EDWIN ABBOTT, in his 1884 book Flatland, created a fictional 2D landscape full of lines, triangles, squares and circles that have no notion of up or down. One day, a 3D Sphere visits Flatland and whisks away a Square to a higher dimensional world. Square learns that Flatlanders are mere 2D projections of 3D beings. He then has the audacity to suggest that Sphere may be a shadow too – of a shape in four dimensions. “The very idea of it is utterly inconceivable,” says the appalled Sphere.
Henry Markram thinks we might be suffering from a similarly blinkered perspective when considering the workings of our own brains. “We look at the brain, we see its immense complexity, but if it’s a shadow projection from a higher dimension, we’ll never understand it,” Markram says. Those aren’t idle words: he and his colleagues of the Blue Brain Project at the Swiss Federal Institute of Technology in Lausanne (EPFL) have been using algebraic topology, a field of mathematics used to characterise higher-dimensional shapes, to explore the workings of the brain.
What they have found beggars belief. As our brains think, learn and remember, they create elaborate but ephemeral structures in at least seven mathematical dimensions, and possibly many more. What’s more, these transient structures, which appear and disappear like sandcastles on a beach, could help us understand how the brain creates our thoughts and feelings. They might even unravel the greatest mystery of them all: consciousness. “Algebraic topology is the mathematics to take neuroscience out of Flatland,” says Markram.
The Blue Brain Project was launched in 2005, with the aim of simulating the entire human brain inside a computer. That’s an ambitious goal and far from fruition. In late 2015, however, the team announced it had recreated a sliver of the rat brain that is involved in sensing touch. The real brain tissue is only 0.5 millimetres wide and 2 millimetres long, but its digital analogue consists of 31,000 neurons of more than 200 different types, with some 8 million connections between them (see “How to build a brain”).
