In 1670 French mathematician Pierre de Fermat famously left the world a puzzle, although he had been dead for five years when he did so. His son had set out to collect and publish his papers for posterity, and amongst Fermat's library was a recent translation of Diophantus' Arithmetica, originally written during the second century AD. The book consisted of mathematical problems; whilst pondering them, Fermat doodled his thoughts in the margins, and one day he came upon the idea that no number, when raised to a power greater than two, produces the sum of two other numbers raised to that same power. He earned his mathematical stripes by analysing the nature of curves - what were they, where did they come from, how did they work? - but it was this doodle that earned his place in history.
A curve, at the Heygate Estate, LondonFor example, let's take the numbers three and four. They're ours now; no-one else can use them for the next few minutes. We will feed them, care for them, and let them go once we have used them. Three to the power of three is three times three times three equals 27, which is a horrible number. Four to the power of three is 64, which is much nicer. Add them together and you get 91. Now try and find a number that equals 91 when you raise it to the power of three.
Five? No, that's 125. Obviously not four, because we know that's 64. It can't be a number greater than five, or less than four, which leaves us with nothing. Yes, in theory you could create a new number in between four and five, such as for example schwemmberg, which is a number I have just created in my head which is equal to four point four nine seven nine four one four four and so on. But let's imagine that you can't use any of these in-between numbers. You can only use pure, ordinary, proper numbers, even including the bad ones like five and seven. In which case there is no number which, when raised to the power of three, produces the sum of three and four also raised to the power of three.
Ulorin Vex, who is possessed of curves But there are many numbers. What if we decided to raise 379 to the power of 15, and add it to 675 added to the power of 15? We'd have a huge number. Surely there must be another whole number somewhere that, when raised to the power of 15, produces the sum of 37915 + 67515? Or any other case of xn + yn = zn? I'll just have a think.
(years pass)
No, there isn't.
(longer pause)
Hang on, I've worked out why.
(even longer pause)
No. In fact I haven't. Now I'm an old man, and I've wasted my life. Damn.
Famously, Pierre de Fermat thought he had. Worked out why. But the margin of his copy of Arithmetica was too small to write it down. "Cujus rei demonstrationem mirabilem sane detexi", he wrote (in Latin). "Hanc marginis exiguitas non caperet". If you say that slowly in a low voice, it sounds awesome.
Fermat never revisited his proof, at least not that history records, and by the time his marginalia was shared with the world he had been dead for five years. You know, in Fermat's day people had loads of deep thoughts, but no space to write them down; and even if they did so, there was a good chance their words would be lost with time, their books burned, ripped up and turned into packing material, never read by other people because there was no way to broadcast that information. Nowadays it seems that we have infinite space but no deep thoughts, only shallow ones not worth preserving or sharing. Earlier today I went to the shop and bought some Lithium AA batteries, because they are lighter and last seven times longer than conventional NiMH rechargeable batteries. Later I will have pasta for tea. "I'm wearing a four-button double-breasted wool and silk suit, a cotton shirt with a button-down collar by Valentino Couture, a patterned silk tie by Armani and cap-toed leather slipons by Allen-Edmonds."
Ultimately a proof was found, in the 1990s, but it took supercomputers using mathematics that would have been beyond Fermat's puny French 17th-century mind. Mathematics that would have freaked him out. The proof couldn't have been Fermat's proof, which leaves two possibilities. Firstly, Fermat was wrong. This would explain why he never revisited the proof, but how can we be sure that he didn't? His original copy of Arithmetica is long-gone - it would be worth a fortune if someone found it nowadays, but seemingly his son threw it away - and we can never be certain that he didn't write out a proof on some paper that was subsequently lost. Alternatively, it could be that he was right all along, but he had a simpler proof that has defied centuries of thought.
"Nothing is forgotten. Nothing is ever forgotten."
