However, the irreducible symmetric spaces can be classified. As shown by Katsumi Nomizu, there is a dichotomy: an irreducible symmetric space "G"/"H" is either flat (i.e., an affine space) or formula_6 is semisimple. This is the analogue of the Riemannian dichotomy between Euclidean spaces and those of compact or noncompact type, and it motivated M. Berger to classify semisimple symmetric spaces (i.e., those with formula_6 semisimple) and determine which of these are irreducible. The latter question is more subtle than in the Riemannian case: even if formula_6 is simple, "G"/"H" might not be irreducible.