The Sirens of Eleven Dimensions

While most theorists are tied to the mast of four dimensions, some have found it irresistible to speculate about eleven dimensions, the domain of M-theory. We outline a program which starts from the light-cone description of supergravity, and tracks its divergences to suggest the existence of an infinite component theory which in the light-cone relies on the coset $F_4\mathrm{/}SO(9)$, long known to be linked to the Exceptional Jordan Algebra.