Being colour-blind in a world of infinite colours

The notion of classical physics is usually thought of as that of long-distance, low-energy physics that is described by a set of PDEs rather than a path integral. Furthermore, the complexity of a given problem is usually expected to increase with the number of degrees of freedom. It was therefore very surprising when 't Hooft realised in 1973 that quantum chromodynamics theory not only simplifies in the limit of an infinite number of colours, but in fact becomes classical. The colour-neutral bound states, which are accessible to a low-energy observer, interact with one another weakly and classically. The fundamental constituents still interact strongly, and give the bound states non-trivial internal structure and mass spectrum. This limit is therefore a highly non-trivial approximation scheme which assumes no weak coupling. In this talk, I will briefly review the theory behind this limit, and argue why semiclassical physics arises for a colour-blind observer in a world of infinite colours.