  A non-commutative formula for the isotropic magneto-electric response of
disordered insulators under magnetic fields is derived using the methods of
non-commutative geometry. Our result follows from an explicit evaluation of the
Ito derivative with respect to the magnetic field of the non-commutative
formula for the electric polarization reported in Ref. 1. The quantization,
topological invariance and connection to a second Chern number of the
magneto-electric response are discussed in the context of 3-dimensional,
disordered, time-reversal or inversion symmetric topological insulators.
