STRUCTURE OF THE UNIVERSE—HEAPS 181 
conspiracy of nature to prevent man from acquiring too much detailed 
information. A conspiracy of nature is a law of nature; we cannot 
pass it over as being of no importance. It is as if nature had erected 
a wall of impenetrability around the smallest particles and forced us 
to see them only partially, as if through the cracks in the wall. 
It appears, therefore, that we are asking a meaningless question 
when we ask just where an electron is when it has a certain definite 
momentum. No possible operation can be thought of by which an 
answer to this question can be obtained without violating a law of 
nature. The conclusion is that the electron cannot have an exact 
velocity and an exact momentum simultaneously. There is an essen- 
tial fuzziness in the very foundations of nature herself. Time and 
space are a little peculiar in the microscopic region, most certainly. 
Someone has said that “the infinite, whether the infinitely large, 
or the infinitely small, seems to carry disaster in its wake.” I do 
not think the word disaster is happily chosen in this connection. 
It is true that the two infinities at either end of our linear lay-out 
have shattered the beautiful, crystal-clear mechanical system which 
described the universe during most of the nineteenth century—when 
the luminiferous ether was as definitely material as a piece of iron, 
and when a scientist could say that practically all pioneer research 
in physics was over and nothing remained except to measure things 
with increasing accuracy. This complacent attitude is fortunately 
gone forever, and the two infinities have had a great deal to do with 
its disappearance. The new problems presented, the paradoxes, the 
uncertainties, all combine to give us a picture of modern science 
once more struggling, once more growing. It seems better to change 
the quotation to read, “The infinite, whether the infinitely large or 
the infinitely small, seems to have carried renaissance in its wake.” 
In summing up the subject we may say that the small part of the 
universe, open to everyday experience, has given us a simple concep- 
tion of nature, a simple body of laws, which seems unable to cope 
with problems either in the region of the supernebulae or in the 
region of the extremely small particles. 
In the latter field we have found that, properly speaking, descrip- 
tions of phenomena must be mainly mathematical. Such descrip- 
tions are quite adequate at present, and we feel that the main prob- 
lems of explanation are well in hand. But we must be careful not 
to expect the same type of explanation that is used for objects of 
ordinary size, and we must remember that here there is a certain 
indefiniteness of behavior. We do not say that a small particle can 
never get over a high hill when it does not have enough energy to 
carry it tothe top. We say that the probability of its getting over is 
