Pure love of learning, of course, was a less compelling motive for those who became educated for careers other than teaching. Students of law in particular had a reputation for being materialistic careerists in an age when law was becoming known as the ‘lucrative science’ and its successful practice the best means for rapid advancement in the government of both church and state. Medicine too had its profit-making attractions. Those who did not go on to law or medicine could, if they had been well trained in the arts, gain positions at royal courts or rise in the clergy. Eloquent testimony to the profit motive behind much of 12th-century education was the lament of a student of Abelard around 1150: ”Christians educate their sons . . . for gain, in order that the one brother, if he be a clerk, may help his father and mother and his other brothers, saying that a clerk will have no heir and whatever he has will be ours and the other brothers.” With the opening of positions in law, government and the church, education became a means for advancement not only in income but also in status. Most who were educated were wealthy, but in the 12th century, more often than before, many were not and were able to rise through the ranks by means of their education. The most familiar examples are Thomas Becket, who rose from a humble background to become chancellor of England and then archbishop of Canterbury, and John of Salisbury, who was born a ‘plebeian’ but because of his reputation for learning died as bishop of Chartres.
The instances of Becket and John of Salisbury bring us to the most difficult question concerning 12th-century education: To what degree was it still a clerical preserve? Despite the fact that throughout the 12th century the clergy had a monopoly of instruction, one of the outstanding medievalists of our day, R. W. Southern, refers with good reason to the institutions staffed by the clergy as ‘secular schools’. How can we make sense out of the paradox that 12th-century schools were clerical and yet ‘secular’?
Let us look at the clerical side first. Not only were all 12th-century teachers except professionals and craftsmen in church order, but in northern Europe students in schools had clerical status and looked like priests. Not that all really were priests, but by virtue of being students all were awarded the legal privileges accorded to the clergy. Furthermore, the large majority of 12th-century students, outside of the possible exception of Italy, if not already priests became so after their studies were finished. For these reasons, the term ‘cleric’ was often used to denote a man who was literate and the term ‘layman’ one who was illiterate. The English word for cleric, clerk, continued for a long time to be a synonym for student or for a man who could write, while the French word clerc even today has the connotation of intellectual.
Despite all this, 12th-century education was taking on many secular qualities in its environment, goals, and curriculum. Student life obviously became more secular when it moved out from the monasteries into the bustling towns. Most students wandered from town to town in search not only of good masters but also of worldly excitement, and as the 12th century progressed they found the best of each in Paris. More important than environment was the fact that most students, even though they entered the clergy, had secular goals. Theology was recognized as the ‘queen of the sciences’, but very few went on to it. Instead they used their study of the liberal arts as a preparation for law, medicine, government service, or advancement in the ecclesiastical hierarchy.
This being so, the curriculum of the liberal arts became more sophisticated and more divorced from religion. Teaching was still almost exclusively in Latin, and the first book most often read was the Psalter, but further education was no longer similar to that of a choir school. In particular, the discipline of rhetoric was transformed from a linguistic study into instruction in how to compose letters and documents; there was a new stress on logic; and in all the liberal arts and philosophy texts more advanced than those known in the early Middle Ages were introduced.
Along with this new logic came the translation of Greek and Arabic philosophical and scientific works. Most important was the translation of almost all the writings of Aristotle, as well as his sophisticated Arabic commentators, which helped to bring about an intellectual revolution based on Greek rationalism. On a more prosaic level, contact with Arabs resulted in the introduction in the 12th century of the arithmetic system and the concept of zero.
Though most westerners first resisted this and made crude jokes about it, the material quickly became widely accepted as useful. When it was understood, the system they used their study of liberal arts as preparation for law, medicine, government service, or advancement in the ecclesiastical hierarchy.


