a doctoral candidate working on my thesis and finding that I needed numerical tools that I should have
been taught years before. In the intervening decades, little has changed except for the worse. All fields
of science have undergone an information explosion while the computer revolution has steadily and
irrevocability been changing our lives. Although the crystal ball of the future is at best "seen through a
glass darkly", most would declare that the advent of the digital electronic computer will change
civilization to an extent not seen since the coming of the steam engine. Computers with the power that
could be offered only by large institutions a decade ago now sit on the desks of individuals. Methods of
analysis that were only dreamed of three decades ago are now used by students to do homework
exercises. Entirely new methods of analysis have appeared that take advantage of computers to perform
logical and arithmetic operations at great speed. Perhaps students of the future may regard the
multiplication of two two-digit numbers without the aid of a calculator in the same vein that we regard
the formal extraction of a square root. The whole approach to scientific analysis may change with the
advent of machines that communicate orally. However, I hope the day never arrives when the
investigator no longer understands the nature of the analysis done by the machine.
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