Plus Blog

April 1, 2008
Tuesday, April 01, 2008

Climate change and composing computers

Last night, Plus attended an excellent talk at the Edinburgh International Science Festival by Professor Chris Rapley, who was awarded the Edinburgh Medal. The Edinburgh Medal is awarded each year to those within science whose professional achievements are judged to have made a significant contribution to the understanding and well-being of humanity.

Profesor Rapley's talk was entitled "Great while it lasted; now what?" referring to how humans have exploited carbon-based energy sources for the last century, but now must confront the fact that we are exceeding the safe limits of such use. Professor Rapley is a systems scientist and has studied the Earth mathematically as a complex system through roles as Director of the British Antarctic Survey, Executive Director of the International Geosphere-Biosphere Programme, and Professor of Remote Sensing Science and Associate Director of University College London's Mullard Space Science Laboratory.

Professor Rapley is now Director of the Science Museum in London, and considers that the best way to study the Earth is to bring together "many -ologists — geologists, biologists, sociologists etc." As a complex system, the Earth has many inbuilt checks and balances — the oceans and the biosphere can act as carbon sinks, reducing the amount of carbon dioxide in the atmosphere. However, Rapley thinks that the Earth will also have a "tipping point" whereby the ocean and biosphere can no longer take-up carbon dioxide. Using recent ice melts in the Antarctic and Greenland as examples, he highlighted the incredibly difficult task in modelling the Earth as a complex system. Describing the Earth as "the most complex system in the Universe", he said that the Earth system "has many surprises and can't be modelled too much." He added, soberly, that whilst the greenhouse effect was understood in the 1800s by mathematician Joseph Fourier , the Earth now:

"...has no user's manual, and no spares... . Many senior economists act like they don't understand this."

He likened our current situation to that of the next day after a great party. Burning immense amounts of carbon has given humans a much higher quality of life than before the use of carbon fuels, however the carbon dioxide is the "hangover." He attacked sceptics of climate change by saying that the weight of scientific opinion supports the assertion that climate change is real and man-made, highlighting that 90% of climate change is anthropogenic.

Another interesting, and perhaps unfortunate, point (well, for me anyway) was that meat-eaters contribute far more than vegetarians to climate change. This is because much more energy goes into meat production than vegetarian foods.

Professor Rapley's talk was preceded by an oration by Dr James Lovelock. Dr Lovelock is a systems modeller and is well-known for proposing the Gaia hypothesis — that living and non-living parts of the Earth are a complex interacting system that can be thought of as a single organism, and that all living things have a regulatory effect on the Earth's environment that promotes life overall. Lovelock and Rapley have recently proposed a radical idea to "Help the Earth heal herself" in a letter to Nature Magazine. The proposal is to use huge pipes to pump lower ocean water, rich in nutrients, to the surface, stimulating the growth of algae and plankton in the upper ocean. The surface layer of the ocean is increasingly starved of nutrients such as phosphates and nitrates. These nutrients are needed by the algae to grow, but as the surface warms, there is less mixing with the nutrient-rich water layers beneath. The mixing of ocean layers would encourage algal blooms — the algae take up more carbon dioxide, which is eventually locked up in the tiny shells of plankton when they die and fall to the bottom of the ocean. This proposal essentially assumes that it's too late for carbon emission controls and other alternatives to have any effect on climate change — the damage is already done.

To read more on the mathematics of climate change, read the Plus article Maths and climate change: the melting Arctic.

Another interesting session that Plus attended was on a computer that had been taught using hidden markov models to harmonise melodies in the style of Johann Sebastian Bach. A hidden Markov model is a statistical model in which the system being modelled is assumed to be a Markov process with unknown parameters, and the hidden parameters need to be determined from the observable parameters. Hidden Markov models are known for their application in pattern recognition such as speech, handwriting, musical score following and bioinformatics.

