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.

[答案与考点解析]

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

【考点解析】本题是一道审题定位与关键词语题。通过本题题干中的“physicists”可将本题的答案信息来源迅速确定在第二段的倒数第二句。通过阅读本句以及它的前后句，尤其是它后面的一句话(第二段的尾句)，我们可以推断出本题的正确选项应该是表达“healthy”(有益的)含义的选项A，因为该选项中的“practical”是一个表示肯定的词语。考生在解题时一定要善于审题定位，更要善于理解句间关系所表达的内容。

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。

[参考译文]

计算机程序员经常说计算机器会执行任何愚蠢的命令，因为它们完全缺乏辨别力。当然，其原因在于计算机的智力在其感知细节上的狭窄固定性——它不能被冗长的上下文所引导。三个相关的形容词可以用来对计算机进行心理上的描述：单一的思维，刻板的思维，简单的思维。在认识到这一点的同时，我们也应该认识到这种单一的思维，刻板的思维，简单的思维同样可以用来(尽管只是在较低的程度上)描述理论数学。

由于科学总是处理现实的问题，即使最精确的科学也通常在或多或少的不完全理解的近似的基础上探讨现实，对此，科学家必须保持适当的怀疑。例如，当数学家得知关于氢原子的薛定谔方程并不是对这种原子的精确的描述，而只是在考虑了旋转、磁极以及相对论作用的基础上一个稍微正确的近似方程，并且这个所谓的正确方程自身也只是对一个无穷量子理论场的不完美的近似时，他们一定深感震惊。当物理学家看到最初的薛定谔方程时，他们从中感知到在可见的各种关系之外，仍然存在着许多不可见的关联，而这种感知就会激励物理学家合理地忽略方程中纯技术的特色。这种非常有益的怀疑态度对于数学领域而言则是较为陌生的。

数学家必须研究精确界定的情况。因此，数学家依赖数学以外的努力来对数学照字面意义理解的近似性加以详细的说明。当给予数学家一个不确定程度较小的情形时，他们会把它转化成一个完全确定的状态。这种转化可能是合适的，也可能是不合适的。在某些情形下，数学家的这种刻板思维可能会产生不幸的后果。数学家把科学家的理论假设，也就是科学家分析重点的权宜之点，转化成公理，然后依据精确字义理解这些公理。他们可能还会说服科学家依据字义理解公理，这就会带来危险。科学家调查的中心问题，在数学领域则成为极其扰乱人心的问题，因而被忽略——如果公理不严谨会发生什么情况?

物理学家惧怕精确的论断是对的，因为一个仅仅因其精确性而使人信服的论断，当它所基于的假设略微改变时，其说服力就会丧失殆尽，而一个尽管不精确却具有说服力的论断，却会在它的基础假设受到小干扰时，依旧岿然不动。