Boson-Fermion duality in four dimensions: Neutrinos from photons and vice versa

We present a construction of bosons from fermions in any space dimension. In three dimensions, photons can be constructed from neutrinos, and posses the correct P, C, T and rotational properties. A new massless particle is required, identical to the photon except that it is even under charge conjugations. In a special sense, a photon is $\text{7}\text{8}$ of a neutrino. The inverse construction, neutrinos from these massless bosons, suggests that none of these is truly fundamental.