In chemistry the molecules of a compound are assumed to consist of
the atoms of the elements contained in the compound. These atoms are
supposed to be at certain distances from one another. It sometimes
happens that two compound substances differ in their chemical or
physical properties, or both, even though they have like chemical
elements in the same proportion. This phenomenon is called isomerism,
and the generally accepted explanation is that the atoms in isomeric
molecules are differently arranged, or grouped, in space. It is
difficult to imagine how atoms, alike in number, nature, and
relative proportion, can be so grouped as somehow to produce
compounds with different properties, particularly as in
three-dimensional space four is the greatest number of points whose
mutual distances, six in number, are all independent of each other.
In four-dimensional space, however, the _ten_ equal distances
between any two of _five_ points are geometrically independent, thus
greatly augmenting the number and variety of possible arrangements
of atoms.
This just escapes being the kind of proof demanded by science. If
the independence of all the possible distances between the atoms of
a molecule is absolutely required by theoretical chemical research,
then science is really compelled, in dealing with molecules of more
than four atoms, to make use of the idea of a space of more than
three dimensions.