The mathematics of magic

 
Guest post by Matt Parker

When Derren Brown ‘explained’ how he predicted the lottery, I suddenly experienced something psychologists must be familiar with. An impressive piece of television magic was followed by an expose episode full of pseudo-mathematical smoke-screen. Psychologists breathed a sigh of relief as this time Derren wasn’t using their subject as a decoy explanation for his impressive conjuring skills, while, as a mathematician, I was ready to throw a calculator at the TV screen.

What has impressed me though is that now when I run mathematics lessons in various secondary schools, the students will suddenly get very excited when Derren Brown is mentioned. Discussions on how he actually did the illusion aside (such as split-screens and - my favourite - long-distance laser etching), the students want to talk about the mathematical red-herrings he threw out.

For the pedantic record: both the Wisdom of the Crowd and the Heads-Tails game are well understood bits of mathematics. Wisdom of the Crowd is a lovely example of how even though people make mistakes when trying to estimate a value, the errors follow a delightfully predictable distribution. If you average across everyone’s guess, the under-estimates compensate for the over-estimates and you get a fairly accurate answer; but only when people make consistent mistakes. Which is not the case when predicting a random future event, such as the lottery numbers. The Heads-Tails game is a probability trick to give yourself a seemingly-impossible advantage when predicting a coin flip. I’ve used it to win many a free drink, and if you want to learn how, the details are here.

So now I’ve ended up being extremely grateful to Derren Brown for continuing the age-old overlap between magic and mathematics. For generations, mathematicians have dabbled in magic and visa-versa (the magician S. Brent Morris completed a mathematics PhD based on techniques develop for his magic tricks). My colleague, and professor of computer science, Peter McOwan is also an amateur magician and uses magic in his lectures. He says “It’s no surprise that some mathematicians and computer scientists are also keen amateur magicians. Day-to-day we work on the maths that underpins our modern society, but from time-to-time it’s just good fun to use maths for entertainment too.”

This is also perfect for modern mathematics teaching. To teach maths in a secondary school, you need to engage the students in the subject and nothing does this better than showing them how the maths can be used to perform a magic trick. If a student knows he can use prime numbers to amaze his friends with a card trick, they will suddenly become much more engaged in the lesson. This is why I have worked with Professor McOwan to produce a Manual of Mathematical Magic. All copies of the book, each with a magic kit, are available free to schools. Any school nationwide can request a copy and this week we have posted a copy to every school in London. We hope that teachers will be able to use it in their class, or at the very least give it to an enthusiastic student. If you work in a secondary school, or send your child to one, please locate the copy we sent to the mathematics department and make sure it is being used.

Before we posted the Manual of Mathematical Magic to all the London schools, I ran an estimation-based competition to win one of five advance copies. Not entirely unexpectedly, one entry simply read “the average of all other guesses” and sure enough, they were one of the winners. If more maths teachers use magic to engage their students, we’ll end up with a more mathematically literate society and of course, more people winning free drinks in the pub.

Schools can get more information about the Manual of Mathematical Magic kit and order a free copy from: www.mathematicalmagic.com. Production and distribution of the kit is funded by the Higher Education Funding Council for England.

Matt Parker is based in the School of Mathematical Sciences at Queen Mary, University of London. He also gives talks about Mathematics to schools and wider audiences across the UK.

Comments

[not given]

Excellent idea and book - but awful 'school text book' cover design.

[not given]

(contd) .. if you want to make a difference and have people otherwise not excited by maths read it and be inspired by it the cover should feature exiting images relating to magic .. not mathematical symbols which just bring your average maths hating 14 year old out in a cold swat.

[not given]

(contd) .. if you want to make a difference and have people otherwise not excited by maths read it and be inspired by it the cover should feature exiting images relating to magic .. not mathematical symbols which just bring your average maths hating 14 year old out in a cold sweat.

[Ian Leslie]

Great work and fascinating stuff. Ignore silly anonymous person above.

[Ian Kemmish]

Martin Gardner's friend Dr Matrix did it for me in the 1960's. Truly there is nothing new under the sun.