming out of the house of wisdom,
electricity and and it's that language which enables you to just sort of work out why that magic always happens.
It will happen, whatever. And it's at the hall to say Fermat's Proof.
It's an algebraic relationship between numbers, which eventually gives the heads of why primes on Division Boys,
for which the remainder one might be pulled apart, makes way swings.
Yes, ma'am. I just wondered whether everyone's choice of reptiles might be influenced by just flat screen televisions,
because, you know, most of these are like the wide format.
And, you know, I'm Paisley that I just never up in there looking for my first musical panoramic and you presented
something new looking and of course there are artists who like wide rectangles like Ivan comes to mind.
I'm just wondering whether you knew anything about the way people design due diligence and the proportions and mathematics of the brain.
I mean, I don't know.
But I'm sure that as you compete with was probably the film would say, well, there are all these choices of what the proportions that you all work in.
And if you're watching a film on your laptop, you know, you see I have more, you know,
baseline we can see as a solution and there will be decisions about what I want, why those ratios are good choices.
And again, are what we enjoy looking at as a screen is probably I mean, you, it's probably the other way around.
Those choices were probably made by you by showing the load of screens and everyone saying, well, I like that one and and you don't move.
Most of the canvases, the majority of canvases will be closer to the golden ratio than anything else.
But if, of course, you look at all these long days, it's disrupting those expectations.
And so to have something long and thin actually challenges what your expectations.
But I think there's something very special about that golden ratio,
which something someone might be able to really see because because that actually spirals
that face inside they're actually but the focus of your eye focus is not on the dead centre.
You have to swear you'll be dead centre. They won't be too controlling about that being the place where something dramatic said.
But actually there are four different places where these spirals and often in a Leonardo painting you draw these.
There is something of interest there and it's almost like you're you're drawn to those lines.
He disrupts the the golden ratio of that canvas.
You want to have that that active spiral drawings in that place.
So I think that also is a motivation for why and art is kind of like that particular shape
because he's doing things to the viewer that they're not aware of bringing into place,
which isn't so obvious to. Yes.
And the question here. You send it off.
An Iraqi said that this is very difficult to make mathematics and you talk about it.
He's very famous, for example, and mathematics, I guess.
I just wondered whether you had another examples of authors who also say these ideas.
Well, one of my favourites is actually kind of the 20th century movements in France, George Perec.
I mean, he's very famous for writing this novel. We never saw the letter E anywhere, so.
But actually on his book of the lines is as magic, which is a story of a building.
And actually, he used its mathematical structure for a massive square.
It's a bit like Sudoku, but it's a way of if you take an example of a Latin writer's square, you take the core course and I can call.
So you call Jack Queen King.
I saw each scene.
The challenge is to arrange in a full line all grades such that no line has the same seats and no line has the same call card in it as well.
And same thing you can do that.
It is a Latin slang for my four pack uses a ten by ten, which is really difficult to construct in the construction of that whole.
So there are a few there are 99 chapters.
So this is one angles very deliberately, but each of those represents a room in his building and he has a set of cool cars and suits.
He has different kind of ideas on all things or something,
and he will try to place these in each of the each of the rooms, in particular control like this Nazi breakfast lamp.
And again, it's this kind of idea of, okay, what happens if I put that constraint on?
I'll get pushed somewhere, which I just let myself.
Okay, let's write a story about an apartment block with 99 rooms and that's too much you and it comes out on your see,
it's actually quite interesting to be pushed somewhere by the constraints of a set of lights.
And I think that's often like why does anyone she's right but what poetry,
you know quality is about the the music of the words but actually also was fun I think in poetry is when you put those constraints,
it sort of forces you to find kind of interesting ways to say things because of the the rhyme structure of the rhythm structure.
And I mean, for example, Shakespeare, you can find the most kind of mathematical mind is something that forces in my head.
I think this is page, but there's a lot of interesting use of numbers in that prime numbers as well,
which is I don't think it's very clear whether anybody.
Simon Chase It was really deliberate, but it's so so I think there are there are see a lot more examples being released.
I mean, there's a nice novel that many of you may have read I saw on the beach and
one of the kids goes off to islands in the forest and tests all the winners.
But he also wrote his second book is called The Tesseract. And it's a very interesting story, I think, set in Manilla.
And the idea that all you get the perspective that a tesseract is that unwraps for dimension.
Q So the idea is that the novel is kind of four dimensional.
You never see that you can never get a full position when you see the whole story.
So you just get these perspectives from different characters.
And it's almost like you're taking this shadow, this shadow, this shadow, and it captured in the back of his mind.
It's quite grey, something where you, you never quite completely know what's going on.
Each character has this difference and I think that sort of ideas are in place until you find the frames.
Copenhagen that's an exercise in quantum physics.
And he runs this meeting between Heisenberg and Born Again and again.
Each time he does it, you observe the experiment, it starts something different.
So it's almost like that the quantum physics is embedded in the structure of the play.
I will go on this some of the question here.
And you mentioned the difficulty in having to choose between since I was at school.
Do you think there'd be any value in a different approach towards the boundaries between art and science in any education?
Absolutely. I think we can suffer from this compartmentalisation of education as students go from school,
from the history lesson to the music to the math and science lesson, and they don't realise that connection between these things.
And actually, I think a lot of people just I have into mathematics just because I researched research.
But if you find a different way and I mean I did this program for the BBC about the history of mathematics.
Now, history is a wonderful way in to do something, to show that mathematics is created by people.
It's connected to particular times in history, cultural changes, for example, imaginary numbers, squared minus one,
quite a little time that it's actually the moment you got to accept it was ties in real closely to the French Revolution.
It's that suddenly accepting new ideas, new changes might be very relevant to that change in the acceptance of something so dramatically challenging.
