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  Computer programmers often remark that computing machines, with a perfect lack of discrimination, will do any foolish thing they are told to do. The reason for this lies, of course, in the narrow fixation of the computing machine’s “intelligence” on the details of its own perceptions — its inability to be guided by any large context. In a psychological description of the computer intelligence, three related adjectives come to mind: single-minded, literal-minded, and simple-minded. Recognizing this, we should at the same time recognize that this single-mindedness, literal-mindedness, and simple-mindedness also characterizes theoretical mathematics, though to a lesser extent.

  Since science tries to deal with reality, even the most precise sciences normally work with more or less imperfectly understood approximations toward which scientists must maintain an appropriate skepticism. Thus, for instance, it may come as a shock to mathematicians to learn that the Schrodinger equation for the hydrogen atom is not a literally correct description of this atom, but only an approximation to a somewhat more correct equation taking account of spin, magnetic dipole, and relativistic effects; and that this corrected equation is itself only an imperfect approximation to an infinite set of quantum field-theoretical equations. Physicists, looking at the original Schrodinger equation, learn to sense in it the presence of many invisible terms in addition to the differential terms visible, and this sense inspires an entirely appropriate disregard for the purely technical features of the equation. This very healthy skepticism is foreign to the mathematical approach.

  Mathematics must deal with well-defined situations. Thus, mathematicians depend on an intellectual effort outside of mathematics for the crucial specification of the approximation that mathematics is to take literally. Give mathematicians a situation that is the least bit ill-defined, and they will make it well-defined, perhaps appropriately, but perhaps inappropriately. In some cases, the mathematicians literal-mindedness may have unfortunate consequences. The mathematicians turn the scientists’ theoretical assumptions that is, their convenient points of analytical emphasis, into axioms, and then take these axioms literally. This brings the danger that they may also persuade the scientists to take these axioms literally. The question, central to the scientific investigation but intensely disturbing in the mathematical context — what happens if the axioms are relaxed? — is thereby ignored.

  The physicist rightly dreads precise argument, since an argument that is convincing only if it is precise loses all its force if the assumptions on which it is based are slightly changed, whereas an argument that is convincing though imprecise may well be stable under small perturbations of its underlying assumptions.

  1. The author discusses computing machines in the first paragraph primarily in order to do which of the following?

  [A] Indicate the dangers inherent in relying to a great extent on machines.

  [B] Illustrate his views about the approach of mathematicians to problem solving.

  [C] Compare the work of mathematicians with that of computer programmers.

  [D] Provide one definition of intelligence.

  2. It can be inferred form the text that scientists make which of the following assumptions about scientific arguments?

  [A] The literal truth of the arguments can be made clear only in a mathematical context.

  [B] The arguments necessarily ignore the central question of scientific investigation.

  [C] The arguments probably will be convincing only to other scientists.

  [D] The premises on which the arguments are based may change.

  3. According to the text, mathematicians present a risk to scientist for which of the following reasons?

  [A] Mathematicians may provide theories that are incompatible with those already developed by scientists.

  [B] Mathematicians may define situations in a way that is incomprehensible to scientists.

  [C] Mathematicians may convince scientists that theoretical assumptions are facts.

  [D] Scientists may come to believe that axiomatic statements are untrue.

  4. The author suggests that the approach of physicists to solving scientific problem is which of the following?

  [A] Practical for scientific purposes.

  [B] Detrimental to scientific progress.

  [C] Unimportant in most situations.

  [D] Expedient, but of little long-term value.

  5. The author implies that scientists develop a healthy skepticism because they are aware that

  [A] mathematicians are better able to solve problems than are scientists.

  [B] changes in axiomatic propositions will inevitably undermine scientific arguments.

  [C] well-defined situations are necessary for the design of reliable experiments.

  [D] some factors in most situations must remain unknown.




  1. 【答案】B

  【考点解析】这是一道写作手法题。旨在考察考生的语言基本功和对文章段落结构的认识。这是一道比较难的题目。通过仔细阅读第一段并且把第一段和本文其它段落相联系,可推导出本题的正确选项是B。原文作者借用大家所熟悉的“computing machines”作为例子来帮助我们更好的了解“theoretical mathematics”的特点。考生在解题时一定要识别出作者的写作手法和意图。

  2. 【答案】D

  【考点解析】这是一道审题定位与引申推导题。通过本题题干中的“arguments”一词可将本题的答案信息来源迅速确定在尾段。通过仔细阅读理解尾段的内容并且根据尾段的内容进行推导,可得知本题的正确选项应该是突出“the premises…may change”的选项D。考生在解题时即要具备迅速审题定位的能力,又要具备理解原文深层含义的能力。

  3. 【答案】C

  【考点解析】这是一道审题定位与细节推导题。根据本题题干中的“risk”一词可将本题的答案信息来源确定在原文倒数第二段的倒数第二句,通过仔细阅读倒数第二段的倒数第二句和第三句,尤其是倒数第二句中“danger”一词后面的同谓语从句,我们可以推断出本题的正确选项是突出“theoretical assumptions are facts”的选项C。考生在解题时一定要善于深入理解原文的含义,千万不能只停留在文字的表面。

  4. 【答案】A


  5. 【答案】D

  【考点解析】这是一道指代词题型。根据本题题干中的“healthy skepticism”可将本题的答案信息来源迅速确定在第二段的尾句,该句中的指代词“this”暗示我们本题的真正答案信息来源在第二段的倒数第二句,通过仔细阅读和理解倒数第二段的第二句话,我们可以得知强调“invisible”的选项D是本题的正确选项,因为该选项中含有“unknown”一词。考生在解题时应注意指代词的作用和功能,更要注意对原文细节的理解和把握。







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