Sophisticated maths in everyday life.
On Monday 20 November 2017, Simon Singh MBE came to The Perse to deliver a lecture as part of our Community Lecture Series.
The beginning of Simon Singh’s lecture encapsulated the theme that runs through his work on an eclectic mix of scientific and mathematical subjects, using the gobbledegook created when you play Led Zeppelin’s Stairway to Heaven backwards. The first time we heard this clip, no-one in the audience could glean any meaning at all from the garbled backwards singing. Then, Simon told us that, in fact, this famous song backwards contains a coherent paragraph, beginning ‘so here’s to my little sweet Satan’ and going on to describe ‘a little toolshed, where he made us suffer, sad Satan’. When Simon played the clip again, almost everyone in the audience heard these exact words, where before there had been nonsensical sounds. Then he owned up – there is no such secret message about Satan if you play Stairway to Heaven backwards, just meaningless noise. So what was going on? Our brains are evolved to find patterns, so when we were primed to expect coherent prose that bears a slight resemblance to the sounds that are actually there, this is what we believed we had heard. Throughout Simon’s career, as a research scientist, a journalist and a writer of popular science and maths books, his quest has been to encourage people to question their beliefs, so that they are not easily tricked or open to suggestion.
However, using mathematics and science to find the truth is about far more than simply avoiding misinformation. This was illustrated by the first video clip Simon shared with us, from a Horizon documentary he had worked on about Fermat’s last theorem. As part of this programme, Professor Sir Andrew Wiles, who proved Fermat’s Last Theorem after it had baffled mathematicians for three centuries, described mathematical research as like entering a dark mansion, in which you cannot see where you are going and keep bumping into the furniture, but eventually, after six months or so, it is like a light has been switched on and everything is illuminated. Simon used this image, and the emotion Wiles clearly felt when recalling his astonishing breakthrough, which he already knew would be the greatest moment of mathematical discovery he would ever experience, to convey the beauty that mathematicians see in their subject, and the passion it can generate.
Simon then showed us another clip from the documentary, of which he admitted to being less proud. The video explains why there is still a need for mathematical proofs in a world where computers can run through lists of millions of numbers. Professor John Conway explains that if there are infinite numbers to be tried, when you have tested one number there are infinitely many left, but when you have tested millions of numbers there are still infinitely many left, so you actually haven’t tested very many numbers. The implication of this is that there is a need for general proofs that are not restricted to trying out specific numbers. However, when the documentary was filmed, Conway did not describe testing numbers, but testing primes – because when you test Fermat’s last theorem by trying numbers, you get all the non-prime numbers ‘for free’ if you just test the primes. Simon was unsure how many of the programme’s audience would remember what a prime number is, or know that because all non-prime numbers can be expressed as the product of prime numbers, testing all the primes is essentially the same in this context as testing all the numbers. Therefore, he took the decision to change the word ‘prime’ to the word ‘number’ in Conway’s explanation, to avoid making the subject matter inaccessible to viewers. Simon defended his decision, as he did not distort the truth of the sentence, and the change was made with the benefit of the audience in mind. Nevertheless, it was a thought-provoking example of the difficult editorial decisions journalists face when explaining scientific and mathematical concepts, and the fine line they have to walk between educating and alienating their audience.
Later in his lecture, Simon gave an example of a programme he believed had twisted the truth, which prompted him to complain to the BBC, as well as embark on a mission to test the effectiveness of alternative medicine. This was the BBC 2 documentary Alternative Medicine: The Evidence, which showed its viewers astonishing footage of a patient undergoing open heart surgery in Shanghai without general anaesthetic, with her eyes open as surgeons operate on her heart. The only method of pain relief that appears to be being used is the 2,000-year-old method of acupuncture. Simon was astonished by this, and started to investigate how it could be possible. His enquiries led him to the Royal College of Anaesthetists, who had been given access to the raw footage of the surgery in the documentary. They confirmed that no general anaesthetic had been given to the patient, and acupuncture had been used, but that the patient had also been given three of the world’s most powerful sedatives, so it did not actually matter that she was not under general anaesthetic. The documentary did admit that the patient had been given ‘some numbing to the chest’, but the fact that she was under the influence of sedatives was not mentioned. Simon made a complaint to the BBC, which was rejected, but when he took his complaint to the board of trustees it was upheld. He believes this kind of footage, in which the truth is obscured or distorted, is deeply misleading, and this experience prompted him to write Trick or Treatment: Alternative Medicine on Trial.
