tag:blogger.com,1999:blog-3175577296727913212016-04-14T14:47:36.257+01:00Finding Moonshine"Finding Moonshine: a mathematician's journey through symmetry" is a new book by the author of The Music of the Primes. In twelve chapters, one for each month of his working year, Marcus du Sautoy explores the nature of symmetry and gives an unparalleled insight into the working life of a mathematician.Marcus du Sautoyhttp://www.blogger.com/profile/09231135591825316245noreply@blogger.comBlogger48125tag:blogger.com,1999:blog-317557729672791321.post-39807738302895198232016-01-04T13:41:00.003+00:002016-01-04T13:43:17.319+00:00The Code on US Netflix<a href="http://3.bp.blogspot.com/-Hta2vNAGmbA/Vop1bplTZ8I/AAAAAAAAAUc/NXmmASsyjII/s1600/starlings.jpg" imageanchor="1" ><img border="0" src="http://3.bp.blogspot.com/-Hta2vNAGmbA/Vop1bplTZ8I/AAAAAAAAAUc/NXmmASsyjII/s320/starlings.jpg" /></a> Very exciting that my 3 part BBC series The Code is now available on US Netflix. Some viewers have written to me very excited to have freeze framed an extraordinary pattern made by the flock of starlings that we filmed in Denmark, the so-called black sun (which I've posted above). Was this some amazing message the starlings were trying to communicate? Is the answer to life the universe and everything 6 not 42. So perhaps I should explain... When The Code first aired in the UK we ran an online competition which involved spotting clues in the show. It was made with the great game developer <a href="http://www.sixtostart.com/">http://www.sixtostart.com/</a> who also do the fantastic Zombies, Run app. Here is an article from Wired about the competition. <a href="http://www.wired.co.uk/news/archive/2011-07/27/the-code">http://www.wired.co.uk/news/archive/2011-07/27/the-code</a>One of the clues was the number 6 hidden in the flock of starlings. There was another clue for example painted onto the nails of one of the Rock-Paper-Scissors competitors. There were also online games you needed to play. One of my favourites was Master of the Mosaics, all about reading symmetry in the walls of Moorish Palace like the Alhambra. You can play an extended version of the game here <a href="http://www.open.edu/openlearn/science-maths-technology/mathematics-and-statistics/mathematics/the-code-grandmaster-mosaics">http://www.open.edu/openlearn/science-maths-technology/mathematics-and-statistics/mathematics/the-code-grandmaster-mosaics</a>The Open University here in the UK helped create a lot of supporting material that you can find here <a href="http://www.open.edu/openlearn/whats-on/tv/ou-on-the-bbc-the-code">http://www.open.edu/openlearn/whats-on/tv/ou-on-the-bbc-the-code</a>It was a really great competition culminating in an extraordinary Code Book you had to download and complete once you'd unlocked the password. The first three to complete the book the were involved in a grand finale at Bletchley Park. The winner got a unique mathematical sculpture designed by Californian sculpter Bathsheba Grossman. You can find out more about the sculpture here: <a href="http://www.bbc.co.uk/blogs/thecode/2011/07/the-treasure-unveiled.shtml">http://www.bbc.co.uk/…/…/2011/07/the-treasure-unveiled.shtml</a>There is more here about the competition. <a href="http://www.sixtostart.com/the-code/">http://www.sixtostart.com/the-code/</a>and a video here of the finale <a href="https://www.youtube.com/watch?v=iZvQDdPz-JM">https://www.youtube.com/watch?v=iZvQDdPz-JM</a>Marcus. <a href="https://www.netflix.com/title/80063658">https://www.netflix.com/title/80063658</a>Marcus du Sautoyhttp://www.blogger.com/profile/09231135591825316245noreply@blogger.com0tag:blogger.com,1999:blog-317557729672791321.post-46416091097101942862014-02-13T13:26:00.000+00:002014-02-13T13:26:22.283+00:001+2+3+4+...=-1/12The equation <br /><br /> 1+2+3+4+...=-1/12 <br /><br /> is shorthand for how to meromorphically continue the Riemann zeta function beyond its region of convergence. <br /><br /> If you add up the integers there is no way you will get anything other than infinity. The equation needs to be understood in its context. The Riemann zeta function is defined as <br /><br /> <a href="http://2.bp.blogspot.com/-rrUbzdFHxqQ/UvzDNHCfj_I/AAAAAAAAATo/oW94QLtCY4s/s1600/zetafunction.jpg" imageanchor="1" ><img border="0" src="http://2.bp.blogspot.com/-rrUbzdFHxqQ/UvzDNHCfj_I/AAAAAAAAATo/oW94QLtCY4s/s320/zetafunction.jpg" /></a> <br /><br /> If you put s equal to any number bigger than 1 then the infinite sum of fractions converges. For example put s=2 and the function says add together 1+1/4+1/9+1/16+... This infinite series can be added up and you get rather beautifully <br /><br /> <a href="http://3.bp.blogspot.com/-w_tlqGJ2KM0/UvzEMHLo7EI/AAAAAAAAATw/6sqwy2M7lIk/s1600/zeta(2).jpg" imageanchor="1" ><img border="0" src="http://3.bp.blogspot.com/-w_tlqGJ2KM0/UvzEMHLo7EI/AAAAAAAAATw/6sqwy2M7lIk/s320/zeta(2).jpg" /></a><br /><br /> However if you put s equal to a number less than 1 the infinite series doesn't make sense. For example put s=-1 and you get 1+2+3+4+... <br /><br /> But if you now allow s to be a complex number (not just a real number) then there is a unique way to smoothly extend the definition of the function into the region where it doesn't converge. It is essentially taking another formula which will make sense for values of s less than 1 but which seamlessly meshes with the function you have already defined. It is essential to put this in the context of complex numbers because we have a theorem which says there is a unique way to do this. So if you can extend the function there is only one way to do it. This new function gives the value -1/12 when you put in s=-1. <br /><br /> The story of this equation is discussed more in chapter 4 and chapter 6 of The Music of the Primes. <br /><br /> Do not trust physicists bearing divergent series. You will lose your wallet. Marcus du Sautoyhttp://www.blogger.com/profile/09231135591825316245noreply@blogger.com0tag:blogger.com,1999:blog-317557729672791321.post-75195790590121503042013-06-01T15:22:00.000+01:002013-06-01T15:22:27.488+01:00Geometric Unity<a href="http://2.bp.blogspot.com/-aUOwqPUX1iQ/Uan_tAPLCQI/AAAAAAAAASI/c83gCKWt2_8/s1600/Geometric+Unity.jpg" imageanchor="1" ><img border="0" src="http://2.bp.blogspot.com/-aUOwqPUX1iQ/Uan_tAPLCQI/AAAAAAAAASI/c83gCKWt2_8/s320/Geometric+Unity.jpg" /></a><br /><br />Physics has a problem. In fact quite a few problems. Why are there three generations of fundamental particles, each seemingly just a heavier copy of the generation before? What is dark matter? Why is the expansion of the universe accelerating? How can one reconcile Einstein’s Field Equations which control the curvature of space time and represent our theory of gravity with the Yang-Mills equations and the Dirac equation which represent our theory of particle interactions on a quantum level? <br /><br />Two years ago Eric Weinstein, working from outside the academic system, came to me with some bold and unorthodox ideas that he had come up with as an attempt to answer these problems. My initial reaction to this was the same as to any such proposal of this type: skepticism. Like many academics I regularly receive hundreds of emails, letters, books from a whole range of people claiming the discovery of a theory of everything or proofs of the Riemann Hypothesis or the Goldbach Conjecture. However I have always kept in the back of my mind the story of Ramanujan writing out of the blue to GH Hardy. Ramanujan’s approaches had been rejected by two academics in London before Hardy responded positively to his letters. So I try to give serious proposals a hearing regardless of whether they come from inside or outside the academy. <br /><br />My initial skepticism began to wane though as I heard Weinstein’s ideas unfold. By the end of our meeting I was intrigued enough to dedicate time during the last two years to work through the ideas. I don’t understand every detail, but the ideas are beautiful and I believe extremely natural. It is a highly mathematical story but with clear implications to questions of physics. His approach is in line with Einstein’s belief in the power of mathematical geometry. Einstein talked about his conviction that the universe was made of marble not wood. Weinstein’s proposal which he calls Geometric Unity realizes Einstein’s dream. <br /><br />Geometric elegance is of course no guarantee that the mathematical universe that Weinstein describes must match the reality of our universe. However, if the details survive scrutiny it will still be a beautiful mathematical landscape Weinstein has uncovered, as well as one with uncanny similarities to the world we inhabit. <br /><br />Weinstein has kept many of these ideas to himself for nearly three decades. It took some courage for him to discuss the ideas with me. I was sworn to secrecy. Weinstein has also been discussing the ideas in secret with mathematician Ed Frenkel and physicist David Kaplan. But as I spent time with the ideas I believed that they were too important to be kept private and needed to be discussed more broadly. <br /><br />I debated with myself whether it was appropriate for me to host a lecture where Weinstein could begin to explain his ideas. Was this an appropriate use of my position as the Simonyi Professor for the Public Understanding of Science? Charles Simonyi prepared a manifesto when he endowed my chair to guide the holders of the chair in their mission. I would like to quote one part of the manifesto: <br /><br />“Scientific speculation, when so labelled, and when the concept of speculation and its place in the scientific method has been made clear to the audience, can be very exciting. It is a very effective communication tool, and it is by no means discouraged.” <br /><br />It was in the spirit of this part of my mission as the Simonyi professor that I decided to persuade Weinstein to give a special lecture in which he could start to propose the ideas he has been working on. The decision to try to publicise his ideas was not taken lightly as all attempts at a Unified Theory have failed so far. However, a little thought reveals that whenever a final theory is at last found, it will first begin its public life with an overwhelming statistical likelihood of failure. <br /><br />As Charles Simonyi suggested let me make very clear how the scientific method can work. If you have new ideas it is perfectly acceptable to try to articulate these ideas through a seminar or lecture before publishing a paper. The ideas might go through some revision and evolve through dialogue with other scientists. Ultimately these ideas must be written down and evaluated by the communities to which they are relevant. The lecture that Weinstein gave last week was the beginning of that process. A paper which Weinstein is currently working on will in due course appear. <br /><br />As Charles Simonyi expressed in his manifesto “scientific speculation can be very exciting”. It is an excitement that I think the public can share. No one other than the relevant scientific communities will be able to evaluate the merit of the work, but why shouldn’t the public see science in action? It can help communicate the challenging problems that physics still faces. <br /><br />It took a lot of courage for Weinstein to come forward and talk about his ideas. He comes as something of an outsider but with the sensibilities and knowledge of an insider, a difficult place from which to propose bold ideas. He has a PhD from Harvard, post-doctoral experience from MIT and the Hebrew University. Not a bad grounding. But rather than staying in academia he went a more independent route working in economics, government and finance. But I have always been a believer that it doesn’t matter who the person is and what is their background, it is the ideas that speak for themselves. I believe science has much to gain if the ideas turn out to be correct and little to lose if they turn out to be wrong. <br /><br />For a general description of the ideas being proposed check my <a href="http://www.guardian.co.uk/science/2013/may/23/eric-weinstein-answer-physics-problems">Guardian blogpost</a> Marcus du Sautoyhttp://www.blogger.com/profile/09231135591825316245noreply@blogger.com5tag:blogger.com,1999:blog-317557729672791321.post-7931893889418548372013-02-24T12:26:00.002+00:002013-02-24T13:22:13.023+00:00BBC Radio 6: Maths and Music with Miranda Sawyer<a href="http://4.bp.blogspot.com/-oAsI547aARw/USoGzT004vI/AAAAAAAAARg/QRhKNmcy2SE/s1600/5:4.png" imageanchor="1" ><img border="0" src="http://4.bp.blogspot.com/-oAsI547aARw/USoGzT004vI/AAAAAAAAARg/QRhKNmcy2SE/s320/5:4.png" /></a><br />I did an interview for Miranda Sawyer on BBC Radio 6 for her forthcoming series which will include a programme about maths and music. I did a radio series about maths and music for The Essay on BBC Radio 3 some years ago which you can listen to <a href="http://people.maths.ox.ac.uk/dusautoy/flash/2soft/sound/">here</a> That series was mostly concerned with my love of classic music. So I was interested to find out about good examples of maths in popular music. Radiohead, Bjork, Gorillaz all have good examples of interesting time signatures and mixtures of beats which give an unsettling feel of not quite knowing where the beat is. For example: Radiohead 15 Step is in 10/8, Gorollaz 5/4 does what it says on the tin...moves between 5 and 4 beats per bar in an unsettling way, Bjork's Crystalline is in 17/8 (I think Messiaen would have enjoyed that!). <br /><br />But I was intrigued to know about other examples. So who better to ask than my twitter followers. Below are some of their replies. I thought it worth sticking them here because it's hard sometimes for everyone to see all the interesting responses. It's also worth checking out the <a href="http://en.wikipedia.org/wiki/List_of_musical_works_in_unusual_time_signatures">wiki entry</a> which is full of good examples of songs with interesting rhythms and metres. <br /><br />One of the most striking examples was Tool's <a href="http://www.youtube.com/watch?v=wS7CZIJVxFY">Lateralus</a> which uses the Fibonacci Series via @SalisburyHill Reminded me of my post on <a href="http://findingmoonshine.blogspot.co.uk/2010/07/twitter-fibs.html">fibs</a><br /><br />Here are some of the replies I had from twitter: <br /><br />Jon Saunders @fygaro146 the Birdie Song is based on fractals. However hard you listen it remains just as annoying as it was before. <br />Paul O'Hagan @pmohagan Golden Brown by Stranglers has that extra beat in the instrumental. Think it goes 6/8 to 7/8 v. effective <br />MaST@EdgeHill @EdgeHill_MaST @RobertSmyth Golden Brown by Stranglers is in 13/4 time <br />Richard Hopkins @dadhopdog Golden Brown by the Stranglers is in 3 time but sticks in a 4 beat bar on the 4th bar between verses. <br />Julian Peace @JulianPeace1 As mentioned, Lateralus by Tool varies from 9/8 - 8/8 - 7/8. 