In general problem solving I have gone on record[l] as being convinced that if there
is a genuine choice between solving a problem manually or by computer, then it is
better done manually: all the intermediate steps of calculation are checked and thought
about as they are done; errors of logic or emphasis may be spotted even at a late
stage in the numerical work; there is the opportunity to bend the calculations of
particular cases to make them more realistic; there is the chance of avoiding the
brittleness of inflexible methods. And above all, there is not the temptation to assume
that just by putting in the input data and observing the output everything will be all
right, and forgetting the imperfections of the program hidden inside the black box.