  I propose a discrete model for the Gell-Mann matrices, which allows them to
participate in discrete symmetries of three generations of four types of
elementary fermions, in addition to their usual role in describing a continuous
group $SU(3)$ of colour symmetries. This model sheds new light on the
mathematical (rather than physical) necessity for `mixing' between the various
gauge groups $SU(3)$, $SU(2)$ and $U(1)$ of the Standard Model. In particular
it shows how the anti-Hermitian version of Pauli matrices can act non-trivially
on a unitary version of the Gell-Mann matrices, which leads to a non-trivial
mixing between the weak and strong nuclear forces.
  The unitary version of the Gell-Mann matrices can in turn act non-trivially
on a quaternionic version of Dirac matrices, which leads to a non-trivial
mixing between the strong force and the shape of spacetime defined by the Dirac
matrices. Hence this model implies a mixing between the electro-weak-strong
forces on the one hand and gravity, as described by General Relativity, on the
other. This mixing in turn implies the necessity for both general relativistic
corrections to the Standard Model of Particle Physics, and quantum corrections
to General Relativity. Contrary to general expectation, both types of
corrections seem to be large enough to be tested experimentally.
