The quantitative data obtained in any physical experiment are recorded as finite, ordered sets of rational numbers. All such sets are discrete. However, when a physicist sits down to make sense of such data, the tools he or she employs are generally based upon the continuum: analytic (or at least smooth) functions, differential equations, Lie groups, and the like. It is the view of many eminent mathematicians that ‘bridging the gap between the domains of discreteness and of continuity … is a central, presumably even the central problem of the foundations of mathematics’, yet Fritz London did not seem to have had the slightest hesitation in writing, in the very first paragraph of his book on superfluidity, ‘that new differential equations were required to describe [the observed behaviour of]… “superfluid” helium…’ The physicist had stepped over the gap which has occupied philosophers for two millenia without even noticing that it existed!

This gap is but a fragment of one that separates theoretical from experimental physics. Some of the most important physicists of the first half of the twentieth century have expressed themselves on the subject, and it is instructive to compare their views. Dirac, for example, had the following to say: