Weird Maths: At the Edge of Infinity and Beyond

by David Darling

A genuine four-dimensional observer looking at something in our world would be able to see everything inside a thing simultaneously, in addition to its three-dimensional surface. So, for example, if you had some valuable items locked up in a safe, a 4D being would see not only all sides of the safe at a single glance but everything inside it as well (and would be able to reach in and take those things if it so chose!). This isn’t because the being would have something like X-ray vision that allowed it to see through the walls of the safe, but simply because it had access to an extra dimension. We would similarly have a privileged view of an enclosed space in a 2D world. Draw a square on a piece of paper, to represent a two-dimensional safe, with some items of jewellery inside it. A Flatlander, embedded in the 2D surface, could see only a view of the outside of his safe – a mere line. We, looking from above the sheet of paper that was his world, would be able to see the lines that formed the walls of the safe and all its contents at a single glance and could reach in and lift out the 2D pieces of jewellery.