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The problems we have really solved do not have to be done over again; the downfall of past societies is but the wiping off the slate of a mass of elaborate failures. “Rule it all out down to that first line and begin again!” says the teacher.

We are quite clever at simple examples in units, but very weak on fractions. We could see how one man affected another in the short radius of a limited early group, but the long-range effects of our widening interhuman activities have been beyond us, and we are slowly working out in heavy centuries those problems of liberty and justice, of honesty and love, the mastery of which is as essential to our further progress as was the early mastery of metallurgy and mechanics.

A mistake in short and simple addition is easily seen, but as the examples grow more complex the errors are more difficult to trace.

They spread wider and last longer, and by the time a society begins to meet the punishment due to the behaviour of its misguided constituents, those worthies have long since died in the odour of sanctity and a new generation is piously producing the incipient errors which will destroy its grandchildren. The vigour of our basic life processes sustains us through wide reaches of experiments and mistakes.