While on the local level we are trained to think of space as having three dimensions, general relativity paints a picture of a four-dimensional universe, and string theory says it has 10 dimensions – or 11 if you take an extended version known as M-Theory.
There are variations of the theory in 26 dimensions, and recently pure mathematicians have been electrified by a version describing spaces of 24 dimensions.
All this raises a liberating possibility, for if mathematics allows for more than three dimensions, and we think mathematics is useful for describing the world, how do we know that physical space is limited to three? Although Galileo, Newton and Kant had taken length, breadth and height to be axiomatic, might there not be more dimensions to our world?
While Square is arguing for other dimensions of space, he is also making a case for other dimensions of being – he’s a mathematical queer. In his ‘special theory of relativity’, time was added to the three classical dimensions of space.
In mathematics, 24-dimensional space is rather special – magical things happen there, such as the ability to pack spheres together in a particularly elegant way – though it’s unlikely that the real world has 24 dimensions.
A leading proponent of new ways of thinking about space is the cosmologist Sean Carroll at Caltech, who recently said that classical space isn’t ‘a fundamental part of reality’s architecture’, and argued that we are wrong to assign such special status to its four or 10 or 11 dimensions.