Aspects of science

By J. W. N. Sullivan

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Title: Aspects of science

Author: J. W. N. Sullivan

Release date: October 5, 2025 [eBook #76989]

Language: English

Original publication: London: Richard Cobden-Sanderson, 1923

Credits: Tim Lindell, Laura Natal and the Online Distributed Proofreading Team at https://www.pgdp.net (This file was produced from images generously made available by The Internet Archive/Canadian Libraries)

*** START OF THE PROJECT GUTENBERG EBOOK ASPECTS OF SCIENCE ***

ASPECTS OF SCIENCE

_By_ J. W. N. SULLIVAN

LONDON
RICHARD COBDEN-SANDERSON
17 THAVIES INN

PREFACE

The papers which make up this volume have been selected because,
although they deal with different aspects of various scientific ideas,
yet they do illustrate, more or less, one point of view. That point
of view may be described, perhaps as æsthetic, but rather better as
humanistic. Scientific ideas have a history; they arose to satisfy
certain human needs; to see them in their context is to see them as
part of the general intellectual and emotional life of man. What they
exist to do they do better than does anything else, and the needs they
satisfy are not peculiar to scientific specialists. These papers try
to show one or two of the many reasons why, for people who are not
specialists as well as for those who are, science may be interesting.

J. W. N. SULLIVAN.

CONTENTS

PAGE

THE INTEREST OF SCIENCE 9

A PHYSICIST ON PHYSICS 23

SCIENCE AND CULTURE 36

JAMES CLERK MAXWELL 41

ASSUMPTIONS 49

ON LEARNING SCIENCE 72

THE ENTENTE CORDIALE 77

POPULAR SCIENCE 82

PATIENT PLODDERS 89

THE AMATEUR ASTRONOMER 95

SCIENTIFIC CITIZENS 100

THE SCEPTIC AND THE SPIRITS 105

THE SCIENTIFIC MIND 112

THE SCIENTIFIC CONTRIBUTION 116

THEORIES AND PERSONALITIES 122

THE IDEAL SCIENTIFIC MAN 128

PARALLEL STRAIGHT LINES 133

THE NEW SCIENTIFIC HORIZON 139

THE HOPE OF SCIENCE 145

THE RETURN OF MYSTERY 151

MATHEMATICS AND MUSIC 159

HUMAN TESTIMONY 177

THE INTEREST OF SCIENCE

The conception of science as a body of thought embracing the whole
of our rational convictions about reality has hardly yet been
generally reached. Man is still so far from being a rational animal
that the application of rational methods of inquiry to all branches
of his experience is still instinctively resisted--as if reason
were an alien and hostile intruder. Beliefs which are held with
passion, being the expression of instinctive preferences, are felt
not to belong to the “sphere” of science. On all questions where
his passions are strongly engaged, man prizes certitude and fears
knowledge. Dispassionate inquiry is welcomed only when the result is
indifferent. Nearly every great scientific generalisation has incurred
the _odium theologicum_--which is not the exclusive possession
of theologians--from the Copernican hypothesis to the theory of herd
instinct. That science, although continually wounding men, should
nevertheless have progressed, is evidence that it serves impulses
deeply rooted in man’s nature. The great scientific innovator, like
the great altruist, is treated with ignominy by the society whose
deepest instincts he lives to serve.

Science, the child of irrational impulse, has inherited something
of the parental character. Its history reveals it as purblind and
fumbling, with no clear vision of its aim, no premonition of its
imperial state. Unlike philosophy, it did not aspire to universal
dominion. It was content to investigate the particular instance,
and did not reject a certain incoherence in explanation rather than
accept a generalisation which did not spring from its own ground. It
refused foreign assistance, but kept its independence. That scientific
men did not always understand that science must, from its nature, be
autonomous, is evident from the history of every particular science.
Even as late as Descartes it was considered quite natural to deduce
phenomena from metaphysical principles; and an admixture of mythical
elements is not entirely absent from some branches of science, even at
the present day. Science has not yet reached full consciousness of its
proper ground and aims.

The values served by science, in terms of which its claim to
consideration is to be judged, have become more numerous as science has
developed. The earliest scientific researches were concerned wholly
with the particular event, with, at most, the vaguest inkling of large
perspectives. The savage who discovers that the branch lying partly
in the stream is not really bent, is prompted by the same localised
and detached curiosity which led to most of the early scientific
discoveries. Interest in the oddity of an event is undoubtedly the
root of scientific observations. The more closely the events concern
us, the more pregnant they may be with possible pleasure or pain,
the greater the degree of abstraction necessary to see them in their
relations. Human beings remain miracles to us long after we have
learned to predict the motion of a planet. Psychology is the latest
of the sciences, not so much because of the intrinsic difficulty of
its subject-matter as because our interest in the subject-matter is so
vehement that it is almost impossible to be indifferent to the results.
An intelligent fish would probably have found most of the painfully won
results of human psychology fairly obvious.

From the accumulation of facts and the attempt to see them in
relation springs the scientific theory. With the construction of
theories science enters on a new phase in its development, and
serves a different set of human values. Its facts, the products
of local curiosities, now take on an order, and serve the desire
for comprehension. The apparently dissimilar becomes related; law
supervenes on chaos. The desire for knowledge becomes transformed into
the desire for _significant_ knowledge--significant primarily
for contemplation, and secondarily for practice. It is the scientific
theory alone that gives to science its true being and makes it worthy
of a deep concern. The desire for comprehension is deeply rooted in
human nature. Religious myths and philosophical systems arose in
obedience to this impulse. Science also exists to satisfy this craving,
and the terms on which it does so are altogether to its advantage. The
fact that it is an extension of common knowledge, and infers nothing
that cannot be verified, differentiates it from myth, and is the secret
of the grave and serious satisfaction it affords. Those accustomed
to this homely, invigorating atmosphere find the rarer air of much
traditional philosophy quite insupportable. A certain indifference to
other methods of describing reality becomes more evident as the years
advance and the domain of science becomes more and more extended.
Peaceful penetration takes the place of open warfare, and in face of
rival systems men of science feel less inclined to disprove what they
feel more at liberty to ignore.

Science still falls far short of affording complete comprehension or
of providing so finished a picture of reality that we feel no need
of other speculations. The different sciences do not yet conspire to
form one single coherent body of truth. The interstices between them
are still sufficiently large to admit foreign interpretations. But the
impulse to comprehension, which created science, will be justified by
it: we may have so much faith. Even that moiety of mankind who care for
little beyond pure immediacy will find that science alone can give
them much of what they desire. Scientific theories possess a value
even to those who are strangers to the pleasures of contemplation, for
science has powerful reactions in the world of practice. To those who
have lost their birthright it can offer a mess of pottage.

Besides serving curiosity, comprehension and practice, science offers
richly satisfying objects to the æsthetic impulse. The language of
æsthetics is not far to seek in the writings of men of science, and
were it not that the word arouses such a proprietary fury, we should
agree, reviewing their motives and the kind of their satisfactions,
to call them artists. The matter of the highest art, like that of
true science, is reality, and the measure in which science falls
short as art is the measure in which it is incomplete as science. All
good philosophy, art or science partakes of the nature of the other
two. When these three are regarded as one, each will have reached its
apotheosis.

It is unfortunately true that as a science advances it grows more
complex. Not only does its language depart more and more from ordinary
speech by the accumulation of technical terms, but the terms in current
use at any time are defined in terms of others which are defined in
terms of others--something after the manner of the description of
the house that Jack built. The most obvious case of this Chinese box
kind of language is, of course, that of mathematics. A mathematical
theorem occupying one line of type might very well occupy a volume if
written out in ordinary prose in which no terms were used which were
not common property. For this reason modern mathematical discoveries,
except in very special instances, cannot be made intelligible except
to mathematicians. To learn the language of a highly developed science
like mathematics takes about as long as to learn Chinese, but the
task of translation into English is very much harder. For this reason
mathematicians cannot hope for intelligent popular recognition; they
must be content to be regarded either as vaguely impressive figures
or else as mild lunatics busied with incomprehensible and probably
trifling abstractions. Compared with writers, musicians or painters,
they are, for social purposes, mental outlaws. It is apparent, however,
that mathematics was not always so remote. It was possible for Voltaire
to take an interest which was, at any rate, enthusiastic, in the work
of Newton. This was doubtless due, in some degree, to the obviously
dramatic quality of Newton’s discoveries, but it was also due to the
fact that his discoveries could be expressed in comparatively simple
language. Again, physics and chemistry at that time, and for some years
later, were not only intelligible to men without special training, but
such men could actually make valuable discoveries in these sciences.
As these sciences progressed their language became more and more
forbidding and their fundamental notions more and more abstract. Men
without special training, but with scientific curiosity, turned their
attention to the biological sciences. They collected birds’ eggs and
butterflies; they bought microscopes and wrote little papers on the
sea-shells they discovered in a morning’s walk. But biology has now
developed a technical language, and the days of the untrained observer
are almost over. The one science which is still, to some extent,
accessible to these amiable people is psychology. It is growing more
technical, it is true, but the majority of the books dealing with
psychology may still be read almost as easily as a treatise on the
history of the Balkans. And the “psychological” novelist can still
regard himself as being, from one point of view, a scientific man.
Psycho-analysis is, as yet, a favourite subject of discussion in
advanced drawing-rooms where discussions of the principle of relativity
are comparatively rare.

The divorce between science and the general intellectual world is
unfortunate, but inevitable. It is unfortunate both for the scientific
man and for the general _intelligentsia_. The scientific man,
mentally companionless except for the little circle of his immediate
co-workers, becomes less complete as a human being; he fails as a
humanist. He too often accepts his outlawed position and turns his
special interests into his exclusive interests, as if, through some
inverted generosity, he refused to take where he could not give. He
may grow to ignore the other intellectual activities of his time,
as Darwin, to his distress, found he had grown to ignore poetry,
or he may actually become intolerant of such activities and so add
contempt to the ignorance with which his preoccupations are regarded
by the outside world. For the outside world, also, this divorce is
unfortunate. For science, in its own way, satisfies just the same
impulses as do other intellectual interests, and some of them it
satisfies more completely and in a richer way. A great waste of mental
energy and much inconclusive discussion would be avoided were certain
scientific results more generally known, and, more particularly, were
the advantages of the scientific method more widely recognised and the
method itself more extensively practised. An air of superiority is
often noticed in the references of scientific men to certain current
discussions. It is a fault of manner, but one difficult to avoid.
“Inside” information usually has this effect on the possessor, and
when it is information that cannot be shared the attitude is apt to
become chronic. Both sides, then, are the poorer for their lack of
intercourse. But this state of affairs seems to be inevitable. The
claims of the Latin and Greek literatures to attention, whether they
are justified or not, have led to the study of these languages being
imposed on perhaps the majority of the people in this country who are
predominantly interested in intellectual affairs. It is a training
which consumes several years: is a training in the sciences to be
added? This is manifestly impossible. Even if our whole educational
system were radically altered, only those sciences, such as biology and
psychology, which may be understood with comparatively little training,
could ever become objects of common knowledge. But sciences where, in
addition to a severe and prolonged discipline, special aptitude is
necessary, must always be the property of the few. As, every year,
all the sciences grow more complex, so the difficulty of obtaining an
adequate knowledge of them increases. A dead language may be learnt
once for all, but the language of a science must be learnt afresh every
few years. The popular article of Huxley’s day, the link between the
man of science and the general public, is now the link between the more
and less advanced students of the same science. A so-called “popular”
account of Relativity Theory, for instance, is like an annotated
edition of Pindar; a very fair knowledge of the language is assumed
beforehand. It might be thought that the process of reduction, as it
were, could be continued, until finally an account was prepared where
no technical terms were used. But such an account would be, at best,
like a translation of Greek poetry; the essential quality would be
gone. Such translations have, of course, their uses, but the attraction
of science for the scientific man, like the attraction of a poem for
the poet, is not to be communicated in this way. In art the separation
of matter and form is not really possible, and the same is true of the
sciences.

III

In their apologias, which have now become so common, men of science
never weary of pointing out that it is the method of science which
is really worthy of adoption by philosophers and that the results of
science are merely provisional. The philosopher who bases his system
upon the results reached at any given time by any given science has
ensured the ultimate downfall of his system. He is sometimes told that
the adoption of scientific methods, on the other hand, will enable him
to make sure progress. At first sight there seems to be a contradiction
here, for if the scientific method is infallible why are the results
reached by it provisional? To judge from the history of science, the
scientific method is excellent as a means of obtaining plausible
conclusions which are always wrong, but hardly as a means of reaching
the truth. The contradiction is only apparent, however, for it will
be found that there is a part of every discarded hypothesis which is
incorporated in the new theory. The discarded hypothesis proves to
have been too general; the scientific man made a mistake of the same
kind as the philosopher who uses the hypothesis as the basis of a
general system. It is now known, for instance, that Newton’s theory of
gravitation is very probably not exactly true; in most cases, however,
it remains very nearly true, and there are large regions of dynamical
astronomy which are unaffected by the alteration. The Newtonian laws
of motion, again, are not sufficient to describe the motion of bodies
moving with very large velocities, but they are very nearly true
for all ordinary velocities. That the theories which have taken the
place of those abandoned are exactly true is very improbable; they
are, however, nearer the truth. We may say, therefore, that while the
scientific method may, quite possibly, never enable us to reach the
exact truth, successive applications of it enable us to approximate
nearer and nearer to the exact truth. In this lies its chief difference
from the methods usually adopted in philosophy, which aim at obtaining,
at one blow, theories which shall never need revision. It is for this
reason that philosophy does not progress.

