THE PRESIDENTIAL ADDRESS 7 
minutest details, but the motion was quite inconsistent with the 
mechanistic determinism of the Newtonian mechanics. The elec- 
tron did not move continuously through space and time, but jumped, 
and its jumps were not governed by the laws of mechanics, but to 
all appearance, as Einstein showed more fully four years later, by 
the laws of probability. Of 1000 identical atoms, 100 might make 
the jump, while the other g00 would not. Before the jumps oc- 
curred, there was nothing to show which atoms were going to jump. 
_ Thus the particle-picture conspicuously failed to provide an answer 
- to the question ‘ What will happen next ?’ 
Bohr’s concepts were revolutionary, but it was soon found they 
were not revolutionary enough, for they failed to explain more 
complicated spectra, as well as certain other phenomena. 
Then Heisenberg showed that the hydrogen spectrum—and, as 
we now believe, all other spectra as well—could be explained by the 
motion of something which was rather like an electron, but did not 
move in space and time. Its position was not specified by the 
usual co-ordinates x, y, 2 of co-ordinate geometry, but by the 
mathematical abstraction known as a matrix. His ideas were rather 
too abstract even for mathematicians, the majority of whom had 
quite forgotten what matrices were. Itseemed likely that Heisenberg 
had unravelled the secret of the structure of matter, and yet his 
solution was so far removed from the concepts of ordinary life that 
another parable had to be invented to make it comprehensible. 
The wave-parable serves this purpose ; it does not describe the 
universe as a collection of particles but as a system of waves. ‘The 
universe is no longer a deluge of shot from a battery of machine- 
guns, but a stormy sea with the sea taken away and only the abstract 
quality of storminess left—or the grin of the Cheshire cat if we can 
think of a grin as undulatory. This parable was not devised by 
Heisenberg, but by de Broglie and Schrodinger. At first they 
thought their waves merely provided a superior model of an ordinary 
electron ; later it was established that they were a sort of parable 
to explain Heisenberg’s pseudo-electron. 
Now the pseudo-electron of Heisenberg did not claim to account 
for the spectrum emitted by a single atom of gas, which is something 
entirely beyond our knowledge or experience, but only that emitted 
by a whole assembly of similar atoms ; it was not a picture of one 
electron in one atom, but of all the electrons in all the atoms. 
In the same way the waves of the wave-parable do not picture 
individual electrons, but a community of electrons—a crowd—as 
for instance the electrons whose motion constitutes a current of 
electricity. 
In this particular instance the waves can be represented as travel- 
ling through ordinary space. Except for travelling at a different 
