  Over the past few years the arithmetic Langlands program has proven useful in
addressing physical problems. In this paper it is shown how Langlands'
reciprocity conjecture for automorphic forms, in combination with a
representation theoretic notion of motives, suggests a framework in which the
entropy of automorphic black holes can be viewed as a probe of spacetime that
is sensitive to the geometry of the extra dimensions predicted by string
theory. If it were possible to produce black holes with automorphic entropy in
the laboratory their evaporation would provide us with information about the
precise shape of the compact geometry.