In what, then, does the scientific method consist? It would be
difficult to give a precise definition; it has, however, two main
characteristics, the choice of facts and the treatment of facts. It
does not seem to be generally recognised that scientific men do choose
their facts; there are many people who suppose that all facts are of
equal interest to scientific men, and that information respecting the
number of nightingales heard in Hertfordshire during a certain month,
for instance, is a contribution to scientific knowledge. It should
be obvious, however, that a mere random collection of facts is very
unlikely to aid either practice or theory. The aim of science is not to
form catalogues, but to form theories describing phenomena, and to this
end some facts are pertinent and a very great number are not. All men,
faced with a problem of any kind, choose such facts for examination
as they consider relevant. Sherlock Holmes often bewildered Watson by
pondering over facts that Watson considered irrelevant, but Watson’s
surprise was a proof that even he had a standard of relevance. The
history of any science shows that the facts first chosen were those
most likely to be repeated. Such facts obviously lead to statements
which have a greater or less degree of generality. That an unsupported
stone falls to the ground is a fact of this kind. The facts chosen
by the man of science are those that permit generalisation. For this
reason they usually differ entirely from the facts of interest to
historians. After selecting, in accordance with this principle, the
facts which are to be examined, the next step consists in establishing
relations between sets of these facts. The precise expression of these
relations is called a law of nature, to use a somewhat old-fashioned
terminology. If now all the relations between certain sets of facts
can be expressed in one general statement, that general statement is
called a scientific theory. The ultimate aim of the scientific method
is to create scientific theories. The scientific theory, however,
usually introduces an element which has not been or cannot be directly
observed, and also, as we have seen, usually proves to have been too
hasty a generalisation. Its function is to co-ordinate known phenomena
and to predict hitherto unobserved phenomena. The extent to which it
does this is the measure of its success as a scientific theory, and,
since the primary object of the scientific theory is to express the
harmonies which are found to exist in nature, we see at once that these
theories must have an æsthetic value. The measure of the success of a
scientific theory is, in fact, a measure of its æsthetic value, since
it is a measure of the extent to which it has introduced harmony in
what was before chaos.

It is in its æsthetic value that the justification of the scientific
theory is to be found, and with it the justification of the scientific
method. Since facts without laws would be of no interest, and laws
without theories would have, at most, a practical utility, we see that
the motives which guide the scientific man are, from the beginning,
manifestations of the æsthetic impulse. The reason why certain facts
and not others interest the scientific man, the reason why he makes a
choice, is because truth without beauty is as uninteresting to him as
to any other artist. In the words of Poincaré: “Le savant n’étudie pas
la nature parce que cela est utile; il l’étudie parce qu’il y prend
plaisir, et il y prend plaisir parce qu’elle est belle. Si la nature
n’était pas belle, elle ne vaudrait pas la peine d’être connue, la vie
ne vaudrait pas la peine d’être vécue.”

A PHYSICIST ON PHYSICS

The well-meant and industrious efforts of professional metaphysicians
to explain to men of science in what sense science is true, in what
sense it has meaning and in what its value really consists, practically
all suffer from the defect that men of science do not recognise the
subject of investigation as being science at all. It is almost true to
say that the professional philosopher is only convincing when he is
talking about the Absolute, for that is a subject with which nobody
else is concerned; but when he devotes his attention to subjects with
which other people are familiar, it often becomes possible to put
the book down before finishing it. Thus treatises on æsthetics are
usually convincing to everybody but poets, painters and musicians,
and philosophical writings on science are probably in great demand
amongst classical scholars. Nevertheless, since philosophising on these
subjects is an agreeable mental exercise, we find that some artists
are now engaged in developing an æsthetic for themselves, and some
men of science are engaged in trying to find out what science is.
In each case the work consists chiefly in making explicit processes
which are instinctive. This fact is of the greatest importance, for,
if the instinctive equipment be lacking, the results will inevitably
be unsatisfactory. There are treatises on æsthetics, for instance,
whose chief effect on the poet is to make him doubt whether the author
could tell a good poem from a bad one; this is an absolutely fatal
objection. If poets cannot recognise what they call poetry as being
the subject of the discussion, then, as a discussion of poetry, that
discussion is worthless. Practitioners, whether artists or men of
science, seldom have the inclination to uncover and dissect what is
to them an instinctive and delightful process; but it is quite easy
for them to see (or, rather, to feel) that a suggested explanation
is unsatisfactory, although they may find it wholly impossible to
give reasons for their dissatisfaction. Nevertheless, when this
dissatisfaction is due to an inability to recognise the subject-matter,
the explanation must be condemned. It is perfectly possible, for
instance, that psycho-analysis, by introducing a mother-complex, an
inferiority-complex, and two or three more, might “explain” the Ode to
a Nightingale. But if this explanation left out everything which made
poets regard that composition as a poem, it would not be a satisfactory
explanation.

We have treated this point at some length because Dr. Campbell, in
a recent valuable book on the Elements of Physics, insists that the
physics he is talking about is that of physicists. He has endeavoured
to supply a criticism of the terms used in Physics, to find what is
meant by a Law, by a Theory, what a physicist means when he says a
proposition is “true,” or that something “exists,” or that a theory has
“meaning.” Mr. Campbell is perfectly aware that all these subjects have
already been treated by the professional metaphysician, but he claims,
and we have no doubt that his claim is just, that he is speaking not
only for himself but for the great majority of scientific men when
he says that in these discussions he not only does not recognise
the subject-matter, but he does not recognise any subject-matter.
Such words as “reality” and “existence,” as they are employed by
metaphysicians, he finds productive of nothing but great discomfort and
intense mental confusion. As he unhesitatingly rejects the hypothesis
that metaphysicians are imbeciles, he thinks this confusion can be due
only to the fact that these words are used by metaphysicians in senses
quite different from those they bear to men of science. He has not
been able to explain precisely in what the difference consists, since
he has not been able to discover what meanings metaphysicians attach
to these words. Accordingly he has confined himself to explaining the
meanings these words have in science. The result is a subtle, fairly
clear, and frequently entertaining piece of analysis. He acknowledges
that his two masters have been Poincaré and Bertrand Russell, and he
shows complete familiarity with other writers of the kind. But part
of his reason for publishing the book, he tells us, is that even the
mathematical philosophers occasionally misrepresent science as the
experimental physicist knows it. That they are mathematicians and
not physicists is a little too evident in some of their conclusions.
Thus Mach’s idea that the object of science is to economise thought
is only plausible, he thinks, to a mathematician; and a fundamental
proposition that Russell and Whitehead find quite necessary to thought
Mr. Campbell does not find necessary at all. He thinks it quite likely,
also, that scientific thinking is illogical, but not therefore invalid.
The point of view, in fact, is that there are different kinds of minds
with different needs and different satisfactions, and Mr. Campbell
claims that physicists, for example, belong to a certain species and
that the science of physics is something which exists in the minds of
physicists. Therefore this book, as he insists, is not only written
by a physicist, but it is written for physicists. He is confident
that what he has to say will be found an explicit statement of their
instinctive processes, and he thinks the highest compliment that could
be paid to his book would be for physicists to say they knew it all
before.

Now it is true that nobody but a physicist could have written this
book and that nobody ignorant of physics could understand it. It may
also be true that none but a practising physicist could understand it
with the intimacy that Mr. Campbell desires. But any reader who is
not, in Mr. Campbell’s sense, half-educated (the other half consists
of science--preferably physics) will find the book not only valuable,
but delightful. The slight touch of _brusquerie_ that the
metaphysician or the equally unfortunate “half-educated” person might
attribute to Mr. Campbell from the above exposition is not in the
least that of the horny-handed son of toil, but is the half-humorous
impatience of a subtle and vigorous thinker who is by no means naïve.
There is no reason why the audience that reads Poincaré’s popular four
volumes should not also read this book, and there are many reasons why
it should. Many of the questions raised there are here developed more
fully; most of the questions, in fact, raised by the speculations of
such men as Poincaré, Russell, Mach, etc., in so far as they affect
science, are here given systematic treatment. We hope to devote a
future article to the exposition of some of Mr. Campbell’s more
interesting results; we are concerned here to indicate the nature and
scope of the book.

The present volume is in two pretty distinct parts, the first part
being concerned with the propositions of science, and the second part
with measurement. These are to be followed by Part III. on Space and
Time, Part IV. on Force, and Part V. on Energy, although, regarding
these parts, Mr. Campbell says: “I have not the remotest idea when,
if ever, they will be published.” Without anticipating a future
discussion of the more technical parts of Mr. Campbell’s work, we may
refer here, because of the general interest taken in the subject, to
the explanation he gives of the fact that while the outside world
resolutely marks off Science from Art, yet this distinction is not at
all clear to scientific men. It is difficult, for example, in studying
the life of a great man of science, to resist the conclusion that his
incentives and satisfactions are indistinguishable from those of a
great artist. Yet it seems to be undoubtedly true that a work of Art
is something personal, whereas Science is obviously impersonal. Mr.
Campbell asks us to distinguish between truth and meaning. The truth
of science is something impersonal, but its meaning is personal. The
achievement of Newton and Maxwell is as personal as that of Giotto,
Shakespeare and Bach. Their dreams were not less personal, nor less
delightful, and it is nothing to their discredit that their dreams also
came true. And the fact that the meaning of a scientific theory is
something that exists, perhaps, only for men of science, has an obvious
parallel in Art. The following passage from Mr. Campbell’s book is one
to which every man of science would give instant assent:

Nobody who has any portion of the scientific spirit can fail to
remember times when he has thrilled to a new discovery as if it were
his own. He has greeted a new theory with the passionate exclamation,
“It must be true!” He has felt that its eternal value is beyond
all reasoning, that it is to be defended, if need be, not by the
cold-blooded methods of the laboratory or the soulless processes of
formal logic, but, like the honour of a friend, by simple affirmation
and eloquent appeal. The mood will and should pass; the impersonal
enquiry must be made before the new ideas can be admitted to our
complete confidence. But in that one moment we have known the real
meaning of science, we have experienced its highest value; unless such
knowledge and such experience were possible, science would be without
meaning and therefore without truth.

What kind of Physics would be developed by a man alone on an island?
We are assuming, of course, that this favourite figure of speculative
writers enjoys the properties usually attributed to him; he is
remarkably intelligent, and can create by a word any scientific
apparatus he requires. The point is that he has no need to take into
account the judgments of other people. Let us choose an experiment
designed to make clear the consequences of his isolated state.
Suppose our islander, after looking at a red patch, glances at a
white ceiling. He sees a green patch. Now suppose that he heats a
copper wire in the flame of a Bunsen burner. The flame turns green.
Will our islander proceed to construct a physics which shall embrace
both these observations? Before we can answer this question we must
consider why our own physics distinguishes so sharply between them.
In the first place, it may be said that all observers, except the man
who contemplated a patch of red, agree that the colour of the ceiling
is unchanged, whereas, in the case of the copper wire, all observers
agree that the flame has turned green. In the first case, therefore,
we say that there has occurred a change in the observer, and in the
second case a change in the flame. We invoke the criterion of universal
assent. But it can readily be shown that we have not, in fact, invoked
this criterion, for in saying that the flame has turned green, we have
left out the testimony of colour-blind persons. Not everybody would
agree that the flame has turned green, and on what principle are we to
decide between the conflicting opinions of different observers? Mr.
Campbell’s examination of this question appears to take us to the root
of the matter. Universal assent is involved, but also something more,
and it is the something more which will probably enable our islander
to form a physics like our own. Let us first consider the way in which
universal assent is involved in science.

We must obviously leave out judgments of colour; similarly, science
does not now measure electrical quantities in the manner of Cavendish,
by comparing the intensities of electric shocks experienced by the
observer. Science makes a choice of the judgments it shall consider;
it does not even embrace all judgments for which universal assent may
be obtained. The judgments on which science is based, and for which
universal agreement may be obtained, are divided by Mr. Campbell into
three groups: (1) Judgments of simultaneity, consecutiveness and
“betweenness” in time;[1] (2) Judgments of coincidence and betweenness
in space; (3) Judgments of number, such as, The number of the group
A is equal to, greater than or less than, the number of the group
B. Now it is judgments of this kind that are involved in physical
observations: the deflection of a spot of light on a scale, the reading
of a stop-watch, and so on. These judgments are fundamental to science
and are such that universal assent may be obtained for them. Let us
now consider the case of the copper wire in the Bunsen flame. We have
said that not all people will agree that the flame has turned green.
But the light from the Bunsen has other properties than its colour;
it has a measurable refrangibility and a measurable wave-length. The
important point for physics is that all observers, both “normal”
and colour-blind, would agree on these measurements, since they are
connected with the fundamental judgments mentioned above. The fact that
different observers associate these same measurements with different
colours is a fact of no importance for physics; “colour” is not a
notion essential to physics at all; when phrases containing such words
as “red” or “yellow” occur in physics they may always be replaced by
words depending for their meaning solely on fundamental time, space and
number judgments. It is for this reason, then, that science builds on
perfectly sure foundations; its foundations can only be denied by an
imposter, that is, by one whose actions show that he actually believes
what he says he denies. Now, how does this apply to our islander?
We may assume that he can measure refrangibility and wave-length.
He finds that, in these particulars, the light from the ceiling is
unaltered, while the light from the Bunsen flame is altered. But these
observations have no greater support than his colour judgments. On both
occasions the only testimony is his own. But he would notice a great
difference directly he began to establish the laws connecting these
phenomena. The laws derived from the second set of observations would
be much more satisfactory than those derived from the first set. He
would undoubtedly prefer them and would unhesitatingly adopt them. When
it is put in this way, there certainly seems something arbitrary about
the process by which science selects its fundamental judgments. They
are selected because they fall neatly and satisfactorily into laws. Mr.
Campbell further suggests that the laws used in science are selected
from amongst other possible laws because the selected laws fit into
theories, “the form of which is dictated chiefly by preconceived ideas
of what a theory should be.” It may be stated at once that Mr. Campbell
admits the presence of an arbitrary element in science, but it is
precisely his case that this arbitrary element gives to science its
value.

