¹ In terms of the cultures involved, the data would relate overwhelmingly to the Classic, Islamic, and Western civilizations. They would include both military-political and aestheticintellectual achievements (though in an unknown proportion), but practically exclude economic and technological attainments and events.

¹ If Pirenne's view of the West as undergoing recession from about 700 on as the result of Muslim expansion is correct, the Grays’ trough at 710 might represent the Arab land and sea closure as well as the end of Merovingian decadence. But the Grays’ curve seems to validate the Carolingian Renaissance as an advance by its definite rise from 710 to 850. Medievalists have perhaps by now decided how far Pirenne was essentially right or how far his cause and effect stand in disproportionate relation. Their reaction to the problem would be extremely helpful.