  We argue that higher spin fields originate from Hamiltonian mechanics and
play a role of gauge fields ensuring covariance of geometric observables such
as length and volume with respect to canonical transformations in the same way
as a metric tensor in Riemannian geometry ensures covariance with respect to
diffeomorphisms. We consider a reparametrization invariant action of a point
particle in Hamiltonian form. Reparametrization invariance is achieved in the
standard way by coupling to the auxiliary world-line metric. Identifying
Hamiltonian function with a generating function for higher spin fields this
action can be viewed as an action for the point particle in a higher spin
background, while canonical transformations act as higher spin symmetries. We
define the gauge invariant length as a proper time of a particle moving along
the geodesic. Following the usual geometrical interpretation we introduce the
volume form and the scalar curvature for a combined lower spin sector. As for
the general case, we show that notions of local volume and scalar curvature are
not compatible with symplectic transformations. We propose symplectically
invariant counterparts for the total volume of the space and Einstein-Hilbert
action.