Which leads us to the topic of today's post. Fast-forward to 1975. After leaving Simon & Garfunkel - he was Simon - US singer-songwriter Paul Simon embarked on a solo career which was very successful in the United States but generally a bust here in the UK, where he is remembered as the man who did "Call me Al" in the 1980s. In 1975 he had a big hit in the US with "Fifty Ways to Leave your Lover", a song notable for its drum pattern. Steve Gadd, drummer to the stars, had come up with a style he called Lazy Drumming, whereby he only had to move one limb at a time. This conserved energy, which was a big topic in the mid-1970s. Here's a pair of Converse All-Stars, photographed with an infrared camera, because I could:
You know, I've always wondered why drummers don't put sticks on their heads, or little bells. After all, the head is a limb. It can move, do things, hit things. And yet drummers only use their arms and legs. Also, cock drumming. That's six limbs. But I digress.
Famously, Simon only presented five different ways to leave your lover. One of them - "just get yourself free" - was too vague to be of practical use. There wasn't space in the song to fit all of the fifty ways; it would have been too long to play on the radio. And so his fifty ways remained hypothetical.
Until now.
After years of study I present The Most Efficient Fifty Ways to Leave Your Lover. Scientifically chosen to fit the metre of the song. Sorted upwards in order of efficiency. These aren't necessarily the fifty ways that Paul Simon intended - we will never know what was going through his mind, in 1975 - but they are fifty ways, and there are fifty of them, and they are ways. Scientifically-proven ways. Proven, by science.
-The Most Efficient Fifty Ways to Leave your Lover
Go, Jo
Fly, Eli
Blow, Moe
Dash, Ash
Deny, Kai
Ebb, Webb
Fade, Ade
Cut, Mutt
Run, Alun
Adieu, Boo
Bolt, Walt
Buzz, Buzz
Dust, Just
Hike, Mike
Quit, Brit
Scram, Sam
Skim, Akim
Skip, Chip
Split, Kit
Cease, Rhys
Chill, Phil
Depart, Art
Shirk, Dirk
Shoot, Knut
Unass, Cass
Whizz, Aziz
Break, Blake
Desert, Bert
Drive, Clive
Flee, Leslie
Go 'way, Jay
Jet, Ornette
Leave, Steve
Move on, Ron
Recede, Said
Rotate, Nate
Secede, Bede
Swerve, Merv
Unload, Joad
Forsake, Jake
Retreat, Pete
Conclude, Jude
Creep, Pradeep
Retire, Squire
Unhitch, Mitch
Vamoose, Moose
Withdraw, Thor
Detour, Seymour
Disappear, Amir
Melt, Roosevelt
For the curious, the next seven ways are:
Abscond, Armond
Scarper, Harper
________, _____*
Decamp, Beauchamp
F--- off, Kristoff
Take flight, Dwight
Tergiversate, Drake
* Newspeak; Clive is an unperson.
I'd just like to thank the English language, which has an abundance of words that mean almost but not quite the same thing. In technical terms, English has multiple redundancy, like a fighter jet. Which is useful in case some of the words are forgotten, or fall out of fashion. Perambulate, for example, was all the rage in the 19th century, whereas nowadays it's just a baroque flourish, no longer an organic part of the language. If it was the only word that meant what it meant, we would nowadays have no way to express the concept of perambulating, except by waving our hands and/or hips, as in for example this documentary about people who seem to have forgotten a tonne of words. They forgot words and learned something else instead.
Fortunately we have lots of words that mean the same thing as perambulate, so we can give that one a rest and use the others instead. Like shoes. Wear one pair today, the other pair tomorrow, repeat. I wonder if at some point in the past a fundamental concept was lost to humankind - a concept akin to love, or hate, lust, desire - and ever since then we have been unable to express it, except by some ritualistic gesture-echo, because there are no words to describe it. That might explain the root of our unease. Lurking within us like a sub-oceanic bubble. Just waiting to break the waves and suffocate us all.
