The Secret You: Horizon BBC2

Horizon: THE SECRET YOU

BBC2 Tuesday 20 October 2009 9pm

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.

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.

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.

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.

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.

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.

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.

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.

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.

Bonus feature: Hole in the hand

Also check out an article on BBC News Online

The Times Cheltenham Literature Festival

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.
Book online.

Simetria

The Spanish edition of Finding Moonshine was published this week by Acantilado.
I was in Spain this week promoting the book. I gave a talk in Madrid at the prestigious Residencia de Estudiantes, 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.
I also gave a talk in Barcelona at the CosmaCaixa museum. It is a fantastic science museum and I thoroughly recommend it to anyone visiting Barcelona.

Here are some reviews that have appeared in Spain:

El Pais: La Alhambra es un microcosmos de simetrías
Agencia EFE: El científico Marcus Du Sautoy dice que "la simetría es un lenguaje fundamental"

Simonyi Lecture

JOIN TIMOTHY GOWERS

For this years

CHARLES SIMONYI LECTURE

at OXFORD PLAYHOUSE



Friday 2 October at 5pm



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.



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.



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.



Tickets for The Charles Simonyi Lecture at Oxford Playhouse are available from the Box Office on 01865 305305 or Oxford Playhouse Website

TED

The subject of TEDGlobal 2009 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.
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:



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.
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.

TED blog entry about my talk

Twitter Snapshot: Marcus du Sautoy on symmetry

Groups for Charity 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.

The Complete Sexy Maths

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.

1 Jul 2009 Oh, it’s such a perfect day. We have discovered 47 perfect numbers — the largest has nearly 26 million digits.

24 June 2009 How to avoid a grudge match. Never mind Arsenal against Spurs. How about NP versus P?

17 June 2009 Arithmetic eases swine flu. Figuring out the rate of contagion can make you feel better

10 June 2009 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.

27 May 2009 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.

20 May 2009 A game of 12 pentagons. Why a football match is actually geometry in motion.

13 May 2009 in search of the poetry of Muslim symmetry. Galois’s group theory allowed mathematicians to articulate the theory of symmetry.

6 May 2009 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.

29 April 2009 The lemming theory. There is no mass suicide pact keeping the numbers of lemmings down.

22 April 2009 What's unique about the number 1,729?

15 April 2009 The Fibonacci sequence's prime rate.

8 April 2009 Drawing parallels in geometry. This year's Abel Prize honours some of the most revolutionary contributions to geometry since those of Euclid.

25 March 2009 Go fourth... into another dimension.

18 March 2009 Twists and turns that make a rollercoaster ride.

11 March 2009 A number-munching celebration.

4 March 2009 Ditch the GPS, just follow the colour code.

25 February 2009 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.

18 February 2009 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.

11 February 2009 Why Palladio's proportions are pleasing on the eye and the ears.

4 February 2009 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.

28 January 2009 It's true, young Muggles. Maths can be magic.

21 January 2009 Rubik's Cube returns.

14 January 2009 Solving wobbly restaurant tables. Wedging beer mats or bits of paper under that annoying table leg is no more. Try the mathematical solution instead.

7 January 2009 Survival of the mathematician.

31 December 2008 How to be a perfect timekeeper.

17 December 2008 Warm up with a few festive candles.

10 December 2008 The symmetry of sneezing. Viruses blight many people's lives in winter but the molecular structure of many are things of mathematical beauty.

26 November 2008 Skills of a chess grandmaster.

19 November 2008To infinity - and beyond

12 November 2008 Get the upper hand at poker.

5 November 2008 Why democracy is an ass.

29 October 2008 Get your teeth into this.

22 October 2008 Why the taxman has your number.

15 October 2008 Sexy maths: a calculating approach to love. Mathematics can help you to maximise your chances of landing the best flat – or the best partner.

8 October 2008 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.

1 October 2008 Primes of passion.

Finding Moonshine in Paperback

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.

Click here to buy the paperback from Amazon

To Infinity and beyond

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.

To infinity and Beyond...

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.

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.

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.

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.

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.

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,…

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.




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…

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.

1 ↔ 3.1415926…
2 ↔ 2.7182818…
3 ↔ 1.4142135…
4 ↔ 1.6180339…
5 ↔ 0.3331779…

…

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".

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.

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".

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.

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".

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.

Twitter

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.

Follow Marcus du Sautoy.

Alan and Marcus Go Forth and Multiply

"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.
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.
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?"

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.

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."

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 Sunday Times.

You can see some clips of the programme on the BBC website.

The maths of the beautiful game "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."

Why maths lacks common sense "Comedian Alan Davies - who has hated maths since school - has embarked on a maths odyssey with the help of mathematician Marcus du Sautoy.
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.

From Ecstasy to Infinity

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.

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.

15 Mar 2009, 21:30 on BBC Radio 3

A Disappearing Number

I was the mathematical advisor on Complicite's play A Disappearing Number. PLUS magazine have just released a podcast including interviews with me about my collaboration.

You can see clips from the show at Complicite's website

I also helped devise workshops in connection with the play for maths and drama teachers. More details can be found in the Education section of Complicite's website

Too hard...?

Somebody just sent me this quote from Terry Prachett's Thief of Time. Susan is a teacher talking to her Head teacher:

"What precisely was it that you wanted madam?" she said. "It's just that I have left the class doing algebra and they get restless when the've finished".
"Algebra?" said madam Frout............"But that's far too difficult for seven-year-olds!"
"Yes but I didn't tell them that, and so far they havn't found out" said Susan....................

Story of Maths on BBC World

Our journey round the world to uncover the story of Maths is appropriately going to be shown on BBC World throughout January. The programmes originally broadcast on BBC4 in October and were available on BBC iPlayer but those outside the UK were unable to catch the series. Now is your chance.

SHOWING TIMES for Programme One: The Language of the Universe.
Showing Saturday 10th January at 0810 GMT.
Repeated: Saturday at 1810 GMT and Sunday 11th at 0210 and 1410 GMT.

If that isn't possible then the series is also available on DVD from the Open University although I'm afraid it is a little pricey which is a shame.

Exciting news: the BBC has chosen The Story of Maths as one of its entries for the Royal Television Awards in Science and History.

BBC World website