987 being the 16th Fibonaci number. <br />Julian Peace @JulianPeace1 Lateralus by Tool is worth looking at. It's all rather clever... <br />Paul Firth @TedInCanada Check out the information online about tool, particularly the album lateralus. fibonnaci rhythms! Tool's Lateralus uses Fibonacci Series via @SalisburyHill@msmirandasawyer Check out http://www.youtube.com/watch?v=wS7CZIJVxFY …and http://findingmoonshine.blogspot.co.uk/2010/07/twitter-fibs.html … <br />Damian Armitage @iAxiom78 All You Need is Love, by the Beatles swap between 3/4 and 4/4. Some think it's 7/8 but its not <br />Damian Armitage @iAxiom78 Excuse my language but "Bastard" by Ben Folds mixes it up; 3/2, 3/4, 4/4, 5/4, 6/4 & 7/4. <br />Stuart @20Hotels Jeff Buckley’s “So Real” moves from 4/4 to 6/8 to 2/4 in space of a few bars. Quite unnerving. Cream “White Room” opens 5/4 <br />Brett Callacher @bcbluesy Jacobs Ladder by Rush alternates 5/4 6/4 and 6/8 7/8. Results in a really ominous feel. <br />Brett Callacher @bcbluesy also intro: this song was originally done in 1968 but we are going to do it 4/4 so you can clap along. <br />Geoff Smith @GeoffBath "Strawberry Fields Forever" is all over the shop. <br />Robert Smyth @RobertSmyth two faves: tessellate by Alt J, and Dodecahedron by Beth Jeans Houghton <br />Michael Sheen @SheenNotHeard And the overture to Class's Akhnaten uses the same phrase but in 1/4 notes, then 16th notes, then 32 notes <br />Michael Sheen @SheenNotHeard More popularly, Kashmir by Led Zep: the riff is 3/4 or 6/8, and the drums 4/4. Black Dog is similar. <br />Michael Sheen @SheenNotHeard Math rock and metal acts like Meshuggah will play a riff in 17/8 etc over a 4/4 drum so the accent shifts <br />Eddie Rumkee @eddrumkee Penguin Cafe Orchestra's Perpetuum Mobile has 15 beat phrases. <br />Mike Pitt @mhpitt Serenade by Derek Bourgeois. Cuts from 11/8 (3323) to 13/8 and 7/8 etc. Wedding march for his wife...http://www.windrep.org/Serenade_(Bourgeois) … <br />Mike Pitt @mhpitt I assume you've got Brubeck on the list... <br />Leighton Pritchard @widdowquinn Not time sig, but 'phasing' may also be of interest: e.g. http://en.wikipedia.org/wiki/Piano_Phase … and http://en.wikipedia.org/wiki/Clapping_Music … <br />EP @Phonosexual Conlon Nancarrow even experimented with using irrational and even transcendental musical proportions! <br />EP @Phonosexual Blackened, by Metallica also goes through a range of time signatures. <br />EP @Phonosexual Soft Machine also play a lot with time signatures. And Debussy allegedly used measures the length of Fionacci numbers. <br />EP @Phonosexual Lobachevsky, by Tom Lehrer! Frank Zappa's Little House I Used To Live In also has am interesting time sig. <br />Tariq Desai @tariqDesai Also, interesting thing about the Gorillaz song is the 20-beat phrasing; 20 being LCM of 5 and 4. <br />Tariq Desai @tariqDesai Pink Floyd's Money is interesting: 7/4 over melody but 4/4 over the guitar solo; illusion of speeding up. <br />Tariq Desai @tariqDesai Outkast's Hey Ya features a queer combination of 4/4 and 2/4 bars. <br />RespectMyCrest @RespectMyCrest @msmirandasawyer money changes sigs as Gilmore couldn't do a solo in original sig, unlike the saxophonist <br />Dave Brown @youldave http://en.m.wikipedia.org/wiki/Xenochrony <br />David Gower @Gowerly Skimbleshanks (from cats) starts in 13/8 and Gershwin's Chichester Psalms changes time whenever it wants <br />hooperdave @hooperdave Wikipedia claims Meheeco by Sky is 8/8 and 7/8. I'm sure they've done one in 3/4 and 4/4 or arguably 15/4 <br />Jon Dickenson @Newtonfrisky Didn't 'Money' by Pink Floyd do 7/8 or 7/4 with 4/4 or something? It does sound a bit odd?! <br />Peter Jeal @redziller http://www.youtube.com/watch?v=dIuDwESKjZc … Second part (from ~ 7mins) 4s & 3s classic Edgar Froese <br />Si Prentice @Mr_fermion Under a Glass Moon by Dream Theater, it's all over the show. <br />John Wilson @JohnWilson14 Try Radiohead's Pyramid Song - 7/8 time or something? - But you mean songs that interchange time sigs? <br />Laura Fearn @oulaura Some sections of Radiohead's Paranoid Android are in 7/8 timing in contrast to the general 4/4 <br />Steve Skipper @SteveSkipper Nine Inch Nails March of the Pigs http://en.m.wikipedia.org/wiki/March_of_the_Pigs#section_1 … plus @trent_reznor had an interest in maths <br />Stephen J Henstridge @HenstridgeSJ I think "Money" (Pink Floyd) used a combination of 7/4 & 4/4 <br />Alabaster Crippens @AlabasterC Outkast's Hey ya is probably the biggest pop hit of recent years to be so off kilter. <br />Alabaster Crippens @AlabasterC Blue Rondo alla Turk, 15 Steps, Money, Hey Ya!, two differently time signatured versions of Morning Bell. <br />davidjwbailey @davidjwbailey so many: for starters Foo fighters have intros in 7/4, and Genesis messed about with rhythm endlessly <br />Helen Ferguson @HelenFerguson5 love plus one by Haircut 100. What's the total? <br />Jane Bromley @jmbromley I like "New Math" composed and sung by Tom Lehrer. <br />Chris Marshall @oxbow_lakes American Pi: apparently it's 4 <br />Helen Ferguson @HelenFerguson5 Senses Working Overtime by XTC. All together now 1, 2, 3, 4, 5 etc <br />Mark Fletcher @mdfletcher I am the Walrus: I = he as you = he therefore you = me and we are all together <br />FrankH @2FrankH Mathematic by Cherry Ghost <br />Jim Spinner @Vim_Fuego I believe when Queen recorded We Will Rock You @DrBrianMay used delay times that were prime numbers on the intro. <br />Raymond Vander Metal @MetalJudge Obvious - Karma Police "arrest this man he talks in maths" Radiohead <br />Matt Foster @matt_j_foster Quasimoto - Microphone Mathematics (which samples De La Soul) or The Pointer Sisters - Pinball Number Count <br />andy hilton @iamandyhilton The amazing Kate Bush and Pi <br />Johnny Daukes @jdaukes Violent Femmes 'Add it up...' <br />Richard Hopkins @dadhopdog I've always loved the five beat rhythm of Take Five or the seven beat rhythm of Sabine-Gould's Gabriel song <br />Alfred Walker @donawalf Bobby Darin's multiplication. <br />Dz3k0 @JamesDafydd Calculus rhapsody on youtube. <br />Jerry Roche @JerryRoche no. 6 on this article might be what you're looking for: http://www.cracked.com/article_18896_10-mind-blowing-easter-eggs-hidden-in-famous-albums.html … #biglink <br />david kelner @davidkelner The album A Grounding In Numbers by Van Der Graaf Generator has a track called 5533 among other mathematical delights <br />Jenny Jacoby @pixiecake obviously, three is the magic number. Even with the sums as lyrics I don't remember the three times table. <br />Cheesy winner Bruno Mars U can count on me like 1 2 3 I'll be there. And I can count on u like 4 3 2 U'll be there <br />Michael Seaton @mikeo_s Tom Lehrer's New Math and Lovachevsky - arithmetic method vs. results and mathematical plagiarism. :) <br />Malcolm Chalmers @UrsaMal Jonathan Coulton - Mandelbrot Set. Contains a (slightly adapted) version of the entire formula. <br />Phil Marsh @Hey_Marshy anything by Joy Division <br />Justified Left @justified_left Big Audio Dynamite: E=mc2http://www.youtube.com/watch?v=wRyZyrnVsFA … <br />Paul O'Hagan @pmohagan 2 4 6 8 Motorway. (2 times table for the keen eyed). <br />Lorna @LornaRedpath Inchworm with Danny Kaye - maths isn't just for the classroom! http://www.youtube.com/watch?v=fXi3bjKowJU … <br />Joel Tibbitts @TibbittsJoel It has to be Three is the magic number by Bob Dorough.Kate Bush's song Pi about pi is also good. <br />sam wollaston @samwollaston Hit Me With Your Logarithm Stick by Ian Dury #bbcradio6 #MathsMusic <br />Robert Smyth @RobertSmyth The whole Bjork's Biophilia album. One is 17/4. <br />Louise Brown @LouiseBrown definitely @applesinstereo. Robert did a whole episode of Relatively Prime on it @Samuel_Hansen <br />James Fowkes @fowkc check out Klein four "finite simple group of order two" http://m.youtube.com/watch?v=UTby_e4-Rhg&desktop_uri=%2Fwatch%3Fv%3DUTby_e4-Rhg&gl=GB … <br />Norman Dunbar @NormanDunbar One and One is One by Medicine Head? I think they got it wrong! <br />Oliver Prior @InfraredPanda Most time signature changes in a song for some ~(relaxing) Sunday listening: http://www.progarchives.com/forum/forum_posts.asp?TID=69410 … Marcus du Sautoyhttp://www.blogger.com/profile/09231135591825316245noreply@blogger.com0tag:blogger.com,1999:blog-317557729672791321.post-41465249340480208102012-10-15T09:27:00.001+01:002012-10-15T09:29:11.670+01:00Queen given dominion in hyperspace<div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-9-QxJpOhS9Y/UHu6ApYIRZI/AAAAAAAAAQ0/3fB6MxxhNjA/s1600/15689_Marcus_Queen_hyperspace.jpg" imageanchor="1" style="margin-left:1em; margin-right:1em"><img border="0" height="213" width="320" src="http://4.bp.blogspot.com/-9-QxJpOhS9Y/UHu6ApYIRZI/AAAAAAAAAQ0/3fB6MxxhNjA/s320/15689_Marcus_Queen_hyperspace.jpg" /></a></div> An Oxford University mathematician will give Her Majesty The Queen an unusual Diamond Jubilee gift: her very own piece of mathematical infinite dimensional hyperspace. Professor Marcus du Sautoy of Oxford University’s Mathematical Institute has named a new symmetrical object he has discovered ‘The Diamond Jubilee Group’ in Her Majesty’s honour. However, The Queen won’t be able to take a stroll around her new mathematical domain as this symmetrical object exists beyond our three-dimensional universe. Instead, she will receive a framed certificate from Professor du Sautoy describing in mathematical language the contours of her strange new dominion. The contours of this new shape encode three important numbers: 1952, the year of The Queen’s accession to the throne, 2012, and 60 (the years she has reigned). The Queen’s new symmetrical object is one of a seam of such shapes that du Sautoy has uncovered in hyperspace. He has decided to allow members of the public to name some of the other new shapes in a drive to involve the public in the fundamental research that is done in Oxford. In exchange for a donation to an educational charity that du Sautoy supports he will allow the donor to name one of these as yet unidentified symmetrical objects floating in hyperspace. Visit <a href="http://www.maths.ox.ac.uk/naming_symmetries">http://www.maths.ox.ac.uk/naming_symmetries</a> to name your own symmetrical object. ‘Unlike bell towers, ocean liners and Olympic Parks this creation will stand the test of time because mathematical discoveries last forever,’ Professor du Sautoy said: ‘I hope this initiative will give the public a chance not only to get involved in mathematics but also to join The Queen in hyperspace to celebrate her Diamond Jubilee.’ Symmetry is one of the most important concepts in science and underpins many parts of the natural world. Diamond gets its strength from the symmetry of the arrangement of Carbon atoms. The symmetry of a flower is key to attracting bees. Even the particles we’re hunting for in the Large Hadron Collider in CERN are discovered because underlying symmetries tell us where to look. So the discovery of a new symmetrical object always has the potential for exciting new revelations. Naming mathematical shapes has a long history: The fives symmetrical shapes that make good dice are named after Plato: the Platonic solids. Symmetrical shapes like the classic football made from hexagons and pentagons are named after Archimedes: the Archimedean solids. But a strange symmetrical shape with more symmetries than there are atoms in the sun that lives in 196883 dimensional space, discovered in the 1970s, was so daunting it was named ‘The Monster’. Oxford University has a very strong research team exploring the world of symmetry. Professor du Sautoy’s new symmetrical object forges a link with one of the great mysterious in mathematics: solving equations called elliptic curves. Ever since the Ancient Greeks, mathematicians have been trying to find solutions to different equations. Fermat’s Last Theorem, solved by Oxford mathematician Andrew Wiles, proved that equations that generalize Pythagoras’s famous equation do not have solutions. Elliptic curves are the next great challenge. Reported on in <a href="http://people.maths.ox.ac.uk/~dusautoy/Times1.pdf">The Times</a> , <a href="http://www.bbc.co.uk/news/uk-england-oxfordshire-19920702">the BBC Website</a> , <a href="http://www.bbc.co.uk/news/uk-england-oxfordshire-19936501">BBC TV</a> , <a href="http://www.wired.co.uk/news/archive/2012-10/13/queen-hyperspace">Wired Magazine</a>Marcus du Sautoyhttp://www.blogger.com/profile/09231135591825316245noreply@blogger.com2tag:blogger.com,1999:blog-317557729672791321.post-53442126880933353602012-06-11T13:12:00.001+01:002012-06-11T13:14:50.793+01:00Maths on Stage: The Dramatic Life of Numbers<a href="http://1.bp.blogspot.com/-02H7Z0UzZsQ/T9Xf1PiZ7yI/AAAAAAAAAQM/LqRk3wX7DAs/s1600/Hay2012.jpg" imageanchor="1" style="margin-left:1em; margin-right:1em"><img border="0" height="200" width="320" src="http://1.bp.blogspot.com/-02H7Z0UzZsQ/T9Xf1PiZ7yI/AAAAAAAAAQM/LqRk3wX7DAs/s320/Hay2012.jpg" /></a> <p> A packed tent for double maths at 10 on a Saturday morning at the Hay Festival was a very gratifying sight as I came on stage for the first of three events I did at the Hay Festival this year. And the stage was the right place to be discussing the exciting fusion of maths and theatre that has emerged over the last few years. I was exploring my collaboration with Complicite on their award-winning show A Disappearing Number and a new show that I am devising and acting in with actress Victoria Gould. This new show is in some sense a baby of A Disappearing Number as it is growing out of many of the themes we explored while developing the play Complicite did on the extraordinary collaboration between Hardy and Ramanujan. We will be giving people a sneak preview of our work in progress on this new piece at <a href="http://www.latitudefestival.co.uk/line-up/artist/complicite_presents_twin_primes_theatre_companys_production_of_xay_with_marcus_du_sautoy">Latitude Festival</a> this year when we perform Act 1. <p> In my event at Hay I wanted to show the audience why the world of mathematics and theatre are actually much closer than you might imagine. On the spur of the moment I decided to use my event to create our own little bit of mathematical theatre at Hay. I wasn't sure whether it was going to work but in the end it was surprisingly effective. A lot of the theatre games that Complicite use to devise their theatre depend on setting up very simple rules that allow the actors just to concentrate on reacting to their fellow actors. Being given the freedom of the stage and being asked to improvise something can quickly lead to a creative freeze. Simple theatre games often allow something unexpected to emerge that no one could plan. <p> We started with an exercise that I think can look magical. 20 members of the audience came up on stage. I asked each person to silently choose two others on the stage. When I said "go" they had to move to try to create an equilateral triangle with the two people they'd chosen. (The person and the two they've chosen must be an equal distance from each other). Of course the two people you've chosen are unlikely to have chosen you so a strange dance starts to emerge on stage. As the audience members still in their chairs watched on they observed an extraordinary crowd ebbing a flowing on stage, something that would have been impossible to choreograph without the simple mathematical rule. It was chaos in action...and it was very funny to watch. Three girls did end up choosing each other and very quickly stabilised as a still triangle in the chaos. As the scene developed the others began to get close to stability. A stillness across the group seemed to emerge but then one person moved very slightly, obviously trying to get their equilateral triangle perfect. That caused other triangles to become unequal and more people began to adjust. Very soon manic chaos had flooded the stage again. <p> The second exercise I did was one that actually appeared in the production of A Disappearing Number. I got 5 volunteers from the audience. They came on stage and immediately formed a group of 3 on one side of the stage and 2 on the other. This is called a "partition of 5". The exercise was to find how many different ways there are to partition the 5 people, how many different groupings were there? The members in each of the groups doesn't matter. It's how many there are in each group that is important. When I said "go" 1 member of the group of 3 peeled off. Suddenly we had 2+2+1. One of the couples separated. We had 2+1+1+1. 