Surrealism and the Mathematician :: Wessex Scene Online

Surrealism and the Mathematician

15th August 2005
Chris Lane

Rate this story

Feb 05 - Even the gherkins were electrified
Aug 05 - A load of Rubbish
Aug 05 - Adventures in '80s TV
Sep 05 - Songs, skits and squaredances
Oct 05 - United they could conqueur, divided they will fall

More by Chris Lane

Feb 05 - SOC scientists survey tsunami source
Feb 05 - Even the gherkins were electrified

Stop what you are doing and get a mirror.

It doesn’t matter where from – just polish up the nearest shiny surface or grab the nearest high-maintenance girl’s handbag and steal her compact. Hold it in front of your face, but before you look at your reflection... close your eyes. Think. What do you expect to see?

Open your eyes and there should be no surprises. This is because we have an innate knowledge about the physical laws that control our environment; we know how light behaves, including how it reflects.

But what if light didn’t obey normal physical laws?

What if parallel lines bent away from each other, and our normal 2D representation of the world wasn’t flat, but saddle-shaped? Welcome to the crazy world of Cormac Long: Southampton mathematician and keen climber.

Cormac investigates problems in hyperbolic, or ‘bendy’, space; a world view that is, well, bendy. He explains, "Draw a triangle on a sphere and measure it’s interior angles. The sum of these angles is greater than 180 degrees.

"On a plane (Euclidean space) the sum is exactly 180 degrees. In hyperbolic space, the sum is less than 180 degrees – the sides of the triangle ‘bend in’ towards the middle."

Cormac builds 3D images to describe events in hyperbolic space, including reflections. He computes 3D visualisations analogous to the 2D interlocking tiles, or tessellations, that 1950’s artist M.C. Escher used as the basis for his surreal mathematical artwork. Escher used art to represent mathematical concepts, often using unusual perspective and viewpoints.

His brain-teasing works include an endless staircase, that seems to simultaneously ascend and descend, a waterfall that flows uphill, and hands that draw themselves.

So how do people like Escher and Cormac keep their sanity in a world where straight lines are bent, and reality is the reflection of a dimension that is separate from normality?

Cormac explains, "In some ways it is like sculpture: Start with an amorphous blob of stuff, then hack at it until you get something strange but beautiful. Your only limit is your imagination."