Marcus du Sautoy
http://www.newstatesman.com/writers/marcus_du_sautoy
en<![CDATA[Self-awareness by numbers]]>
http://www.newstatesman.com/sci-tech/sci-tech/2013/02/self-awareness-numbers
<div class="field field-name-field-node-image field-type-image field-label-hidden view-mode-fulltext"><div class="field-items"><figure class="clearfix field-item even"><a href="/sci-tech/sci-tech/2013/02/self-awareness-numbers"><img typeof="foaf:Image" class="image-style-fullnode-image" src="http://www.newstatesman.com/sites/default/files/styles/fullnode_image/public/20120808104208-0.jpg?itok=YHSa2Cjb" width="510" height="348" alt="" /></a></figure></div></div><div class="field field-name-field-nodeimage-title field-type-text field-label-hidden view-mode-fulltext"><div class="field-items"><div class="field-item even">Golgi stained neurons in the dentate gyrus of an epilepsy patient. Image: WikiCommons</div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden view-mode-fulltext"><div class="field-items"><div class="field-item even" property="content:encoded"> <p>What is consciousness? In the past, this question was the preserve of theologians, psychologists and philosophers. Scientists seemed unable to find a way to probe the grey matter between our ears. Now that has changed. The study of the brain has experienced a renaissance.</p>
<p>We are in a moment similar to that when the telescope provided a way for the likes of Galileo to explore the outer reaches of the solar system. The development of the fMRI (functional magnetic resonance imaging) scanner, techniques of transcranial magnetic stimulation (TMS) and EEGs (electroencephalograms) has given scientists a way to ask the brain new questions. One of the most intriguing proposals to emerge is that mathematics might hold the key to unlocking the mystery of consciousness.</p>
<p>To understand what makes something conscious, one can look at the converse question of what contributes to things being unconscious. Every night, when we fall into dreamless sleep, our consciousness disappears. So what is happening in the brain that causes us to lose our sense of self until we wake or dream?</p>
<p>In the past, it was impossible to ask the sleeping, dreamless brain questions. New TMS techniques allow us to infiltrate the brain and artificially make neurons fire. By applying a rapidly fluctuating magnetic field to the brain, we can activate specific regions when people are awake and, more excitingly, when they are asleep. So how do the conscious and sleeping brains respond to this stimulation of neurons?</p>
<p>Experiments conducted by Giulio Tononi and his team at the Centre for Sleep and Consciousness at the University of Wisconsin-Madison have shown that the brain’s reaction to TMS when it is awake is strikingly different from when it is dreamlessly sleeping. The first part of the experiment involves applying TMS to a small region of the participants’ brains when they are awake or conscious. Electrodes attached to the head record the effect using EEG. The results show that different areas far away from the stimulated site respond to the stimulation at different times in a complex pattern that then feeds back to the original site of the stimulation. The brain is interacting as a complex, integrated network.</p>
<p>Participants are then required to fall asleep and, once in deep, “stage-four” sleep, TMS is again applied to the brain in the same location, stimulating the same region. Unlike in the conscious state, the electrical activity does not propagate through the brain. It’s as if the network is down. The tide has come up, cutting off connections. The implication is that consciousness has to do with the complex integration in the brain.</p>
<p>Our gut has as many neurons as our brain, yet we don’t believe it is conscious. Is this because the neurons are not wired to have this integrated feedback behaviour? Tononi has even developed a mathematical coefficient of consciousness that measures the amount of integration present in a network. Called “phi”, it is a measure that can be applied to machines as well as the human brain and offers a quantitative mathematical approach to what makes me “me”.</p>
<p>Could Tononi’s phi help us understand if a computer, the internet or even a city can achieve consciousness? Perhaps the internet or a computer, once it hits a certain threshold, might recognise itself at some point in the future. Consciousness could correspond to a phase change in this coefficient, rather like the way water can change state when its temperature passes the threshold for boiling or freezing.</p>
<p>If consciousness is a spectrum encoded by this coefficient, measuring from the consciousness of a stone to the consciousness of the human mind, who are we to say there might not be consciousness beyond where evolution has taken the brain? The fMRI scans that have been done on Tibetan monks as they meditate seem to show that the act of meditation takes them into an altered brain state that might well be an increased level of consciousness. The brain appears to be organised into two networks: the extrinsic network and the intrinsic – or default – network.</p>
<p>When people are performing tasks external to themselves, such as playing a musical instrument or filling the kettle, it is the extrinsic portion of their brain that is active. When individuals are reflecting more on themselves and their emotions, it the default network that appears to be more dominant.</p>
<p>The interesting observation is that these two networks are rarely fully active at the same time. One side of the see-saw needs to be down in order to allow the other side to play its part in enabling an individual to concentrate on whatever task is at hand. Yet evidence from scanning the Buddhist monks during periods of meditation indicates that they seem to be able to raise both sides of this neural see-saw at the same time.</p>
<p>The research opens up the thrilling possibility that there are ways to increase your levels of consciousness. And so, on 2 March, as part of the Barbican’s and the Wellcome Trust’s season “Wonder: Art and Science on the Brain”, I will be collaborating with the musician James Holden to see whether we can use music to take the collective phi of our audience and turn it up to 11.</p>
<p><em>Marcus du Sautoy is the Simonyi Professor for the Public Understanding of Science at the University of Oxford. “Wonder: Art and Science on the Brain” will run at the Barbican Centre, London EC2, from 2 March to 10 April</em></p>
</div></div></div>Thu, 28 Feb 2013 05:31:09 +0000Marcus du Sautoy193173 at http://www.newstatesman.com<![CDATA[Maths is the language of the universe]]>
http://www.newstatesman.com/education/2010/10/problem-science-mathematics
