This passage in this part is followed by questions based on its contents. Read the passage carefully and choose the best answer for each question.
Humans have probably always been surrounded by their kin – those to whom they have been related by blood or marriage. But the size, the composition, and the functions of their families and kinship groups have varied tremendously. People have lived not only in the “nuclear family”, made up of just the parents and their offspring, which is standard in the West and has been found almost everywhere, they have lived in extended families and in formal clans; they have been “avunculocal”; they have been “ultrolateral”, they have been conscious of themselves as heirs of lineages hundreds of generations deep. However constructed, the traditional kinship group has usually provided those who live in it with security, identity, and indeed with their entire scheme of activities and beliefs. The nameless billions of hunter-gatherers who have lived and died over the past several million years have been embedded in kinship groups, and when people started to farm about ten thousand years ago, their universe remained centered on kinship. Now that there was a durable form of wealth which could be hoarded – grain – some families became more powerful than other; society became stratified, and genealogy became an important means of justifying and perpetuating status.
During the past few centuries, however, in part of the world – in Europe and the countries that have been developing along European lines – a process of fragmentation has been going on. The ties and the demands of kinship have been weakening, the family has been getting smaller and, some say, less influential, as the individual, with a new sense of autonomy and with new obligations to himself (or, especially in the last decade and a half, to herself), has come to the foreground. A radically different mental order – self-centered and traceable not to any single historical development as much as to the entire flow of Western history since at least the Renaissance has taken over. The political and economic effects of this rise in individual self-consciousness have been largely positive: civil rights are better protected and opportunities are greater in the richer, more dynamic countries of the West; but the psychological effects have been mixed, at best. Something has been lost: a warmth, a sanity, and a supportiveness that are apparent among people whose family networks are still intact. Such qualities can be found in most of the Third World and in rural pockets of the U.S., but in the main stream of post-industrial society the individual is increasingly left to himself, to find meaning, stability, and contentment however he can.
An indication of how far the disintegration of traditional kinship has advanced is that a surprising number of Americans are unable to name all four of their grandparents. Such people have usually grown up in step-families, which are dramatically on the rise. So is the single-parent family – the mother-child unit, which some anthropologists contend is the real nucleus of kinship, having already contracted to the relatively impoverished nuclear family, partly as an adaptation to industrialization. Kinship seems to be breaking down even further. With the divorce rate in America at about fifty percent and the remarriage rate at about seventy five, the traditional Judeo-Christian scheme of marriage to one person for life seems to be shading into a pattern of serial monogamy, into a sort of staggered polygamy, which some anthropologists, who believe that we aren’t naturally monogamous to begin with, see as “a return of normality”. Still other anthropologists explain what is happening somewhat differently; we are adopting delayed system of marriage, they say, with the length of the marriage chopped off at both ends. But many adults aren’t getting married at all; they are putting “self-fulfillment” before marriage and children and are having nothing further to do with kinship after leaving their parents’ home; their family has become their work associate or their circle of best friends. This is the most distressing trend of all; the decline in the capacity of long-term intimate bonding.


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: