At 48 I’ve probably left it too late to win Wimbledon or join Fabio Capello in South Africa next year to help England lift the World Cup. But I still harbour secret hopes of conjuring up the definitive explanation of physical reality in a grand theory of everything, and from there it would be a mere quantum jump to the Lucasian Professorship of Mathematics at the University of Cambridge, the chair once held by Sir Isaac Newton.
(OK, I admit I was disappointed with my C grade Higher Maths A-level in 1979, but it would have been a different story if I’d remembered that the curve of a washing line is called a catenary – and on a good day I might have known that!)
Last week I learnt of a new setback for my cosmological ambitions.
I’d been pipped to the Lucasian post by one of the world’s most brilliant theoretical physicists, a founding father of string theory called Michael Green. He succeeds some of the greatest names in the history of science – not just Newton, but Charles Babbage, Paul Dirac and Professor Stephen Hawking, who’s had the job for the last 30 years.
I was devastated to be overlooked, but I’ve already adjusted. My new plan is to use the internet to make sure I’m ready when the position comes around next time.
The late American astronomer Carl Sagan is still a good place to start. I can just about follow his explanation on YouTube, from a television show way back when, of how to think in four dimensions.
But 10 or 11 dimensions is the norm for today’s proponents of M-theory, which is scientists’ best shot so far at fusing the two main theoretical foundations of contemporary physics: Albert Einstein’s general theory of relativity and the quantum mechanics of Max Planck.
I don’t mind admitting I’ve lost sleep trying to visualise more than three dimensions. Here’s my best (Euclidean) stab at it so far:
Imagine a cube. Then imagine it packed with an infinite number of infinitely small light bulbs, so that every point in the cube can have its brightness turned up and down independently. That’s your fourth dimension – x, y, z and “b” for brightness. Superimpose further sets of infinitely small lightbulbs to represent other variable qualities – such as “spiciness”, “slinkiness”, “sassiness”, whatever takes your fancy – and you can twiddle imaginary knobs to mix in as many dimensions as you like.
If only Carl Sagan could do the video for me: How to escape from inside a cube whose “solid” walls exist only at one particular level of brightness (or even “sassiness”).
But apparently our universe is stranger even than this. According to string theory, we’re unaware of dimensions other than space and time because they are “curled up very tightly”.
So that’s farewell to Euclidean geometry then. I remember from my schooldays that if you draw a triangle on the surface of a sphere the angles in its corners will add up to more than 180 degrees – and that if you travel in any direction on that surface you’ll follow a curl back to your starting point. I must have been listening after all.
But how to visualise the multiple curled-up dimensions of M-theory?
Perhaps a cube packed with an infinite number of infinitely small combination locks. Each lock has a number of separate dials spinning from zero round to nine and then on to zero again, and each dial represents a curled-up dimension.
Cambridge’s new Lucasian professor has his own imagery. In a 1986 article for Scientific American, Michael Green wrote:
The idea of unobservably small dimensions can readily be understood by considering a simple, two-dimensional analogy. A hose is a two-dimensional surface that appears to be one-dimensional when it is observed at scales too coarse to resolve its thickness. In superstring theory it is likely that the size of the six curled-up dimensions is approximately the same as the length of the string. The world appears to have three spatial dimensions in the same sense that the string acts like a point particle.
Well I understand the first part. It seems I have a lot more studying to do. Warm congratulations on your appointment, Mr Green.