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Slight traces of Pythagoreanism are to be found in the mystical

number of the State, in the number which expresses the interval

between the king and the tyrant, in the doctrine of

transmigration, in the music of the spheres, as well as in the

great though secondary importance ascribed to mathematics in

education.

But as in his philosophy, so also in the form of his State, he

goes far beyond the old Pythagoreans. He attempts a task really

impossible, which is to unite the past of Greek history with the

future of philosophy, analogous to that other impossibility,

which has often been the dream of Christendom, the attempt to

unite the past history of Europe with the kingdom of Christ.

Nothing actually existing in the world at all resembles Plato's

ideal State; nor does he himself imagine that such a State is

possible. This he repeats again and again; e.g. in the Republic,

or in the Laws where, casting a glance back on the Republic, he

admits that the perfect state of communism and philosophy was

impossible in his own age, though still to be retained as a

pattern.