The Meaning of Dimensions

We review the current status of dimensions, as the result of a long and controversial history that includes input from philosophy and physics. Our conclusion is that they are subjective but essential concepts which provide a kind of book-keeping device, their number increasing as required by advances in physics. The world almost certainly has more than the four dimensions of space and time, but the introduction of the fifth and higher dimensions requires a careful approach wherein known results are embedded and new ones are couched in the most productive manner.