the competing essayists were forced to introduce into their text on a
liberal scale is that of non-Euclidean geometry. The entire formulation
of the General Theory of Relativity is in fact an exercise in this. The
essayists--good, bad and indifferent alike--were quite unanimous in
their decision that this was one thing which the reader would have
to assume the responsibility of acquiring for himself. Certainly they
were justified in this; for the Editor has been able to explain what
non-Euclidean geometry is only by using up considerably more space
than the contestants had for an entire essay. No effort has been made
to set forth any of the details of any of the various non-Euclidean
geometries; it has simply been the aim to draw the dividing line
between Euclidean and non-Euclidean, and to make the existence of
the latter appear reasonable, so that when the essayists come to talk
about it the reader will not feel hopelessly at sea. In other words,
this is another case of providing the mental background, but on such
a scale that it has seemed necessary to give a separate chapter to it.