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. “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. Henry Markram thinks we might be suffering from a similarly blinkered perspective when considering the workings of our own brains. “The very idea of it is utterly inconceivable,” says the appalled Sphere. He then has the audacity to suggest that Sphere may be a shadow too – of a shape in four dimensions. Square learns that Flatlanders are mere 2D projections of 3D beings. One day, a 3D Sphere visits Flatland and whisks away a Square to a higher dimensional world. 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.
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