3 partitions of 5 people had already been found. But then the one that broke off went to join one of the other actors on their own. We'd returned to 2+2+1. It was a different arrangement of people but the same pattern as the second partition. Gradually they went through the other partitions. 3+1+1, a single group of 5 people. Then suddenly one broke off. We had a group of 4 and one actor on his own. You could feel his sense of loneliness, rejection by the group, the strength of the group of 4 staring at him. We'd got 6 partitions. I said that there was one they'd missed. They thought for a while. And then suddenly all separated into individuals on the stage. 5 groups of 1. 1+1+1+1+1. The exercise had discovered all 7 different ways of partitioning 5 actors. But in the process they'd created a poignant piece of theatre. Partition Numbers are a sequence of numbers that Hardy and Ramanujan had great success investigating. If you have a 100 actors how many ways are there to partition them? Hardy and Ramanujan discovered a formula for telling you. <p> While working on A Disappearing Number I did a number of workshops with Complicite for Drama and Maths teachers. The Drama teachers of course all want to come to a Complicite workshop but maths teachers are a little more reluctant about doing some physical theatre workshops. So we made it a condition that the drama teacher from a school could only come if they also bought a maths teacher with them. Apparently this was the first time many of them had talked to each other in the school common room. As the teachers gathered at the beginning of the session it was quite easy to spot who were the maths teachers and who were the drama teachers. Half of them were waving their arms around, shaking their legs, rolling their shoulders, warming up for a physical workout. The other half were in a corner looking rather shyly at their shoes. However it didn't take long to get everyone buzzing. The maths teachers came into their own and felt more confident as we took them all off on a journey to explore why one infinity might be bigger than another. The Complicite <a href="http://www.complicite.org/pdfs/A_Disappearing_Number_Resource_Pack.pdf">website</a> has a work-pack that was developed out of the workshops which teachers and others might enjoy. <p> I might add some more to this post but got to rush down to the National Theatre to do some maths with the cast of A Curious Incident of the Dog In The Time. More maths on stage!Marcus du Sautoyhttp://www.blogger.com/profile/09231135591825316245noreply@blogger.com0tag:blogger.com,1999:blog-317557729672791321.post-80324912501566646512012-05-28T20:55:00.000+01:002012-05-28T21:49:15.572+01:00Dara O'Briain's School of Hard Sums<div class="separator" style="clear: both; text-align: center;"><a href="http://4.bp.blogspot.com/-0ml_TvG5fZo/T8OBw4jrczI/AAAAAAAAAPQ/_5J83brt4Mc/s1600/Dara.jpg" imageanchor="1" style="margin-left:1em; margin-right:1em"><img border="0" height="180" width="320" src="http://4.bp.blogspot.com/-0ml_TvG5fZo/T8OBw4jrczI/AAAAAAAAAPQ/_5J83brt4Mc/s320/Dara.jpg" /></a></div> <p>I am co-hosting a mad comedy maths game show with Dara O'Briain on the TV channel <a href="http://uktv.co.uk/dave/series/tvseries/257755">Dave</a>. <p>I was away filming for another series last week when an episode was aired that required some calculus. I got lots of tweets and emails about the problem so thought it worth just explaining how you solve it. It's got some great maths in it. <p>Problem: A lifeguard at the beach spots a swimmer in distress in the water. They need to run across the sand to the water and then swim out to rescue the swimmer. But what is the fastest path to take? If he can run twice as fast as he can swim, should he run as far as possible to swim the shortest distance possible? Or should he take a shorter path even if it involves more swimming? Here are the dimensions of the beach and locations of the lifeguard and swimmer. <div class="separator" style="clear: both; text-align: center;"><a href="http://3.bp.blogspot.com/-pdrB4zLfm04/T8PN9QhERCI/AAAAAAAAAPg/miXiQCie1ow/s1600/Picture.jpg" imageanchor="1" style="margin-left:1em; margin-right:1em"><img border="0" height="159" width="320" src="http://3.bp.blogspot.com/-pdrB4zLfm04/T8PN9QhERCI/AAAAAAAAAPg/miXiQCie1ow/s320/Picture.jpg" /></a></div> <p>Lets suppose the lifeguard's running speed is v1 and swimming speed is v2. The task is to find x which will minimise the time taken to travel along D1 and D2. The time taken is exactly T=D1/v1+D2/v2. <p>We note that v1=2*v2. Since v1 is a constant instead of minimising T we minimise v1*T i.e. v1*T=D1 +2D2. Now by Pythagoras D1=√(x<sup>2</sup>+2<sup>2</sup>) and D2=√((75-x)<sup>2</sup>+25<sup>2</sup>). To minimise v1*T we differentiate the right hand side with respect to x and set this derivative to zero. We solve for x and this gives us the critical value for x. Explicitly, once the maths is done we compute that x=60.58m. This you can get by Newton approximation method. <p>There is also a cute physical way you could use to solve this puzzle. Once you realise that you are having to minimise D1+2*D2 you can then take a piece of string which you run from the red spot round the yellow spot and then back to the point where the string crosses the dividing line. You then drag this point on the dividing line along the line and see where the string length is smallest. At x=60.58 you’ll get a point where suddenly you need more string to move in either direction. <p>When you set the differential to 0 and expand it then they will get a quartic polynomial. If you want to find the exact value (rather than an approximate value) then you are going to need to know how to find roots of a quartic! Also there are 4 solutions. Two are complex but there is another real solution at 89.43. This corresponds in the equation to taking different roots of the square root. <p>At school you learn about a formula for solving quadratic equations. There is also an extraordinary formula for solving quartic equations discovered by Italian mathematician Ferrari. Details are <a href="http://mathworld.wolfram.com/QuarticEquation.html">here</a>. Feeding in the coefficients of our quartic gives the exact solution in the following form: <div class="separator" style="clear: both; text-align: center;"><a href="http://2.bp.blogspot.com/-pQYBZJqmvx0/T8PR_pS-tuI/AAAAAAAAAPw/JdBz6cPuEMs/s1600/Show1.2ExactSolution.jpg" imageanchor="1" style="margin-left:1em; margin-right:1em"><img border="0" height="230" width="320" src="http://2.bp.blogspot.com/-pQYBZJqmvx0/T8PR_pS-tuI/AAAAAAAAAPw/JdBz6cPuEMs/s320/Show1.2ExactSolution.jpg" /></a></div> <p>Glorious...if you like that kind of thing. <p>Why do we need to do quadratic equations at school? The problem Dara had to solve is an example where a problem of trying to find the optimal solution reduces to solving an equation. This one has x raised to the power 4 which we call a quartic. In school we learn how to solve a quadratic equation using a bit of algebra <p>Solving quadratic equations is something we do every time you catch a ball. If someone throws, kicks or hits a ball and you want to work out where to stand to catch it then the trajectory is described by a quadratic equation and solving it tells us where to stand. So Wayne Rooney is actually solving quadratic equations in his head every time he works out where to stand in the box to volley a ball in the back of the net. <p>This skill is very important in warfare too. If you want to hit a target then again you need to solve a quadratic equation to be able to decide the angle to fire the missile at. <p>We have been solving quadratic equations for millennia. The method we use dates back to ancient Babylon. The mathematicians of Babylon found a cunning way to solve these equations. They were interested in quadratic equations because they also describe areas of land. <p>But already in the tablets of ancient Babylon you can see people solving these equations not for practical reasons but for the fun of it. A quadratic equation is a bit like a cryptic crossword that hides the solution in some encrypted equation. Your challenge is to undo that cryptic description to reveal the answer to the puzzle. <p>The problem of finding a formula for solving cubics (things with x to the power 3) was one of the big challenges of the sixteenth century. Mathematical duelling was a public sport and great crowds would gather to watch mathematicians jousting with each other. Mathematicians would offer a cubic equation up and declare “solve that!” Tartaglia was an Italian mathematician who discovered the secret to solving these equations and made a lot of money in this public mathematical jousts. But he was tempted into revealing his secret to Cardano in exchange for the promise of future support. But Cardano betrayed his trust and told his student Ferrari who then saw how to generalize it to solving the quartic equation (x to the power 4 like in our problem). They published and poor Tartaglia lost the credit! <p>The problem of solving quintic equations (x to the power 5) turned out to be impossible with a simple formula and began the study of group theory which seeks to understand the world of symmetry. <p>You can find lots about this story in my book Finding Moonshine. <p>In order to find the value of x for which the time travelled is minimal we used the calculus. The calculus discovered by Newton and Leibniz is an extremely powerful tool for finding the optimal solution to practical problems. This idea of the power of the calculus to home in on the most efficient solutions to problems is one of the reasons it is a central tool in all modern science. It is used to do this day across the industrial and financial world. Investors use it to maximize profits. Engineers exploit it to minimize energy use. Designers apply it to optimize construction. It has now become one of the lynchpins of our modern technological world. <p>The calculus tries to make sense of what at first sight looks like a meaningless sum: what is zero divided by zero. Such a sum is what you are faced with calculating if you try to understand the instantaneous speed of an accelerating object. Take the famous apple that legend has it fell from the tree onto the young Newton’s head in the garden at Woolsthorpe and inspired his theory of gravity. The speed of the apple is constantly increasing as gravity pulls the apple to the ground. So how can you calculate what the speed is at any given instance of time. For example after one second how fast is the apple falling? Speed is distance travelled divided by time elapsed. So I could record the distance it drops in the next second and that would give me an average speed over that period. But I want the precise speed. Well I could record the distance travelled over a shorter period of time, say ½ a second or ¼ of a second. The smaller the interval of time the more accurately I will be calculating the speed. But ultimately to get the precise speed I want to take an interval of time that is infinitesimally small. But then I am faced with calculating 0 divided by 0. The invention of Newton’s calculus made sense of this calculation. He understood how to calculate what the speed was tending towards as you made the time interval smaller and smaller. It was a revolutionary new language that managed to capture a changing dynamic world. The geometry of the ancient Greeks was perfect for a static frozen picture of the world. But Newton’s mathematical breakthrough was the language that could describe a moving world. Mathematics had gone from describing a frozen still life to capturing a dynamic moving image. In our case we are trying to understand the behaviour of the distance D(1)+2D(2) as the distance x changes. If you draw a graph of this you get a curved graph. The calculus helps you to find the point where this graph reaches its minimum. <div class="separator" style="clear: both; text-align: center;"><a href="http://1.bp.blogspot.com/-KwsldA7WcBU/T8PS7uKlf1I/AAAAAAAAAP8/GiNdyR3Z5bE/s1600/graph.jpg" imageanchor="1" style="margin-left:1em; margin-right:1em"><img border="0" height="218" width="320" src="http://1.bp.blogspot.com/-KwsldA7WcBU/T8PS7uKlf1I/AAAAAAAAAP8/GiNdyR3Z5bE/s320/graph.jpg" /></a></div> <p>Work has been done by Timothy J. Pennings (Associate Professor of Mathematics at Hope College in Holland, Michigan) that suggests dogs are very good at finding such optimal solutions. See <a href="http://www.maa.org/features/elvisdog.pdf">here</a> and <a href="http://mathdl.maa.org/images/upload_library/22/Polya/minton356.pdf">here</a> Of course the dog isn’t really doing calculus (in the same way Wayne Rooney isn’t really solving quadratic equations) but it illustrates and important point that evolution has wired our brains to be good intuitive mathematicians. Those who can do maths survived. But it is by externalizing this maths that we can solve problems that defy our intuition. <p>The optimal path lifeguard is also the one light would choose if it travelled twice as fast in air as in water. In actual fact light travels only 1.33 times faster in air than in water so its path would be slightly different. However, this bending of the light waves (called refraction) produces many strange phenomena, such as making a straight pencil seem bent when it is put in water. Total internal reflection can be observed while swimming, if one opens one's eyes just under the water's surface. If the water is calm, its surface appears mirror-like. Another very common example of total internal reflection is a critically cut diamond. This is what gives it maximum sparkle. <p>The science behind this principle is known as Snell’s law. Snell's law states that the ratio of the sines of the angles of incidence and refraction is equivalent to the ratio of phase velocities in the two media. Using Snell’s law you can create total internal reflection. This occurs when, instead of light travelling from one substance to the next, the light reflects. This is a crucial physical phenomenon that allows us to use optical fibres. The light enters the plastic, and travels until it hits one of the walls. However, when it hits the wall, it is reflected instead of travelling through the clear plastic.Marcus du Sautoyhttp://www.blogger.com/profile/09231135591825316245noreply@blogger.com1tag:blogger.com,1999:blog-317557729672791321.post-68097485556472747882011-06-17T21:40:00.002+01:002011-06-17T22:34:26.205+01:00Maths in the City<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://2.bp.blogspot.com/-cpTKpFRh6DI/TfvIWQGLqkI/AAAAAAAAAMI/nY8Q3qSA4WE/s1600/mathsinthecity.jpg"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 200px; height: 78px;" src="http://2.bp.blogspot.com/-cpTKpFRh6DI/TfvIWQGLqkI/AAAAAAAAAMI/nY8Q3qSA4WE/s320/mathsinthecity.jpg" border="0" alt=""id="BLOGGER_PHOTO_ID_5619305244678400578" /></a><br />I have started an exciting new project called Maths in the City.<br />Maths in the City aims to highlight the fundamental role that maths plays in society by viewing the urban environment in a mathematical way. Conventionally, the urban environment is used to explore local history, architecture and culture - but it can also provide us with adventures in mathematics.<br />Maths in the City is an EPSRC funded public engagement project led by myself. The project is produced and managed by the Technology–Assisted Lifelong Learning (TALL) unit of the University of Oxford Department for Continuing Education.<br />We’d like to hear your mathematical stories of the city no matter who you are — young, old, students, teachers, researchers, member of the public, journalists... Anyone is welcome to shine a mathematical spotlight on their city!