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　　(D) Explain the rational elements in Gothic painting that corresponded to craftsmanship in Gothic architecture

　　(E) Show the increasing sophistication of artists after the Gothic period

　　(The passage below is drawn from an article published in 1962.)

　　Computer programmers often remark that com- puting machines, with a perfect lack of discrimina- tion, 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 simpleminded. Recognizing this, we should at the same time recognize that this single- mindedness, literal-mindedness, and simplemindedness 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 mathe- maticians 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 some- what 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.

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