You can read more on Machine Learning at the Edinburgh Festival on yesterday's blog, and you can read more about Markov Processes in the Plus article Formulaic football. And to read more on using hidden Markov Models to analyse Bach, see the group's publication Harmonising chorales by probabilistic inference.

This afternoon, I eagerly await the screening of Pi in the maths film festival. For more information and a comprehensive program, see the Festival website. The event runs until April 6.

posted by westius @ 10:12 AM


March 31, 2008
Monday, March 31, 2008

Machine learning and clever 8-year olds

This week, Plus is attending the Edinburgh International Science Festival — an educational charity aiming to engage society in the value of science and technology, placing a particularly strong emphasis on providing experiences of science that are inspiring and confidence building. The Festival is internationally well-regarded and one of the biggest science events in the UK. Its timing suggests we are now well into science festival season, with roughly another 10 city-wide events to be held around the country, in addition to the recently run Cambridge and Brighton Science Festivals. In 2007, Plus attended the BA York Science Festival — you can read more on the Plus Blog.

There is a comprehensive range of talks from some of the world's leading scientists, and last evening Plus attended a talk by Chris Bishop, Deputy Director of Microsoft Research in Cambridge, on Machine Learning. Compared to humans, machines are very bad at recognising some patterns — for instance, recognising that a photo of a cow is actually a cow and not a dog or a shadow or even a spoon — they simply do not innately know these things and must be taught. Whilst humans are very good at understanding messy handwriting — a subtle task — computers must learn. Bishop's work involves developing computers that can learn and so become smarter in completing their tasks. To read more about the mathematics involved, see the Cambridge team's introduction to applied mathematics for machine learning.

Central to machine learning is the Turing Test. English mathematician Alan Turing — instrumental in breaking the Enigma code during World War II — is widely regarded as one of the founders of modern computer science — see the Plus article What computers can't do. In a 1950 paper, he described what he called the Imitation game, now known as the Turing Test, in which a person (in a separate room) tries to distinguish between human and computer test subjects by asking them each a series of questions. If the person can't distinguish between the computer and the human, the computer is deemed to be intelligent. There is a (currently unclaimed) prize of $100,000 for a computer that can pass the Turing Test. Bishop talked about the Forza Motorsport X-box game, in which you race against other players or against the computer. The computer car can be taught to drive like a human — you can create a "Drivatar" which will learn from the way you drive and then drive like you. The word Drivatar comes from avatar, which in gamer-speak is the player's representation within the game. Participants in trials have said that they cannot tell the difference between a human playing and a computer, and so within a very limited context, the Drivatar passes the Turing Test.

Bishop also talked about other developments in machine learning, from Spam email detection — see the Plus article CAPTCHA if they can — to websearches and modern developments in HIV detection. New software is being developed to look for patterns in the HIV protein code. This code evolves over time, and so searching for the same string of amino acids each time is likely not to work. He also discussed developments in the way computers play the games Chess and Go. He stated that whilst the IBM Deep Blue chess-playing computer was able to beat world chess champion Garry Kasparov in 1997, it was not because of any particular advances in machine "intelligence" — the success was largely due to advancements in computer memory and speed that allowed the computer to analyse the game very thoroughly. If at each turn you can make around 30 possible moves, and then there are around 30 possible replies by your opponent, and then in turn another 30 possible moves you can make, and so on, then a human could never hope to analyse each and every scenario. However, Deep Blue was able to look at the full set of possible moves and then make the best one (although it did have the intelligence to look within a set of smart moves). With the game Go however, at each turn there are around 200 possible moves, meaning that it is impossible currently to completely analyse each scenario before playing a move. Bishop is working with computers that are learning by playing against humans.

I have also attended Wonderama and the mathematical puzzles at the Museum of Scotland. Wonderama is designed for the whole family and hosts many free activities and events for budding scientists, aspiring surgeons, wannabe adventurers and trainee archaeologists. Thankfully, my time around science festivals means that I wasn't outdone by 8-year olds in the mathematical puzzle department. Actually, that is not completely true...