<br />We are also happy for you to either create a Site individually or in a group. If you and your friends or your family have an idea you’d like to work on together, or if you’re a teacher and would like your class to produce a Site, then we’d love to hear from you.<br />Go to <a href="http://www.mathsinthecity.com">www.mathsinthecity.com</a> to check out examples of sites and to add your own.<br />To launch the site we ran a competition to find examples of maths in the cities around the world. Five winners were chosen that came to Oxford to celebrate. As part of their prize I constructed some special symmetrical objects which I named after the winners.<br /><br />The Edward Mak Group: Set [C[1], C[2], C[3], C[4]]=[18, 6, 2011, 1] Corresponds to an elliptic curve of conductor 365504323038715. Maths in the City site: Burj Khalifa, Dubai, United Arab Emirates.<br /><br />The Samantha Keung Group: Set [C[1], C[2], C[3], C[4]]=[18, 6, 2011, 2] Corresponds to an elliptic curve of conductor 365537511174131. Maths in the City site: Most stable shape – triangle.<br /><br />The Nick Simmonds Group: Set [C[1], C[2], C[3], C[4]]=[18, 6, 2011, 3] Corresponds to an elliptic curve of conductor 365570706018123. Maths in the City site: Route Planning – the perfect walking tour.<br /><br />The Liz Meenan Group: Set [C[1], C[2], C[3], C[4]]=[18, 6, 2011, 4] Corresponds to an elliptic curve of conductor 365603907571075. Maths in the City site: The mathematics of tiling.<br /><br />The María Ángeles Gilsanz Group: Set [C[1], C[2], C[3], C[4]]=[18, 6, 2011, 5] Corresponds to an elliptic curve of conductor 365637115833371. Maths in the City site: Wallpaper groups, Segovia.<br /><br />Competition entries were so strong that we decided that five other entries deserved to be recognised as highly commended. These are:<br /><br />Hong Kong Space Museum (East Wing) by Cassandra Lee<br />The Gateway Arch – A Trigonometric delight by Ronan Mehigan<br />The Golden Ratio in Manchester by Sam Watson and Nicky Watmore<br />The Wobbling Bridge by Thomas Woolley<br />Topology on the Metro by Christian PerfectMarcus du Sautoyhttp://www.blogger.com/profile/09231135591825316245noreply@blogger.com0tag:blogger.com,1999:blog-317557729672791321.post-55195805633529828322011-01-02T16:54:00.003+00:002011-01-02T17:04:28.390+00:00Objects for the Future on the BBC World TonightOver the Christmas period the BBC World Tonight programme did a series of features where people proposed an object for the future. Listen <a href="http://people.maths.ox.ac.uk/dusautoy/flash/2soft/sound/OBJECT%201%20DU%20SAUTOY.mp3">here</a> if you want to hear my proposal: a conscious-ometer.Marcus du Sautoyhttp://www.blogger.com/profile/09231135591825316245noreply@blogger.com0tag:blogger.com,1999:blog-317557729672791321.post-11825109380577631872010-12-23T16:36:00.008+00:002010-12-24T16:51:36.594+00:004D Godless Christmas festivities<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://4.bp.blogspot.com/_VXvJUb9b-Xw/TRN6s6CnFYI/AAAAAAAAALY/7tue0AGAGTQ/s1600/NineLessons.jpg"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 225px; height: 320px;" src="http://4.bp.blogspot.com/_VXvJUb9b-Xw/TRN6s6CnFYI/AAAAAAAAALY/7tue0AGAGTQ/s320/NineLessons.jpg" border="0" alt=""id="BLOGGER_PHOTO_ID_5553917677390992770" /></a><br /><br />9 Lessons and Carols for Godless People is a show celebrating science at this festive time of year. In its third year, this was my first time performing alongside people like Simon Singh, Robin Ince, Dobby from Peep Show and Chris Addison from In The Thick of It and many other amazing performers.<br /><br />My spot looked at some of the fun maths in the festivities at this time of year. Take the Jewish festival of Chanucka for example. Already a holiday I love because you have to work modulo 19 to work out when it takes place. Celebrated over 8 days, one of the rituals involves lighting candles on each day. On the first day you light 2 candles, second day 3 candles...until on the last day you light 9 candles. The question every nerdy Jewish kid gets asked: how many candles do you need to celebrate Chanucka?<br /><br />You could just add up the numbers from 2 to 9 but there is a cleverer way to do this calculation. Look at the triangle of candles you are trying to count:<br /><br />C C<br />C C C<br />C C C C<br />C C C C C <br />C C C C C C <br />C C C C C C C<br />C C C C C C C C<br />C C C C C C C C C<br /><br />If I take another copy of the triangle and invert it then I can put the two triangles together to make an 11 x 8 rectangle which has 88 candles in. So one triangle has 44 candles in it.<br /><br />Not to be outdone, Christmas has its own mathematical problem. While Chanucka involves 2D triangles, the Christmas problem goes one dimension up and uses 3D pyramids. The problem relates to the famous Christmas song: The Twelve Days of Christmas.<br /><br />On the first day of Christmas, my true love gave to me...A Partridge in a Pear Tree.<br />On the second day of Christmas, my true love gave to me...2 Turtle Doves And a Partridge in a Pear Tree.<br />On the third day of Christmas, my true love gave to me...3 French Hens, 2 Turtle Doves And a Partridge in a Pear Tree.<br />...and so on, until the last verse:<br />On the twelfth day of Christmas, my true love gave to me...<br />12 Drummers Drumming<br />11 Pipers Piping<br />10 Lords-a-Leaping<br />9 Ladies Dancing<br />8 Maids-a-Milking<br />7 Swans-a-Swimming<br />6 Geese-a-Laying<br />5 Gold Rings<br />4 Colly Birds<br />3 French Hens<br />2 Turtle Doves<br />And a Partridge in a Pear Tree.<br /><br />So the maths problem: How many presents did I get from my true love over the twelve days of Christmas? Calculating the number of presents on each day is the same sort of problem as counting the candles at Chanucka. For example on the 12th day I get 12+11+10+...+3+2+1 presents. But how many do I get over the whole of Christmas?<br /><br />This time you need to stack all the triangles in layers so that you build up a pyramid. On the top is the first Partridge in the Pear Tree. On the second layer: a Partridge and two turtle doves. Here is a picture of 4 layers of the pyramid which I made for the performance. <br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://4.bp.blogspot.com/_VXvJUb9b-Xw/TROCG0XDEJI/AAAAAAAAALg/N6WKFe_cCwY/s1600/boxes.jpg"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 247px; height: 320px;" src="http://4.bp.blogspot.com/_VXvJUb9b-Xw/TROCG0XDEJI/AAAAAAAAALg/N6WKFe_cCwY/s320/boxes.jpg" border="0" alt=""id="BLOGGER_PHOTO_ID_5553925819124093074" /></a><br />My arts and crafts skills were pushed to the limits. It took me ages making those little boxes so I gave up after 4 layers. That's why I chose maths...you don't have to get your hands dirty with all that UHU glue.<br /><br />But how can I calculate quickly the number of boxes I would have had to have made to do all twelve layers. Well it turns out that if you take 6 of these pyramids you can rearrange them all to make a rectangular box with dimensions 12x13x14. So the total number of boxes in one pyramid is 12x13x14/6=364. So one present for every day of the year except Christmas!<br /><br />If Chanucka is a two dimensional festival (triangles), Christmas is a three dimensional festival (pyrmaids) then I thought I should invent a 4D festival to celebrate at the 9 Lessons and Carols for Godless People. <br />Here is the formula for Chanucka: \sum_{i=2}^{9} i<br />The formula for Christmas is a double summation: \sum_{j=1}^{12} \sum_{i=1}^{j} i<br />So the formula for a 4D Godless festivity is a triple summation: \sum_{k=1}^{N} \sum_{j=1}^{k} \sum_{i=1}^{j} i<br />where N is the number of days in our 4D Godless festival.<br />I've been getting people to help me via my twitter account (@MarcusduSautoy) to build up this 4D celebration of science. It is also based on a song...<br /><br />On the first day of Godless Christmas my geek friend sent to me...a boson in the LHC.<br />On the second day of Godless Christmas my geek friend sent to me... 2 twin primes and a boson in the LHC ... (but to make it a 4D puzzle we have to repeat the previous day so you also get another)... and a boson in the LHC.<br />On the third day of Godless Christmas my geek friend sent to me... 3 laws of motion, 2 twin primes and a boson in the LHC ... (and to get it 4D we repeat all the presents from the previous day so)...2 twin primes and a boson in the LHC ... and a boson in the LHC.<br /><br />So here are the suggestions via twitter for each additional present. <br /><br />4 pairing bases<br />5 Platonic Solids<br />6 Quarks a spinning<br />7 base units Measuring<br />8 bits a byte-ing<br />9 Heegner numbers prime generating<br />10 Rorschach Inkblots diagnosing<br />11 dimensions a-stringing<br />12 astronauts moon-walking<br />13 Neptune moons an-orbiting<br /><br />There has also been some debate about how many days the 4D Godless festival should have:<br />42 was suggested during one show - a good geeky number.<br />Infinite was suggested in another show - A very long festival ... especially towards the end.<br />Someone suggested via twitter 28 since it is a perfect number. Quite like that one.<br />I've gone for 13 at the moment as that proves I'm not superstitious. <br /><br />But how many presents would we get from our geeky friend? Well that requires building shapes in 4 dimensions. Something that is beyond my arts and crafts skills.Marcus du Sautoyhttp://www.blogger.com/profile/09231135591825316245noreply@blogger.com0tag:blogger.com,1999:blog-317557729672791321.post-18473242680283440222010-11-17T09:58:00.001+00:002010-11-17T10:00:57.871+00:00The Beauty of Diagrams<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://4.bp.blogspot.com/_VXvJUb9b-Xw/TOOn0NNWx1I/AAAAAAAAAK4/AMSk0uX0J9E/s1600/beauty%2Bof%2Bdiagrams%2BTx%2Bcard%2Bfinal%2B12.11.gif"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 320px; height: 166px;" src="http://4.bp.blogspot.com/_VXvJUb9b-Xw/TOOn0NNWx1I/AAAAAAAAAK4/AMSk0uX0J9E/s320/beauty%2Bof%2Bdiagrams%2BTx%2Bcard%2Bfinal%2B12.11.gif" border="0" alt=""id="BLOGGER_PHOTO_ID_5540456481936557906" /></a><br /><br /><br />BBC 4 (6 x 30 mins)<br /><br />Transmitting weekly on BBC 4 at 20.30 and 22.00 from Thur 18th November 2010, BBC HD at 23.35<br /><br /> <br />Why do complex scientific theories and equations often only make sense when portrayed in pictures? How have scientific diagrams, drawings, sketches and graphs revolutionised our understanding of science?<br /><br />One of the most pervasive myths about science is that it doesn’t require art. Science, we’re told, is about the logic of numbers, hard cold facts and the recording of experiences purposefully stripped of emotion. Nothing could be further from the truth.<br /><br />In this new six part series I will illustrate and explore that far from being a reluctant visual medium, science is actually at the forefront of the design and creation of a number of iconic visual diagrams. From Newton’s Prism to Da Vinci’s Vitruvian Man to Watson and Crick’s extraordinary diagram of the Double Helix diagrams have successfully shaped and defined our understanding of complex scientific theories and over time have become accepted in society as astonishing illustrations in their own right. In this new series I will navigate viewers through the numerous diagrams, graphs, sketches and designs that have revolutionised our understanding of the world around us.Marcus du Sautoyhttp://www.blogger.com/profile/09231135591825316245noreply@blogger.com0tag:blogger.com,1999:blog-317557729672791321.post-29688094178986241102010-07-11T10:22:00.002+01:002010-07-11T10:47:31.542+01:00Twitter Fibs<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://2.bp.blogspot.com/_VXvJUb9b-Xw/TDmNwGFSNeI/AAAAAAAAAKY/X4jT9iwpuSE/s1600/ledbury.jpg"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 320px; height: 293px;" src="http://2.bp.blogspot.com/_VXvJUb9b-Xw/TDmNwGFSNeI/AAAAAAAAAKY/X4jT9iwpuSE/s320/ledbury.jpg" border="0" alt=""id="BLOGGER_PHOTO_ID_5492577077961045474" /></a><br />I'm speaking at the <a href="http://www.poetry-festival.com/talks.html">Ledbury Poetry Festival</a> today about the connections between maths and poetry.<br />Among other things, I am going to be talking about Fibs: a peom with 1,1,2,3,5,8,13 syllables per line. The numbers follow the famous Fibonacci sequence first discovered, not by Fibonacci in fact, but by Indian poets counting the number of rhythms possible with long and short beats.<br />They were recently championed by Gregory Pincus who created this Fib to describe the form:<br />One , Small, Precise, Poetic, Spiraling mixture: Math plus poetry yields the Fib.<br /><br />I set a challenge on my twitter @marcusdusautoy for people to send me Fibs and I would choose the best to present during my talk. The one I chose is the following by @benbush<br />Tweet/Tweet/Marcus/Here's my fib/(An unwise ad lib?)/Wait: fib? On Twitter? I'm confused/How many of my 140 have I used?<br /><br />Here are a selection of the other great twitter fibs I got sent. Thanks everyone for all your efforts. Really enjoyed reading them.<br /><br />From @angelt42 <br />Shell/Snow/Spiral/Sunflower/Natural music/Beautiful living and growing/Mathematics labels the natural growth of life<br /><br />From @declankh <br />one/ two/ yahoo/ lets make three/ now five is harder/ 8 is slightly contrived i think/ bugger, 13 doesnt scan very elegantly<br /><br />From @bongerman <br />Broad/ Bean./ You're green./ And starchy./ I caress your skin;/ Helps keep my finger on the pulse/And - randomly - engenders dreams of Fibonacci.<br /><br />From @Col_in_UK <br />Let, Me, Twitter, Youmyday, Firstofallbreakfast, Thenlunch,dinner&suppertoo, Finallyit'stimeforbed,justonemoretorestmyhead.<br /><br />From @CtCw_BIGTOE <br />Black/ then/ White are/ all I see/ in my infancy/ Red & Yellow then came to be/ reaching out to me lets me see there is much in me<br /><br />From @pjbryant<br />In<br />Time<br />When you<br />Remember<br />Things will seem quite clear<br />Home - the place where you can return<br />Is the place where you can relax and ease all your fear<br /><br />From @daniellekurant (and thanks for the plug for my new book)<br />I/ love/ numbers/ just as a/ fish out of water/ loves to be cast into the sea/ what sweet freedom is found in these Number Mysteries<br /><br />From @floppymonkey a mini Fib<br />Yes We Have some Bananas!<br /><br />From @mrgrasshead the first Fib to be written by a potplant<br />I/ Love/ Water/ But also/ Pure Mathematics./ Hydrodynamics is my thing!<br /><br />From @dudegalea who tweeted after sending me half a dozen fibs: ""What A Rotten Thing to do! Saturday morning Wasted writing silly poems!<br />Shall/ I/ Compare/ Math poems/ To Shakespeare's sonnets?/ Thou art more geeky, and formal!<br /><br />From @JaneLMcGrath <br />Maths/ And/ Poems/ Do not mix/ They say but you lure/ The logical mind to capture/ English and confine it into constricted beauty<br /><br />From @Kateviola (who worried about how many syllables Ledbury has)<br />O, Hi, Marcus, du Sautoy, Ledbury Festival, Innovative Fibonaccist, Combining words & numbers in true Renaissance style.<br /><br />From @christianp (who wanted the first line as "Er, Dork, Author" but felt that was a bit disrespectful then noticed he'd missed the number 3. But I like the message so included it here:<br />hey! you! marcus! we have got to talk / your convoluted verse structure / tends to prose as the length of the poem increasesMarcus du Sautoyhttp://www.blogger.com/profile/09231135591825316245noreply@blogger.com0tag:blogger.com,1999:blog-317557729672791321.post-61929180042252595962010-04-09T13:06:00.031+01:002012-06-24T15:09:11.154+01:00Symmetry4Charity<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://1.bp.blogspot.com/_VXvJUb9b-Xw/S78bovCBMqI/AAAAAAAAAKQ/6H2c0-0i0Kk/s1600/NameAGroup.jpg"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 320px; height: 92px;" src="http://1.bp.blogspot.com/_VXvJUb9b-Xw/S78bovCBMqI/AAAAAAAAAKQ/6H2c0-0i0Kk/s320/NameAGroup.jpg" border="0" alt=""id="BLOGGER_PHOTO_ID_5458111660029981346" /></a><br /><br />I am trying to help Common Hope get a permanent presence on the UK Global Giving website which will allow UK donors to the charity to benefit from Gift Aid where tax is added to the donation.