Simon also took us on a whistle-stop tour of the many instances of mathematics in The Simpsons. This long-running and popular cartoon about a dysfunctional American family probably contains more maths than any other prime time show, thanks to many of its writers having an impressive academic pedigree in maths, science and engineering. Maths crops up in countless Simpsons episodes, from small details, such as Springfield’s cinema being called the Googolplex (a googol is 10100, while a googolplex is 10googol), to whole equations such as Euler’s identity, often believed to be the most beautiful equation in mathematics, which appears in a pile of Lisa’s books. Even Homer, not usually known for his intellectual prowess, sometimes gets his maths very nearly right. Simon recalled the episode that first drew his attention to maths in The Simpsons, The Wizard of Evergreen Terrace, in which Homer decides to become an inventor. The episode includes a blackboard covered in equations, the first of which predicts the mass of the Higgs boson. Simon, whose PhD involved working on the Higgs boson at CERN, commented that if you plug the various fundamental parameters into the equation it is not a bad guess, particularly as the episode was aired 14 years before the Higgs boson was experimentally confirmed to exist in 2012. Futurama, the sister series of The Simpsons, also showcases the writers’ love of mathematics, sometimes even requiring its viewers to be astonishingly quick with numbers to get the joke. In the episode The Honking, the characters are confronted with a perplexing message in binary code written in blood on a wall, 0101100101, or 357 in decimal. What can this mean? 357 does not seem to have any particular significance. However, Bender, the robot character, turns around and sees the number reflected in a mirror, which turns it into 1010011010, or 666, the sign of the devil. He screams and runs away, but never explains why he does this. To get the joke, you need to be able to convert the binary number to decimal in a split second, a mean feat for even the most nimble-minded mathematician.
Simon ended his lecture with another song, this time with easily discernible lyrics, but which could nevertheless be misleading. Katie Melua’s 2005 hit Nine Million Bicycles contains the following lyrics: “We are 12 billion light years from the edge, that’s a guess, no one can ever say it’s true, but I know that I will always be with you”. In an article in The Guardian soon after the song was released, Simon took issue with the accuracy of Katie’s astronomy-inspired lyrics; scientists now believe the universe to be around 14 billion light years old, and this is far from ‘a guess’, but based on careful research. He ended his light-hearted article proposing alternative lyrics: “We are 13.7 billion light-years from the edge of the observable universe, that’s a good estimate with well-defined error bars,
Scientists say it’s true, but acknowledge that it may be refined, and with the available information, I predict that I will always be with you”. Soon after the article was published Simon’s phone rang – it was Katie Melua. Luckily, she had taken the article in good humour, and had actually been a keen member of her school’s astronomy club as a child. She offered to meet Simon at the BBC and re-record the verse with his lyrics. The result, which Simon played to us, showed that the truth is not always catchy or easy to convey, as Katie stretches the song to accommodate Simon’s many additional syllables. Nevertheless, it encapsulated the essence of Simon’s talk: the truth is worth pursuing for its own sake, however difficult or unpalatable, but that this quest for accuracy need not be undertaken with straight-faced seriousness. The truth can be beautiful, awe-inspiring, and even funny.
The Perse holds termly Community Lectures, open to all in the community, whether or not they have a link to the School. Information about upcoming lectures can be found here.