When people who are talking don’t share the same culture, knowledge, values, and assumptions, mutual understanding can be especially difficult. Such understanding is possible through the negotiation of meaning. To negotiate meaning with someone, you have to become aware of and respect both the differences in your backgrounds and when these differences are important. You need enough diversity of cultural and personal experience to be aware that divergent world views exist and what they might be like. You also need the flexibility in world view, and a generous tolerance for mistakes, as well as a talent for finding the right metaphor to communicate the relevant parts of unshared experiences or to highlight the shared experiences while demphasizing the others. Metaphorical imagination is a crucial skill in creating rapport and in communicating the nature of unshared experience. This skill consists, in large measure, of the ability to bend your world view and adjust the way you categorize your experiences. Problems of mutual understanding are not exotic; they arise in all extended conversations where understanding is important.
When it really counts, meaning is almost never communicated according to the CONDUIT metaphor, that is, where one person transmits a fixed, clear proposition to another by means of expressions in a common language, where both parties have all the relevant common knowledge, assumptions, values, etc. When the chips are down, meaning is negotiated: you slowly figure out what you have in common, what it is safe to talk about, how you can communicate unshared experience or create a shared vision. With enough flexibility in bending your world view and with luck and charity, you may achieve some mutual understanding.
Communication theories based on the CONDUIT metaphor turn from the pathetic to the evil when they are applied indiscriminately on a large scale, say, in government surveillance or computerized files. There, what is most crucial for real understanding is almost never included, and it is assumed that the words in the file have meaning in themselves—disembodied, objective, understandable meaning. When a society lives by the CONDUITmetaphor on a large scale, misunderstanding, persecution, and much worse are the likely products.
Later, I realized that reviewing the history of nuclear physics served another purpose as well: It gave the lie to the naive belief that the physicists could have come together when nuclear fission was discovered (in Nazi Germany!) and agreed to keep the discovery a secret, thereby sparing humanity such a burden. No. Given the development of nuclear physics up to 1938, development that physicists throughout the world pursued in all innocence of any intention of finding the engine of a new weapon of mass destruction—only one of them, the remarkable Hungarian physicist Leo Szilard, took that possibility seriously—the discovery of nuclear fission was inevitable. To stop it, you would have had to stop physics. If German scientists hadn’t made the discovery when they did, French, American, Russian, Italian, or Danish scientists would have done so, almost certainly within days or weeks. They were all working at the same cutting edge, trying to understand the strange results of a simple experiment bombarding uranium with neutrons. Here was no Faustian bargain, as movie directors and other naifs still find it intellectually challenging to imagine. Here was no evil machinery that the noble scientists might hide from the problems and the generals. To the contrary, there was a high insight into how the world works, an energetic reaction, older than the earth, that science had finally devised the instruments and arrangements to coart forth. “Make it seem inevitable,” Louis Pasteur used to advise his students when they prepared to write up their discoveries. But it was. To wish that it might have been ignored or suppressed is barbarous. “Knowledge,” Niels Bohr once noted, “is itself the basis for civilization.” You cannot have the one without the other; the one depends upon the other. Nor can you have only benevolent knowledge; the scientific method doesn’t filter for benevolence. Knowledge has consequences, not always intended, not always comfortable, but always welcome. The earth revolves around the sun, not the sun around the earth. “It is a profound and necessary truth,” Robert Oppenheimer would say, “that the deep things in science are not found because they are useful; they are found because it was possible to find them.”
...Bohr proposed once that the goal of science is not universal truth. Rather, he argued, the modest but relentless goal of science is “the gradual removal of prejudices.” The discovery that the earth revolves around the sun has gradually removed the prejudice that the earth is the center of the universe. The discovery of microbes is gradually removing the prejudice that disease is a punishment from God. The discovery of evolution is gradually removing the prejudice that Homo sapiens is a separate and special creation.
For any natural number $k$, let $a_k = 3^k$. The smallest natural number $m$ for which \[ (a_1)^1 \times (a_2)^2 \times \dots \times (a_{20})^{20} \;<\; a_{21} \times a_{22} \times \dots \times a_{20+m} \] is: