Relativity says we live in four dimensions. String theory says it’s 10. What are ‘dimensions’ and how do they affect reality?
'Writing away at my desk, I reach my hand up to turn on a lamp, and down to open a drawer to take out a pen. Extending my arm forward, I brush my fingers against a small, strange figurine given to me by my sister as a good-luck charm, while reaching behind I can pat the black cat snuggling into my back. Right leads to the research notes for my article, left to my pile of ‘must-do’ items (bills and correspondence). Up, down, forward, back, right, left: I pilot myself in a personal cosmos of three-dimensional space, the axes of this world invisibly pressed upon me by the rectilinear structure of my office, defined, like most Western architecture, by three conjoining right angles.
Our architecture, our education and our dictionaries tell us that space is three-dimensional. The OED defines it as ‘a continuous area or expanse which is free, available or unoccupied … The dimensions of height, depth and width, within which all things exist and move.’ In the 18th century, Immanuel Kant argued that three-dimensional Euclidean space is an a priori necessity and, saturated as we are now in computer-generated imagery and video games, we are constantly subjected to representations of a seemingly axiomatic Cartesian grid. From the perspective of the 21st century, this seems almost self-evident.
Yet the notion that we inhabit a space with any mathematical structure is a radical innovation of Western culture, necessitating an overthrow of long-held beliefs about the nature of reality. Although the birth of modern science is often discussed as a transition to a mechanistic account of nature, arguably more important – and certainly more enduring – is the transformation it entrained in our conception of space as a geometrical construct.
Over the past century, the quest to describe the geometry of space has become a major project in theoretical physics, with experts from Albert Einstein onwards attempting to explain all the fundamental forces of nature as byproducts of the shape of space itself. 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. But what are these ‘dimensions’? And what does it mean to talk about a 10-dimensional space of being?
In order to come to the modern mathematical mode of thinking about space, one first has to conceive of it as some kind of arena that matter might occupy. At the very least, ‘space’ has to be thought of as something extended. Obvious though this might seem to us, such an idea was anathema to Aristotle, whose concepts about the physical world dominated Western thinking in late antiquity and the Middle Ages.'
Read more: Radical dimensions