Laziness, lottery and lemmings

After an unforgivable two-month silence, it’s Haggis here reporting back from the Edinburgh International Science Festival.  It’s certainly been a mathemagical experience so far and we’re not finished yet!  First off, we had 5 days of presenting the Magical Möbius strip at the National Museum of Scotland for the University’s “Discover Science” programme.  It was fantastic to see the eyes of old and young alike light up at the wonders of topology (photos hopefully forthcoming!).  Yesterday there was a heated debate about “Maths, Money and Magic” in which a scientist, a mathematician and a banker discussed the causes of the current financial crisis. (More debate will probably continue in a future blog post!)

Me and Marcus

Tonight we had the most exciting mathematical event so far: a lecture by the bestselling author and renowned maths ambassador Marcus du Sautoy.  I decided to arrive early in order to get him alone for a photo opportunity, to which he was happy to oblige on one condition: that I donate some money to help children in Guatemala.  This seemed like a perfectly reasonable bargain to me, and it became much more so when Marcus explained that not only would I get a photo, but I would also get a mathematical group named after me!  If I choose my group carefully then it could just end up being the last piece of the puzzle to prove the Riemann hypothesis or something.  Then fame and immortality will be mine forever!  (If you want to have your own piece of mathematical glory, the donation website is www.tiny.cc/symmetry4charity and Marcus is looking to raise £1000 by the end of April.)

Is Beckham a mathematician?

So, I got my photo and it was time to sit back and watch the show.  The event was chaired by none other than my flatmate Julia, and though she was a bit nervous I think she managed to say all the right things at the right time. Marcus gave a great opening by telling the story of how his football team Recreativo managed to get high up in the league rankings by switching all the players’ shirts to prime numbers.  An amazing coincidence it may well have been, but the prime numbers (those which have no factors other than themselves and 1) do hold a lot of secrets and a lot of power when used in the right place.  Anyone who can discover the pattern of the primes is in line for a prize of $1 million from the Clay Institute and a lot of kudos from the mathematicians!  We really are a lazy bunch and love to have formulas that predict things so that we can stop having to do boring calculations.

Next up after the primes was the lottery.  The audience members were each asked to pick 6 numbers out of 49 and Marcus performed his own lottery draw, with a volunteer picking six bright pink balls out of a box.  Marcus then used the power of mathematics to predict how many people had got 0, 1,2,3 or 4 of the numbers correct, and he was frighteningly accurate!  About half the audience had failed to predict any of the numbers, about an eighth had got at least two numbers, only three people (out of 150) had got three numbers and (surprisingly) there was someone who got 4 numbers.  Even more surprisingly, Marcus told us that about half of lottery results contain two consecutive numbers, e.g. 31 and 32.  So there you go: a tip for next time you play!  This strategy will also make it less likely that you’ll have to split your winnings since not many people opt for pairs of numbers close to each other.

Pendulum around 3 magnets

The rest of the lecture was about showing different examples of chaos theory in action.  The picture on the left shows what happens if you have a pendulum swinging between three magnets (blue, yellow and red).  If you start the pendulum swinging in a red region, it will end up orbiting the red magnet and similarly for the other colours.  Away from the magnets, the motion is totally chaotic: a tiny move from a starting point and your pendulum will orbit a completely different magnet.  I thought it was amazing that the picture looked so similar to mixing in a pot of paint and wonder if there is some kind of connection.

More exciting than pendulums was, of course, lemmings.  Why do they commit suicide every 4 years?  According to Marcus, it’s because of maths.  Suppose that there are N lemmings at a certain time.  If each of them has one baby, there will then be 2N lemmings in the population, but with the increase in population comes a decrease in food for everyone.  The formula for working out how many lemmings will die as a result of this is

(N x 2N)/10

If you plot a graph of the number of lemmings over time (starting with, for example, N=2 lemmings), then you find that the number of lemmings eventually becomes fixed at a constant stable value.  If instead of one baby you allow each lemming to have two babies, the formula becomes (N x 3N)/10, and then the population goes through cycles of growing and shrinking.  So far, so simple.  The interesting bit comes if you let the lemmings have more than 2.5 children each, since then the population graph goes pretty wild and chaotic and unpredictable!  At the 2.5 mark exactly, the population is still quite predictable but you get these crazy years when almost all of the population dies off.  You have to feel sorry for the lemmings really, being killed because of the maths of having the wrong number of babies.

Finally, it was not so unpredictable that Marcus would finish as he opened with his favourite pastime of football.  He explained how chaos was responsible for Roberto Carlos’ swerving free kick against France in 1997.

It was a great pleasure to watch Marcus speak, as it was clear that he had a genuine enthusiasm for the subject and could infectiously spread this to the rest of the audience.  It was as though he was speaking of all these great mathematical results for the first time, rather than that he was repeating the same old mantra to just another group of people.  It is this attitude which has cemented him as today’s foremost maths populariser and I have no doubt that he will continue to inspire many thousands of people through his great work.

Tomorrow night we can look forward to another great don of the mathematical outreach world, Ian Stewart, giving us a glimpse of what is inside his new book “Cows in the Maze”.  Stay tuned!

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