<br /><br />Common Hope need to raise £1000 from 50 unique donors by the end of April. <a href="http://www.commonhope.org">Common Hope</a> is an educational charity supporting and empowering children and their families in Guatemala. <br /><br />To help them reach their goal I have set up a Symmetry4Charity project to name symmetrical objects after people who donate to the site.<br /><br />In exchange for a minimum donation of £10 to the charity, I will create and name a symmetrical object for you. Donations can be made at <a href="http://www.tiny.cc/symmetry4charity">my fund-raising site</a>. A clue to why this is my charity of choice can be found in Chapter 12: July of Finding Moonshine.<br /><br />If you would like to give the group of symmetries as a birthday present or to celebrate an anniversary then email me details of the significant date and I will weave the date into the construction of the symmetry group. Please email me to alert me to the fact that you have left a donation. dusautoy@maths.ox.ac.uk<br /><br /><span style="font-weight:bold;">Stop Press</span> Thanks to all those who donated, Common Hope achieved their target on 24th April and now have a permanent place on the UK Global Giving Website. <br /><br />Here is a list of the groups created so far that have helped change the lives of children in Guatemala.<br /><br /><br />The Tom Critchlow Group Set [C[1], C[2], C[3], C[4]]=[31,0,8,1983] Corresponds to an elliptic curve of conductor 3489405992393. <br /><br />The Aoife McLysaght Group Set [C[1], C[2], C[3], C[4]]=[1976,0,2004,2006] Corresponds to an elliptic curve of conductor 60613926650500572088192.<br /><br />The Carol Jones Group Set [C[1], C[2], C[3], C[4]]=[0,0,0,2610] Corresponds to an elliptic curve of conductor 48441600.<br /><br />The Raffaele Malanga Group Set [C[1], C[2], C[3], C[4]]=[2087 0 2089 2099] Corresponds to an elliptic curve of conductor 10860662998996528897934.<br /><br />The Antonio Cangiano Group Set [C[1], C[2], C[3], C[4]]=[2111 0 2113 2129] Corresponds to an elliptic curve of conductor 188766474306629521300694.<br /><br />The Adam Tonks Group Set [C[1], C[2], C[3], C[4]]=[2131 0 2137 2141] Corresponds to an elliptic curve of conductor 201253543919366765652458.<br /><br />The Tim Goldberg Group Set [C[1], C[2], C[3], C[4]]=[14 0 1 2010] Corresponds to an elliptic curve of conductor 368874666643. Named by Michael O'Connor for Tim's birthday.<br /><br />The Dawn Denyer Group Set [C[1], C[2], C[3], C[4]]=[28 0 1 1974] Corresponds to an elliptic curve of conductor 1926277419109.<br /><br />The Allen Edwards Group Set [C[1], C[2], C[3], C[4]]=[2143 0 2153 2161] Corresponds to an elliptic curve of conductor 16190845034753857655278.<br /><br />The Christopher Rath Group Set [C[1], C[2], C[3], C[4]]=[2179 0 2203 2207] Corresponds to an elliptic curve of conductor 119528325153563319394762.<br /><br />The Jennifer Mallery Group Set [C[1], C[2], C[3], C[4]]=[23 0 1 4] Corresponds to an elliptic curve of conductor 1883254.<br /><br />The Mr Grasshead Group Set [C[1], C[2], C[3], C[4]]=[15 0 7 2002] Corresponds to an elliptic curve of conductor 1740062254. Named by Pat Galea to celebrate Mr Grasshead's repotting.<br /><br />The Joyce Hynds Group Set [C[1], C[2], C[3], C[4]]=[6 0 8 1943] Corresponds to an elliptic curve of conductor 120494204588. Named by Matt Jensen in memory of his mother-in-law.<br /><br />The Harris Philpott Wong Lau Mak Leung Oswald Group Set [C[1], C[2], C[3], C[4]]=[15 0 6 2010] Corresponds to an elliptic curve of conductor 14226022458. Named by Chris Oswald for his Upper Sixth Further Maths class at Campbell College, Belfast.<br /><br />The Keith Marshall Group Set [C[1], C[2], C[3], C[4]]=[2213 2221 0 2237] Corresponds to an elliptic curve of conductor 53847539164253317.<br /><br />The Joyce Brown Group Set [C[1], C[2], C[3], C[4]]=[440 415 5040 1958] Corresponds to an elliptic curve of conductor 112390621233323209184. Interesting choice of numbers: "440 (I play the cello and that is standard pitch), 415 (I play the viol and that's Baroque pitch), and 5040 (From my bellringing - 7!, the full extent of all the permutations of 7 bells, and the minimum required for a peal) (I do a masterclass talk on the maths of bellringing); 1958 (Year I was born)."<br /><br />The Haggis Group Set [C[1], C[2], C[3], C[4]]=[242 4 228 43112608] Corresponds to an elliptic curve of conductor 6500621248808920956132. Named by Julia Collins for Haggis, the mathematical sheep. Check out Haggis's blog at http://haggisthesheep.wordpress.com/<br /><br />The Judith Cantrell Group Set [C[1], C[2], C[3], C[4]]=[2239 0 2243 2251] Corresponds to an elliptic curve of conductor 71088728997276867992782.<br /><br />The Frances Allsop Group Set [C[1], C[2], C[3], C[4]]=[24, 0, 9, 1939] Corresponds to an elliptic curve of conductor 839108955077. Named by Richard Allsop.<br /><br />The Gwyn Bellamy Group Set [C[1], C[2], C[3], C[4]]=[0 0 0 1983] Corresponds to an elliptic curve of conductor 125833248. <br /><br />The Dave Phillips Group Set [C[1], C[2], C[3], C[4]]=[30 0 5 1945] Corresponds to an elliptic curve of conductor 554774344225. Named by Lucy and Rosana for Dave's birthday.<br /><br />The Beatrice and Henry McBain Group Set [C[1], C[2], C[3], C[4]]=[20, 3, 31, 7] Corresponds to an elliptic curve of conductor 451166557. Named by James McBain.<br /><br />The Maria Beljajev Group Set [C[1], C[2], C[3], C[4]]=[2267 0 2269 2273] Corresponds to an elliptic curve of conductor 309080878106951538630038. <br /><br />The bykimbo Group Set [C[1], C[2], C[3], C[4]]=[4 0 3 1824] Corresponds to an elliptic curve of conductor 43484568627. To mark the date the RNLI was founded.<br /><br />The Thomas Dunham Group Set [C[1], C[2], C[3], C[4]]=[2281 0 2287 2293] Corresponds to an elliptic curve of conductor 64819437055680114154570. <br /><br />The Peter and Laurie Komorowski Group Set [C[1], C[2], C[3], C[4]]=[7 5 3 2] Corresponds to an elliptic curve of conductor 17299. Named by Isaac Abdullah.<br /><br />The Neil Davies Group Set [C[1], C[2], C[3], C[4]]=[2297 0 2309 2311] Corresponds to an elliptic curve of conductor 170755749787700804711146. <br /><br />The James Nicholson Group Set [C[1], C[2], C[3], C[4]]=[2333 0 2339 2341] Corresponds to an elliptic curve of conductor 378769980499583140602578. <br /><br />The Kiss Chops Hunter Group Set [C[1], C[2], C[3], C[4]]=[13 0 1 1968] Corresponds to an elliptic curve of conductor 381310485302. Named by Neil Brewitt for his girlfriend "The geekiest present ever."<br /><br />The Nancy Whitney Group Set [C[1], C[2], C[3], C[4]]=[2371 0 2377 2381] Corresponds to an elliptic curve of conductor 424434490670520944020538.<br /><br />The Niamh and Owain Elsey Group Set [C[1], C[2], C[3], C[4]]=[7, 8, 13, 26] Corresponds to an elliptic curve of conductor 349310. Named by David Elsey for his children<br /><br />The Hafsa Farhana Group Set [C[1], C[2], C[3], C[4]]=[2383 0 2389 2393] Corresponds to an elliptic curve of conductor 439684906279538095624430.<br /><br />The Colin Jenkins Group Set [C[1], C[2], C[3], C[4]]=[2399 0 2411 2417] Corresponds to an elliptic curve of conductor 463431595209250290763706.<br /><br />The Margaret Nicholson Group Set [C[1], C[2], C[3], C[4]]=[2423 0 2437 2441] Corresponds to an elliptic curve of conductor 497218761743202211331006.<br /><br />The Sean Goddard Group Set [C[1], C[2], C[3], C[4]]=[11 0 7 1997] Corresponds to an elliptic curve of conductor 478893859786. Named by his mother Karen Goddard. Sean's team recently won the UKMT Junior maths challenge in the Cumbria regional finals. Congratulations.<br /><br />The Nigel Metheringham Group Set [C[1], C[2], C[3], C[4]]=[2447 0 2459 2467] Corresponds to an elliptic curve of conductor 8322830442423051970094.<br /><br />The Laura Nicholson Group Set [C[1], C[2], C[3], C[4]]=[2473 0 2477 2503] Corresponds to an elliptic curve of conductor 286963521763982408250722.<br /><br />The Charlotte Campbell Group Set [C[1], C[2], C[3], C[4]]=[2521 0 2531 2539] Corresponds to an elliptic curve of conductor 40930035288396217940662. Named by her mother Christine Campbell to inspire her daughter to become a mathematician.<br /><br />The Joanne Nicholson Group Set [C[1], C[2], C[3], C[4]]=[2543 0 2549 2551] Corresponds to an elliptic curve of conductor 346036497122670226830634.<br /><br />The Jenny Pearson Group Set [C[1], C[2], C[3], C[4]]=[2557 0 2579 2591] Corresponds to an elliptic curve of conductor 365494968738038567029426. Named by her husband Andrew.<br /><br />The James Crick Group Set [C[1], C[2], C[3], C[4]]=[2593 0 2609 2617] Corresponds to an elliptic curve of conductor 800984866525168371236674.<br /><br />The Pringle Group Set [C[1], C[2], C[3], C[4]]=[2 12 17 25] Corresponds to an elliptic curve of conductor 1024603.<br /><br />The Patrick Joseph O'Hara Group Set [C[1], C[2], C[3], C[4]]=[23 0 5 1930] Corresponds to an elliptic curve of conductor 120500736670. Named by Shaun for his father's 80th birthday.<br /><br />The Michaela Schmid Group Set [C[1], C[2], C[3], C[4]]=[2621 0 2633 2647] Corresponds to an elliptic curve of conductor 431360159413383233262178.<br /><br />The Louise Nicholson Group Set [C[1], C[2], C[3], C[4]]=[2657 0 2659 2663] Corresponds to an elliptic curve of conductor 469183075585812482668954.<br /><br />The Andrew Burbanks Group Set [C[1], C[2], C[3], C[4]]=[2671 0 2677 2683] Corresponds to an elliptic curve of conductor 122143989488324550049210.<br /><br />The Graham Elliott Group Set [C[1], C[2], C[3], C[4]]=[2687 0 2689 2693] Corresponds to an elliptic curve of conductor 1015048834019033780426498. Named by Andrew Burbanks for the retirement of his colleague in the maths department at the University of Portsmouth.<br /><br />The Euclidian Boxes Group Set [C[1], C[2], C[3], C[4]]=[325 0 265 5] Corresponds to an elliptic curve of conductor 1088438966488150. Named by John Edwards after his xbox gamertag and twitter id.<br /><br />The BCME2010 Group Set [C[1], C[2], C[3], C[4]]=[6 0 4 2010] Corresponds to an elliptic curve of conductor 261881545824. I donated the fee that I was due for the talk I gave to BCME 2010 to Common Hope in order to help them achieve their first place status on the fund-raising challenge.<br /><br />The Louise Egerton Group Set [C[1], C[2], C[3], C[4]]=[2699 0 2707 2711] Corresponds to an elliptic curve of conductor 525923505004979530688566.<br /><br />The Richard Bunch Group Set [C[1], C[2], C[3], C[4]]=[2713 0 2719 2729] Corresponds to an elliptic curve of conductor 1091390907796059056481182.<br /><br />The Nandin G. Rau Group Set [C[1], C[2], C[3], C[4]]=[5 0 5 2010] Corresponds to an elliptic curve of conductor 6586199050. Named by James B. Glattfelder.<br /><br />The Leon P. Grothe Group Set [C[1], C[2], C[3], C[4]]=[8 0 8 2005] Corresponds to an elliptic curve of conductor 523803243328. Named by James B. Glattfelder.<br /><br />The Adam Timothy Jackson Group Set [C[1], C[2], C[3], C[4]]=[2731 0 2741 2749] Corresponds to an elliptic curve of conductor 1145536771536211777040122. Named by Anne Jackson.<br /><br />The Daniel Hagon Group Set [C[1], C[2], C[3], C[4]]=[2753 0 2767 2777] Corresponds to an elliptic curve of conductor 1215991556499890529439214. <br /><br />The Mara Lytrokapi Group Set [C[1], C[2], C[3], C[4]]=[2789 0 2791 2797] Corresponds to an elliptic curve of conductor 1318270795656516690423226. Named by Leptourgos Pantelis for his girlfriend<br /><br />The Polly Sinnett-Jones Group Set [C[1], C[2], C[3], C[4]]=[4 0 2 1981] Corresponds to an elliptic curve of conductor 499555204208. Named by John Shimwell for his daughter's maths teacher.<br /><br />The John Reynolds Group Set [C[1], C[2], C[3], C[4]]=[2801 0 2803 2819] Corresponds to an elliptic curve of conductor 340825568103087059408246. <br /><br />The Marcus Tomlinson Group Set [C[1], C[2], C[3], C[4]]=[24 0 2 2002] Corresponds to an elliptic curve of conductor 414748597288. Marcus came and interviewed me as part of the NCTEM Special Leaders Award for STEM.<br /><br />The Senhenn Lewis Group Set [C[1], C[2], C[3], C[4]]=[424, 1109, 787, 1110] Corresponds to an elliptic curve of conductor 10656159592614961931. Created in memory of Alexander Lewis's grandfather.<br /><br />The Simon Baines-Norton Group Set [C[1], C[2], C[3], C[4]]=[10, 0, 12, 1971] Corresponds to an elliptic curve of conductor 13734429036. From Jacquelyn Arnold for her partner's birthday.<br /><br />The Joseph Daly Group Set [C[1], C[2], C[3], C[4]]=[2833 0 2837 2843] Corresponds to an elliptic curve of conductor 368225749767160780343246. From his Mum to help distract him from a very painful fractured arm.<br /><br />The Susan Wonnacott Group Set [C[1], C[2], C[3], C[4]]=[15 0 12 2010] Corresponds to an elliptic curve of conductor 61438942062. To remember my visit to Bath to receive an honorary DSc.<br /><br />The Laura Evison Group Set [C[1], C[2], C[3], C[4]]=[2851, 0, 2857, 2861] Corresponds to an elliptic curve of conductor 1540697762342693708321498.<br /><br />The Reverend Jay Ridley's Retirement Group Set [C[1], C[2], C[3], C[4]]=[30, 0, 1, 2011] Corresponds to an elliptic curve of conductor 2792409422309. Named by Mark Ridley for his Dad's retirement.<br /><br />The Andy Green Group Set [C[1], C[2], C[3], C[4]]=[763, 0, 035, 0] Corresponds to an elliptic curve of conductor 157093058. Named by Marcus Tomlinson to mark Andy Green's land speed record of 763.035 mph.<br /><br />The Leonard Marson Group Set [C[1], C[2], C[3], C[4]]=[3, 0, 4, 1981] Corresponds to an elliptic curve of conductor 501755813227. Named by Susan Mulligan in memory of her father "who loved maths and taught me to be curious".<br /><br />The Jessica Williams Group Set [C[1], C[2], C[3], C[4]]=[19, 0, 9, 1995] Corresponds to an elliptic curve of conductor <br />504655734. From a maths loving family to their daughter for scoring 100% on her GCSE maths and wishing her luck as she embarks on A level maths.<br /><br />The Johan Nordin Group Set [C[1], C[2], C[3], C[4]]=[2879, 0, 2887, 2897] Corresponds to an elliptic curve of conductor 1655404146508213187596826. A symmetrical object in hyperspace to adorn your new apartment from Torbjörn Jansson.<br /><br />The Ebtisam Hatem Group Set [C[1], C[2], C[3], C[4]]=[2903, 0, 2909, 2917] Corresponds to an elliptic curve of conductor 1750705875861273269012114. From Torbjörn Jansson to celebrate solving "Ett litet problem".<br /><br />The Claire Corner Group Set [C[1], C[2], C[3], C[4]]=[28, 0, 5, 2000] Corresponds to an elliptic curve of conductor <br />7504706935. From Marcus Tomlinson for Mrs Claire Corner as a thank you for being such a wonderfully kind and inspiring teacher.<br /><br />The Charlotte Macro Group Set [C[1], C[2], C[3], C[4]]=[19, 0, 8, 1984] Corresponds to an elliptic curve of conductor <br />3096766. From Marcus Tomlinson for Miss Charlotte Macro for all her really kind help with maths and chess.<br /><br />The Louise Springer Group Set [C[1], C[2], C[3], C[4]]=[6, 0, 7, 1990] Corresponds to an elliptic curve of conductor <br />515190151459. From Djamschid Safi to celebrate Louise Springer's birthday.<br /><br />The Lamis Group Set [C[1], C[2], C[3], C[4]]=[2927, 0, 2939, 2953] Corresponds to an elliptic curve of conductor <br />1865831301990171792354578. A gift from Torbjörn Jansson to Lamis, the Norwegian National Council of Teachers of Mathematics.