For 10 points, name this number, the number of fundamental forces.
In a toy Yang-Mills theory of this dimension, the computation of scattering amplitudes is simplified by the positive Grassmanian, also known as the amplituhedron. The Higgs field has this many components, all but one of which are "eaten" by gauge bosons, manifesting as longitudinal polarization components. Relatedly, the electroweak interaction also features this many gauge bosons. Particle number is a natural variable for this many standard thermodynamic potentials. For a uniform rod, the moment of inertia about one end exceeds the moment about its center by this factor. This is the dimension of the vectors acted on by Lorentz transforms in special relativity, whose setting of Minkowski spacetime has this many dimensions. For 10 points, name this number, the number of fundamental forces.
In a toy Yang-Mills theory of this dimension, the computation of scattering amplitudes is simplified by the positive Grassmanian, also known as the amplituhedron.
four [or word forms; accept N = 4; accept four-vector]