174 DANGEROUS THOUGHTS

The principles of mechanics discovered by Stevinus, Galileo,
Hooke, Huyghens, and Newton have very little relevance to the
mechanisms with which a boy is familiar. In real life he never
meets perfectly smooth bodies sliding down perfectly flat slopes
without any friction. He has more experience of motor bicycles
which seize because of overheating. If he were enterprising
enough to calculate the trajectory of Big Bertha when it shelled
Paris, he would find that the actual range Snd height were less
than half what would be inferred from the formula given in the
text-book. Of course few boys would be so enterprising. The
boy who was would have the making of a scientist in him, and
the best way of training a scientist is not to start him off with
wrong ideas about the way the world works.

As long as the teacher has to prepare pupils to pass examinations
in mechanics conducted in the usual way he will find his task
easier if he tells the whole truth. Half the truth, of course, is that
the principles of mechanics in the Newtonian epoch were not
designed to deal with modern mechanisms. So we must not be
surprised or disappointed if they have to be supplemented by
much more information before they can give us a useful guide
to conduct in the everyday life of a secondary school pupil who
lives in the age of the light car and the autogyro. A conscientious
teacher will generally point this out and leave the pupil wondering
why it is necessary to learn the principles if they do not fit the
facts. So the other half of the truth, more rarely disclosed, is
equally important. Galilean mechanics did provide a very useful
guide to conduct in an age when sailing ships were first
undertaking westerly courses to uncharted oceans.

In contradistinction to the "so what?" problem of allaying the
sense of unfamiliarity or futility which discourages effort in pure
mathematics, the Hack sheep problem of realism in applied
mathematics may be discussed at various levels of relevance and
at different levels of sophistication. At the lowest we may recall
examples in compound proportion concocted to illustrate the
untruth that too many cooks never spoil the broth. At a later
stage we should distinguish between two different ways of