We cannot here summarise his exposition, because it would be
unintelligible except to readers with a scientific training, since Mr.
Campbell has adopted the very sound method of analysing the actual
laws and theories current in physics. We may indicate, however, the
general lines of his investigation. He attempts to analyse the kind of
relation involved in a scientific “law.” It has been generally assumed
by philosophers that this relation is the “causal” relation, but, in
fact, it is very doubtful whether this relation is ever used in the
statement of laws. It is a very special kind of relation, and its
supposed importance to science seems to rest on a confusion between the
psychological process in an observer performing an experiment and the
relation stated to exist between his observations. Thus, in Ohm’s Law,
does the potential difference enter as cause or effect of the current?
The question is sufficient to show that the causal relation is not
concerned. Mr. Campbell admits that he has not succeeded in making a
final analysis of the propositions called laws, but we think that he
has certainly established several points of great value. It is more to
our present purpose, however, that this analysis shows more clearly
how an arbitrary element enters into scientific laws. A law does
not simply relate concepts in a manner consistent with observation;
it would be perfectly possible, for instance, to replace Ohm’s Law,
expressing simple proportionality between current and potential
difference, by a much more complicated expression which should agree
equally well with observation. There are always several laws which will
satisfy the observations; the one that is chosen is chosen for its
simplicity, i.e., because of the mental satisfaction it affords. The
fact that it does fit the observations gives it what Mr. Campbell calls
its “truth,” and the fact that it affords intellectual satisfaction
gives it what he calls its “meaning.”

When we pass from laws to theories we find that the element of
“meaning” becomes much more prominent. Now the truth of a law is
something that rests on universal assent; this is not the case,
however, for the meaning of a law. It may be that the contemplation
of Ohm’s Law gives you no satisfaction whatever; if it satisfies me,
however, then to me it has meaning. It is only necessary, therefore,
that scientific laws should have meaning for scientific men; their
truth, however, is the same for all. When we come to consider theories
we find that, concerning their meaning, there is much more difference
of opinion. This difference, in fact, almost follows national lines,
so that of the two great classes of theories, the “mechanical” and the
“mathematical,” the former is largely a product of British physicists,
while continental physicists prefer the second type. Mr. Campbell
analyses very acutely the differences between the two classes as
well as the elements they have in common. As he says, there may be a
“taste” for certain kinds of theories, as there is a taste for oysters.
The result of this analysis is to show very clearly in what respects
science is impersonal and in what respects personal; it also helps to
make clear what science is. It is true that the impersonal element in
science is the most important, in this sense, that if any law or theory
can be shown not to be true, then, however much meaning it may have,
it must be at once rejected. It is also true that it is the meaning
of laws and theories, particularly theories, which gives them their
value to scientific men. We therefore reach once more the conclusion,
sufficiently familiar, but seldom so satisfactorily prepared, that the
value of science is in the æsthetic satisfactions it affords. In Mr.
Campbell’s words, “Science is the noblest of the arts.”

FOOTNOTES:

[Footnote 1: Assuming, in accordance with the principle of Relativity,
that all observers have the same motion.]

SCIENCE AND CULTURE

The influence of scientific discoveries on that vaguely defined
complex of beliefs and intellectual interests called culture seems, at
first sight, to have something paradoxical about it. There can be no
question that this influence is very widespread, and there can be as
little question that ignorance of scientific discoveries is equally
widespread. If our admittedly cultured classes were submitted to such a
_questionnaire_ as the workers in Sheffield were recently called
upon to answer, we should doubtless find that such questions as Who
was Dante? Who was Plato? would act like holes in a dam; but it is to
be feared that the questions under the heading _Science_ would
evoke the merest trickle of information. And yet many of the questions
in other parts of the _questionnaire_ would be answered very
differently were it not for those scientific discoveries of which the
examinee can give no satisfactory description. The apparent paradox is
resolved by remembering that it is only the broadest generalisations
of science, and only certain aspects of those, which exert a marked
influence on the rest of a man’s beliefs. The varied and highly
complicated studies which make up modern astronomy, for instance,
can be known, in any real sense, to but a few specialists; the one
significant thing, for purposes of general culture, that emerges from
these studies, is that the earth is materially insignificant in the
universe. We need not mind if so much knowledge and no more percolates
through the barriers of a literary education; the damage is done;
the rest of the man’s beliefs begin to be profoundly affected. In
the papers on geology and biology the majority of cultured people
would fail; they would all be amused, however, at the idea that the
earth was formed in 4004 B.C. and that man was a special and
separate creation. Psychological studies have not yet reached, perhaps,
a great and easily understood generalisation, but there is a growing
charity vis-à-vis the “criminal classes” and other moral outcasts. Our
Victorian parents’ hearty condemnation of everybody they disliked is
now just a little more difficult. Such generalisations as we have been
mentioning are important to general culture because of what we may
call their perspective effect. Their bearing on the rest of a man’s
mental furniture is not direct; they put the furniture in a different
setting. A change of residence, if the difference between the two
houses be sufficiently marked, may well lead to a change of habits,
and the furniture which looked quite well in four rooms may seem a
little inadequate in forty. Those writers who declare that there is
no “real” conflict between science and religion, for instance, may be
perfectly good logicians; the point is whether a particular religion
looks adequate in the modern universe of science. It is not a question
of destroying the furniture; it is whether the contents of a bijou
villa adequately furnish Salisbury Plain. The influence of science
on philosophy is similarly indirect. Perhaps there is no philosophy
which does not still find defenders; our objection to many of these
philosophies is not that they are illogical, but that they look so
funny.

When we come to study the influence of science on the arts we see that
there is yet another way in which science modifies culture. Many of the
pleasurable emotions associated with the arts are not unknown to the
student of science. The study of such sciences as astronomy, physics
or biology awakens emotions not readily distinguishable from those
evoked by even the greatest works of art. It is as if the universe with
which science deals was itself a work of art; it is, to an increasing
number of people, the greatest of all works of art. Such students often
acquire a new standard of æsthetic excellence. Darwin’s indifference to
poetry in his later years was probably the result, not of the atrophy
of a faculty, but of its fuller exercise elsewhere. The young William
Thomson, reading at night in the library, and drawing great breaths of
rapture over Lagrange’s _Mécanique Analytique_, was experiencing
emotions probably not very different from those of Swinburne when
reading Shakespeare. Before such satisfactions become accessible to the
ordinary cultured classes more is required than that vague acquaintance
with outstanding generalities to which we have referred. In such a
science as astronomy the mere results are often sufficiently attractive
to rouse pleasurable emotions in the reader, although the actual march
of the investigation by which the results were obtained is often of
equal interest. At the present day both results and the broad lines
of the investigations are in many cases accessible to the ordinary
cultured person, with the result that his intellectual interests are
added to, or at least find a new field for deployment. A greater number
of æsthetic objects people his world, and it may even happen that the
new arrivals affect the estimate in which he held the old. He may
discover an unsuspected futility in some of his earlier occupations; he
may, in fact, change his ideals of culture.

But it is, in truth, impossible to trace precisely the effect on an
individual of a new belief or of a new interest. Psychologists have
made us aware of the fact that the mind is not only immensely complex,
but that the connections between its elements are often of the most
unsuspected character. Destruction of an old belief or the grafting
of a new interest may issue in results as unlike their cause as the
butterfly is unlike the chrysalis. The effect of the impact of science
on the old culture cannot be foreseen; it has, however, already
produced such changes that the culture of the comparatively near future
will probably differ from ours by more than ours differs from that of
Babylon.

JAMES CLERK MAXWELL

The place that will be held by James Clerk Maxwell in the history of
physics is not easy to determine. That it will be a very high place is
obvious, that he will emerge as the greatest of the physicists of the
nineteenth century is probable, but the student of Maxwell must feel
that this kind of ranking is somehow irrelevant, or likely to become
irrelevant, to his peculiar effect. The unique impression produced by
Maxwell’s achievement is not adequately described by being referred to
his “originality.” There are different ways of being original; it is
not a sufficiently penetrating term. A number of Maxwell’s scientific
contemporaries were original men, but one is conscious that they
had more in common with one another than Maxwell had with them. An
exception from this statement is found in W. K. Clifford, who, as has
often been remarked, had a genius curiously akin to Maxwell’s. Both men
were exceptionally _independent_ thinkers, both men resisted the
attraction of the high road; both men, if the term may be permitted,
had a personal and unique angle of approach to the problems of their
time. But this, though true, is not a sufficient description. It is
important that in neither case do we feel their individual quality
to be an eccentricity; their work has a power, and, still more, a
comprehensive serenity, which is never the product of mere oddity--the
oddity, for instance, of a Samuel Butler. If we try to get closer to
this elusive and important characteristic we do not meet with much
success; but we may suggest that the ideas of these men have the
effect of springing from an unusually rich, subtle and comprehensive
_context_. The fundamental ideas of the science of their time were
subtly modified by reception into these minds; they were connected in a
personal and unusual web of implications.

It is doubtless worth noting in this connection that Maxwell, unlike
most of the scientific men of his time, was genuinely interested in
metaphysical speculation. This was not merely another interest of
his; it was, at most, another field of attention; he brought the same
attitude of mind to all the objects with which he was concerned. We
cannot make an exception even in the case of his religious views; to
this man the problems of metaphysics, of physics, of morality, are
almost arbitrary divisions of the one object of his thought. He was
expressing a real difference from himself when he said that some men
seem to have water-tight compartments in their minds. When we study the
kind of homogeneity characteristic of Maxwell’s mental life it is easy
to understand those who call him a mystic. Even as a purely scientific
man, his rational faculty, as evidenced by his mathematical reasoning,
was a distinctly more fallible thing than his intuition. This is not to
say that he was not a fine mathematician, but it is his intuitive grasp
of a physical problem which gives him his high position, and not his
purely mathematical verifications. His mathematics, in fact, was not
always impeccable, as Sir Joseph Larmor points out in the new edition
of _Matter and Motion_. But it is characteristic of Maxwell, that,
even when his proofs were faulty, his results were usually sound. His
own way of confirming a difficult intuition was not to provide a formal
mathematical verification, but to make appeal to easier intuitions--in
fact, to construct mechanical models. He always liked to _see_ the
way things worked. It is important to remember that this desire for a
particular kind of verification was not due to any lack of power to
form abstractions; it was due to something quite different, to a lack
of ease when faced by a purely logical chain of deduction. On Maxwell’s
famous _Treatise on Electricity and Magnetism_, Poincaré comments
that its difficulty resides precisely in its great abstraction. It is
this presentation of his theory to which one has to turn; nevertheless
Maxwell, as if for his private satisfaction, developed some extremely
complicated models which seemed to him to make his theory clearer. It
was doubtless this combination, a great power of abstraction on the one
hand, and a desire for very definite, even unnecessarily definite,
confirmation on the other, which enabled him to be at once extremely
original and remarkably sound.

In his boyhood he was constantly making all kinds of experiments with
common substances, drawing complicated diagrams, constructing solid
geometrical figures, even knitting elaborate pieces of wool-work;
practically all these pursuits were dictated by the same desire, the
desire to see an abstract principle embodied in a concrete instance.
No man was less at the mercy of words. But it was, nevertheless,
the abstract principle with which Maxwell was concerned; he merely
wished to be quite sure that he understood it. His occasional trick of
supplying an unexpectedly simple proof of a difficult theorem is due to
this habit of realisation. Platitudes acquired a wealth of implication
in Maxwell’s hands. During his student life at Cambridge, when he seems
to have been chiefly occupied in making a survey of things in general,
we find the same desire to reduce everything to a few principles; but
the principles must first stand a rigorous examination. Merely vague
unifications provoked his irony, and where no principle could be made
to work, then, in spite of his love for coherent and inclusive systems,
he would admit ignorance. And, in spite of his need for principles,
and the tenacity with which he clung to those that met his need, he
claimed no “absolute” quality for his beliefs. In his own words,
“Nothing is to be _holy ground_ consecrated to Stationary Faith,
whether positive or negative.” And, later, “Again, I assert the Right
of Trespass on any plot of Holy Ground which any man has set apart....”
Such questioning as Maxwell applied to himself was to be applied to
all other men. He was conservative, but not on exterior authority. His
scepticism was, in truth, very profound, and it was always present.
It informs his criticism, which is often extremely penetrating. The
letters he wrote on the death of his friend Pomeroy, shortly after
Maxwell had become a Fellow of Trinity, are very instructive from this
point of view. His distrust of the “rationalisations” that men give of
their beliefs extends to the beliefs themselves. As he says, men “are
ignorant even of their own true faith till something brings it into
action.” This was a deep-rooted conviction with him, and is responsible
for the flavour of irony which is never long absent from his comments
on philosophic matters, indefatigable student as he was. He can direct
this scepticism against himself, as in the entry in his programme of
future study: “4. Metaphysics--Kant’s _Kritik of Pure Reason_
in German, read with a determination to make it agree with Sir W.
Hamilton.” On another occasion he writes to a friend pointing out that,
in reading an author, he had to find out first of all, not what the
author meant, but that it was not what he was convinced must be meant.
A little experience of criticism persuades us that this is, indeed, a
very necessary procedure.

This aspect of Maxwell, as a critic at large, as it were, would
well repay study, and it is unfortunate that our material for it is
contained in a scarcely ideal biography. He differed from the run of
scientific men, whose absorption in one pursuit makes their mental life
unrepresentative; his chief problems are not found in his scientific
writings, and they are the problems of us all. There was nothing
superficial in Maxwell, and he had no easily won conclusions. It is
the path he followed that gives interest to his goal. We should like
to know, for instance, what experiences, what reflections, enabled him
to write: “Long ago I felt like a peasant in a country overrun with
soldiers, and saw nothing but carnage and danger. Since then I have
learned at least that some soldiers in the field die nobly, and that
all are summoned there for a cause.” That Maxwell, either suddenly
or gradually, developed a mystic consciousness of life, is borne
out by many passages of his correspondence. We can attach no other
significance to his description of his “nostrum”: “an abandonment of
wilfulness without extinction of will, but rather by means of a great
development of will, whereby, instead of being consciously free and
really in subjection to unknown laws, it becomes consciously acting by
law, and really free from the interference of unrecognised laws”; and
his letters to his wife, dealing with passages from the Bible, abound
in interpretations which are indubitably mystical. Yet we have no
evidence that he was acquainted with the literature and terminology
of mysticism; he is speaking of personal experiences, not of acquired
doctrines.

