  On logarithmic paper some real algebraic curves look like smoothed broken
lines. Moreover, the broken lines can be obtained as limits of those curves.
The corresponding deformation can be viewed as a quantization, in which the
broken line is a classical object and the curves are quantum. This generalizes
to a new connection between algebraic geometry and the geometry of polyhedra,
which is more straight-forward than the other known connections and gives a new
insight into constructions used in the topology of real algebraic varieties.
