On the 16th April 1964 the Beatles, George Harrison, Paul McCartney, John Lennon and Ringo Starr, were on the cusp between stardom and mega-stardom. Groundbreaking albums, hit films, cartoons, royal honours, Sgt. Pepper, Indian mysticism, and an acrimonious break up all lay in their future as did the murder of Lennon and attempted murder of Harrison by separate mentally disturbed fans. That was all to come. Their task that night was to record an impressive opening track for their forthcoming debut film and the album to accompany it. Their producer, George Martin, wanted something spectacular: ‘We were looking for something big to open it with, an introduction. It needed a strong chord, a dramatic thing’ (p487 of Dominic Pedler, The Songwriting Secrets of the Beatles, Omnibus Press, 2003). Those present in the Abbey Road studio to record Lennon’s song A Hard Day’s Night could not have imagined that 50 years later the events would still be analyzed and dissected. Particularly since the focus of the analysis is almost not a piece of music, it’s a short sound, less than 3 seconds long, a crashing, ringing, chiming sound that has caused arguments and discussions between Beatles’ fans and musicologists ever since it was recorded. The noise is impossible to describe accurately in words – the famous quote ‘writing about music is like dancing about architecture’ comes to mind. The sound can be heard here: http://www.kevinhouston.net/blog/wp-content/uploads/2014/12/original-chord3.wav The central question is simple: What is it? That is, what notes are played and who is playing them? Many versions have been suggested. In his massive Beatles book, The Songwriting Secrets of the Beatles, Dominic Pedler collects twenty one educated guesses from various sources and devotes over 40 pages to discussion, including his own theory. It is not difficult to produce a chord that is close – strumming a guitar without fretting produces a similar sound. It’s close. But close is not exact, right? So, what is it really? In 2004 a mathematician claimed to have discovered this musical holy grail by applying mathematics. Once and for all, the riddle was solved because, after all, mathematics is not wrong and you can’t beat the scientists with their fancy abstract toys. Except there was a problem. He got it horribly wrong. Here, for the honour of all mathematicians, I would like to put the record straight — or at least straighter. The mathematical tale of the Beatles’ Magical Mystery Chord is a tale of 18th century mathematicians, the study of heat, Karaoke tricks and a measure of luck. The quest begins I am a mathematics lecturer who enjoys promoting mathematics to school children and the general public. My introduction to the mystery of the chord came not from a love of the Beatles music but a desire to show off in front of my parents. My mathematics promotion involves giving talks all over the country but as I live in the north of England and my parents live in a secluded part of the north east of Scotland, they would under normal circumstances be unable to see their second son on a stage explaining mathematics. Back in 2011 I heard that the British Science Festival would be held the following year in Aberdeen which is close to where my parents live. The festival is held in a different city in the UK each year and aims to engage the general public in science. Hundreds of events take place over a week in September with debates, demonstrations and hands-on exhibitions at the local university as well as theatres and even, like maths busking, in the street. (Maths busking is as it sounds. Mathematicians go out in the street and do mathematics to entertain passers-by. I’ve tried it and it is hard. See my report here.) All I had to do was offer to give a talk, get accepted and I would get my chance to impress...

## Another Hard Day’s Night...

posted by Kevin Houston

I haven’t posted in a while for many reasons. One of which is that I’ve been trying to finish a textbook. My target date is July 31 to have the final draft finished. I’m not sure I’m going to make it… Anyhow, I noticed that the Beatles’ first film A Hard Day’s Night is being rereleased. ‘But what’s the opening chord to the title song?’ I hear you say. Funny you should ask, that gives me a chance to show again my modest attempt at solving the...

## Persi Diaconis Lecture on Martin Gardner at BMC...

posted by Kevin Houston

The name Martin Gardner is familiar to most mathematicians. He wrote numerous on mathematics from a culture and leisure viewpoint. (You can find his books on Amazon.) Next week Persi Diaconis will give a talk at the British Mathematical Colloquium (BMC) on the life and work of Martin Gardner. The BMC is an annual gathering of research mathematicians in the UK and beyond. Diaconis’ talk is a public lecture so anyone may attend but a (free) ticket is required. Details of the talk are here. I’ll be attending so do say hello if you see me. For all of those unable to attend but want to know a bit more about Gardner then Diaconis has co-written a biography of Gardner (as well as a great mathematical magic book). There is also a recent article in the New York...

## Mathematics of Love

posted by Kevin Houston

Today is St. Valentine’s Day, the day in much of Western culture arbitrarily designated to be the day for love. So let’s see what mathematics has to say on the subject. Finding a relationship with someone special is often about being introduced to people and sifting out the inappropriate. It seems clear that there is plenty of scope for the application of statistical techniques to the processes of meeting and weeding. First up is a great video from the ever-so-slightly geeky Amy Webb, who used mathematics to calculate the odds of finding a mate in Philadelphia. After producing a figure of 35 suitable men satisfying her criteria in a city of 1.5 million people she realized that she would have to turn to maths for help. There’s even a book, Data, a Love Story. Over on Wired, Chris McKinlay’s attempts to hack OKCupid’s online dating service is profiled. The article left me in two minds. Is this is great use of mathematics or is it just a bit creepy? Seemingly, the approach worked for him and no one is reported injured, so perhaps I shouldn’t judge. As a bonus, Wired also produced a handy infographic slideshow describing tips for improving online dating profiles. Top tips: Avoid Karaoke, get into surfing. My favourite though is that it is more attractive to mention “cats” than “my cats”. If everything goes well with the dating, then how do you arrange the wedding? “With maths” is not the standard answer. The Guardian reports on a statistically modelled wedding. This solves the centuries old problem of how to write the guest list. After all, you don’t want too few guests or too many accepting. Next post: Calculating the likelihood of...

## Rafael Araujo – A New Escher?...

posted by Kevin Houston

One needs only look at some of Fomenko’s monstrosities to see that mathematics and art don’t always mix well. Exceptions are rare with Escher the benchmark for excellence. A recent Wired article on the Venezuelan artist, Rafael Araujo, describes how he produces his mathematically constructed pictures. I can see these joining Escher’s pictures on the walls of mathematicians throughout the world over the next few years. The full article is here but you can also see stunning examples on his...

## Hilbert Hotel Video

posted by Kevin Houston

Belated Happy New Year! Here’s another of those short educational TED videos. This time on the Hilbert Hotel. (A cartoon Hilbert does seem to make an appearance but it is hard to tell as he isn’t wearing the hat. Do you think Hilbert wore that hat just once and had the misfortune of having it appear in his most famous picture?) Anyhow: You can find out more at the TED Education page for the video. Oh, and this week is the last chance to win a signed copy of Simon Singh’s book on The Simpsons! See...