The maintenance of a mystical outlook on life, together with a
perfect realisation of the implications of physical science, was
accomplished, in Maxwell’s case, by denying the ordinary conception of
the _direction_ of scientific progress. It is the idea which would
inevitably occur to him, for it is the peculiar merit of his own work
that it was not the result of straightforward progress. He made a new
way of thinking necessary just as, in our own time, Quantum Theory and
Relativity Theory have fundamentally disturbed our most unquestionable
assumptions. The way Maxwell actually approached the problem we have
mentioned was by insisting on what he called, by a mathematical
analogy, the “singular points” of existences, that is, the points where
the equations break down, and he postulated that the more there were
of these singular points the higher the rank of the existence. At a
“singular point” influences which are usually negligible may assume a
dominating importance, and Maxwell saw the science of the future as
being largely concerned with these lapses in continuity--as, in fact,
science since his time has been. In this way he escaped determinism. In
his own words:

If, therefore, those cultivators of physical science from whom the
intelligent public deduce their conception of the physicist, and
whose style is recognized as marking with a scientific stamp the
doctrines they promulgate, are led in the pursuit of the arcana of
science to the study of the singularities and instabilities, rather
than the continuities and stabilities of things, the promotion of
natural knowledge may tend to remove that prejudice in favour of
determinism which seems to arise from assuming that the physical
science of the future is a mere magnified image of that of the past.

This speculation, the problem of evil, and in what sense the individual
may be said to persist in Time, are the kind of questions which
concerned him during the last years of his life. It would be merely
fanciful to mention these things as evidence of that “context” of which
we spoke, but we think it is possible to understand more intimately the
origin of the Electromagnetic Theory of Light if we remember that it
originated in a mind which also constantly entertained these other, and
apparently disconnected, speculations.

ASSUMPTIONS

It has been remarked that man’s senses were given him, not to
philosophise with, but to help him in the struggle for existence;
Boltzmann, the great German physicist, was frankly distrustful of
many of the natural motions of the mind. He could admit that Science,
although often very abstract, had a certain validity, since it issues
in the prediction of events which are accessible to sense perception.
But philosophy, he insisted, was in an altogether different case, and
he thought the chances considerable that its impalpable conclusions
were the merest moonshine. It is a speculation that must have exercised
everyone who has whole-heartedly accepted the evolutionary account of
the rise of intelligence. Why should this instrument be adapted to
other than its original uses? Doubts of this kind, however, are both
too vague and too comprehensive to serve any useful purpose. They
do not tell us in what way and to what extent our intelligence is
untrustworthy; they do not enable us to make one step towards drawing
up an Index of Forbidden Subjects. At the most they enable a man with
a constitutional dislike of philosophic speculations to indulge his
contempt for that occupation with an easy conscience. Nevertheless,
a tincture of this doubt is very wholesome, and more particularly if
it be the result of an acquaintance with the history of human thought
rather than the product of a kind of lazy _a priori_ scepticism.
A student of the history of science, for instance, is inevitably led
to reflect on the curious nature of the barriers to further advance
which the mind itself has set up. It is as if the mind could only take
exercise within some imaginary prisoner’s yard, and that the great
advances were really the result of liberations. These liberations are
only partial; the mythical boundaries are set a little further off, but
it is agreed that the high walls exist.

It is interesting to review the progress of Science from this point of
view, to see it as a gradual secession from unwarrantable assumptions.
The exceedingly cautious, the almost groping character, of the
advance of knowledge, becomes very apparent. And, although such a
survey may lead us to become very conscious of this particular mental
limitation, we are not one whit nearer being enfranchised. It is still
the prerogative of genius to be innocent, to turn surprised eyes on
one of our most arbitrary assumptions, and to say: But that is not
necessary. The history of Astronomy, of course, provides some of the
best examples of mental prison yards. That the planets must move in
circles because the circle is the perfect figure is an assumption now
sufficiently remote from our acquired sense of probability to seem
exceedingly strange. That it was an assumption possessing a high degree
of obviousness is apparent from the fact that even Copernicus did not
question it. The attempt to enter into this assumption, to see it as
obviously reasonable, would be a useful exercise for the historian,
since it involves, very largely, a reconstitution of the mental life
of that age. It acquired its obvious character from the fact that it
_fitted in_; it was the natural companion of a great number of
other equally obvious assumptions; it was not an isolated eccentricity
of the mind. It is for that reason that Copernicus never freed himself
from it, and that Kepler only succeeded after a difficult struggle.
Kepler was required to question not merely an isolated doctrine, but to
escape from a veritable _Zeitgeist_. The Inquisitorial examination
of Galileo, also, was not directed merely to correcting the erroneous
statement of an isolated fact; it was, in truth, a whole system of
thought that stood on trial. It is this double aspect of any given
abandoned assumption that accounts for our unimaginative surprise on
learning that very intelligent men once mistook it for an obvious
truth. We are judging the assumption, not on its own merits, as it
were, but from the standpoint of an alien system of thought.

We can form a juster estimate of the degree of credulity manifested by
the contemporaries of Copernicus by considering assumptions that have
been but recently questioned, or rather, which have only recently been
generally questioned. The assumptions regarding animal psychology form
a vivid example. Such men as Darwin and Romanes found it quite natural
to assume that the emotions and many of the intellectual processes of
which they were conscious in themselves furnished an adequate key to
animal behaviour. It is an assumption which the average educated man
of to-day makes quite readily, although he may not share Aristotle’s
views on the perfection of circles. We now know that there is no reason
whatever to suppose, for example, that the psychology of snails has
the slightest resemblance to the psychology of human beings. We may be
confident that, in a very few years, the assumptions of Darwin and most
other people will appear almost inexplicably gratuitous. It will take
longer, we think, for the Freudian ideas about man himself to become
acclimatised; man will take a long time to learn that in trusting his
immediate awareness of himself he is making a number of unwarrantable
assumptions. The system of thought into which his present assumptions
fit is so profound and extensive that it is impossible, even now, to
picture the thoroughly enfranchised man.

A general acceptance of the Einsteinian ideas of space and time is
easier to predict. The current conceptions of space and time, although
Euclidean when reduced to a logical scheme, are not, in fact, present
as a logical scheme in the mind of the ordinary man. He is sufficiently
vague about his fundamental assumptions to offer no strenuous
resistance to their subtle modification. We think that part of his
general bewilderment about Einstein’s space and time is due to his
bewilderment on thinking about space and time at all. His assumptions
on these questions, whatever those assumptions may be, are not really
part of a general scheme of beliefs. Nothing that greatly concerns him
is incompatible with non-Euclidean geometry, and we confidently expect
that the grandchildren of the ordinary man will as blandly believe they
have swallowed Einstein as the contemporary ordinary man believes he
has swallowed Euclid. For an assumption which is not an integral part
of a general scheme of thought is readily abandoned. It is the lopping
of connections which the mind resists. It is no paradox to say that the
mathematician and philosopher finds it harder to accept Einstein than
does the ordinary man. That is because the mathematician’s acceptance
involves both believing more and disbelieving more.

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.

III

If we contrast ancient with modern scientific theories we find
that the chief distinguishing characteristic of the former is that
they employ principles drawn from other branches of knowledge or
speculation. It would be, perhaps, rash to say that modern science,
in all its branches, is yet completely autonomous; sometimes, for
instance, it seems to make assumptions which are the result of an
uncritical philosophy, but even the grossest of these examples,
compared with many celebrated early scientific theories, shows how
great is the purification that has been effected. The chief error of
the old speculators consisted in imagining that the world is a more
obvious unity than we have now any reason to suppose. Hence they were
always willing to argue by “analogy,” comparing terms between which
we cannot now find the slightest resemblance. The method was not only
illegitimate, but sometimes led to quite unnecessary complexities of
explanation. The Ptolemaic system of astronomy, for instance, conceived
as the theory that the heavenly bodies revolve round the earth, was
a perfectly reasonable and satisfactory theory. It was capable of
explaining all the observed planetary motions, except a few minute
irregularities requiring precise measurements for their detection. Its
proper development required, of course, complete docility in face of
the facts. But in its actual development it was forced to accommodate
itself to quite other considerations. It had to take into account the
venerable principle that, the celestial bodies being obviously sublime,
incorrupt and perfect, their orbits must be perfect and described with
uniform velocities. The only possible perfect orbit was as obviously
a circle. Hence the Ptolemaic theory was loaded with the task of
explaining the observed heavenly motions on two grounds: first, that
the earth was stationary and at the centre of the system, and second,
that the planetary orbits were circular and described with unvarying
velocities. Alternative hypotheses were not only stupid but impious.
The task thus set to the early astronomers was one of considerable
difficulty.

The observed path of a planet, say Mars, or Jupiter, or Saturn, is
by no means simple. If its motion amongst the stars be watched from
night to night it is seen to be moving sometimes from east to west
and sometimes from west to east. Further, in changing its direction
of motion it does not retrace its path amongst the stars. Its actual
observed path exhibits irregular loops, and, more rarely, a twisted
line. It was at once obvious that a circular orbit, traversed with
uniform velocity, would not suffice to explain these appearances.
Nevertheless, the principle must be preserved. The astronomers
overcame this difficulty by a device that strikes one as being almost
disingenuous. They imagined a small circle whose centre traversed the
circumference of the big circle with a constant velocity and round
whose own circumference the planet moved with a constant velocity. By
assigning suitable velocities to these two motions the crude features
of the planet’s actual observed motion could be represented--it would
sometimes be retrograde and sometimes direct. This is ingenious, but it
is questionable whether it preserves the principle. The planet’s motion
is obtained by circular motions, it is true, but it is not itself a
circular motion with reference to the earth as centre. The astronomers
have entered on a slippery path. We view them with the same suspicion
with which we watch a Broad Churchman expounding the Thirty-Nine
Articles. But they had to go further. The theoretical and the observed
motions did not fit well enough. On the little circle it was necessary
to imagine a still smaller circle, and to place the planet on its
circumference. After all, this interpretation of “circular motion” once
admitted, there was no reason why it should not be followed up. But
progress in this direction soon came to a halt. It became evident that
this method would not, by itself, reconcile observation and theory.
The principle had to be strained again, and this time in an almost
indefensible manner. It was declared that the big circle was eccentric
with respect to the earth and that the little circles were eccentric
with respect to their supposed former centres. This assertion must have
been a great strain on the faith of the orthodox believer. He may well
have wondered whether, by this time, the pure doctrine of his fathers
had not been subtly undermined. Circular motion was still preserved, in
a way, it is true, but with so many circles, and their centres all over
the place--this must have appeared something very different from what
he supposed the principle to mean.

The same difficulty was felt by simple minds in modern times, when the
correct explanations of statements in Genesis were worked out by the
theologians. And just as the simple story of the Creation in Genesis
became transformed into an extremely obscure and ambiguous anticipation
of the discoveries of Geology, so the interpretation of circular motion
advanced from complexity to complexity. Immutable principles must
exist, of course--it is part of the glory of man that he should have
been able to discover so many of them--but they sometimes seem more
trouble than they are worth. The old astronomers found that yet again a
more liberal interpretation must be given to the principle of circular
motion. This time it was found that the circles do not all lie in one
plane. Each circle has its own plane, which may be inclined at any
angle to the others. By this time the theorists, whom we might call the
“commentators,” had forged a very powerful method. Circles could be
multiplied; their centres could be placed anywhere; their planes could
be inclined at any angle. The rich content of the principle of circular
motion was now fully revealed. With all these variables to play with a
very close correspondence between theory and observation was effected.

The rise of the “higher criticism” of this system leads to the history
of modern astronomy. It is to be noted, however, that the first higher
critic, like the first higher critics in other departments, was not
wholly emancipated from his early teaching. Copernicus effected the
immense revolution of placing the sun in the centre of the system, but
he did not abandon circular motion. So he had to retain parts of the
epicyclic apparatus. The revolution was first completely effected by
Kepler, but even he conducted his early researches as a semi-believer,
a kind of very Broad Churchman. He made nineteen successive attempts
to explain the motions of Mars by the arrangements of eccentric
and epicyclic motions, and only then did he frankly throw the great
principle of circular motion overboard, and state that the actual paths
of the planets were ellipses. And so, in a few years, a great immutable
principle, a whole system of beliefs, the industry and thought of
generations went for nothing, and now exist merely as an occasional
cold reference in a treatise on Astronomy to the Ptolemaic system as a
“monument of misplaced ingenuity.”

We may divide scientific theories into two classes, which have recently
been distinguished by Einstein as theories of construction and theories
of principle. His own theory of relativity is a theory of principle,
and its attraction resides in its logical perfection. Such theories,
whatever charm they may have for the logician, are not, man being
constituted as he is, felt to be sufficient. A principle which natural
phenomena obey, and which enables equations to be deduced expressing
the relations between phenomena, is, to a few austere souls, all with
which science need concern itself, but the majority of men require, in
addition, something they call an “explanation” of the relations deduced
from the principle. They desire to see events described in terms with
which they are familiar. Thus, a description of the behaviour of the
material universe in terms of the mutual impacts of little billiard
balls would afford genuine satisfaction to the mind, and important
advances have been made in science by the attempt to describe phenomena
in these terms. The assumptions which underlie some such attempts
may seem, to the logician, preposterous, but there is no doubt that
the mind is impelled to make such assumptions. Our familiarity with
the motions of matter in bulk makes it quite natural that we should
endeavour to give, as far as possible, dynamical explanations of
events, although, if we stop to ask ourselves why nature should be
flexible enough to admit of descriptions in such terms, we are at a
loss for an answer.

