The ancients devoted a lifetime to the study of arithmetic; it required days to extract a square root or to multiply two numbers together. Is there any harm in skipping all that, in letting the school boy learn multiplication sums, and in starting his more abstract reasoning at a more advanced point? Where would be the harm in letting the boy assume the truth of many propositions of the first four books of Euclid, letting him assume their truth partly by faith, partly by trial? Giving him the whole fifth book of Euclid by simple algebra? Letting him assume the sixth as axiomatic? Letting him, in fact, begin his severer studies where he is now in the habit of leaving off? We do much less orthodox things. Every here and there in one’s mathematical studies one makes exceedingly large assumptions, because the methodical study would be ridiculous even in the eyes of the most pedantic of teachers. I can imagine a whole year devoted to the philosophical study of many things that a student now takes in his stride without trouble. The present method of training the mind of a mathematical teacher causes it to strain at gnats and to swallow camels. Such gnats are most of the propositions of the sixth book of Euclid; propositions generally about incommensurables; the use of arithmetic in geometry; the parallelogram of forces, etc., decimals.

The complexity of contemporary biology has led to an extreme specialization, which has inevitably been followed by a breakdown in communication between disciplines. Partly as a result of this, the members of each specialty tend to feel that their own work is fundamental and that the work of other groups, although sometimes technically ingenious, is trivial or at best only peripheral to an understanding of truly basic problems and issues. There is a familiar resolution to this problem but it is sometimes difficulty to accept emotionally. This is the idea that there are a number of levels of biological integration and that each level offers problems and insights that are unique to it; further, that each level finds its explanations of mechanism in the levels below, and its significances in the levels above it.

The explosive component in the contemporary scene is not the clamor of the masses but the self-righteous claims of a multitude of graduates from schools and universities. This army of scribes is clamoring for a society in which planning, regulation, and supervision are paramount and the prerogative of the educated. They hanker for the scribe’s golden age, for a return to something like the scribe-dominated societies of ancient Egypt, China, and Europe of the Middle Ages. There is little doubt that the present trend in the new and renovated countries toward social regimentation stems partly from the need to create adequate employment for a large number of scribes. And since the tempo of the production of the literate is continually increasing, the prospect is of ever-swelling bureaucracies.

There was this huge world out there, independent of us human beings and standing before us like a great, eternal riddle, at least partly accessible to our inspection and thought. The contemplation of that world beckoned like a liberation.

Those who see their lives as spoiled and wasted crave equality and fraternity more than they do freedom. If they clamor for freedom, it is but freedom to establish equality and uniformity. The passion for equality is partly a passion for anonymity: to be one thread of the many which make up a tunic; one thread not distinguishable from the others. No one can then point us out, measure us against others and expose our inferiority.