Abstract: The individual polarization components of nonlinear Thomson scattering arise from the separate dimensions of electron figure-8 motion caused by a linearly polarized laser field. We present the first measurements of nonlinear Thomson scattering in both emission hemispheres. In the electron average rest frame, the shape of the electron figure-8 path is symmetric about the laser polarization dimension. However, the periodic electron velocity is intrinsically asymmetric. The full scattering emission pattern reveals this asymmetry and the direction that electrons move around the figure-8 path.