Spin and non-commutative geometry

The divide between quantum theory and general relativity, more generally classical physics, has persisted. It is argued here that this is because the latter has, in the words of Witten, a Bosonic space-time underpinning, while the former has a Fermionic or non-commutative space-time underpinning: the purely quantum mechanical spin-half implies non-commutative space-time and vice versa.