Read the passage carefully and choose the best answer for each question.
How quickly things change in the technology business! A decade ago, IBM was the awesome and undisputed king of the computer trade, universally feared and respected. A decade ago, two little companies called Intel and Microsoft were mere blips on the radar screen of the industry, upstart start-ups that had signed on to make the chips and software for IBM’s new line of personal computers. Though their products soon became industry standards, the two companies remained protected children of the market leader.
What happened since is a startling reversal of fortune. IBM is being ravaged by the worst crisis in the company’s 79 year history. It is undergoing its fifth restructuring in the past seven years as well as seemingly endless rounds of job cuts and firings that have eliminated 100,000 jobs since 1985. Last week IBM announced to its shell-shocked investors that it lost \$4.97 billion last year – the biggest loss in American corporate history.
And just when IBM is losing ground in one market after another, Intel and Microsoft have emerged as the computer industry’s most fearsome pair of competitors. The numbers on Wall Street tell a stunning story. Ten years ago, the market value of the stock of Intel and Microsoft combined amounted to about a tenth of IBM’s. Last week, with IBM’s stock at an 11-year low, Microsoft’s value surpassed its old mentor’s for the first time ever (\$26.76 billion to \$26.48 billion) and Intel (\$24.3 billion) is not far behind. While IBM is posting losses, Intel’s profits jumped 30% and Microsoft’s rose 44%.
Both Intel, the world’s largest supplier of computer chips, and Microsoft, the world’s largest supplier of computer software, have assumed the role long played by Big Blue as the industry’s pacesetter. What is taking place is a generational shift unprecedented in the information age – one recalls a transition in the US auto industry 70 years ago, when Alfred Sloan’s upstart General Motors surpassed Ford Motor as America’s No. 1 car maker. The transition also reflects the decline of computer manufacturers such as IBM, Wang, and Unisys and the rise of companies like Microsoft, Intel, and AT\&T that create the chips and software to make the computers work. “Just like Dr. Frankenstein, IBM created these two monster competitors,” says Richard Shaffer, publisher of the Computer Letter. “Now even IBM is in danger of being trampled by the creations it unleashed.”
Although Intel and Microsoft still have close relationships with Big Blue, there is little love lost between IBM and its potent progeny. IBM had an ugly falling-out with former partner Microsoft over the future of personal computer software. Microsoft developed the now famous disk operating system for IBM-PC – called DOS – and later created the operating software for the next generation of IBM personal computers, the Personal System/2. When PS/2 and its operating system, OS/2, failed to catch on, a feud erupted over how the two companies would upgrade the system. Although they publicly patched things up, the partnership was tattered. IBM developed its own version of OS/2, which has so far failed to capture the industry’s imagination. Microsoft’s competing version, dubbed New Technology, or NT, will debut in a few months and will incorporate Microsoft’s highly successful Windows program, which lets users juggle several programs at once. Windows NT, however, will offer more new features, such as the ability to link many computers together in a network and to safeguard them against unauthorized use.
IBM and Intel have also been parting company. After relying almost exclusively on the Santa Clara, California company for the silicon chips that serve as computer brains, IBM has moved to reduce its dependence on Intel by turning to competing vendors. In Europe, IBM last year began selling a low-cost line of PCs called Ambra, which runs on chips made by Intel rival Advanced Micro Devices. IBM also demonstrated a sample PC using a chip made by another Intel enemy, Cyrix. And that October IBM said it would begin selling the company’s own chips to outsiders in direct competition with Intel.
IBM clearly feels threatened. And the wounded giant still poses the biggest threat to any further dominance by Intel and Microsoft. Last year, it teamed up with both companies' most bitter rivals – Apple Computers and Motorola – to develop advanced software and microprocessors for a new generation of desktop computers. In selecting Apple and Motorola, IBM bypassed its longtime partners. Just as Microsoft’s standard operating system runs only on computers built around Intel’s computer chips, Apple’s software runs only on Motorola’s chips. Although IBM has pledged that the new system will eventually run on a variety of machines, it will initially run only computer programs written for Apple’s Macintosh or IBM’s OS/2. Its competitive juice now flowing, IBM last week announced that it and Apple Computer will deliver the operating system in 1994 – a year ahead of schedule.


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: