Probability is, of course, the guide of life. If all our assumptions
were expressed, we should find the phrase “it is reasonable to suppose”
occurred more frequently than any other, whether we were engaged
in crossing a street or in writing a philosophical essay. Yet our
perception of the reasonableness of anything rests on a sentiment
which is often very delicate and extremely difficult to define. The
mathematicians have succeeded in giving exact expression to some of the
simplest manifestations of this sentiment, but most of the cases we
are called upon to solve in ordinary daily life cannot be dealt with
by their analysis. It is the great strength of science that it builds
wholly upon this sentiment. We are not called upon to “transcend”
reason by faith; we are asked to believe nothing that sins against
our sense of probability. It is admitted, of course, that there are
scientific theories that do not sound reasonable on a first hearing;
indeed, they sometimes outrage common sense, and every scientific
engineer knows the difficulty of persuading the “practical” man that
the obvious thing is not always the right thing. Nevertheless, it is
claimed for science that, on the evidence, its conclusions are the
most reasonable ones even when they are wrong. The sense of what is
reasonable depends upon the evidence, but the word “evidence” must
often be taken to include a great deal of which the mind is not fully
conscious. It was at one time thought quite reasonable that the
heavenly bodies should move in circles round the earth. The belief was
not wholly a matter of astronomical evidence. It was considered that
there was something peculiarly and inherently reasonable in circular
motion for heavenly bodies. We can see that this expectation was
connected with the æsthetic properties of the circle, and we now think
that expectations based on such considerations are, in astronomical
matters, illegitimate. Something akin to such considerations still
plays a part in science, however, although in a less obvious form.
Other things being equal, a simple explanation of natural phenomena is
preferred to a more complicated one, although, as Fresnel remarked,
there is no _a priori_ reason to suppose that Nature takes any
account of analytical difficulties. The history of the Copernican
theory of the solar system is instructive from this point of view. The
notion that the Earth and other planets went round the sun immediately
made a number of puzzling things clear. It seemed, on the whole, a very
reasonable notion. It was attended, however, by one great difficulty.
If, at the end of six months, the earth were really at opposite ends
of a long line, it should follow that the stars, viewed from these
two points, should seem to shift their relative positions in the sky,
just as the trees in a wood seem to change their relative positions as
we pass them in a train. Tycho Brahe, one of the greatest astronomers
who ever lived, was so impressed by the fact that this expected change
does not occur, that he could not accept the Copernican theory as it
stood. He invented a curious hybrid theory of his own, according to
which, while the other planets went round the sun, they, together with
the sun, revolved round the earth. He does not seem to have made many
converts to this view; it somehow offends one’s sense of probability.
The Copernican hypothesis persisted, in spite of the difficulty we have
mentioned, but not without causing considerable mental discomfort. When
Horrebow at last thought that he had obtained evidence of the apparent
annual motion of the stars he published his discovery under the title
_Copernicus Triumphans_. It was found, however, that the supposed
differences were caused by temperature changes affecting the observer’s
clock, and the old difficulty persisted. It might be thought that the
correct solution was obvious; one had only to assume that the stars
are so far away that, with such instruments as were then used, their
apparent motion is imperceptible. We now know that this solution is
the right solution, but in the eighteenth century it did not appear
a reasonable solution. It was felt that if the stars were really at
such immense distances as this hypothesis required, then Nature showed
a grave lack of economy in space. Such enormous stellar distances
pointed, so far as these astronomers could see, to a most unreasonable
waste of space. No farmer would behave in such a fashion, and although
the eighteenth-century astronomers would have denied that they viewed
the universe as a gigantic farm, yet this delicate and elusive notion
of what is reasonable was, in this case, greatly influenced by farming
considerations. It is not possible to form reasonable expectations
except on the basis of experience, and sometimes the most irrelevant
considerations play a part in our estimate.
As instruments improved, however, the expected motion was observed,
and the distances of some stars calculated. They proved to be
enormous; the great waste of space does occur. God is not a farmer.
This being established, one could approach the general problem of
stellar distribution free from certain prepossessions. One’s sense
of the reasonable acquired a different orientation, as it were. But
it still remains reasonable to suppose that the brighter stars are,
on the whole, nearer to us than the fainter stars. This assumption
must, however, be employed with caution. If a list be formed of
the nearest stars from amongst those whose distances have actually
been determined, we reach some rather unexpected results. Knowing
the apparent magnitudes of these stars, and their distances, we can
calculate their actual luminosity compared with the sun as a standard.
The apparent magnitudes range from Sirius, which is considerably
brighter than a first-magnitude star, to stars of more than the ninth
magnitude, that is, to stars quite invisible to the naked eye. Some
of the nearest stars may be fainter yet, for determinations of the
distances of stars fainter than magnitude 9.5 are lacking. The actual
luminosities of these stars range from forty-eight times that of the
sun to four-thousandths that of the sun. The actual distribution of
the nearer stars is not at all that which would appear reasonable
if we were guided by considerations of apparent brightness. Some of
the very brightest stars, such as Canopus, must be at inconceivable
distances, and their actual brightness must be thousands of times,
perhaps very many thousands of times, that of the sun. Here again our
unsophisticated notion of what is reasonable is apt to be more of a
hindrance than a help. Excellent as a guide through not too unfamiliar
country, it is apt to lead us sadly astray when we advance into
completely unknown territory. Nevertheless, it is the only guide we
have.