The history of theories of the æther is particularly instructive from
this point of view, because the irrational nature of the impulse is
here most clearly apparent. The attempt to explain phenomena in terms
of an æther has led to some very remarkable theories of the nature of
matter itself. It has been supposed, for instance, that the ultimate
particles of matter are vortical whirls in the æther, or, again, points
of a very special kind of strain in the æther. Nevertheless, a theory
of the æther is regarded as unsatisfactory which is not couched in
terms of the observed behaviour of ordinary matter as we know it. A
dynamical explanation is always sought after, and a great part of the
scientific effort of the nineteenth century was devoted to describing
the æther as an elastic solid. But men of science were not content
with showing that the laws of dynamics could be applied to the æther;
many of them endeavoured to devise models which should represent, on a
large scale, the actual construction of the æther. It is difficult to
know to what extent their authors supposed these models to correspond
to the reality; it is probably not sufficient, however, to say that
they regarded them merely as furnishing useful tools for subsequent
investigations. The models were usually extremely complicated, for,
from the very beginning, the æther proved somewhat recalcitrant to this
attempt to represent it as an elastic solid. The most obvious objection
to this representation was provided by the observed motions of the
planets. It could be proved that, if there were any resistance to their
motions round the sun, it must be excessively minute, and how was this
to be combined with the hypothesis that they were moving with great
speed through an elastic solid? The answer was found in cobbler’s wax.
Sir George Stokes noticed that cobbler’s wax, although rigid enough to
be capable of elastic vibration, is yet sufficiently plastic to permit
other bodies to pass slowly through it. We have only to imagine that
in the æther these qualities are much exaggerated, and the motion of
the planets presents no difficulty. If no substance like cobbler’s
wax happened to be known it is difficult to know what satisfactory
answer could be returned to the objection. Here we have the first
glimpse of the remarkable combination of qualities with which it was
found necessary to dower the æther. The mathematical examination of
the properties of the æther, undertaken by such men as Navier, Cauchy,
Poisson, Green, was continually leading to queer and unsatisfactory
results, unsatisfactory, that is, in the light of our experience of
the properties of matter. Cauchy, in particular, deduced a number of
remarkable physical properties which were irreconcilable with one
another, although one of his theories, that of the æther considered as
a kind of foam, attracted the attention of Lord Kelvin.

With the rise of Maxwell’s electromagnetic theory, the elastic solid
æther received less attention. Maxwell himself, in his great treatise,
gives no mechanical explanation of his theory; he merely shows that
an infinite number of mechanical explanations are possible. With the
publication of Einstein’s first principle of relativity in 1905,
however, the æther began to disappear; and now, with the generalised
theory of relativity, it has become a mere ghost. There are still
sturdy champions of the æther, and, indeed, it seems a pity to have
to abandon the mechanical explanations it promised. But possibly
the attempt to find dynamical explanations of this kind is doomed
to failure; perhaps, after all, nature is not flexible enough. The
orientation of modern science is in another direction. It is towards
a more abstract class of theories altogether--theories which tell us
nothing about the mechanism of a process, but tell us the principles
the process must obey. Such theories effect a vast unification of
knowledge. They are magnificently comprehensive, and it is possible
that they contain all that we can really know, although men will long
be reluctant to abandon all hope of ever approaching reality with the
intimacy that the theory of the æther seemed to promise.

Whether or not it be true that the proper study of mankind is man, it
is certain that he finds great difficulty in studying anything else.
His first impulse, when he thinks about the universe at large, is to
consider it in reference to himself, and to explain it in terms of his
own actions and desires. In Astronomy, for example, it long seemed
quite reasonable that in the peculiarities of men’s bodies should be
found the system on which the universe is constructed. The arguments
of Galileo’s contemporaries amuse us now, for we have learned modesty,
but the tendency to explain all things in purely human terms, as it
were, is by no means yet extinct, and is still a hindrance to science.
It is even hinted that man’s explanation of himself is not free from
bias; psychologists inform us that a man’s account of his own actions
is not always to be trusted, that the true springs of his conduct
are usually those he would blush to own. But if we are to say that
man’s speculations about the universe show an overwhelming sense of
his own importance we must allow him also a certain generosity. Until
quite recent times he was willing to dower almost anything, animate or
inanimate, with his own attributes. He credited stones with life and
trees with desire, while the whole animal world were his brothers. He
could admire the loving sentiments of the dove and weep for the sorrows
of the crab. A pathetic confidence in man as the type and exemplar
of the universe informed nearly all the early writings on animal
psychology, and Descartes’ theory that animals were automatic roused
a sentimental indignation which has not yet subsided. Nevertheless,
comparatively recent investigations tend to overthrow the natural
assumption that worms and insects are little men inhabiting strange
bodies. The modern biologist refuses to be conscience-stricken when
referred to the industry of the bee or the conjugal perfections of the
dove. It is only recently that he has become so heartless. Darwin,
in a celebrated passage, describes with simple reverence the mutual
affection existing between snails. The intelligence of these little
creatures was also estimated highly by Romanes. Loeb, the great
American biologist, did much to upset this naïve anthropomorphism.
He took some worms who are “always attracted by light,” and showed
that this movement did not testify to a “more light” cry in these
little souls, but was a purely automatic proceeding. The worm places
itself so that both sides of its body are equally illuminated. It is a
mechanical action due to the influence of light on the living matter of
its body. If there are two lights the worm passes between them, thus
securing equal illumination of its two sides.

The crab which, being held by a claw, sheds that claw and hurries to
the nearest rock for shelter, is found to do the same thing after its
eyes or brain have been destroyed. Dr. Georges Bohn, who has made many
experiments to determine how far the actions of the lower animals are
purely mechanical, gives an interesting account of a certain parasitic
worm which attaches itself to the fish called the torpedo. He finds
(1) that if the amount of salt in the water be varied the reactions
of the worm alter; (2) that if light be allowed to play first on one
part and then on another part of the worm, its reactions alter; (3) if
the animal has already taken up its position, attached to the glass,
for instance, and a shadow be passed over the top of the vessel, the
whole body of the worm turns itself into the vertical in such a way
that if the shadow were caused by a passing torpedo, the worm could
attach itself to the fish. If, however, it be already attached to a
torpedo, it does not raise itself at a passing shadow. Here, then, is
an _association_ between the region of the body excited by light
and the part fixed to the fish. It was found, also, that the crab which
abandons its claw only does so when held by a certain part. The action
appears to be purely automatic. If it were dependent in any way on the
crab’s simultaneous visual perceptions, for instance, an associative
phenomon would be established. But experimental tests find no such
correspondence. As the result of numerous experiments of this kind
biologists have become very wary of offering psychical explanations of
the actions of the lower animals. Even when genuine associations are
established one must be careful not to interpret them in terms of human
psychology. In the very description of experiments an unwarrantable
turn may be given to the phenomena by the fact that words of ordinary
language inevitably call up associations which may be out of place in
the discussion. To say that an amœba _learns_ to reject certain
foreign particles in a solution, for instance, is a statement that
requires careful interpretation. How are we to picture an amœba
_learning_ something?

But, indeed, the danger of anthropomorphic interpretations becomes
very obvious when we reflect on the purely physical phenomena which
accompany man’s own emotions. If the James-Lange theory be correct,
it is in terms of these physical phenomena that we must understand
man’s emotions. Now consider the example given in Washburn’s book,
_The Animal Mind_. An angry man has a quickened heartbeat, altered
breathing, a change in muscular tension, and a change in the blood.
Consider a wasp. It has no lungs, but breathes through its tracheæ;
the circulation of its blood is fundamentally different from that in
man; all its muscles are attached internally because its skeleton is
everywhere external. What, then, is an “angry” wasp? It seems clear
that if a man is to study anything but man he must forget himself as
far as possible.

ON LEARNING SCIENCE

It is a well-known fact that a really intelligent child finds great
difficulty in believing that the earth is round. Stupid children,
on the other hand, believe anything they are told. The difficulty
experienced by the first child is due to the fact that, in however
elementary a way, it is conscious of the implications of the statement.
The stupid child seems to be unaware that the statement has any
implications; it seems able to accept almost any statement in some
curiously bare, unrelated fashion. Hermann Bahr has an interesting and
amusing story of how profoundly his faith in his father was shaken when
the latter, _à propos_ of a sunset, told the young boy that in
reality it was the earth that turned round and not the sun. Completely
overwhelming objections to this statement rose instantly in young
Hermann’s mind, and, outraged by this insult to his intelligence, he
preserved a hurt and dignified silence that lasted for days.

We notice the same essential difference in schoolboys and university
students, and, in fact, in men of any age. Perhaps the majority
of men, and less certainly of children, have but little sense of
the implications of a statement. The sense of implications does not
necessarily involve the ability to discover the implications--that is
a comparatively rare gift. It acts rather in a negative manner, making
the student restless under a subtly illogical presentation of a case,
or leaving the schoolboy frankly mutinous at the end of a sermon. It
is not a gift which makes a rapid learner, although its absence will
prevent a man from ever knowing a subject properly. It is unfortunate
that education, as practised in this country, does not sufficiently
take into account this very desirable inhibition. The text-book plays
a very large part in contemporary education, and most text-books are
designed for those who can swallow statements at great speed. That
delicate web of doubt, of half-seen alternative explanations, which
comes into the mind of the intelligent student when confronted with
the highly dogmatic statements and somewhat perfunctory “proofs” of
many modern text-books, counts as sheer loss in the examination race.
This is especially true of scientific text-books, which are usually
conceived on an entirely wrong plan, judged from the standpoint of
rational education. Statements which are the final expression of
very difficult and slowly acquired abstractions are presented in all
their nakedness, and followed by a collection of “examples.” The glib
student learns these statements as if he were learning a foreign
language, and soon masters the tricks necessary to apply them. I
have known such students able to solve very difficult problems and
yet entirely unable to meet, in any way, a sceptical attack upon
the fundamental theorem they employ. The fact is that this method
of teaching science is psychologically unnatural, and the knowledge
acquired on this method is largely sham knowledge. While it may not
be true that the child passes through “cultural epochs” in its mental
growth, it is true that it will feel many of the hesitations and
difficulties experienced by the men who first formulated the concepts
now presented to it for its instant acceptance. It is for this reason
that the best method of teaching a science is probably the historic
method. In this way not only are many doubts fairly met instead of
being merely repressed, but the exact _portée_ of a statement and
possible lines of extension are much more clearly seen. The effect of
the modern text-book is to make the intelligent student feel that he is
remarkably unintelligent; the text-book writer is so terribly cocksure.

But if the historic method must be rejected as too lengthy one may
plead for its partial application. Let the text-book give the broad
outlines, and let the student supplement these by reading, wherever
possible, the standard memoirs written by the original discoverers.
In this way he will gain something much more valuable than a more
thorough acquaintance with his subject; he will learn something of the
mental gesture of the true man of science, something very different
from the glittering efficiency of the text-book writer. Consider, for
instance, the following passage from Newton, writing on the theory of
light: He discusses a corpuscular theory, and continues:

But they, that like not this, may suppose light any other corporeal
emanation, or any impulse or motion of any other medium or æthereal
spirit diffused through the main body of æther, or what else they
can imagine proper for this purpose. To avoid dispute, and make this
hypothesis general, let every man here take his fancy; only whatever
light be, I suppose it consists of rays differing from one another in
contingent circumstances, as bigness, form, or vigour.

The subject here becomes alive in a way it never does in the text-book.
It is of the greatest importance that the student should see, not
merely the results, but the avenues of approach. He will gain more
confidence in his own powers and more interest in the subject.

For those people also who, without being students, take an interest in
science, the reading of original memoirs may be recommended. Much of
the science they learn in this way will be wrong, but they will see it
as something thoroughly human and, it may be, as something thoroughly
sympathetic. The text-book has an air of infallibility which is very
repellent, and it is difficult to avoid associating this with the
scientific man. But it is merely a manifestation of the same tendency
that produces stereotyped restaurants. A reading of the old memoirs
shows science as tentative, imaginative, courageous. They show that the
man of science is a humanist.

THE ENTENTE CORDIALE

Those who are interested in current “serious” literature, and more
particularly that branch of it which deals in a speculative way
with those vague but impressive problems which have always haunted
men, the existence of God, the “meaning” of the Universe and so on,
cannot have failed to notice the unaccustomed prestige now enjoyed by
science. The supposed contributions of science to these discussions
are now listened to with a gravity and politeness, with a kind of
serious hush, which was formerly reserved for quotations from Plato
and Aristotle. Compared with the crude materialists of Huxley’s day,
it is evident that the modern man of science has greatly improved his
social standing; he now frequently talks to the best people, on equal
terms, on such subjects as the Good and the Beautiful. The underbred,
pushing, clamorous self-assertion of the Victorian scientist is a rare
note in these improving conversations between philosophers and men
of science. A man like Haeckel is dismissed as a mere vulgarian; no
one would trouble to refute him; his loud voice and hob-nailed boots
are sufficient condemnation. Even Huxley is felt to be a rather noisy
person; the modern expositor of the relations of Science and Religion
or Science and Philosophy no longer borrows his technique from the Hyde
Park orator; he has adopted rather the insinuating charm of the curate.
There are, of course, survivals on both sides; sweetness and light
are not yet universal; the general atmosphere of mutual forbearance
and respect is still occasionally marred by the harsh note of some
exceptionally fanatic or insensitive partisan. One or two grave lapses
of this kind may be detected amongst the mass of recent books devoted
to cosmical questions. There are still one or two literary men and
philosophers who hint at those dreadful early days of science, before
it went to Oxford, and there are still one or two provincial men of
science, _farouche_, suspicious, who attend a modern cultured
salon carrying their obsolete life-preserver in their pocket. But on
the whole good manners prevail everywhere. It is realised that there is
no reason why anybody should feel awkward at meeting anybody else in a
world which is so indulgent of the difference between a man’s private
and public capacities.

