  We give an interpretation of the maximal number of linearly independent
vector fields on spheres in terms of the Spin(9) representation on R^16. This
casts an insight on the role of Spin(9) as a subgroup of SO(16) on the
existence of vector fields on spheres, parallel to the one played by complex,
quaternionic and octonionic structures on R^2, R^4 and R^8, respectively.
