The Freudenthal Problem and its Ramifications (Part III)

The movie “Romanoff and Juliet” (Universal International Studios, 1961) shows Peter Ustinov as the Prime Minister of the tiny, peaceful, sleepy nation of Concordia, only a few miles across somewhere in Europe. It is the time of the cold war, and Concordia is squeezed between East andWest. Americans and Soviets are fiercly determined to dominate the neutral country. Prime Minister Ustinov learns by chance from the American Ambassador that the Americans know about the latest top secret Soviet manoeuvre in this contest to control Concordia. After a bit of reflection, Ustinov visits the Soviet Ambassador and tells him in a voice fraught with significance: “They know.” The Soviet Ambassador is not impressed: “We know they know.” Ustinov goes back to the American Ambassador: “They know you know.” The American Ambassador smiles: “But we know they know we know.” Ustinov returns to the Soviet Ambassador: “They know you know they know.” The Soviet Ambassador replies triumphantly: “We know they know we know they know!” Once again Ustinov returns to the American Ambassador. Wearily he says: “Well, they know you know they know you know.” The American Ambassador repeats it after him, counting on his fingers. “What?” he suddenly cries in horror. “They know we know they know we know?”