TEDxOxford - Marcus du Sautoy - The Two Cultures: A False Dichotomy

I thought you're going to say he's also very fit but you then said to do the job so I was good when were at school were often asked to make a choice Shakespeare or the second law of thermodynamics Ruben's or relativity Debussy or DNA art or science and when I was at school I was deeply frustrated by this sort of desire for the education system to put me into this art or science box when I was about 12 or 13 I sort of started to fall in love with the world of mathematics I enjoyed the way this language kind of explained the way the world word Mei helped us to make predictions about where we were going next it's incredible logical sides and I also fell in love with science but at the same time actually I started learning the trumpet started to play a lot of music really enjoyed the musical world did a lot of theater and things and so I found it deeply frustrating that I've somehow asked to make a choice about my career path my educational path about choosing to be a scientist or to be an artist I supposed to call this the two cultures of false dichotomy the two cultures of course comes from this lecture that CP snow gave about the problem of the two sort of a divide between these two camps now I actually turned out to be better at doing maths than playing the trumpet and so I chose the scientific route but ever since I've been doing my science becoming a mathematician proving theorems I've always kept a love of the Arts and music I listened to a lot of music when I'm doing my mathematics and I've done a lot of collaborations with artists over the time I collaborated with complicity on their theatre works with some composers and so I've always been interested in really is this sir is it really true there is sort of two different camps and as I've explored these two areas I realize actually we're often interested in exactly the same things about structures structures our interest us and intriguingly the structures that artists often are drawn to often the same sort of structures that I find interesting from a mathematical perspective so in this talk is so I have got enough time to to look at the whole of the arts and the sciences so I just chose a particular example to illustrate this kind of dialogue between the world of art and science and I suppose the dialogue between mathematics and music has always been one that people have talked about so I token a particular composer one of my favorite composers who is olivier messiaen olivier messiaen was a composer french composer during the 20th century and a lot of his music deliberately seeks out mathematical structures he loved mathematics in order to create certain effects one of my favorite pieces of messy anne is a quartet he wrote some called the quartets for the end of time this quartet he wrote whilst he was a prisoner of war in germany during the second world war in the prisoner of war camp there was an upright piano he played piano and he discovered there was a clarinetist a violinist and a cellist also in the camp and say red is quartet to express the kind of terrible times that happening and wanted to create a sense of timelessness in this first movement the liturgy - Crysta in order to create a sense of unease and never-ending time what he did was to use a bit of mathematics he knew about prime numbers prime numbers are these indivisible numbers like 7 and 17 things can't be divided by and think for themselves and one and he used these Prime's to create this sense of unending time so in the first movement so the clarinet and the violin exchange bird themes he was very obsessed by bird themes but it's in the piano where you see these use of these prime numbers to create this sense of unease I'm so in the piano piece and this is the score for the piano piece the piano plays a 17 note rhythm sequence and after 17 notes it repeats the same rhythm again and again throughout the piece let's see we're pressing there we go that's the red line there so the rhythm starts it starts crotchet crotch at crotch it then does nice syncopated rhythm and then repeats after 17 notes crotch it crotchet crotch it again the harmonic sequence however is doing something else it has a 29 nota monic sequence and after 29 notes it then starts repeating itself but at that point the rhythm is only about two-thirds of the way through its pattern when the rhythm finishes again the harmony is somewhere else and so the two things by using the prime 17 and 29 messy a very carefully keeps the two things out of sync a piano just repeats this harmonic sequence 29 notes again and again the rhythm 17 notes again and again but because they never interact in the same way each time they're repeated you get this sense of unease and eventual timelessness because you never you have to hear the thing 17 times 29 times before you hear it actually come full circle again and the piece is finished by that point um so let's hear these prime 17 and 29 in action in the piano piece you spacious starts again harmony is still working its way through its changing line sequence harmony is finished and starts again but the rhythm is somewhere completely different now of course messy and doesn't expect you to hear these prime seventeen and twenty nine because it's such a long sequence of time but he does feel wants you to feel the effect of these structural numbers not interacting keeping them out of sync and interestingly missing on is picking up on something that Nature has been using for a long while it's an interesting insect in North America a cicada which uses the same principle of these primes to keep it out of sync for its evolutionary survival and the species of sacada has extraordinary lifecycle it hides underground doing absolutely nothing for 17 years then after 17 years they the cigar does all emerge on mass from the ground and they party away this is the sound of one Secada you have to