  Comparison is made between the distribution of saddle points in the chaotic
analytic function and in the characteristic polynomials of the Ginibre
ensemble. Realising the logarithmic derivative of these infinite polynomials as
the electric field of a distribution of coulombic charges at the zeros, a
simple mean-field electrostatic argument shows that the density of saddles
minus zeros falls off as $\pi^{-1}|z|^{-4}$ from the origin. This behaviour is
expected to be general for finite or infinite polynomials with zeros uniformly
randomly distributed in the complex plane, and which repel quadratically.
