Mathematics must deal with well-defined situations. Thus,mathematicians depend on an intellectual effort outside of mathematics for thecrucial specification of the approximation that mathematics is to takeliterally. Give mathematicians a situation that is the least bit ill-defined,and they will make it well-defined, perhaps appropriately, but perhapsinappropriately. In some cases, the mathematicians literal-mindedness may haveunfortunate consequences. The mathematicians turn the scientists theoreticalassumptions that is, their convenient points of analytical emphasis, intoaxioms, and then take these axioms literally. This brings the danger that theymay also persuade the scientists to take these axioms literally. The question,central to the scientific investigation but intensely disturbing in themathematical context what happens if the axioms are relaxed? is therebyignored.

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

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

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

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

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