586 DISCUSSION ON THE 
oscillating universes, and those that start from a zero radius, out of account, 
the universe may have been practically stationary at or very near its 
minimum size for an infinite time before starting to expand, or it may 
have contracted during an infinite time and after passing through a 
minimum a few thousand million years ago started to expand again. In 
both cases there appears to be no causal connection between the change 
of size of the universe as a whole and the evolution of the systems which 
it contains. 
It should not be forgotten that all this talk about the universe involves 
a tremendous extrapolation, which is a very dangerous operation. I have 
sometimes called the part of the universe of which we know anything with 
certainty ‘our neighbourhood.’ The limits of this neighbourhood have 
been enormously extended in the last ten or fifteen years by the results 
derived from observations with the large telescopes at Mount Wilson and 
elsewhere, but still it is presumably only a very small portion of the whole 
of the universe. All assertions regarding those portions of the universe 
which lie beyond our neighbourhood either in space or in time are pure extra- 
polations. In making a theory of the universe we must, however, adopt 
some extrapolation, and we can choose it so as to suit our philosophical 
taste. But we have no right to expect it to be confirmed by future 
observations extending to parts now outside our reach. The extra- 
polation that is at the base of the theory of the expanding universe is that 
our neighbourhood is just an ordinary point, or small area, in the universe, 
not differing from any other small area in any essential property. 
This is, of course, a very natural hypothesis to make, and I do not see 
how we can avoid making it, but it remains a hypothesis and an extra- 
polation. It involves, of course, the assertion—the axiomatic truth of 
which can hardly be doubted by any physicist—that the laws of nature 
remain the same at all times and all places. The observed fact is that the 
spectral lines in the light which reaches us from bodies at a great distance 
are displaced towards the red, or, in other words, that light 1s reddened by 
age. Now the only interpretation of a reddening of light consistent with 
the accepted laws of nature in a homogeneous world is a receding 
‘velocity’ of the source. This is the observational evidence of the 
‘expanding universe ’ in a nutshell. 
The dilemma that we are in has some similarity with that by which 
atomic physics was confronted some twenty years ago, when the necessity 
became apparent of ascribing to the atom properties which in a finite 
material body would be contradictory. The concept of the universe as 
a closed entity is, so far as I can see a hypothesis, an arbitrary addition to, 
and extension of, the observed phenomena by our imagination. We must 
be prepared to allow this ‘ Universe’ the freedom to have contradictory 
properties, like we have been forced to grant to the atom, ana in particular 
we must try to accustom ourselves to the idea that the velocity of change 
of the quantity of the dimension of a length, which occurs in the equations, 
and is interpreted as the ‘ Radius of the Universe,’ has nothing to do with 
the rate of evolutionary change of stars and stellar systems. 
It seems to me that the current interpretation, and the consequent 
model of the universe as an expanding closed hypersphere, may be found 
to be too simplistic, and may be displaced in time by one in which the 
a. 
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