To be on amiable terms with everybody is worth a sacrifice, and in
our relief at escaping from the ferocious savagery of the Victorian
controversialists we may well endure the minor discomforts of a
reconciliation between science, philosophy and religion so effective
as to render indistinguishable the separate persons of this trinity.
The particular advantage of this amalgamation that concerns us here
is the fact that it has brought a new branch of literature into
existence. As is usual in an amalgamation, each member profits by the
custom brought by the others, until finally a composite article is
evolved which is, as it were, simultaneously buff and blue. That is
how we get these very curious and interesting modern works on cosmical
questions--works which seem to result from a close collaboration
between, say, a professor of physics, an archdeacon and a Bond Street
crystal-gazer. A very comprehensive _Weltanschauung_ is thereby
afforded, and doubtless a truly “balanced” mind must result from the
perusal of such works, but we may doubt whether each component, as
it were, is presented in its purity. The advantages of association
are only obtained by a certain loss of individuality. We cannot speak
for the philosophy and religion of these works, but we are impelled
to these reflections by detecting a certain quality which pervades
the scientific part of the expositions. It is, as we have admitted,
a good thing for science that it has been taken up in this way. It
moves in an atmosphere of culture; it finds itself being described in
chapters headed with Greek quotations; it is complimented on its strong
vein of poetry; its peculiarities are explained, inaccurately but
sympathetically, in columns of literary causerie, and the unexpected
but gratifying discovery is made that it by no means lacks the bump of
reverence and proper respect for constituted authority.

Yet, kindly as are the surrounding faces, and pleasant as is the
consciousness that one’s clothes and accent excite no comment, there
is, on the part of many scientific men, a persistent uneasy feeling
that one has gained this position on false pretences. It is these
remarkable modern books to which we have referred which render the
feeling acute. At the same time, it is very difficult to state
precisely the elements of this feeling. We understand, however, that
there are young poets and novelists who experience very much the same
emotion when one of the great “official” men of letters talks about
literature. It appears that such people often get everything subtly
wrong, that their criticism never pierces to the real heart of the
matter, that they make literature at once more pompous and more tame
than it really is. These new cultured expositors of science affect
one very much like that. Their indisputable intelligence and their
wide knowledge do not save them; they lack something--it may be a
mere familiar way of talking--which marks the practitioner; we feel
they touch their subject with padded fingers. We attribute no occult
influence to laboratories, but we think the expositor of science who
is not also a creator is something like that curiously unconvincing
creature--the theoretical sailor who has never been to sea. For
that reason we are uneasy in the presence of these numerous modern
expositions. Such work of the kind as was done in the old days was done
by real men of science in their spare time. They had the competence,
if also something of the crudity, of the workman in the factory who
explains to you how his machine works. The modern writers are so much
more like those frock-coated “attendants” at Exhibitions. One is
oppressed with the same suavity, the same incredible readiness, the
same secret doubt whether he has ever handled a tool in his life....

Such being our estimate of our modern teachers, we may be permitted to
be sceptical concerning the complete satisfactoriness of their account
of the present disposition and relations of science. When they vouch
for the complete respectability and harmlessness of science we wonder
if they are not a little too kind. We have an absurd nervousness, as
in the presence of a reformed burglar. He looks well-dressed enough
and his hands are not impossibly horny; moreover, we are told that
the two very respectable gentlemen with him find him a most charming
companion. We are prejudiced, we suppose; but to our thinking there
is a coarseness about the jaw, an occasional hard glint in the eye,
which would make us reluctant to accept him as, at any rate, a sleeping
companion. We wonder if those two gentlemen, the one reverend and the
other nearly so, ever feel a little apprehensive during the night?

POPULAR SCIENCE

The Victorian Age was unquestionably the great age of physical science.
It was not only the number and quality of the scientific men whose
working lives were covered by this period that were responsible for
this--although no period in history makes a braver show--but it was
due also to the fact that the scientific discoveries of that age were
often of the kind that rouses a vast amount of public attention. The
attention of a cultured minority was no new thing in the history
of science. Newton’s discoveries, largely through the influence of
his indefatigable populariser Voltaire, speedily became, in a more
or less adequate form, the common property of the cultured part of
Europe. But from the time of Newton to that of Davy there was no such
general attention paid to science; England and the Continent largely
lost touch, even technical students working in comparative isolation,
so that the great French advances in Newtonian philosophy were not
appreciated for several years in England, and the cultured public in
England itself no longer considered the intelligent observation of
scientific progress to be one of its chief duties. It never did regain
this outlook; science, becoming increasingly technical, became more and
more completely the affair of a small and specialised class, until, by
the middle of the nineteenth century, it was the most dissociated of
intellectual activities. The great recrudescence of general interest
in science was brought about by the discovery that this dissociation
was merely a consequence of lack of attention, and that, in fact,
scientific discovery was not unconnected with the major interests of
mankind.

The publication in 1859 of Darwin’s _Origin of Species_ persuaded
the men of that time, rightly or wrongly, that science and religion
were very intimately connected, and science, at one blow, obtained
a degree of public attention without precedent in its history. The
interest thus evoked was not always very intelligent, but it was
intense and widely diffused; it extended to other branches of science,
influenced the educational system of the country and gave rise to an
enormous extension of “popular” science lectures and articles. This
popular interest was of a different kind from the leisurely interest
previously shown by the cultured classes. The latter was, indeed, much
more genuinely an interest in science for its own sake; the former
had a different emotional basis and was merely the diversion of an
interest in religious or social questions. There is a controversial
air about nearly all the popular scientific writings of that time; the
scientific man, like his audience, was fully aware that he was talking
about a good deal more than the ostensible subject of discussion.
Science, the creature of the least popular of man’s activities,
patient and unprejudiced ratiocination, became associated with violent
emotions. With Biology and Geology this association was inevitable and
immediate; their subject-matter happened to be that of the first few
chapters of Genesis. But the more exact sciences, when public attention
turned their way, could offer no such excitements. They seem to have
compromised by specialising on “marvels.” The “Marvels of Science”
became a familiar heading, and the unsophisticated public were stunned
by figures: the distances of the stars, the number of molecules in
a cubic centimetre of water, the weight, in tons, of the earth, the
incredible minuteness of light-waves, and so on, the whole object of
such discourses being, as Maxwell unkindly put it, to prevent the
audience realising that intellectual exhaustion had set in until the
hour had elapsed.

We readily admit that popular science of a very different kind was
also provided. Faraday, Kelvin, Huxley, Tyndall, Maxwell himself, did
their best to make the lay public acquainted with scientific methods
as well as results, to present their results as part of a coherent
theory instead of as items in catalogue of marvels. But it is the
marvel-mongers who have proved most tenacious of life, so that
“popular” science has now become a term of contempt, and any statement
whatever, provided it has the right marvellous flavour, may be printed
in our newspapers as scientific information. In America such marvellous
statements, not only inaccurate but meaningless, occupy pages of the
Sunday supplements, so that that meritorious organ, _The Scientific
American_, has to announce, in self-defence, that it publishes, not
“popular” science, but merely non-technical science. In our own country
that sober periodical _Nature_ used to print extracts from the
more marvellous scientific items provided by the daily press, thus
furnishing a little light relief from its own austere pages. The fact
that this quackery exists is not unimportant. If it does no more, it
often leads to a waste of time, for there has been more than one worthy
gentleman who has imagined himself to be attacking the pernicious
doctrines of science, when, as his argument makes clear, it is this
kind of quackery he has in mind. The cure for this kind of thing would
seem to be the development of a conscience in newspaper editors, unless
we prefer to wait patiently until a tincture of science forms part of
the education of an English adult.

But, turning to the popular but accurate scientific article, we may ask
what purpose it serves. Should its object be to supply the deficiencies
of a defective general education, to provide an easy introduction
to science? Doubtless such articles or lectures have served such a
purpose; Faraday himself, as we know, was won over to science by the
blandishments of Mrs. Somerville, and there is more than one case where
the current of a man’s life has been definitely changed by a lantern
lecture. It is, nevertheless, a mistake to suppose that the attentive
perusal of a number of popular science articles is equivalent to a
scientific education, a mistake which is unfortunately very common. The
fact is that the scientific treatise and the popular science article,
so far from being rivals, serve entirely different ends, and may be
read with profit by the same man. Broadly speaking, the function of
the popular science article is to present science in its humanistic
aspect. It should, while dealing with as definite a scientific problem
as the author chooses, hint at the relations between this problem and
the other interests of mankind. Very often these relations are implicit
in the subject; such subjects are, in fact, usually chosen, and for
that reason. But there is another type of article which has for its
object the exposition of relations which are not obvious, and this
exposition may be the result of a genuine and valuable intellectual
effort on the part of the writer. Such articles are really essays in
criticism and are not essentially different from the best type of
literary criticism. Some of the best articles of this kind--some of
those by W. K. Clifford, for example--are as truly “research” work as
is the technical paper. A third type of article may, either by way
of history or by way of logic, show the position occupied by a given
theory or fact in a scheme of knowledge. This type is usually of more
interest to the scientific student than to the general reader, since a
general acquaintance with the whole subject is presupposed, and in this
connection it is interesting to note that a powerful plea has recently
been made for the more effective endowment of the teaching of the
history of science.

If a popular science article serves none of these three purposes,
it must inevitably be nothing but the description of a “marvel.” In
competent hands this may be agreeable enough; the appetite for marvels
is vigorous and universal, and its indulgence cannot be condemned as a
vice. To look at a marvel for the pleasure of gaping is not, however,
a very intelligent occupation, and, to judge from the number and kind
of phenomena unhesitatingly ascribed to “the electricity in the air,”
merely increases credulity. Regarded as a marvel, wireless telegraphy
is, of course, merely a miracle, a fact extensively exploited by
spiritualists. The human tendency to seize on the merely marvellous
should, in fact, be carefully allowed for by the writer of popular
science articles; he should, if anything, be even more reserved and
pedantically precise than when addressing a scientific audience; an
incautiously flamboyant remark is very likely to be seized upon to
support some preposterous philosophy or religion. Usually, however,
the popular science writer yields to the temptation, to _épater_
his audience, to make himself more readable, as readability is now
understood, and so he may, while speaking the truth, have all the
effect of telling a lie.

Thus the division between the genuine and the quack science article is
not, in practice, clearly defined. The difference between the writers
is definite enough; but it is writer and public together which make the
popular science article. Lack of education is just as great a hindrance
to perception as is lack of sensitiveness. The poet may be subtly and
completely misunderstood because his audience lacks sensitiveness,
and, to compare small things with great, the conscientious retailer of
scientific information may be in a like case for a different reason.
So that if it is true that the best type of poetry is that written
by the poet “for himself,” it is perhaps true that the best type of
popular science article is written for a similar reason--because the
writer is genuinely interested in working out certain speculations or
treating certain facts in a certain way. Some of the very best popular
articles--those by Helmholtz, for example--are of this kind, and have
achieved a relative immortality, although, like the poetry which is
read chiefly by poets, they are probably read chiefly by scientific
men.

PATIENT PLODDERS

It is a melancholy fact that the estimable qualities of patience
and industry do not, by themselves, enable their possessor to
attain eminence in the arts. There is very good reason to suppose
that character, particularly a certain simple type of integrity and
sincerity, is necessary to great artistic achievement, but it is
certain that such gifts are not sufficient; they must be allied with
very unusual mental qualities. In the sciences, however, we often find
work of very great importance being performed by men of quite average
intelligence, but of exceptional tenacity. A pure heart seems to be all
that is necessary. This is not true, of course, of the mathematical
sciences--mathematicians, like musicians, are “born”--but it is very
obviously true of what are called the “observational” sciences. A
history of Astronomy, in particular, is interesting from this point
of view. The fact that the whole of our knowledge of the heavens
comes through the sense of sight, and that we cannot experiment, in
the ordinary way, upon the heavenly bodies, means that the patient
observer, by merely accumulating observations, is performing an
absolutely essential function. There is no other subject which yields
such rich rewards to mere patience. There is no other subject which
has so long a record of valuable discoveries achieved by purely
average ability. It is interesting to notice how often a telescope
and a capacity for sitting still have made their owners immortal. In
the region of stellar astronomy the minuteness of the phenomena which
may be observed has narrowed possible competitors to those possessing
large instruments, and that usually means public institutions and
professional astronomers. But the history of our knowledge of the
nearer heavenly bodies, the sun, the planets and the moon, owes much to
the industrious amateur. No history of planetary and lunar discoveries
would be complete without mention of Schröter, the “Oberamtmann”
of Lilienthal, who watched the moon and planets incessantly for
thirty-four years with a patience only equalled by his enthusiasm. He
died of a “broken heart,” the result of a French atrocity, for after
firing, on the night of April 20, 1813, the Vale of Lilies and thereby
destroying, amongst other things, the whole of Schröter’s books and
writings, the French army under Vandamme broke into and pillaged his
observatory. The old man, then sixty-eight years of age, had not
the means to repair the catastrophe, and, deprived of his one great
interest, he died three years later, leaving, amongst his published
works, some of the most long-winded and entertaining observations in
the history of astronomy.

But although Schröter is undoubtedly the most amusing of all amateur
observers, he has had his prototypes in all countries. Francis Baily,
the “philosopher of Newbury,” is a good example of our more sober
English product. We may have doubts as to what sort of chief magistrate
old Schröter was, but we know that Baily took his profession of
stockbroking with the utmost seriousness. He did not allow astronomy
to interfere with business. Beginning in 1799, he remained on the
Stock Exchange in London for twenty-four years, devoting his leisure
largely to solar observations, particularly those connected with
eclipses. It is with two of these phenomena, the first annular, a
ring of the sun being visible round the moon, and the second total,
that Baily’s name is particularly associated, in each case for the
vivid and accurate account he gave of what he witnessed. The first
phenomenon, a ring of bright points extending round that part of the
moon’s circumference which has just entered on the solar disc, is
merely a consequence of the lunar edge being serrated with mountains.
These “Baily’s beads,” as they were called, were successful, however,
in stimulating interest in the physical aspect of eclipses, with the
result that the next total eclipse, that of 1842, was looked for with
an unprecedented degree of enthusiasm. Astronomers like Airy, Otto
Struve and Arago travelled to Central or Southern Europe to observe
the eclipse, and the indefatigable Mr. Baily accompanied them. He
fitted up his telescope in an upper room of the University of Pavia.
The result was magnificent. At the instant of totality the sun appeared
decorated with a glorious _auréole_, the famous corona. It was
not, of course, an unknown phenomenon, but it had never before excited
so much attention. Mr. Baily, in particular, was moved to write a most
eloquent description of this flaming object. He calls it splendid and
astonishing, but continues: “Yet I must confess that there was at the
same time something in its singular and wonderful appearance that was
appalling; and I can readily imagine that uncivilised nations may
occasionally have become alarmed and terrified at such an object....”
Besides being a specialist on eclipses, Baily was an untiring editor
of star-catalogues, and he also made no fewer than 2,153 laborious
experiments, on Cavendish’s method, to determine the density of the
earth. He was indeed a zealous worker in what Sir John Herschel called
the “archæology of astronomy.” He was noted for his unvarying health,
undisturbed equanimity and methodical habits.

