by Matthew Cobb
According to Douglas Adams, Earth was created as a kind of super-computer to find the question to which the answer was 42, the secret of life, the universe and everything. The Earth was, of course, destroyed by the Vogons just before the programme was due to come up with an answer (or rather, a question).
As a result, ’42’ has taken on a humorous symbolic value – try asking Siri what the secret of life is. But now there’s a new kid on the block, a new number that will probably lead to all sorts of nerdy jokes. And it is a very weird number indeed: – 1/12.
This number is what comes out of attempts to calculate an *infinite* series: 1 + 2 + 3 + 4 + 5 … In other words, instead of the sum of infinite numbers being… infinity, it is in fact a negative fraction.
This is explained in this video from the excellent Numberphile team at Nottingham University. It’s already had > 1.5 million hits on YouTube, and has been covered in the New York Times.
This isn’t a joke, and although there’s some mathematical jiggery-pokery going on to help us poor mortals understand it, more formal and elaborate proofs are around, and have been known literally for centuries – this is the Reimann-Zeta function, first worked out by Euler in the early 18th century, and then developed by Reimann in 1859. It is used a lot in string theory, a highly speculative part of physics.
Before you all start chipping in below pointing out basic mistakes in the maths (I don’t think there are any), read this response by Tony Padilla (I got lost when the Greek letters began) or, for the truly mathematically endowed, watch this extra and more elaborate proof which takes you through Euler’s calculation and read this mind-bogglingly difficult piece.
The key point to remember before you get angry or think you’ve been tricked (you haven’t) is that while if you add up any set number of natural numbers (say 2, 5, 178 or a googleplex of numbers), you get a large positive number, whereas if you were to try and do this with an *infinite* number of natural numbers, you get – 1/12.
Roll over 42—your time is past.