15. The Night-Sky. At night, only our own sun is
turned away from us, but all the other suns (that is
fixed stars) of the universe shine upon us as by daytime.
Yet, the night-sky is dark, meaning that only very little
radiation energy from all the other stars reaches us and
falls on our retinas. It is a leading problem about the
structure of the universe to explain why this is so, that
is, why and how so much radiative energy is “lost”
in space, as it appears to be.
The problem was posed in the first half of the eight-
eenth century; first, somewhat casually, in 1720 by
Edmund Halley, eminent British astronomer, translator
of difficult works from antiquity, and personal friend
to Isaac Newton; and then, quite formally, in 1743,
by the youthful Swiss gentlemen astronomer Jean
Philippe Loys de Chéseaux, owner of an observatory
on his estate (North, p. 18). After that, most unbeliev-
ably, for eighty years nothing happened. Then, in 1823,
the problem was stated anew, quite emphatically, by
the German astronomer H. W. M. Olbers. This stirred
up some notice, but not much, and, unbelievably, the
problem did not move into an area of active attention
for another hundred years. But after Hermann Bondi
had dubbed the problem the “Olbers Paradox” it be-
came generally known, among professionals at any rate
(North, p. 18; Bondi, Ch. 3).
Specifically the problem is as follows. If, à la
Giordano Bruno we make the assumption that the
universe is Euclidean and unchanging; that it houses
infinitely many stars which, on a suitable average, are
uniformly distributed; and that the universe does not
change in time, so that in particular it has “always”
existed in the past; then, by a simple calculation, the
total radiation energy reaching, at any time, a general
point of the universe is not only not small, but is in
fact “infinitely large.” Which means that under these
assumptions the sky would be just as bright by night
as by day. However it is not so, and we thus have the
Olbers paradox.
In the calculation which leads to the paradox most
of the energy comes from distant stars, and the paradox
will be overcome if a suitable change in the above
assumptions will imply that distant stars contribute
little or no radiation (Bondi, Ch. 3). For instance, it
suffices to assume that the universe has not existed
“always,” but, on the contrary, has been created “rela-
tively recently.”
Another change of assumptions, a highly favored
one, is the hypothesis that the universe is expanding.
The expansion produces the red-shift in the traveling
energy waves, that is a decrease of their energy. Very
informally it can be said that a fraction of the radiative
energy is absorbed by the space as “nutriment” for its
growth, and that the fraction is the larger the more
distant the source from which the radiation is emitted.
Finally, the paradox can be overcome by the as-
sumption that the stars, or rather the galaxies, are not
distributed homogeneously, but, on the contrary, are
concentrated in clusters, “hierarachically” so. Thus,
between 1908 and 1922, C. V. I. Charlier advanced
the hypothesis that there are clusters of galaxies
(clusters of the first order), clusters of clusters (clusters
of the second order), clusters of clusters of clusters,
etc. (North, pp. 20-22). This hypothesis is of interest
in our context because it revived a suggestion made
in the eighteenth century by the imaginative mathe-
matician and natural philosopher Johann Heinrich
Lambert in his Kosmologische Briefe... (1761).
This “hierarchic hypothesis” does not have many
adherents, probably because it cannot be easily recon-
ciled with the so-called “Cosmological Principle”
which is in great demand for applications. This princi-
ple was expressly enunciated, and so named, by
Edward Arthur Milne in the 1930's (North, pp.
156-58), and it maintains rather broadly, and not too
specifically, that the total cosmological picture of the
universe, in its meaningful features, is independent of
the vantage point of the observer composing the pic-
ture. The principle is flexible in its specific formula-
tions, and is in this way a great aid in speculative
deductions (Bondi, Ch. 3).
It also ought to be realized that if no radiation from
the stars were lost in space, “... no planet anywhere
in the universe would be cool enough to permit bio-
logical life of any kind” (Coleman, p. 67), as we know
it today.