Another testimonial to the importance of such qualities in astronomical
discovery is furnished by the career of Heinrich Schwabe, of Dessau.
In the hope of escaping his fate as an apothecary he bought a small
telescope in 1826, and began to observe the sun, being advised to do
so by a friend. He continued to observe the sun daily (weather and
health permitting) for forty-three years. Every day he counted the
number of spots visible on the surface of the sun. It was a simple
occupation, but it led to important consequences. His immense record of
sun-spot statistics showed that the increase and decrease in the number
of sun-spots did not occur in a random manner, but fell into periods,
maxima alternating with minima, a complete period occupying about ten
years. This figure has been modified since, but the fact of sun-spot
periodicity is established and is at the present time one of the most
suggestive and probably far-reaching of solar phenomena. Schwabe
displayed no striking quality of mind or character beyond an almost
incomprehensible patience. He was buoyed up in his spot-counting,
however, by the hope of discovering a planet between Mercury and the
sun, and in order to distinguish between the tiny disc of the planet
crossing the face of the sun and a sun-spot, he found it necessary, in
virtue of his instrumental equipment, to count the spots. When he found
that, as a consequence of this pastime, he was world-famous, he likened
himself to Saul who, going forth to seek his father’s asses, discovered
a kingdom. His magnificent serenity of body and mind enabled him to
attain the age of eighty-six.

Part of his mantle fell on Richard Carrington (born 1826), who built
an observatory at Redhill with the intention of devoting himself to
a study of sun-spots throughout a complete cycle. He failed to finish
the cycle completely, as the death of his father made it necessary
for him to divert his energies to controlling a brewery. He achieved
results of great importance, however. His observations were concerned
with the positions and movements of the spots, and from a series of
5,290 such observations he was enabled, amongst other things, to clear
up the uncertainties attending the period of rotation of the sun.
Galileo, apparently not appreciating the importance of the matter, had
said that the sun rotated in “about a lunar month,” and a number of
other observers gave figures varying from 27 to 25 days. Carrington
illuminated this darkness by remarking that there is no single period
of rotation for the sun. The polar regions rotate more slowly than
those in the neighbourhood of the equator; the equator rotates in a
little less than twenty-five days, while in latitude 50° the period is
twenty-seven and a-half days. Thus the mystery was cleared up and a
fresh direction given to solar investigation.

It is difficult to say whether Astronomy still offers such rewards
to industry. It is probable, however, that it still yields more to
character, as distinguished from ability, than any other science, and
incomparably more, alas! than the arts.

THE AMATEUR ASTRONOMER

The indifference of the Englishman is, considered pragmatically,
the same thing as tolerance. It bestows freedom and leaves every
man, within fairly wide limits, at ease to pursue his bent. There is
doubtless a relation between this English characteristic and the fact
that England, above any other country, is the home of the amateur.
In England, compared with the Continent, there are comparatively few
men whose dominant activity is their exclusive activity. There are
many fair specialists, but there are few specialised men. There are
countries such as France, where the _Gemeinplatz_ of intelligent
men is probably larger and more richly furnished than it is in England,
but it is comparatively difficult to meet the type of man who is an
eminent lawyer, an authority on Eastern poisons, and a really good
judge of horseflesh. Such manifestations of a national quality may
sometimes appear almost grotesque, but we believe that the quality
of which they are partial manifestations is the most splendid and
individual characteristic of the English intellect. It is not a
quality which produces many thrice-armed specialists, but it is a
quality which produces a great number of amateurs. The English amateur
in the arts belongs to a family well worth consideration, but our more
immediate concern is with the amateur in science.

There was a time when the scientific amateur abounded in England.
In the time of Huxley and his contemporaries, as we see from their
letters, amateur zoologists, botanists, and, more rarely, amateur
mathematicians and physicists, were scattered all over England and
occasionally had something of interest, or even of value, to report. In
the days when R. A. Proctor edited _Knowledge_ the country seemed
to be full of reverend gentlemen who owned small observatories and
home-made telescopes. This large and interesting family seems now to
be making towards extinction. The increasing complexity of the various
sciences, to say nothing of the variety and cost of modern apparatus,
has made anything but trifling discoveries difficult to the verge of
impossibility for an amateur equipment. Perhaps the amateur who has
suffered least from these changes is the amateur astronomer. There is
good reason for supposing that his numbers have increased. In this
branch of science the English amateur has always been particularly
strong, and this cannot be attributed to the official encouragement
accorded astronomy in this country. There are many more amateur
astronomers in England than in France, although astronomy counts for
more in France than in England, and although, since Newton, France has
played the leading rôle in the history of astronomy.

The popularity of amateur astronomy in England certainly needs
explanation, for it is a pursuit attended by many disappointments in
so capricious a climate, and Englishmen have few opportunities of
seeing a really impressive display of stars. Perhaps the Englishman
is sufficient of a Northerner to be profoundly attracted by the
sheer vastness and the mystery of stellar phenomena. Then the actual
telescope and its accessories probably appeal to the English love of
mechanism. There are few instruments more delightful in themselves
than a properly mounted telescope of moderate aperture. Its adjustment
affords a pleasure as refined as that given by operating a small hand
printing-press, and superior to that of mending a bicycle. Every
telescope has its distinctive “performance,” and one can grow as
enthusiastically partisan about makes of telescopes as one can about
makes of motor-cars or pianos. Whether or not these be the reasons
it is certain that astronomy is the science which most attracts the
English amateur. The existence of the British Astronomical Association,
an amateur society with some hundreds of members, is sufficient proof
of this. It would perhaps be difficult to justify by the results the
amount of time and money spent in amateur stargazing, if one estimated
results from the severe standpoint of the professional astronomer. But
if one adopts a broader outlook and estimates the results in rather
more human terms, then there is probably no pursuit which affords more
innocent pleasure and provides, in itself, a more liberal education.
It is said that the vast photographic telescopes of the present day
have rendered the small instrument valueless. Even Mr. Hinks, in his
excellent volume _Astronomy_ in the Home University Library, says
that the would-be amateur would do well to hesitate before buying a
small telescope, and that a measuring machine, to measure photographs
taken by big instruments, would be a far better investment. This is the
severely professional point of view; it is to mistake the psychology
of the amateur observer. The amateur likes to think that he might some
day make a discovery, but that is only by the way. His real joy is in
doing precisely what the professional cannot do, and that is to enjoy
the _spectacle_ of the heavens. The ordinary run of work in a
big observatory is not much more exciting than work in an ordinary
business office. To sit up half the night measuring photographs would
conceivably add to scientific knowledge, and there are doubtless stern
men who are willing to do it. These, like computers, are the martyrs
of science. The average amateur will continue to prefer his present
pleasant, if ineffectual, method of adding to scientific knowledge. It
is to be feared that, as one result of the war, this amiable occupation
will decline. A little before the war the amateur could purchase a
modest but thoroughly good, instrument at a reasonable price. The same
instrument to-day would cost at least twice as much, and there would
probably be an interval of several months between the order and the
delivery. One large firm of optical instrument makers announces that it
is not now making astronomical telescopes at all. At the present time,
when astronomy is entering on perhaps the most pregnant phase in its
history, and when men are more than ever attracted by anything which
promises escape from the fret of daily life, this lessening of the
opportunities for acquaintance with the most serene of the sciences is
a minor calamity. The decline in amateur astronomy will probably have
no appreciable reaction on the progress of science, but it will lead to
a real, if small decrease in the intellectual pleasures and spiritual
wealth of the nation.

SCIENTIFIC CITIZENS

It would be an entertaining pursuit to compile the characteristics of
the man of science--usually a Professor--as he is depicted in popular
fiction, on the stage, and in the writings of exasperated conservatives
in religious and social matters. It would be found that these
characteristics combine to give one dominant and entirely untruthful
impression: the man of science is represented as being scientific on
all occasions. We may ignore the inferior school that portrays him as
being constantly obsessed by his work--like Dickens’ learned gentleman
who mistook the nature of a dark lantern--and confine our attention
to the Professor who is represented, not as imbecile, but merely as
homogeneous. This imaginary individual is never to be diverted from his
passion for precise statement and strictly logical inference. Whether
the subject be politics or the state of the weather, he brings the same
preliminary scepticism, the same demands for verification, that he
carries into his scientific researches. As we have said, this picture
is untruthful; we think, however, that this is an unfortunate fact,
and that it is highly desirable that men of science should begin to
live up to the story-teller’s conception of them.

We think that, at the present stage of man’s evolution, science is the
one activity in which he displays himself as a truly rational creature.
The reason is, of course, that success is granted on no other terms; in
everything else, philosophy, theology, politics, reason is usually the
handmaid to prejudice. The penalties that visit error in these fields
are not so swift nor so unambiguous. The ideal of truthfulness is
probably more rigorous with the scientist, _qua_ scientist, than
with any other kind of man. But it would appear that this dispassionate
rationality is hardly won and precariously maintained. Outside his
laboratory the scientist may, and usually does, show himself as
simple, as kindly, as credulous, as irrational as any other man. On
Bolshevism, Disestablishment, the Morality of the Public Parks, his
opinions will be indistinguishable from those of any other comfortable
member of the lower middle class; that is to say that opinions on all
such matters are “distributed” amongst scientific men according to
the same statistical rules as they are distributed amongst ordinary
citizens. Outside their views on purely scientific matters there is
nothing _characteristic_ of men of science. The Royal Society may
conceivably issue a unanimous report on some scientific matter; it
would issue a unanimous report on nothing else whatever. Now on the
assumption that men of science are truly rational beings this is a very
strange state of affairs. Dispassionate attempts to sift evidence,
to argue correctly and to base judgments solely on the outcome of
these processes could hardly result in so remarkable a multiplicity
of opinions. We must assume that, for scientific men as a body, their
“scientific” methods of thought function only within very narrow
limits. As a distinct community they are far less coherent than, for
instance, the community of artists--musicians, poets, painters. The
community of artists, with the exception of a few prosperous members,
exhibits a really remarkable homogeneity in matters outside art.
Doubtless this homogeneity is based on feeling--unless we are prepared
to admit that artists, as a whole, are more rational than are men of
science--and it is probable that the scientist’s difference from his
fellow-citizens is more an intellectual than an emotional difference.
But it is surprising that greater emotional sensitiveness should prove
so much more pervasive and dominating a peculiarity than greater
intellectual subtlety.

It is time that men of science assumed a greater position in the
general community. If a scientific training has a tithe of the
_general_ educational value that is claimed for it, it is time
we had some evidence of that fact. Men of science must adopt a higher
ideal of personal honour. At present the man who will conduct a
laboratory experiment with meticulous precision and describe his
results in an agony of honesty will be content to be a prejudiced
observer and a slovenly and inaccurate thinker in all other matters.
This is the chief reason, we are convinced, why men of science count
for so little in public affairs. If the Royal Society elected its own
member of Parliament, who would bother about the political opinion so
expressed? What greater weight would it have than the political opinion
of an equal number of moderately prosperous ordinary citizens? Does not
the scientific man waggle his head just as solemnly over his morning
newspaper as does any unsophisticated voter?

We plead for the development of a class consciousness on the part
of the man of science. We want scientific men to regard their ideal
of evidence, their conception of proof, their really admirable
scientific detachment, not merely as rules making for success in their
particular game, but as principles applicable to every subject that
concerns a citizen. Why should a man of science be merely a Liberal
or a Conservative in politics? The alternative belongs to the stage
of mental development that explained the material universe by saying
that its moving principle was fire, or, alternatively, water. We
expect a more sober contribution to political questions from, say, a
distinguished physicist, than the panacea “Shoot the miners.” All the
questions on which scientific men now adopt “sides” as uncritically
as any simple dupe of the daily press are amenable to scientific
investigation. They can reach a solution only by the application of
scientific methods, and the modern world badly needs deliverance from
the method of charms and incantations by which these questions are at
present treated. How long are these vital matters to remain in the
hands of the witch-doctors? With scientific men content to sit in the
circle and help beat the tom-toms what hope is there of real advance
founded on real knowledge? The artists cannot help us; they are useful
indicators of the value of the product, as it were; they look pleased
or they look disgusted, and that is very helpful in showing us where
we are. It is the scientific man who must show us how to go somewhere
else. So we plead for the conscious formation of a community of men
of science, for scientific men who are at least as pervasively and
constantly scientific as a good Jesuit is Roman Catholic.

THE SCEPTIC AND THE SPIRITS

It is only youth that has the energy to be bothered with everything.
There comes a time when one’s mind is “made up” on all sorts of things
that were once matters of inquiry; we have profited by experience; we
know that some things are not worth investigating. It is one of the
marvellous laws of growth that this increase in wisdom should accompany
physical decay. As our teeth and hair start to fall out our judgment
grows riper. The law of growth is not really as simple as this, for
there are many silly old men and there are one or two wise youths. The
rich, mellow, balanced period is never reached by some people: Solomon,
on the other hand, was noted for his wisdom while still a young man.
There is, it must be admitted, something mechanical about old men’s
wisdom. Truth is one, of course, so that we should expect a certain
unanimity. The answers of the old can usually be predicted. Wisdom can
be simulated; all that one lacks is the conviction, the spirit that
animates the letter.

