  The polarization measure is the probability that among 3 individuals chosen
at random from a finite population exactly 2 come from the same class. This
index is maximum at the midpoints of the edges of the probability simplex. We
compute the gradient flow of this index that is the differential equation whose
solutions are the curves of steepest ascent. Tools from Information Geometry
are extensively used. In a time series, a comparison of the estimated velocity
of variation with the direction of the gradient field should be a better index
than the simple variation of the index.