<br /><br />The Arthur Group Set [C[1], C[2], C[3], C[4]]=[16, 0, 7, 2011] Corresponds to an elliptic curve of conductor <br />284936059387. Bought live on air on BBC Radio 4's Loose Ends by Arthur Smith, Unoffical Mayor of Balham.<br /><br />The Sonja Bartholomew Group Set [C[1], C[2], C[3], C[4]]=[21, 0, 8, 1973] Corresponds to an elliptic curve of conductor <br />265534721713. From Alex Woodcraft for his girlfriend who is a maths teacher and maths geek.<br /><br />The Paul Rispin Group Set [C[1], C[2], C[3], C[4]]=[23, 0, 4, 1970] Corresponds to an elliptic curve of conductor <br />306336944158. From Colleen Usher for her other half.<br /><br />The Bromley High School Group Set [C[1], C[2], C[3], C[4]]=[0, 0, 1883, 2011] Corresponds to an elliptic curve of conductor <br />339962077636651. A gift from maths teacher Jo Munday to the school.<br /><br />The Mitchell Woodman Group Set [C[1], C[2], C[3], C[4]]=[2957, 0, 2963, 2969] Corresponds to an elliptic curve of conductor <br />1990173394038556429897022. A prize from Mel Curran for excellence in mathematics.<br /><br />The Supermole Group Set [C[1], C[2], C[3], C[4]]=[24, 0, 7, 1981] Corresponds to an elliptic curve of conductor <br />121416506771. Named by Joe Malone for his brother's birthday.<br /><br />The Nik Sargent Group Set [C[1], C[2], C[3], C[4]]=[2971, 0, 2999, 3001] Corresponds to an elliptic curve of conductor <br />2084720622014853093541714. <br /><br />The Helen Kent Group Set [C[1], C[2], C[3], C[4]]=[21, 0, 10, 1976] Corresponds to an elliptic curve of conductor <br />66239468098. Named by Dan Kent for his wife.<br /><br />The Adrian Brasnett Group Set [C[1], C[2], C[3], C[4]]=[73, 0, 42, 2011] Corresponds to an elliptic curve of conductor <br />287692484729511. Named by Chris Brasnett for his Dad.<br /><br />The StevenBradleyofLangleyPark Group Set [C[1], C[2], C[3], C[4]]=[1, 0, 8, 1970] Corresponds to an elliptic curve of conductor <br />246142199510. Named by Jen for her brother's birthday.<br /><br />The J.C.P. Miller Group Set [C[1], C[2], C[3], C[4]]=[3011, 0, 3019, 3023] Corresponds to an elliptic curve of conductor <br />1130088249101822428698802. Named by Alison Smith and her family to remember their father's love of maths.<br /><br />The Paul Parker Group Set [C[1], C[2], C[3], C[4]]=[27, 0, 7, 1975] Corresponds to an elliptic curve of conductor <br />852701983546. Named by Benjamin Pring.<br /><br />The Vincent Murphy Group Set [C[1], C[2], C[3], C[4]]=[15, 23, 8, 1969] Corresponds to an elliptic curve of conductor <br />120668102111. Named by Michaela Murphy for her autodidactic husband on his 42nd birthday.<br /><br />The Rodney Jagelman Group Set [C[1], C[2], C[3], C[4]]=[15, 0, 8, 1951] Corresponds to an elliptic curve of conductor <br />315422032951. Named by Rupert Jagelman for his father's 60th birthday.<br /><br />The Penelope Garwood Group Set [C[1], C[2], C[3], C[4]]=[6, 0, 9, 2001] Corresponds to an elliptic curve of conductor <br />176123656377. Named by Adrian and Helen Garwood for their daughter's birthday.<br /><br />The Eleanor Garwood Group Set [C[1], C[2], C[3], C[4]]=[3, 0, 1, 2003] Corresponds to an elliptic curve of conductor <br />128784499418. Named by Adrian and Helen Garwood for their daughter's birthday.<br /><br />The Michelle Doggett Group Set [C[1], C[2], C[3], C[4]]=[4, 0, 10, 2011] Corresponds to an elliptic curve of conductor <br />133766205052. Named by Spencer Doggett for his wife's birthday.<br /><br />The Alasdair Hunter Group Set [C[1], C[2], C[3], C[4]]=[3037, 0, 3041, 3049] Corresponds to an elliptic curve of conductor <br />2397079763494449095534242. Named by Su Knight for her boyfriend.<br /><br />The Peter Baxendall Group Set [C[1], C[2], C[3], C[4]]=[3061, 0, 3067, 3079] Corresponds to an elliptic curve of conductor <br />1269675294767721689908126. Named by Su Knight for her tutor at the OU.<br /><br />The Charles Rule Group Set [C[1], C[2], C[3], C[4]]=[3083, 0, 3089, 3109] Corresponds to an elliptic curve of conductor <br />2676620509058079475578242. Named by Abie Cohen.<br /><br />The Magda Nilges Group Set [C[1], C[2], C[3], C[4]]=[11, 0, 1, 1927] Corresponds to an elliptic curve of conductor <br />203604256438. Named by Guido Stemme to celebrate his mother-in-law's 85th birthday.<br /><br />The Simona Matejova Group Set [C[1], C[2], C[3], C[4]]=[16, 0, 11, 1991] Corresponds to an elliptic curve of conductor <br />26471494049. Named by Jakub Mihalciak.<br /><br />The Ben Whitehead Group Set [C[1], C[2], C[3], C[4]]=[30, 0, 8, 2009] Corresponds to an elliptic curve of conductor <br />3044382914512. Named by Heather Davis.<br /><br /><br />The Howison Group Set [C[1], C[2], C[3], C[4]]=[7, 9, 32, 58] Corresponds to an elliptic curve of conductor <br />12407326. Named by Sam Howison for his parents. <br /><br />The Tim Sprackling Group Set [C[1], C[2], C[3], C[4]]=[3119, 0, 3121, 3137] Corresponds to an elliptic curve of conductor <br /> 70530741503400137394166. Named by Alison Sprackling for her husband's 50th birthday. <br /><br /> The Balan Group Set [C[1], C[2], C[3], C[4]]=[17, 0, 3, 2012] Corresponds to an elliptic curve of conductor <br /> 97286346818. Named by Jo Taylor to celebrate her wedding anniversary. <br /><br /> The Lynne Owen Group Set [C[1], C[2], C[3], C[4]]=[3163, 0, 3167, 3169] Corresponds to an elliptic curve of conductor <br /> 3179359613757754838257882. <br /><br /> The Ian Miller Group Set [C[1], C[2], C[3], C[4]]=[14, 0, 7, 1973] Corresponds to an elliptic curve of conductor <br /> 371762090587. Named by Kathryn Miller for her husband, a maths teacher to celebrate their wedding anniversary. <br /><br /> The Travis Holgate Group Set [C[1], C[2], C[3], C[4]]=[12, 0, 5, 1978] Corresponds to an elliptic curve of conductor <br /> 434448290539. Named by Anna Stanton for her inspiring maths teacher. <br /><br /> The Lewis Austin Bryan Group Set [C[1], C[2], C[3], C[4]]=[3181, 0, 3187, 3191] Corresponds to an elliptic curve of conductor <br /> 1657177978151537627749654. Named by Steve Pettifer to celebrate the completion of Lewis's first year studying maths. <br /><br /> The Mark Thielemans Group Set [C[1], C[2], C[3], C[4]]=[15, 0, 5, 1955] Corresponds to an elliptic curve of conductor <br /> 15257347150. Named by Kris Nordgren. <br /><br /> The Phi-Long Group Set [C[1], C[2], C[3], C[4]]=[3203, 3209, 3217, 1] Corresponds to an elliptic curve of conductor <br /> 3501980459428471078753223. Named by Torbjorn Jansson for good work in Ett litet problem. <br /><br /> The David Cowan Group Set [C[1], C[2], C[3], C[4]]=[3221, 3229, 3251, 1] Corresponds to an elliptic curve of conductor <br /> 3680232669813676781439107. <br /><br /> The Bamkin Group Set [C[1], C[2], C[3], C[4]]=[3253, 3257, 3259, 1] Corresponds to an elliptic curve of conductor <br /> 3880820185442422975005183 Named by Marianne for Roger's birthday. <br /><br /> The Clare Strongman Group Set [C[1], C[2], C[3], C[4]]=[3271, 3299, 3301, 1] Corresponds to an elliptic curve of conductor <br /> 4122888775849334688518817 Named by Luke Renouf. <br /><br /> The Rory Kent Group Set [C[1], C[2], C[3], C[4]]=[3307, 3313, 3319, 1] Corresponds to an elliptic curve of conductor <br /> 4372816226936205513334211 Named by Rory's father Martin to inspire him in his Masters in Astrophysics. <br /><br /> The Melanie Mossman Group Set [C[1], C[2], C[3], C[4]]=[0, 43112609, 0, 1] Corresponds to an elliptic curve of conductor <br /> 725345192111952 Named by Adam Spencer for his wife <br /><br /> The Susan Black Group Set [C[1], C[2], C[3], C[4]]=[4, 7, 24, 1] Corresponds to an elliptic curve of conductor <br /> 125160 <br /><br /> The David Preston Group Set [C[1], C[2], C[3], C[4]]=[18, 0, 6, 1962] Corresponds to an elliptic curve of conductor <br /> 5423339448 Named by Jane Challis for her brother's 50th birthday. <br /><br /> The Gordon Crosby Group Set [C[1], C[2], C[3], C[4]]=[19, 0, 6, 1955] Corresponds to an elliptic curve of conductor <br /> 6333982847 Named by Vicky Crosby for her Dad's birthday.Marcus du Sautoyhttp://www.blogger.com/profile/09231135591825316245noreply@blogger.com1tag:blogger.com,1999:blog-317557729672791321.post-80715884830787299802009-10-19T12:05:00.004+01:002009-10-20T16:05:35.050+01:00The Secret You: Horizon BBC2<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://3.bp.blogspot.com/_VXvJUb9b-Xw/Stxe_WYvVlI/AAAAAAAAAKA/1voG4NinSpo/s1600-h/IMG_0252.JPG"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 240px; height: 320px;" src="http://3.bp.blogspot.com/_VXvJUb9b-Xw/Stxe_WYvVlI/AAAAAAAAAKA/1voG4NinSpo/s320/IMG_0252.JPG" border="0" alt=""id="BLOGGER_PHOTO_ID_5394290896117126738" /></a><br /><br />Horizon: THE SECRET YOU<br /><br />BBC2 Tuesday 20 October 2009 9pm<br /><br />With the help of a hammer wielding scientist, Jennifer Aniston and a general anaesthetic Prof Marcus de Sautoy leaves the certainty of numbers behind and goes in search of answers to one of science’s greatest mysteries: how do we know who we are? It’s a simple question, but one science finds difficult to answer. The feelings and thoughts that make us ‘us’ and make us self aware are easy to experience. But the brain processes that give rise to them are difficult to explain and understanding them is one of the great challenges faced by scientists. <br /><br />To find out what progress they are making Marcus becomes a human guinea-pig in a series of mind probing experiments. He begins by asking when our self awareness emerges and witnesses a cunning test that convincingly reveals a child’s sense of self before they are even capable of talking about what they are feeling. The experiment begs a question: are we alone in the world in being aware of ourselves? He meets Professor Gordon Gallup, a pioneer of animal psychology to find out. <br /><br />But to find out how we become self aware, Marcus needs to delve into the inner machinations of the human brain. He starts of by witnessing a brain dissection, but not before he has the sobering experience of holding a human brain in his hands. <br /><br />Seeing the dissected brain, he wonders when our consciousness disappears and whether answering this question might explain who he is. So Marcus volunteers for a cutting edge medical experiment that will rob him of his sense of self. At the University of Cambridge Wolfson Brain Imaging Centre he undergoes anaesthesia while having his brain scanned. He begins to home in on the areas of the brain that make him who he is.<br /><br />Marcus’ work as a lab-rat continues in Sweden’s Karolinska Institute. Thanks to an ingenious set of spectacles, Marcus is subjected to a disorientating out of body experience, which serves to illustrate how a sense of self is a trick of the mind. <br /><br />Marcus’s journey continues to America where he meets Professor Christof Koch of the California Institute of Technolgy. Christof is looking for evidence of consciousness in one of the smallest units of the brain: the individual neuron. He has made some surprising discoveries, helped by celebrities Jennifer Anniston and Halle Berry. <br /><br />By the time Marcus reaches the University of Wisconsin he is getting closer to an answer to his question. He takes part in an un-nerving experiment featuring transcranial magnetic stimulation – the rapid discharge of electric shocks to a specific region of the brain. Measuring how these shocks travel through the brain’s labyrinthine connections when volunteers are awake and asleep has allowed scientists to demonstrate how the interconnectivity of the brain gives rise to consciousness. <br /><br />The last experiment Marcus takes part in is perhaps the most perturbing. Keen to find out how taking a choice might reveal the secrets of his inner self, Marcus wants to discover the provenance of his decisions. He takes part in a simple experiment overseen by Professor John-Dylan Haynes at the Bernstein Centre for Computational Neuroscience in Berlin. Marcus is shocked to learn that by studying his unconscious brain Professor Haynes is able to accurately predict Marcus’ decisions and that it is his unconscious brain that presides over his conscious mind. <br /><br />Marcus concludes the film with a fuller understanding of the state of brain science, but also a sense of how much remains to be revealed. To help the process on its way he commits to one final experiment – one that will take place after his death – and bequeaths his brain to science.<br /><br />Bonus feature: <a href="http://www.youtube.com/watch?v=BpC0FT7KfAk&feature=player_embedded">Hole in the hand</a> <br /><br />Also check out an article on <a href="http://news.bbc.co.uk/1/hi/health/8314093.stm">BBC News Online</a>Marcus du Sautoyhttp://www.blogger.com/profile/09231135591825316245noreply@blogger.com0tag:blogger.com,1999:blog-317557729672791321.post-5408875831067882672009-10-12T07:28:00.002+01:002009-10-12T07:31:40.997+01:00The Times Cheltenham Literature Festival<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://2.bp.blogspot.com/_VXvJUb9b-Xw/StLM4rKrdRI/AAAAAAAAAJ4/Loc0An04YD8/s1600-h/cheltenham.jpg"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 269px; height: 163px;" src="http://2.bp.blogspot.com/_VXvJUb9b-Xw/StLM4rKrdRI/AAAAAAAAAJ4/Loc0An04YD8/s320/cheltenham.jpg" border="0" alt=""id="BLOGGER_PHOTO_ID_5391596977948161298" /></a><br />I will be appearing at the Times Cheltenham Literature Festival on Friday 16 October 2009 at 10:00 am at the Town Hall talking about Finding Moonshine.<br /><a href="http://cheltenhamfestivals.com/literature-2009/marcus-du-sautoy/">Book online.</a>Marcus du Sautoyhttp://www.blogger.com/profile/09231135591825316245noreply@blogger.com0tag:blogger.com,1999:blog-317557729672791321.post-32548216822610244482009-10-11T19:47:00.003+01:002009-10-11T20:06:37.883+01:00Simetria<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://1.bp.blogspot.com/_VXvJUb9b-Xw/StIpyWwj0SI/AAAAAAAAAJw/bZOMpc6kwCU/s1600-h/simetria.jpg"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 198px; height: 320px;" src="http://1.bp.blogspot.com/_VXvJUb9b-Xw/StIpyWwj0SI/AAAAAAAAAJw/bZOMpc6kwCU/s320/simetria.jpg" border="0" alt=""id="BLOGGER_PHOTO_ID_5391417648995356962" /></a><br /><br />The Spanish edition of Finding Moonshine was published this week by <a href="http://www.acantilado.es/catalogo/simetria-463.htm">Acantilado</a>. <br />I was in Spain this week promoting the book. I gave a talk in Madrid at the prestigious <a href="http://www.residencia.csic.es/en/pres/presenta.htm">Residencia de Estudiantes</a>, home to Dali, Lorca and Bunuel. Other people who have lectured there include Albert Einstein, Paul Valéry, Marie Curie, Igor Stravinsky, John M. Keynes, Alexander Calder, Walter Gropius, Henri Bergson and Le Corbusier. <br />I also gave a talk in Barcelona at the <a href="http://obrasocial.lacaixa.es/nuestroscentros/cosmocaixabarcelona/cosmocaixabarcelona_ca.html">CosmaCaixa</a> museum. It is a fantastic science museum and I thoroughly recommend it to anyone visiting Barcelona.