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''For definiteness, let us suppose that there are nine main roads in the
atom--nine possible orbits for the electron. Then on any occasion there
are nine courses open to the electron; it may jump to any of the other
eight orbits, or it may stay where it is. That reminds us of another
well-known jumper--the Knight in Chess. He has eight possible squares to
move to, or he may stay where he is. Instead of picturing the atom as
containing a particle and nine roads or orbits, why should we not picture the atom as containing a Knight and a Chess-board? It turns out that my suggestion would not do at all. However Metaphorical our usual picture may be, it contains an essential truth about the behaviour of the atom which would not be preserved in the Knight-Chess-board picture. We have to formulate this characteristic in an abstract or mathematical way, so that when we rub out the false picture we may still have that characteristic--the something which made the orbit picture not so utterly wrong as the Knight
picture--to hand over to the mathematician. The distinction is this. If the electron makes two orbit jumps in succession it arrives at a state which it could have reached by a single jump; but if a Knight makes two moves it arrives at a square which it could not have reached by a single move.''  --Arthur Eddington, ''The Theory of Groups,'' chapter of 'New Pathways in Science' 1935