  The equations defining pure spinors are interpreted as equations of motion
formulated on the lightcone of a ten-dimensional, lorentzian, momentum space.
Most of the equations for fermion multiplets, usually adopted by particle
physics, are then naturally obtained and their properties like internal
symmetries, charges, families appear to be due to the correlation of the
associated Clifford algebras, with the 3 complex division algebras: complex
numbers at the origin of U(1) and charges; quaternions at the origin of SU(2);
families and octonions at the origin of SU(3). Pure spinors instead could be
relevant not only because the underlying momentum space results compact, but
also because it may throw light on some aspects of particle physics, like:
masses, charges, constaint relations, supersymmetry and epistemology.