Tonight, I am eagerly awaiting the Edinburgh Medal Address by Professor Chris Rapley, Director of the Science Museum, on the dangers of climate change. The Edinburgh Medal is awarded each year to those within science whose professional achievements are judged to have made a significant contribution to the understanding and well-being of humanity.

For more information and a comprehensive program, see the Festival website. The event runs until April 6.

posted by westius @ 1:57 PM


March 28, 2008
Friday, March 28, 2008

One of the most important international prizes for mathematics has this year been awarded jointly to two outstanding mathematicians — even though one of them was originally unable to find a publisher for his groundbreaking work.



posted by Plus @ 4:23 PM


March 28, 2008
Friday, March 28, 2008

Alexander Grothendiek, one of the most important mathematicians of the twentieth century, turns 80 today.



posted by Plus @ 1:27 PM


March 27, 2008
Thursday, March 27, 2008

Film3 — maths at the movies

Mathematical films will be featured next week in the Edinburgh International Science Festival's mathematics film festival Film3 — maths at the movies.

Pi will be featured on 1 April.

The season of mathematical movies was created by the International Centre for Mathematical Sciences and Filmhouse Cinema to showcase three very different independent films. Each film is based around a mathematical concept, but also provides an element of social commentary.

The season opens on 27 March with the UK premiere of the highly acclaimed animation, Flatland the Film. Based on the 1889 novel by Edwin A. Abbot, the film tackles issues revolving around race, gender, religion and globalisation. Mr A. Square is an average middle-class Flatlander until enlightenment allows him to see his world from a different dimension. He discovers that Flatland is threatened by forces it cannot possibly recognise. Will he be able to save his family and his world? Everyone attending the screening will receive a "goody bag" containing postcards signed by Flatland's director Ladd Ehlinger Jr, a copy of the novel donated by Transreal Fiction, vouchers from Filmhouse and Edinburgh International Science Festival, and other mathematical goodies from ICMS. A discussion led by Maximillian Ruffert of University of Edinburgh and Katie Russell of Heriot-Watt University will follow the film.

You can read the Plus review of the original 1889 novel Flatland in the Plus article 'Flatland'.

Pi is screened on 1 April and explores the life and experiences of Max, a gifted mathematician who believes that everything in the Universe can be expressed mathematically. He becomes obsessed with finding the underlying pattern behind the stock market, but religious and commercial groups try to exploit his research. Can he pass through this philosophical maelstrom and survive unscathed? Giorgos Papageorgiou and Tim Johnson of Heriot Watt University will discuss the film with the audience after the screening.

The final film, Cube, is screened on April 3. Cube investigates the relationships between six apparently unconnected individuals who wake up inside a three-dimensional maze of interlocking cubes. Developing mutual trust is the key to survival as they are forced to collaborate on cracking the code behind the Cube's mechanism. How many will escape to discover the bigger mystery that lies outside their existentialist prison? Science fiction author and mathematician Hannu Rajaniemi will discuss questions arising from the mathematics in Cube with the audience.

Tickets are available for individual films, or at a discounted rate for all three, from the box office at Filmhouse Cinema, 88 Lothian Road, Edinburgh, EH3 9BZ (phone: 0131 228 2688). Each screening will start at 5.45pm, and there will be discussion in the theatre after the screening, and then over coffee and drinks.

Plus will be attending the screening of Pi, so please come and chat to us! You can read more on the Film3 — maths at the movies website.

posted by westius @ 2:57 PM


March 25, 2008
Tuesday, March 25, 2008
A new mathematical object was revealed to great acclaim at the American Institute of Mathematics last week. Ce Bian and Andrew Booker from the University of Bristol showed the first example of a third degree transcendental L-function.

L-functions underpin much of twentieth century number theory. They feature in the proof of Fermat's last theorem, as well as playing a part in the recent classification of congruent numbers, a problem first posed one thousand years ago.



posted by westius @ 4:00 PM


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