  We study a generalized Fermat-Torricelli (S.FT) problem for infinitesimal
geodesic triangles on a C^2 complete surface M with variable Gaussian curvature
a < K < b, for a, b in R, such that the intersection point (generalized
Fermat-Torricelli point) of the three geodesics acquires a positive real number
(subconscious). The solution of the S.FT problem is a generalized
Fermat-Torricelli tree with one node that has acquired a subconscious. This
solution is based on a new variational method of the length of a geodesic arc
with respect to arc length, which coincides with the first variational formula
for geodesics on a surface with K < 0, or 0 < K < c. The 'plasticity' solution
of the inverse S.FT problem gives a connection of the absolute value of the
Gaussian curvature K(F) at the generalized Fermat-Torricelli point F with the
absolute value of the Aleksandrov curvature of the geodesic triangle by
acquiring both of them the subconscious of the g.FT point.