multiply this by millions of these things in the forest but the sound of the voice is so loud that most residents move out during the seventeenth year they tidy away they eat the leaves they mate they lay eggs and then after six weeks of parting they will die fall to the floor the frost goes quiet again for another 17 years before the next brood appears I'm is actually extraordinary life cycle how the sacada is counting to 17 we don't know because there's nothing in the natural cycle which has a 17 year cycle sunspots have 11 years but we're not even too sure what how they manage to do this but why are they choosing 17 prime number is the prime number Messier used in his work is it just a coincidence well we think not there's another species of sacada in North America which appears every 13 years and over in North America you can find different species they either choose 13 or 17 never 12 14 15 16 or 18 just these Prime's 13 and 17 so we think there's something about these primes which is helping these cicadas we're not sure what it is but we think it's the same trick as the Messier we think that this prime number life cycle keeps it out of sync or maybe a predator so for example if there's a predator that appears periodically in the forest say every six years then a sacada that appears every nine years is going to get in sync with the predator very quickly is every 18th year the cicadas and the predator are in the forest so it gets wiped out but it's a condor that has a seven-year lifecycle well because prior the seven is a prime number that can keep out of sync much better of this predator and so the cicadas and the predator only eat meats for the first time in year 42 so those cicadas which have a prime number lifecycle seem to survive much better because they can keep out of sync in the forest in North America that seems to be in a real competition between who knows their Prime's better than the others the cicadas got up to 17 predators white town so a message there if you know your maths you survive in this world but it's interesting because missing I was picking up on something which is already there in the natural world and I think that's often what we're doing we're responding to structures in the natural world around us either I'm from an artistic point of view or from a mathematical point of view but intriguingly sometimes artists are drawn to there in that piece that the quartet for the end of time missing I knew what he was doing he knew his prime numbers he knew how to create this effect but sometimes artists are drawn purely for aesthetic reasons to structures which have huge mathematical significance messy I was actually a follower of Arnold Schoenberg's method of writing music ensuring Berg the beginning of the 20th century they threw away tonal music and replaced it with atonal music where each note of the chromatic scale was given equal value but you need some structure of you're going to throw tonal music away you need to put in new structure that new structure was very mathematical so Schoenberg widsom do a permutation of these twelve notes to create these twelve tone rows so he would arrange the twelve notes of the chromatic scale in some interesting way and then he would do mathematical operations on these he would do reflections translations rotations to create a palette of forty eight ten rows which he would then use to do his composition messy and fell in love with this way of creating a palette of musical themes from which to compose and Chiang Lee and a piece that he wrote for solo piano so this called the eel default to in this piece he chooses to 12 town rows so two permutations of 12 notes which he felt has some interesting relation to each other so when you played them on the piano it sort of had some sort of strange connections with each other now from a mathematical point of view if you view these 12 to 12 tone rows as permutations of two 12 things then it actually generates a symmetrical object in my world the world I research is the world of symmetry and there's an incredibly exciting mathematical object which we call m12 it's rather a it's a symmetrical object I can't show you because it lives in very high dimensional space but the discovery of this at the end of the 19th century gave rise to the discovery of kind of exceptional symmetrical objects out there in the mathematical world now interesting Lee Messier is 212 tone Rose when viewed from a mathematical perspective and you generate the symmetrical object which are associated to these two permutations creates this object m12 that mathematicians have been drawn to purely for mathematical reasons Monsieur knew nothing about this object has only been very recently observed that messieurs peace Ealdor fool to actually captures this symmetrical object so although I can't play you although I can't show you this high dimensional object I can actually play it for you so here's m12 that's the beginning anyway but I prefer the mathematical version I think it's more slightly more beautiful but um and that's interesting because mathematicians often talk about beauty in their subject and talk about aesthetics I mean it's kind of maybe more obvious that artists are plundering the scientific tool box to find interesting structures but I think mathematicians often talk about their subject and talk about the beauty of their proofs and one of the books that really excited me when I was a 12 or 13 year old and got me into doing mathematics was one of the books I've recommended outside I'm pushing it out of print at the moment it's going into a new print it's a book called a mathematicians apology by gh Hardy who's a Cambridge mathematician in the 20s and 30s and he wrote a mathematician like a painter or a poet is a maker of patterns I'm only interested and interested in mathematics as a creative art and actually Graham Greene wrote about this book that this is the best example of being a