Brief Answers to the Big Questions

by Stephen Hawking

Why don’t we live in a history in which eight of the dimensions are curled up small, leaving only two dimensions that we notice? A two-dimensional animal would have a hard job digesting food. If it had a gut that went right through, like we have, it would divide the animal in two, and the poor creature would fall apart. So two flat directions are not enough for anything as complicated as intelligent life. There is something special about three space dimensions. In three dimensions, planets can have stable orbits around stars. This is a consequence of gravitation obeying the inverse square law, as discovered by Robert Hooke in 1665 and elaborated on by Isaac Newton. Think about the gravitational attraction of two bodies at a particular distance. If that distance is doubled, then the force between them is divided by four. If the distance is tripled then the force is divided by nine, if quadrupled, then the force is divided by sixteen and so on. This leads to stable planetary orbits. Now let’s think about four space dimensions. There gravitation would obey an inverse cube law. If the distance between two bodies is doubled, then the gravitational force would be divided by eight, tripled by twenty-seven and if quadrupled, by sixty-four. This change to an inverse cube law prevents planets from having stable orbits around their suns. They would either fall into their sun or escape to the outer darkness and cold. Similarly, the orbits of electrons in atoms would not be stable, so ...