So I would love it if we created a, you know, a school or a curriculum which, which didn't put subjects in these sort of goals.
I think even I think Oxford is a very interesting example of trying to break down these factors because here we are in mathematics department.
Yeah, this is mathematics gets on there. But actually we all have connections with college here at university.
And in that college I spend all my time talking to people from, well, history, philosophy, economics, literature.
And it's it's that's the I've often found most stimulating is that time when both when I was an undergraduate here,
all my friends were doing kind of deconstructing and anxieties and I had to sort of put my body in that context.
And I think it's important subjects sometimes in isolation, we need to push it through.
But also don't forget to put it into a context as well.
And we can do that right as. Question here, and then we'll have a question back there.
Hi. You stand up? Yeah.
I have two questions. Firstly, I think a member of the assembly,
one of them was allowed to make submissions to the the Hayward's call alternative going through this
under the United States and is being taken by these huge mathematical grids there in the first of that.
And I was like, really? Then I know this was based on an scientists.
And so that really might be because of the mental difficulties and issues of connection between studying maths too intensely and going crazy.
But this is my first and the second one was talking about music to show me that I was one of an experimental music.
And then coming some of ABC about how why is it only certain music seems to include the
feeling of anxiety and kind of you know is not easy to listen to and is it possible to
create mathematical randomised music that's actually nice to listen to and what are the
constraints you have on the mathematical models in order to make them pleasant harmonics?
And so that I also went to this exhibition and it was a very interesting example.
I mean that those early grades were actually examples of the last records when he was an artist performing there and the things
that I think they found their way like a calendar and it had residencies with Mayan calendars as a kind of Mayan thing.
To the question,
I think one has to be very careful about this connection between mental health and and doing something like art or mathematics to an extreme.
It's very easy to pick out examples in my panel of people who have been institutionalised because of mental health issues.
And I think one has to be very careful about saying, oh, it's because they push their brains to the extreme.
When you think about cancel who decided to fantasy,
he spent quite a lot of time in a mental health institution and how but you know that he
would have had that mental health issue regardless of whether he was doing the mathematics.
That has to be clear. And I think Nash, for example, beautiful minds.
I think I think it is he spent so much time in a very abstract start.
Well, we know connection to people. Does that accentuates that mental health issue that he might have already?
And I think that's an interesting one to explore.
But I think I find people who just too easily can say the mental health and being is a helpful, connected.
And so I think it's a complicated issue which probably deserves more work.
Now, what's the second question, which is music as well?
And, you know, I think that saying yes, I mean, it's already been a challenge about,
you know, all of this music which has had a disruption, seems can't listen to.
But actually if you go back to the music of golf, which basically out of is one of the most listenable pieces of music,
someone something like that old band Variations does have an old mathematical structure, and ideas of symmetry are things that we're responding to.
We like we like to start saying something goes up and then we hear the same thing.
That's the reason upside down.
We respond to a connection between those two things.
And a friend of mine, actually, Pachelbel's Canon, is one of these tunes everyone seems to love and brings in as well.
Actually, he was able to to write a computer program when she was able to tweet 140 characters reproduced below ten,
and the structure is all it is in just 140 characters in the computer.
So one could say All your longing to listen to what's happening is that generative structure is purely mathematical.
So. So I think, I think recently in a show at the Royal Opera House, I'll be exploring the mathematics of the Magic Flute.
Now, many people love magic, so what they don't know is how much mathematics Mozart was using in order to write music.
He just become a mason seven years earlier, and he learned about things like the old section.
And if you look at the overture, the overture is structured and such.
The key man with a triple chord happens. And as his transformation is, you have 83 bars and 103 bars is the perfect choice.
If you alter a. You're shifting all that old ratio.
There's this sort of moments that it's based on. I think M.J. is deliberately.
Well, I mean, he's doing this, supposedly,
but I think because he spent time with the Masons he knew about the gold rush is very important to a lot of the science symbolism.
So I think I would counter that even the music that we find very listen to.
I think it's possible to find a lot of mathematics, which is which is high minded.
Got it. How you doing this time? You to one more question.
Yeah. We had a question about the breakfast.
I was just wondering on the front line, I was wondering if you thought of the background being in the movie,
the whole movie newest thing, or if it has anything to do with evolution.
Okay. So my oldest would of course, the painting does have the symbol that Pentagram, that's the the symbol used by Masons.
And the reason they use it is also because the devil worshipping it, because hidden inside there is the golden ratio.
If you look at it, it's all over the place and you look at the long length across the top, one point to the other,
and then compare that to the points going all the way to the sort of the angle of the side that is in the golden ratio establishment ratio.
So it's a sort of like a template, but it depends around the temple is a way for an architect.
What am I doing? So, so in mind here is actually creating things with aesthetic and using if you guys in Psychology
London which is next to the Royal Palace outside on the pavements is a pentagram being changed?
Now these backgrounds and the background is an image of the Alhambra.
Alhambra is an example of a combination of art, science and this idea of infinity thing.
One of the reasons them the more advanced is these Islamic artists enjoys playing around with the symmetry and tilings like this.
Is that in a finite wall you can express the sense of Venice because that symmetry tells you exactly what to do.
However, you go on in this,
you see sort of it's sort of like capturing one of the ideas that so obviously captured their idea of gold in some way, things like that.
And that's sometimes why they actually would a little imperfection because they would have nervous of trying to pretend to be gold.
And so they were using this imagery. An Arabic comic, for example, would often have a little arrow there.
So they won't say that I'm I'm on gold creating something that is imperfection.
Well, no, I don't think so. Thank you very much for being a great audience.
After starting a policy seeing country outside of Kosovo and whether or not this is going to be.