Computer programmers often remark that computing machines 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 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 some-what more correct equation taking account of spin, magnetic dipole, and relativistic effects 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 In
situation that is the lens may defined, perhaps appropriately, but perhaps inappropriately some cases, the mathematicians' literal-mindedness may have unfortunate consequences. The mathematicians turn the scimtists thotretical assumptions, that is, their convenient points of analytical emphasis, into axioms, and then take these axioms, literally. This brings the danger that they may alone ade 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.