The key lies in our attitude and practices concerning computation, taken in a most general sense, and its techniques. As we succeed with shifting emphasis from avoidable labor of computation to broader concepts on the one hand and the mathematics of computation on the other, we shall be teaching better 20th-century mathematics. Numerical computation, through the centuries, has often faced up to reality and made things easier. The use of logarithmic tables, even by those who do not know how to recompute them, and of desk calculators and, now, electronic calculators, even by those who cannot repair them, has been a commonplace. Today the 'software' comprising the carefully planned interpretive routines, compilers, and other aspects of automative programming are at least as important to the modern electronic calculator as its 'hardware' of tubes, transis- tors, wires, tapes and the like.

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