creative artist after Henry James's Diaries and so this book talks a lot about the creativity of math and I think most mathematicians if you ask them why they do their subject will not say I do it for utilitarian reasons I do it because I want to solve the problems of the world they'll do it say they do it for similar reasons the artist creates their work they want to create new structures they're interested in it for its own right and there's only the mathematics that I do in the mathematics I appreciate I choose the mathematics that I do because it tells an interesting story and for example one of my favorite mathematical theorems is a theorem of Pierre de fer de ma he proved many beautiful theorems and one he said if a prime is divisible if you take a prime number and you divide it by 4 and you get remainder 1 so something like 41 then you'll always be able to write that prime number as two square numbers added together so 41 we can write as 4 squared plus 5 squared so have a large or prime number is half of them when you divide by 4 have remainder 1 you'll always be able to write them as square numbers now I've never seen this being used in any practical way in the modern world or before however this is a beauty theorem and now she's not the result that's so important but the journey that forever takes you on in the proof because you start with the prime numbers so which lead remainder one on division by four and then as the piece goes on you suddenly see the arguments mutating this prime until it's some magical moment when it starts to become square numbers and it's almost like listening to a piece of music and when I read this proof and I the way I reproofs is very similar to the way I listen to music you can almost feel themes being established somewhere where you're happy and then they start to winter weave and take you on a journey to somewhere new and that's what mathematicians are after they're after telling stories that have exciting journeys and it's not very often just the final result so for example and I don't expect you to understand this but this is my greatest discovery in the world of mathematics which was a new symmetrical object which again lives in this very high dimensional space but I could get a computer to churn out endless new symmetrical objects new mathematical theorems but the role of the mathematician is like the artist I chose this particular symmetrical object to stand up in my seminars to write journal articles about to write books about because it tells an extraordinary story which connects the world of symmetry with a completely different area of mathematics called elliptic curves some area of number theory that we still don't really understand and so mathematics is a lot about choices and those choices often motivated by the same aesthetic decisions that an artist has and the same sort of structures that the artist is drawn to going to end with this quote here I've got another quote after as well but this quote here I want you to think what do you think this is a quote written by a mathematician or an artist to create consists precisely in not making useless combinations invention is discernment choice the sterile combinations do not even present themselves to the mind of the inventor so how many people think that as an artist talking about their subject put your hands up everything as an artist quite a few votes the artists how many people think a scientist a bit more maybe the word inventor you know don't artists then tend to call themselves inventors how many people are not sure could be either after this talk should be perhaps orbiting hands up in Alberta well in fact I mean the wording venture is intriguing because actually Stravinsky used to call himself an inventor um so he felt that he was inventing the music that he developed but it is in fact a mathematician it's a very famous mathematician on rape Juan Corre the discoverer of chaos theory and it certainly expresses what I believe about the mathematical world although the logic of mathematic forces things to be either true or false there are so many true statements out there after all half the statements are true in mathematics it's about making choices about which ones are you going to bother talking about and exciting people about in the seminars and papers that you're right so it's just in the same way as there are infinitely many pieces of music it's about choosing the combinations of notes that say something to the soul and in fact one of the other books that I chose which is outside which is a ray formative book with that I read as a student is a book called the glass speedgame by but by Hermann Hesse and the glass bead game for me I don't know has anybody read the glass bead game here a few readers of God you must read this book this captures for me what we should be doing in our education system and our and Beyond which is breaking down the barriers between all of these subjects stop talking about subjects being maths or history or music or culture or art they're all sides they're all part of the same subject and in this book they play this wonderful thing called the glass bead game which sort of tries to combine all of the subjects into one fusion and I think that's what I've been doing all my life is really trying to play this gas speed game the symbols and formulas of the glass bead game combined structurally musically and philosophically within the framework of a universal language we're nourishing by all the sciences and arts and strove in play to achieve perfection pure being the fullness of reality and that's what I think we should all be doing thank

Channel: TEDx Talks

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Keywords: tedx talks, tedxoxford, talk, mathematics, english, ted, lecture, marcus, ted x, ted talks, tedx talk, science, maths, du sautoy, tedx, ted talk

Id: 2v3IWGiThKA

Length: 18min 27sec (1107 seconds)

Published: Fri Jan 06 2012