<br /><br />Here are some reviews that have appeared in Spain:<br /><br /><a href="http://www.elpais.com/articulo/sociedad/Du/Sautoy/Alhambra/microcosmos/simetrias/elpepusoc/20091009elpepusoc_1/Tes">El Pais: La Alhambra es un microcosmos de simetrías</a><br /><a href="http://www.google.com/hostednews/epa/article/ALeqM5h17amcYCERdyxO4vDZGVOk4ilAWg">Agencia EFE: El científico Marcus Du Sautoy dice que "la simetría es un lenguaje fundamental"</a>Marcus du Sautoyhttp://www.blogger.com/profile/09231135591825316245noreply@blogger.com4tag:blogger.com,1999:blog-317557729672791321.post-7290244598117290262009-09-08T09:39:00.003+01:002009-09-14T07:53:12.531+01:00Simonyi Lecture<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://1.bp.blogspot.com/_VXvJUb9b-Xw/SqYZjyWxyDI/AAAAAAAAAJo/hcBCaZCWZJY/s1600-h/gowers.jpg"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 225px; height: 158px;" src="http://1.bp.blogspot.com/_VXvJUb9b-Xw/SqYZjyWxyDI/AAAAAAAAAJo/hcBCaZCWZJY/s320/gowers.jpg" border="0" alt=""id="BLOGGER_PHOTO_ID_5379014907544062002" /></a><br /><br /><br />JOIN TIMOTHY GOWERS<br /><br />For this years<br /><br />CHARLES SIMONYI LECTURE<br /><br />at OXFORD PLAYHOUSE<br /><br /> <br /><br />Friday 2 October at 5pm<br /><br /> <br /><br />Rouse Ball Professor of Mathematics at Cambridge University and Fellow of Trinity College, Timothy Gowers, gives this year's Charles Simonyi Lecture, the annual lecture for the public understanding of science at Oxford Playhouse on Friday 2 October.<br /><br /> <br /><br />Gowers will talk about his recent involvement in an experimental attempt to solve a serious mathematical research problem publicly and collaboratively on the internet. He will discuss the problem itself, the difficulties involved, the surprising outcome, and what this suggests for the future of mathematics.<br /><br /> <br /><br />The Simonyi Lectures are a series of annual lectures in Oxford, set up in 1999 by Richard Dawkins, in order to promote the public understanding of science. Now in it’s eleventh year, Marcus du Sautoy follows Richard Dawkins as the new Charles Simonyi Professor.<br /><br /> <br /><br />Tickets for The Charles Simonyi Lecture at Oxford Playhouse are available from the Box Office on 01865 305305 or <a href="http://www.oxfordplayhouse.com/show/?eventid=1227">Oxford Playhouse Website</a>Marcus du Sautoyhttp://www.blogger.com/profile/09231135591825316245noreply@blogger.com0tag:blogger.com,1999:blog-317557729672791321.post-38690892085027965662009-07-24T08:43:00.007+01:002009-07-24T09:34:01.875+01:00TED<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://2.bp.blogspot.com/_VXvJUb9b-Xw/SmlmqezhRiI/AAAAAAAAAJY/ned6IPwrBYc/s1600-h/TED.jpg"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 320px; height: 292px;" src="http://2.bp.blogspot.com/_VXvJUb9b-Xw/SmlmqezhRiI/AAAAAAAAAJY/ned6IPwrBYc/s320/TED.jpg" border="0" alt=""id="BLOGGER_PHOTO_ID_5361929711370978850" /></a><br /><br />The subject of <a href="http://conferences.ted.com/TEDGlobal2009/">TEDGlobal 2009</a> held in Oxford this week was the Substance of Things Unseen. My talk, given in the section Curious and Curiouser on Wednesday, attempted to illustrate how mathematics is a powerful language to allow us to get access to things unseen. In particular, symmetry is superficially about something visual, something seen. We say a face is symmetrical because we can see that the left side is a mirror of the right side. But how can we "see" that two walls in the Alhambra for example have the same group of symmetries although they visually look very different. The power of mathematics is to be able to "see" an abstract entity underlying the object. It's like the concept of number. Do you ever "see" the number 5? No. You see visual representations of the number 5. This is the power of the language of symmetry that the French revolutionary Evariste Galois developed at the beginning of the 19th century. It allows us to articulate why two objects have the same symmetries although they visually look very diffferent.<br />It also has the power to prove when we have seen examples of all the symmetries possible. In the Alhambra for example, mathematicians proved that there are only 17 different groups of symmetries possible on a two dimensional wall. There are many more than 17 different wall designs across the palace but they are all examples of one of these 17 symmetry groups. For example, these two walls look very different. But the language of symmetry allows us to explain why the underlying symmetries are exactly the same:<br /><br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://1.bp.blogspot.com/_VXvJUb9b-Xw/SmlpTjB7zII/AAAAAAAAAJg/Pqh1s2EpXlw/s1600-h/632.jpg"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 320px; height: 240px;" src="http://1.bp.blogspot.com/_VXvJUb9b-Xw/SmlpTjB7zII/AAAAAAAAAJg/Pqh1s2EpXlw/s320/632.jpg" border="0" alt=""id="BLOGGER_PHOTO_ID_5361932615903071362" /></a><br /><br />This allows us to explore the symmetries of things seen. But the real power of mathematics is to create symmetries of things unseen. My work concerns creating symmetrical objects that exist beyond our three dimensional visual world. Only with the power of mathematical language can we "see" in 4, 5 even infinite dimensional space.<br />To celebrate TEDGlobal 2009 I constructed a new symmetrical object that cannot be seen but using mathematical language can be explored and played with. It was won in a competition I ran during my 18 minute talk by another of the TED speakers astronomer Andrea Ghez.<br /><br /><a href="http://blog.ted.com/2009/07/marcus_du_sauto.php">TED blog entry about my talk</a><br /><br /><a href="http://blog.ted.com/2009/07/twitter_snapsho_34.php">Twitter Snapshot: Marcus du Sautoy on symmetry</a><br /><br /><a href="http://www.firstgiving.com/findingmoonshine">Groups for Charity</a> If you want your own "unseen" symmetrical object, then a donation through my FirstGiving page to the charity CommonHope will get your name on a new mathematical shape.Marcus du Sautoyhttp://www.blogger.com/profile/09231135591825316245noreply@blogger.com0tag:blogger.com,1999:blog-317557729672791321.post-21655211028099822342009-07-04T08:49:00.008+01:002009-07-04T12:49:47.256+01:00The Complete Sexy Maths<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://1.bp.blogspot.com/_VXvJUb9b-Xw/Sk9Bb8jQBEI/AAAAAAAAAJQ/-NN58WxRT4I/s1600-h/SexyMaths.jpg"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 320px; height: 152px;" src="http://1.bp.blogspot.com/_VXvJUb9b-Xw/Sk9Bb8jQBEI/AAAAAAAAAJQ/-NN58WxRT4I/s320/SexyMaths.jpg" border="0" alt=""id="BLOGGER_PHOTO_ID_5354570430333060162" /></a><br />This week saw the last column in the Sexy Maths series in The Times for the time being. The newspaper is downsizing for the summer. It may reappear in a new reincarnation in the autumn. Here is an archive of links to all the columns that appeared during the year, some including the beautiful illustrations of Joe McLaren who will be illustrating my new book The Num8er My5teries.<br /><br /><a href="http://women.timesonline.co.uk/tol/life_and_style/women/the_way_we_live/article6612248.ece">1 Jul 2009</a> Oh, it’s such a perfect day. We have discovered 47 perfect numbers — the largest has nearly 26 million digits.<br /><br /><a href="http://technology.timesonline.co.uk/tol/news/tech_and_web/article6564213.ece">24 June 2009</a> How to avoid a grudge match. Never mind Arsenal against Spurs. How about NP versus P?<br /><br /><a href="http://technology.timesonline.co.uk/tol/news/tech_and_web/article6512745.ece">17 June 2009</a> Arithmetic eases swine flu. Figuring out the rate of contagion can make you feel better<br /><br /><a href="http://technology.timesonline.co.uk/tol/news/tech_and_web/article6465448.ece">10 June 2009</a> When it pays to play the odds. Mathematicians, and the laws of probability, can tell you whether to have a flutter, or keep hold of your money.<br /><br /><a href="http://technology.timesonline.co.uk/tol/news/tech_and_web/article6366308.ece">27 May 2009</a> A new bicycle reinvents the wheel, with a pentagon and triangle. Guan’s bicycle isn’t the first to exploit these shapes — they have been used by urban planners as manholes.<br /><br /><a href="http://technology.timesonline.co.uk/tol/news/tech_and_web/article6321822.ece">20 May 2009</a> A game of 12 pentagons. Why a football match is actually geometry in motion.<br /><br /><a href="http://technology.timesonline.co.uk/tol/news/tech_and_web/article6274680.ece">13 May 2009</a> in search of the poetry of Muslim symmetry. Galois’s group theory allowed mathematicians to articulate the theory of symmetry.<br /><br /><a href="http://technology.timesonline.co.uk/tol/news/tech_and_web/article6227341.ece">6 May 2009</a> Formula won ... the key to boosting faster travel. How mathematicians can get you to the Grand Prix finishing line — and through an airport — more quickly.<br /><br /><a href="http://women.timesonline.co.uk/tol/life_and_style/women/the_way_we_live/article6188065.ece">29 April 2009</a> The lemming theory. There is no mass suicide pact keeping the numbers of lemmings down.<br /><br /><a href="http://women.timesonline.co.uk/tol/life_and_style/women/the_way_we_live/article6142032.ece">22 April 2009</a> What's unique about the number 1,729?<br /><br /><a href="http://women.timesonline.co.uk/tol/life_and_style/women/the_way_we_live/article6093575.ece">15 April 2009</a> The Fibonacci sequence's prime rate.<br /><br /><a href="http://women.timesonline.co.uk/tol/life_and_style/women/the_way_we_live/article6053197.ece">8 April 2009</a> Drawing parallels in geometry. This year's Abel Prize honours some of the most revolutionary contributions to geometry since those of Euclid.<br /><br /><a href="http://www.timesonline.co.uk/tol/life_and_style/article5969764.ece">25 March 2009</a> Go fourth... into another dimension.<br /><br /><a href="http://women.timesonline.co.uk/tol/life_and_style/women/the_way_we_live/article5926440.ece">18 March 2009</a> Twists and turns that make a rollercoaster ride.<br /><br /><a href="http://women.timesonline.co.uk/tol/life_and_style/women/the_way_we_live/article5883187.ece">11 March 2009</a> A number-munching celebration.<br /><br /><a href="http://women.timesonline.co.uk/tol/life_and_style/women/the_way_we_live/article5840758.ece">4 March 2009</a> Ditch the GPS, just follow the colour code.<br /><br /><a href="http://women.timesonline.co.uk/tol/life_and_style/women/the_way_we_live/article5801747.ece">25 February 2009</a> Tails of a curious submariner. A US Marine with a lot of time on his hands has noticed that a strange thing happens when you keep tossing a coin.<br /><br /><a href="http://women.timesonline.co.uk/tol/life_and_style/women/the_way_we_live/article5755004.ece">18 February 2009</a> How to be a flipping genius. It's possible for me to toss a coin and you, who are somewhere else entirely, to know if I have called honestly.<br /><br /><a href="http://www.timesonline.co.uk/tol/life_and_style/article5704226.ece">11 February 2009</a> Why Palladio's proportions are pleasing on the eye and the ears.<br /><br /><a href="http://technology.timesonline.co.uk/tol/news/tech_and_web/article5653925.ece">4 February 2009</a> Why do snowflakes have six arms? Are your children out of school? Keep their grey matter going with a question that baffled generations of scientists.<br /><br /><a href="http://technology.timesonline.co.uk/tol/news/tech_and_web/article5599504.ece">28 January 2009</a> It's true, young Muggles. Maths can be magic.<br /><br /><a href="http://women.timesonline.co.uk/tol/life_and_style/women/the_way_we_live/article5554655.ece">21 January 2009</a> Rubik's Cube returns.<br /><br /><a href="http://women.timesonline.co.uk/tol/life_and_style/women/the_way_we_live/article5511282.ece">14 January 2009</a> Solving wobbly restaurant tables. Wedging beer mats or bits of paper under that annoying table leg is no more. Try the mathematical solution instead.<br /><br /><a href="http://women.timesonline.co.uk/tol/life_and_style/women/the_way_we_live/article5459742.ece">7 January 2009</a> Survival of the mathematician.<br /><br /><a href="http://technology.timesonline.co.uk/tol/news/tech_and_web/article5419637.ece">31 December 2008</a> How to be a perfect timekeeper.<br /><br /><a href="http://technology.timesonline.co.uk/tol/news/tech_and_web/article5353303.ece">17 December 2008</a> Warm up with a few festive candles.<br /><br /><a href="http://technology.timesonline.co.uk/tol/news/tech_and_web/article5314838.ece">10 December 2008</a> The symmetry of sneezing. Viruses blight many people's lives in winter but the molecular structure of many are things of mathematical beauty.<br /><br /><a href="http://technology.timesonline.co.uk/tol/news/tech_and_web/article5232481.ece">26 November 2008</a> Skills of a chess grandmaster.<br /><br /><a href="http://technology.timesonline.co.uk/tol/news/tech_and_web/article5181874.ece">19 November 2008</a>To infinity - and beyond<br /><br /><a href="http://technology.timesonline.co.uk/tol/news/tech_and_web/article5133268.ece">12 November 2008</a> Get the upper hand at poker.<br /><br /><a href="http://technology.timesonline.co.uk/tol/news/tech_and_web/article5083087.ece">5 November 2008</a> Why democracy is an ass.<br /><br /><a href="http://technology.timesonline.co.uk/tol/news/tech_and_web/article5032299.ece">29 October 2008</a> Get your teeth into this.<br /><br /><a href="http://technology.timesonline.co.uk/tol/news/tech_and_web/article4987235.ece">22 October 2008</a> Why the taxman has your number.<br /><br /><a href="http://technology.timesonline.co.uk/tol/news/tech_and_web/article4943316.ece">15 October 2008</a> Sexy maths: a calculating approach to love. Mathematics can help you to maximise your chances of landing the best flat – or the best partner.<br /><br /><a href="http://technology.timesonline.co.uk/tol/news/tech_and_web/article4902125.ece">8 October 2008</a> Happy (birthday) coincidences. Why Premier League footballers are likely to have dates of birth in common, and how to win more money on the lottery.<br /><br /><a href="http://technology.timesonline.co.uk/tol/news/tech_and_web/article4855363.ece">1 October 2008</a> Primes of passion.Marcus du Sautoyhttp://www.blogger.com/profile/09231135591825316245noreply@blogger.com0tag:blogger.com,1999:blog-317557729672791321.post-47911523337884782772009-05-14T19:26:00.003+01:002009-05-14T19:32:44.406+01:00Finding Moonshine in Paperback<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://lh6.ggpht.com/_VXvJUb9b-Xw/Sgxik-FS3fI/AAAAAAAAAJI/9JQvmM8XKaI/s1600-h/paperback.jpg"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 210px; height: 320px;" src="http://lh6.ggpht.com/_VXvJUb9b-Xw/Sgxik-FS3fI/AAAAAAAAAJI/9JQvmM8XKaI/s320/paperback.jpg" border="0" alt=""id="BLOGGER_PHOTO_ID_5335748045807214066" /></a><br /><br />Finding Moonshine appears in paperback today with a fun cover: the back is a mirror image of the front. It also includes a PS section with a portrait of the author by Roger Tagholm; top ten favourite pieces of music; a symmetry tour round the world; plus the article "Einstein Plato ...and you?" written for the Telegraph about the project to use symmetry to raise money for Common Hope, a charity in Guatemala. <br /><br /><a href="http://www.amazon.co.uk/gp/product/0007214626/ref=s9_csim_gw_s0_p14_i1?pf_rd_m=A3P5ROKL5A1OLE&pf_rd_s=center-2&pf_rd_r=034DT8J9NX08425XNZY5&pf_rd_t=101&pf_rd_p=467128533&pf_rd_i=468294">Click here to buy the paperback from Amazon</a>Marcus du Sautoyhttp://www.blogger.com/profile/09231135591825316245noreply@blogger.com4tag:blogger.com,1999:blog-317557729672791321.post-80082554863531661762009-05-13T12:14:00.004+01:002009-05-13T12:24:24.949+01:00To Infinity and beyond<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://3.bp.blogspot.com/_VXvJUb9b-Xw/SgqsvxpDayI/AAAAAAAAAI4/myQ_crAm0Zo/s1600-h/22102007233.jpg"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 320px; height: 240px;" src="http://3.bp.blogspot.com/_VXvJUb9b-Xw/SgqsvxpDayI/AAAAAAAAAI4/myQ_crAm0Zo/s320/22102007233.jpg" border="0" alt=""id="BLOGGER_PHOTO_ID_5335266645353130786" /></a><br /><br />I've been attempting some Tweetorials on Infinity. For those who would like more than can be expressed in 140 characters (a tough medium to talk about the infinite) here is an account of why there are different infinities.<br /><br />To infinity and Beyond...