<div class="field field-name-field-subheadline field-type-text-long field-label-hidden view-mode-fulltext"><div class="field-items"><div class="field-item even"><p>As governments around the world prepare to slash science research budgets, it is worth remembering h</p>
</div></div></div><div class="field field-name-body field-type-text-with-summary field-label-hidden view-mode-fulltext"><div class="field-items"><div class="field-item even" property="content:encoded"> <!-- Generated by XStandard version 2.0.0.0 on 2010-10-14T08:16:04 --><p>Mathematics can often appear arcane, esoteric, unworldly and irrelevant. Its blue-skies status could easily make it a target for the harsh cuts to science budgets that governments around the world are contemplating. But before the axe falls, it is worth remembering what the 17th-century scientist Galileo Galilei once declared:</p>
<blockquote><p>The universe cannot be read until we have learned the language and become familiar with the characters in which it is written. <br />It is written in mathematical language and the letters are triangles, circles and other geometrical figures, without which means <br />it is humanly impossible to comprehend a single word.</p>
</blockquote>
<p>The scientists at Cern will certainly agree with Galileo. Their ability to make predictions about the particles they are expecting to see inside the Large Hadron Collider is entirely down to mathematics. Rather than triangles and circles, strange, symmetrical objects in multidimensional space - shapes that exist only in the mathematician's mind's eye - are helping us to navigate the strange menagerie of particles that we see in these high-energy collisions.</p>
<p>Biochemists trying to understand the three-dimensional shapes of protein strings will also sympathise with Galileo's sentiments. Each protein consists of a string of chemicals, which are like letters in a book. But to read this language and predict how the one-dimensional string will fold up in three-dimensional space, you need a mathematical dictionary. Studying protein folding is key to understanding several neurodegenerative diseases that are a result of the incorrect folding of certain protein strings.</p>
<p>It is striking, however, how much of my subject remains a mystery: how many mathematical stories are still without endings, or read like texts that have yet to be deciphered.</p>
<p>Take the atoms of mathematics, the primes. Indivisible numbers such as seven and 17 are the building blocks of all numbers because every number is built by multiplying these primes together. They are like the hydrogen and oxygen of the world of mathematics. Dmitri Mendeleev used the mathematical patterns he had discovered in the chemical elements to create the periodic table, the most fundamental tool in chemistry. So powerful were these patterns that they helped chemists to predict unknown elements that were missing from the table. But mathematicians are still to have their Mendeleev moment. The pattern behind the primes that might help us to predict their location has yet to be uncovered. Reading through a list of primes is like staring at hieroglyphs. We have made progress and have unearthed something resembling the Rosetta Stone of prime numbers - but the ability to decode the stone still eludes us.</p>
<p>Mathematicians have been wrestling with the mystery of the primes for 2,000 years, but some of the biggest problems in maths are far more recent. There was a flurry of excitement this summer when the Hewlett-Packard engineer Vinay Deolalikar claimed to have cracked the "P v NP" problem. First posed in the 1970s, this is a problem about complexity. There are many ways to state it, but the classic formulation is the "travelling salesman problem".</p>
<p>An example is the following challenge: you are a salesman who needs to visit ten clients, each located in a different town. The towns are connected by roads, as shown on the following map, but you have only enough fuel for a journey of 238 miles</p>
<p>The distance between towns is given by the number on the road joining them. Can you find a journey that lets you visit all ten clients, stopping in each town only once, and then return home without running out of fuel? (The solution appears at the end of the article.) The big mathematical question is whether there is a general algorithm or computer program that will produce the shortest path for any map you feed in, which would be significantly quicker than getting the computer to carry out an exhaustive search. The number of possible journeys grows exponentially as you increase the number of towns, so an exhaustive search soon becomes practically impossible.</p>
<p>The general feeling among mathematicians is that problems of this sort have an inbuilt complexity, which means that there won't be any clever way of finding the solution. But proving that something doesn't exist is always a tough task. The recent excitement that this problem had been cracked has since evaporated and it remains one of the toughest on the mathematical books.</p>
<p>But the recent solution of another challenging problem, the Poincaré conjecture, gives us hope that even the most elusive problems can be conquered. The Poincaré conjecture is a fundamental problem about the nature of shape. It challenges mathematicians to list the possible shapes into which three-dimensional space can be wrapped up. In 2003, the Russian mathematician Grigori Perelman succeeded in producing a periodic table of shapes from which all other such shapes can be built.</p>
<p>These fundamental mathematical questions are not just esoteric puzzles of interest solely to mathematicians. Given that we live in a world with three spatial dimensions, the Poincaré conjecture tells us ultimately what shape our universe could be. Many questions of biology and chemistry can be reduced to versions of the travelling salesman problem, where the challenge is to find the most efficient solution among a whole host of possibilities. A resolution of the P v NP problem could therefore have significant real-world repercussions.</p>
<p>Modern internet codes rely on properties of prime numbers. So any announcement of a breakthrough on the primes is likely to spike the interest not just of pure mathematicians, but of e-businesses and national security agencies. At a time when blue-skies research without obvious commercial benefits could be under threat from sweeping cuts, it is worth remembering how Galileo concluded his statement about the language of mathematics: without it, we will all be wandering around, lost in a dark labyrinth.</p>
<p><em>Marcus du Sautoy is the Charles Simonyi Professor for the Public Understanding of Science, University of Oxford. His new book, "The Number Mysteries", is published by Fourth Estate (£16.99)</em></p>
</div></div></div>Thu, 14 Oct 2010 08:24:18 +0000Marcus du Sautoy178646 at http://www.newstatesman.com