  We give a physical explanation of the Kontsevich-Soibelman wall-crossing
formula for the BPS spectrum in Seiberg-Witten theories. In the process we give
an exact description of the BPS instanton corrections to the hyperkahler metric
of the moduli space of the theory on R^3 x S^1. The wall-crossing formula
reduces to the statement that this metric is continuous. Our construction of
the metric uses a four-dimensional analogue of the two-dimensional tt*
equations.