<br /><br />The very concept of number illustrates the power of the human mind to abstract mathematical identity from physically very different settings. In fact we seem genetically programmed to be able to detect when things are numerically identical or not. The decision to fight or fly in the face of the enemy depends on an assessment of whether the number in your pack is bigger or smaller than the number in the opposition. Those that can count, survive. <br /><br />This ability of animals to detect numerical identity has been identified in many species. Monkeys, cats and dogs count their young to check they are all there; coots can identify when the number of eggs in their nest has increased indicating someone has added a parasite egg; babies as young as 5 months can tell when dolls are taken away from a pile. Even dogs seem to be able to tell that something fishy is going on when experimenters try to trick them into thinking that 1+1=3. But it is humans who have given names to these numerical identities. <br /><br />Some tribes have only produced names for the first few numbers, lumping together anything too large under the heading “lots”. But even without names for numbers, such tribes are able to compare wealth. The tribe who has numbers “one, two, three, lots” can still say when one member of the tribe has more “lots” than another. If chickens are a mark of wealth then by pairing chickens up we can tell whether one person’s “lots” is bigger than another’s.<br /><br />This idea of comparison lead to mathematicians in the nineteenth century realising that even in our more sophisticated mathematical tribe we could actually compare infinities and say when two infinite sets are identical in size or not. Prior to the nineteenth century this idea of different sizes of infinity had never been considered. In fact when the German mathematician Georg Cantor proposed the idea in the 1870s, it was considered as almost heretical or at best the thoughts of a madman.<br /><br />Using the idea of pairing objects, Cantor was able to propose a way of declaring when two infinite sets were numerically identical or not. For example one might be tempted to declare that there are half as many even numbers as compared to all numbers. However Cantor showed there is a way to line up both sets of numbers so that each number has its pair. For example 1 gets paired with 2, 2 with 4, 3 with 6, and n with 2n. So these two sets have the same size. The tribal member with even numbered chickens is as wealthy as the tribesman with chickens numbered with all whole numbers. These infinite sets are identical in size.<br /><br />You have to be slightly more ingenious to see how to compare all whole numbers against all fractions and prove that both sets are identical in size. At first sight this looks impossible. Between each pair of whole numbers there are infinitely many fractions. But there is a way to match the whole numbers perfectly with all fractions so that no fractions are left unmatched. The procedure starts by producing a systematic way to make a table containing all the fractions. The table has infinitely many rows and columns. The nth colomn consists of a list of all the fractions 1/n,2/n,3/n,… <br /><br />How then do you pair up the whole numbers with the fractions in this table? The trick is to wend a snake diagonally through the fractions in the table as illustrated below. The number 9 for example gets paired with 2/3, the ninth fraction that one meets as the snake slithers through the table of fractions. Since the snake covers the whole table, every fraction will get paired with some whole number. <br /><br /> <br /><a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://3.bp.blogspot.com/_VXvJUb9b-Xw/SgqthtmA5dI/AAAAAAAAAJA/NRQZrbXeQMo/s1600-h/snake.jpg"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 314px; height: 320px;" src="http://3.bp.blogspot.com/_VXvJUb9b-Xw/SgqthtmA5dI/AAAAAAAAAJA/NRQZrbXeQMo/s320/snake.jpg" border="0" alt=""id="BLOGGER_PHOTO_ID_5335267503260100050" /></a><br /><br />This is beginning to look like all infinities are identical in size. Perhaps once a tribal member has infinitely many chickens he won't get beaten by anyone else's collection. Now enter the new big cheese whose chickens are labelled with all the possible decimal expansions there are of numbers. Will the tribal member whose chickens are labelled just with the whole numbers 1,2,3… up to infinity be able to pair his chickens up with this new big cheese? He might start by matching his first chicken with chicken π = 3.1415926…, then the second with e = 2.7182818… <br /><br />Why can we be sure that however hard he tries to match up chickens we can always guarantee an irrational chicken unaccounted for? Let's take one of his attempts to match his chickens with the irrational chickens belonging to the big cheese. <br /><br />1 ↔ 3.1415926…<br />2 ↔ 2.7182818…<br />3 ↔ 1.4142135…<br />4 ↔ 1.6180339…<br />5 ↔ 0.3331779…<br /><br />…<br /><br />We are going to build a number with an infinite decimal expansion such that the corresponding irrational chicken has not been paired up with one of the whole numbers. Each decimal place is a number between 0 and 9. In the first decimal place, we choose a number which is different from the first decimal place of the number paired with chicken number 1. In the second decimal place choose a number different from the second decimal place of the number paired with chicken number 2. For example the irrational chicken with number starting 0.28518… is not paired with the first five whole numbers. In this way we can build up a number labelling a chicken which hasn't been paired up with any whole number. If someone claimed it was the chicken paired with say chicken number 101, we could simply say: "check the 101st decimal place, it's different from the 101st decimal of this new number". <br /><br />There are a few technical points to watch in building this number, for example you don't want to produce the number 0.9999… because this is actually the same as the number 1.000… But the essence of the argument suffices to show that there are more numbers with infinite decimal expansions than there are whole numbers.<br /><br />The great German mathematician David Hilbert recognized that Cantor was creating a genuinely new mathematics. Hilbert declared Cantor's ideas on infinities to be "the most astonishing product of mathematical thought, one of the most beautiful realisations of human activity in the domain of the purely intelligible…no one shall expel us from the paradise which Cantor has created for us". <br /><br />Cantor’s illumination of the different mathematical identities hiding inside the idea of infinity lead to a question that would reveal how subtle numbers are. Cantor wanted to know whether there are sets of numbers which are bigger in size than whole numbers but small enough that they can't be paired with all infinite decimal expansions. In other words can there be a tribal member with numbered chickens that is richer than the man with chickens labelled with whole numbers but poorer than the big cheese with chickens labelled with every possible infinite decimal expansion.<br /><br />The answer to this problem, which finally arrived in the 1960s, rocked the mathematical community to its foundations. Paul Cohen, a logician at Stanford, discovered that both answers were possible. Cohen proved that one couldn't prove from the axioms we currently use for mathematics whether or not there was a set of numbers whose size was strictly between the number of whole numbers and all real numbers. Indeed he produced two different models which satisfied the axioms that we are using for mathematics and in one model the answer to Cantor's question was "yes" and in the second model the answer was "no". <br /><br />Before Cantor, all infinities had been lumped together under one heading. But Cantor was able to distinguish different sizes of infinities. This feature of mathematics to distinguish different mathematical identities is very much a product of nineteenth century movement in mathematics towards looking for abstract mathematical structures underlying physical reality.Marcus du Sautoyhttp://www.blogger.com/profile/09231135591825316245noreply@blogger.com0tag:blogger.com,1999:blog-317557729672791321.post-2064517125889801552009-05-09T17:53:00.004+01:002009-05-09T18:02:55.624+01:00Twitter<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://4.bp.blogspot.com/_VXvJUb9b-Xw/SgW2RcXzvGI/AAAAAAAAAIo/YYl_V8XDFvU/s1600-h/twitter.jpg"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 314px; height: 152px;" src="http://4.bp.blogspot.com/_VXvJUb9b-Xw/SgW2RcXzvGI/AAAAAAAAAIo/YYl_V8XDFvU/s320/twitter.jpg" border="0" alt=""id="BLOGGER_PHOTO_ID_5333869744480304226" /></a><br /><br />Join me on Twitter if you would like to check out my micro blogging. Tweets on everything from Infinity to Nicholas Cage in Knowing, from Sexy Maths to the trials and tribulations of Arsenal football club.<br /><br /><a href="http://twitter.com/marcusduSautoy">Follow Marcus du Sautoy.</a>Marcus du Sautoyhttp://www.blogger.com/profile/09231135591825316245noreply@blogger.com0tag:blogger.com,1999:blog-317557729672791321.post-45644392082615363332009-04-01T21:09:00.001+01:002009-05-09T23:55:29.223+01:00Alan and Marcus Go Forth and Multiply<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://1.bp.blogspot.com/_VXvJUb9b-Xw/SgXjGh83CzI/AAAAAAAAAIw/7nVb38HXWqo/s1600-h/Horizon.jpg"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 320px; height: 178px;" src="http://1.bp.blogspot.com/_VXvJUb9b-Xw/SgXjGh83CzI/AAAAAAAAAIw/7nVb38HXWqo/s320/Horizon.jpg" border="0" alt=""id="BLOGGER_PHOTO_ID_5333919035022576434" /></a><br /><br />"Ever since he was at school, actor and comedian Alan Davies has hated maths. And like many people, he is not much good at it either. But Alan has always had a sneaking suspicion that he was missing out.<br />So, with the help of top mathematician Professor Marcus du Sautoy, Alan is going to embark on a maths odyssey. Together they visit the fourth dimension, cross the universe and explore the concept of infinity. Along the way, Alan does battle with some of the toughest maths questions of our age.<br />But did his abilities peak 25 years ago when he got his grade C O-Level? Or will Alan be able to master the most complex maths concept there is?"<br /><br />In this BBC Horizon that I made with Alan Davies we started out taking as our model the Oz Clarke/James May programmes but instead of wine we did maths. I got to play the posh Oz Clarke character: "what a wonderful bouquet this equation has" while Alan could play the urbane James May of maths. But actually the thing soon evolved into a completely different journey. It waas a mathematical road-trip. From Weymouth to Brighton, from Teddington to...well, actually it was more a road-trip of the mind. From primes to probability, quantum chaos to hyperspace.<br /><br />Alan is a clever guy. The village idiot role he plays on QI is just good acting. The director of our Horizon kept on saying: "Alan. Could you pretend you didn't understand the Riemann Hypothesis so quickly". Amazing what a national icon Alan is. Everywhere we went, people would flock to get his autograph. He was mugged by old grannies in Weymouth saying how much they loved Jonathan Creek to teenagers on Brighton Pier who knew him as the Dad in Angus, Thongs and Perfect Snogging. I kept thinking as I stood on my own on the sidelines: "but don't they know I've got a Theorem named after me." <br /><br />The programme was broadcast on BBC2 at 9pm on the 31st of March 2009. It got 2.3 million viewers. Reviews were mixed but then reviewers love knocking Horizon. One really nice review was in the <a href="http://entertainment.timesonline.co.uk/tol/arts_and_entertainment/tv_and_radio/article6022296.ece?token=null&offset=12&page=2">Sunday Times</a>.<br /><br />You can see some clips of the programme on the BBC website.<br /><br /><a href="http://news.bbc.co.uk/1/hi/education/7968997.stm">The maths of the beautiful game</a> "During his journey to understand the often vilified science of maths, comedian and Arsenal fan Alan Davies hears that footballers are "mathematical geniuses" and learns how maths can help fans of the game."<br /><br /><a href="http://news.bbc.co.uk/1/hi/education/7968941.stm">Why maths lacks common sense</a> "Comedian Alan Davies - who has hated maths since school - has embarked on a maths odyssey with the help of mathematician Marcus du Sautoy.<br />In a game of probability, he was challenged to put common sense aside in order to see the power of logical thinking." Here is an explanation of the infamous Monty Hall Game Show.Marcus du Sautoyhttp://www.blogger.com/profile/09231135591825316245noreply@blogger.com1tag:blogger.com,1999:blog-317557729672791321.post-35066892079705808792009-03-13T07:28:00.003+00:002009-03-13T07:37:46.621+00:00From Ecstasy to Infinity<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://3.bp.blogspot.com/_VXvJUb9b-Xw/SboMDlm49-I/AAAAAAAAAIg/uwH-WQvFolc/s1600-h/borromini.png"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 320px; height: 253px;" src="http://3.bp.blogspot.com/_VXvJUb9b-Xw/SboMDlm49-I/AAAAAAAAAIg/uwH-WQvFolc/s320/borromini.png" border="0" alt=""id="BLOGGER_PHOTO_ID_5312571966211291106" /></a><br />I've spent the two month making a radio programme about the art and science of the baroque for BBC Radio 3 that is due to be aired this Sunday on the Sunday Feature.<br /><br />The Baroque was always a style I'd associated with vulgarity and excess. But in this programme I’ve discovered how much control and structure underpins the spectacle of the baroque. The dramatic and sensational effects of the greatest baroque architects like Borromini and Bernini are founded on sound mathematical principles. Painters like Caravaggio and Rubens are battling with the same problems as Newton and Leibniz in their attempt to capture bodies in motion. And the extravagant sounds of Monteverdi and Bach would not be possible without the mathematical development of new ideas of temperament. It is my world of mathematics and science which allows the artist and musician to play with your emotions. Join me on my journey to the conversion of the delights of the baroque.<br /><br /><a href="http://www.bbc.co.uk/programmes/b00j4j1j">15 Mar 2009, 21:30 on BBC</a> Radio 3Marcus du Sautoyhttp://www.blogger.com/profile/09231135591825316245noreply@blogger.com1tag:blogger.com,1999:blog-317557729672791321.post-26124682478911780102009-02-08T21:19:00.004+00:002009-02-08T21:28:43.295+00:00A Disappearing Number<a onblur="try {parent.deselectBloggerImageGracefully();} catch(e) {}" href="http://3.bp.blogspot.com/_VXvJUb9b-Xw/SY9M8k2j8FI/AAAAAAAAAII/QaaslWLz5M8/s1600-h/complicite.jpg"><img style="display:block; margin:0px auto 10px; text-align:center;cursor:pointer; cursor:hand;width: 320px; height: 235px;" src="http://3.bp.blogspot.com/_VXvJUb9b-Xw/SY9M8k2j8FI/AAAAAAAAAII/QaaslWLz5M8/s320/complicite.jpg" border="0" alt=""id="BLOGGER_PHOTO_ID_5300539890006749266" /></a><br /><br />I was the mathematical advisor on Complicite's play A Disappearing Number. PLUS magazine have just released a <a href="http://plus.maths.org/podcasts/">podcast</a> including interviews with me about my collaboration. <br /><br />You can see clips from the show at <a href="http://www.complicite.org/productions/detail.html?id=43">Complicite's website</a><br /><br />I also helped devise workshops in connection with the play for maths and drama teachers. More details can be found in the <a href="http://www.complicite.org/education/project.html?id=20">Education section of Complicite's website</a>Marcus du Sautoyhttp://www.blogger.com/profile/09231135591825316245noreply@blogger.com1