Deep conviction is a very impressive quality, especially to youth,
which secretly doubts everything. The man of strong convictions is a
cause of optimism in others, for life would appear a sad cheat if the
payment for sixty years of it did not include one certainty. Youth’s
certainties make as much noise, but everybody detects the bluff. A
fearful man shouts to hearten himself, as all the world knows. Between
the certainties of youth and age there is scepticism, a _fine
fleur_ of brief life, an exquisite tempering of the soul, neither
too soft nor too hard, an infinite flexibility. It is a state of
intense activity; life lived at this pace cannot long endure; the tired
spirit relaxes and one finds rest either in credulity or in dogmatism,
accident determining which attitude affords the soundest slumber. It is
not always easy to detect the true sceptic; that honourable title has
often been wrongly bestowed--Voltaire, for instance, was a dogmatist.
Sceptics exist in all ages, but they are more clearly revealed at those
periods that see the birth of some new inquiry. It is essential to
their indubitable manifestation that the inquiry should be attended by
the passionate interest of a large number of people. At the present
day a very good test inquiry is spiritualism. It is a very much better
test than Free Trade and Tariff Reform, for, owing to its comparative
remoteness, the true sceptic of that alternative might live and die in
obscurity. But spiritualism is a subject on which no one is genuinely
indifferent and towards which hardly anyone is genuinely sceptical.
Dispassionate inquiry on this, as on all matters where human interests
are strongly engaged, is usually a pretence. We need not suppose that
the great ones of the Psychical Research Society are less credulous
than the majority of believers or less intolerant than their louder
opponents; it is merely that, their traditions being scientific, they
have better manners.

Psychical literature, as a whole, is as wearisome as theological
literature, as incredible but less amusing than the lives of the
saints. We lack the quality, be it faith, hope or charity, which would
enable us to share these strange excitements. The “exposers,” on the
other hand, are too sturdy in their common sense. We hear the mallet
fall, but we are not always sure that the eggshell is broken. It is a
situation for the sceptic. In the late Lord Rayleigh’s presidential
address to the Psychical Research Society we find that the sceptic has
at last appeared. It is merely a record of his own experiences, very
plain, very simple, and, like the experiences themselves, singularly
elusive. Many years ago, in a friend’s rooms at Cambridge, he witnessed
an exhibition of the powers of Madame Card, the hypnotist. When she had
completed her passes over the closed eyes of those present she asked
them to open their eyes. “I and some others experienced no difficulty;
and naturally she discarded us and developed her powers over
those--about half the sitters--who had failed or found difficulty.”
From hypnotism he passed to spiritualism, his interest aroused by Sir
William Crookes’ experiences. He induced the medium, Mrs. Jencken, and
her husband, to visit his country house as guests. He describes the
results as disappointing:

I do not mean that very little happened, or that what did happen was
always easy to explain. But most of the happenings were trifling,
and not such as to preclude the idea of trickery. One’s coat-tails
would be pulled, paper cutters, etc., would fly about, knocks would
shake our chairs, and so on. I do not count messages, usually of no
interest, which were spelt out alphabetically by raps that seemed to
come from the neighbourhood of the medium’s feet. Perhaps what struck
us most were lights which on one or two occasions floated about. They
were real enough, but rather difficult to locate, though I do not
think they were ever more than six or eight feet away from us.

Another incident was the gradual tipping over of a rather heavy table
at which they had been sitting. “Mrs. Jencken, as well as ourselves
[i.e. Lady Rayleigh and himself. The husband was not admitted to
these séances] was apparently standing quite clear of it.” He found
it very difficult to reproduce the phenomenon himself, using both
hands. He endeavoured to “improve” the conditions for some experiments.
After being shown some writing, “supposed to be spirit writing,” he
arranged paper and pencils inside a large glass retort, which he then
hermetically sealed. Nothing then appeared on the paper at these
séances. “Possibly this was too much to expect. I may add that on
recently inspecting the retort I find that the opportunity has remained
neglected for forty-five years.”

And so he has left the matter. The experiences were certainly strange,
yes, but in his judgment, not strange enough. On the other hand,
he is reluctant to believe they were due to fraud, and he is quite
convinced that he was not a victim of hallucinations. If Mrs. Jencken
were a clever fraud “her acting was as wonderful as her conjuring.”
She practically never made an intelligent remark on any occasion.
“Her interests seemed to be limited to the spirits and her baby.” In
investigating this subject he finds that the attitude of convinced
believers makes a difficulty. They “take no pains over the details
of evidence on which everything depends.” Others attribute all these
phenomena to the devil and will have nothing to do with them. “I have
sometimes pointed out that if during the long hours of séances we
could keep the devil occupied in so comparatively harmless a manner we
deserved well of our neighbours.”

The general disbelief in scientific circles that meteorites really
came from outer space occurs to him. This disbelief was due, he points
out, to the impossibility of producing the phenomena at pleasure in
our laboratories. Nevertheless, the disbelief was unjustified. Spirit
manifestations may be, he thinks, just such sporadic phenomena. The
situation is made worse by the fact that there has undoubtedly been a
great deal of fraud in connection with spiritualist phenomena. Eusapia
Palladino, for instance, undoubtedly practised deception, “but that is
not the last word.” Telepathy puzzles him. If there is such a means of
communication, why should Nature have adopted the laborious method of
building up our very complicated senses? An antelope in danger from
a lion, for instance, depends on his senses and speed. “But would it
not be simpler if he could know something telepathically of the lion’s
intention, even if it were no more than vague apprehension warning
him to be on the move?” He advises the society to continue their
investigations, and mentions that it is quality, not quantity, that
is so desirable in evidence. He concludes by saying that he fears his
attitude, or want of attitude, will be disappointing to some members of
the society. He suggests that after forty-five years of hesitation “it
may require some personal experience of a compelling kind to break the
crust.” He apologises for this. “Some of those who know me best think
that I ought to be more convinced than I am. Perhaps they are right.”

There he leaves us. We do not believe more or disbelieve less, yet we
are completely satisfied. His massive sincerity, his obvious competence
and, above all, that impression of exquisite balance, have charmed us.
So far as present evidence is concerned we feel that while he has said
nothing he has also said the last word. That is the function of the
sceptic.

THE SCIENTIFIC MIND

It is quite common, in reading and in conversation, to find references
to the “scientific mind,” but it is difficult to ascertain precisely
how this mental structure is supposed to differ from other sorts
of mind. The difficulty of defining an object does not, perhaps,
affect the probability of the existence of the object; although it is
difficult for some people to refrain from concluding that because a man
cannot define what he means he does not mean anything. We must suppose
that there is some particular kind of mind called the scientific mind,
in spite of the fact that the numerous references to it tell us little
about it except that it is somewhat extensively disliked. So far as can
be judged from a superficial comparison of different references, the
“scientific mind” is characterised by an inordinate appetite for facts
and an absence of generosity in drawing conclusions from facts. In
ordinary times this absence of generosity is dismissed by most people
as quibbling, while in time of war it becomes unpatriotic. During the
war every Englishman was supposed to believe a great number of things
on very slender evidence or even on no evidence. It was considered that
a right patriotic feeling not only could, but should, supply the place
of evidence, and lead to correct conclusions. The majority of people
in every class of the community found themselves able to adopt this
method of thought without discomfort, and it became evident that the
scientific mind is as rare amongst scientific men as amongst any other
men, while those who could not give this supreme proof of patriotism
were found pretty evenly distributed amongst the different classes. As
a type of mind, therefore, it is not peculiar to scientific men nor do
they all possess it. It cannot be regarded as a distinguishing mark of
this class. But while a just, cautious temperament need not belong to
the man of science as a human being, it might be thought that, as a
mental habit, it is necessary to his work. There is much truth in this,
although it is not wholly true. Alternative explanations are not always
explored by scientists, and if, as sometimes happens, the alternative
explanations are wrong, the scientific man may have reached a correct
result although he worked in a partisan spirit.

But while the characteristics of what is popularly known as the
scientific mind are not peculiar to scientific men, it is true that,
in their actual scientific work, these characteristics have a greater
survival value than they possess in almost any other kind of work.
The extent to which mental habits may be local, confined to some only
of a man’s mental activities, has been made apparent by the war. The
majority of men’s minds are split up into water-tight compartments
in a way truly astonishing, and the various eloquent addresses on
the moral value of scientific studies now make melancholy reading.
We must assume of scientific men, as of any other class, that such
qualities of fairness and deliberation as they exhibit in their work
are imposed upon them as conditions of success, and are not, in
general, the natural manifestations of an exceptionally delicate moral
sensibility. If we adopt William James’ classification of human beings
into tender-minded and tough-minded the dividing line runs through the
scientific camp as through any other. We see this most clearly in the
case of mathematicians, for idealist or empiricist assumptions seem to
be equally reconcilable with the results. Such sciences as physics and
chemistry seem, at first glance, to be given over to the tough-minded;
the official language, as it were, is the language of the tough-minded,
but directly controversy arises on a point having philosophical
bearings we see the dichotomy establish itself.

Nevertheless, it remains true that while scientific men, as human
beings, are of all sorts, they do exhibit, in their own work, a degree
of mental honesty which is unusual. It is easy to see that this virtue,
at any rate, has a strictly utilitarian basis. A scientific man
is honest because he cannot succeed on any other terms in the long
run. The experimental verification always looms ahead. He cannot,
like the mystic who maintains his opinion in face of the world,
take refuge in the deeper insight. His results are communicable and
verifiable or they are not science. Philosophies may be constructed
which no man can verify and no man can refute. Their authors may, with
complete assurance, remain satisfied of their truth and lament the
universal blindness of mankind, just as a poet may present a front of
unconquerable self-esteem to the ignorant derision of the world. But
the whole claim of science is that it is communicable and capable of
verification. It is found, as a matter of experience, that results of
this kind are not usually obtained unless a certain mental habit is
first acquired. It is this mental habit which is usually called the
scientific mind. Where it is the outcome of a natural predisposition it
may be classed as a moral quality, and, as such, is not peculiar to, or
widely distributed amongst, scientific men. But as a tool, as a kind of
technique, it is of more obvious value and is more extensively employed
in the sciences than in any other human activities.

THE SCIENTIFIC CONTRIBUTION

For something like seventy years science has been the dominant
intellectual activity of the Western world. During that period the
range of its material has greatly increased until now the scientific
method is regarded as the method proper to almost any investigation.
Philosophy is still a partial exception, but there is a strong tendency
to regard such philosophic problems as are not susceptible to the
application of the scientific method as being essentially incapable
of solution, or else as incorrectly stated. But although the prestige
of science is so great, and the general attitude towards it so
reverential, there is still much confusion respecting its function and
achievement. Its relations to other human interests and activities are
not yet clearly defined. The attempts to define them by allotting to
science its “sphere” have proved, in the result, to be so ill-judged
that it is now considered safer to waive the question of limitations
altogether. The question is not settled. Everything is left open, but
it is not therefore assumed that science contains or will contain all
we know or all we need to know. Science is not yet the one object of
our contemplation: we have a number of interests which still lead
separate lives. The separation is not complete. Science, if not openly,
then indirectly, has invaded every province of the mind, and even a
modern musical composition counts Copernicus as well as Beethoven
amongst its ancestors. But it is admitted, of course, that we are
not usually reminded of astronomy in listening to music; there is a
sense in which music, and many other things, are autonomous. But it
is interesting to notice that science, to a greater extent than any
other pursuit, can be isolated, although its historical direction has
been influenced, of course, by social and political accidents. Science
has given generously, but has taken comparatively little, and its few
borrowings are in process of being handed back with regret as being,
after all, unsuitable.

What, then, is the precise nature and extent of the contribution of
science to our total stock? Although we do not intend its practical
applications by this question, we cannot wholly ignore them. It is
impossible completely to separate the “material” and “spiritual”
aspects of life, and the sum of the practical applications of science
has even profoundly affected much of our abstract thinking. Where it
has not originated questions it has at least made them acute, if by no
other process than by creating or transforming social conditions. It is
easy to trace the ancestry of whole schools of social philosophy to
the steam engine and the dynamo, and it is probable that the influence
of future applications will be even more extensive. The morality,
art and philosophy of, for example, a disease-less world, where the
average span of human life was two or three times its present value,
would certainly differ greatly from our own. We cannot, then, ignore
the practical applications of science, although they are not, in
themselves, pertinent to our question. But when we turn to consider the
direct spiritual value of science we are conscious, at the outset, of
some hesitation.

It was a common article of the Victorian scientist’s creed that
scientific study was, in itself, an “ennobling” and purifying
influence. He stressed the complete detachment required, in scientific
research, from all prepossessions; the man of science was completely
candid, completely docile in face of the facts. Until one became as
a little child it was no use entering a laboratory. We have realised
since then that scientific men are human, and have their full share of
the unfortunate characteristics proper to that state. But it remains
true that the scientific ideal of detachment and the scientific ideal
of evidence are higher than the corresponding ideals elsewhere. In
spite of the evidence furnished by our newspapers we may, if we are
optimists, believe that science is gradually infecting the whole
community with its conception of these ideals. If this is indeed the
case it must be counted a direct and very important moral gain, as an
indisputably valuable contribution which may be set over against those
somewhat ambiguous practical applications.

A third contribution is to be found in the large store of æsthetic
objects provided by science. Many of its theories are objects of
surpassing beauty. This is particularly true of the mathematical
sciences--indeed, there are a number of mathematicians who have felt
impelled to write of their science in a kind of prose-poetry--but it is
almost equally true of such a science as Geology. We can contemplate
schemes which, in their own way, are as all-embracing as that of the
_Divina Commedia_, and it does not detract from their æsthetic
charm to know that they are also true. The processes by which the
theories are obtained are often as æsthetically important as the
theories themselves. A subtle, elaborate and economical piece of
reasoning often affords great æsthetic pleasure, none the less real
because comparatively few people enjoy it. The fact that the history of
a big scientific investigation, such as the Electromagnetic Theory or
Einstein’s Theory of Relativity, is not generally regarded as a poem
is due merely to an accident of language and education. But we have to
admit that most people are affected by these accidents, and that the
æsthetic objects provided by science count almost as few admirers as
do the “beauties” of chess. If we may judge from the number of popular
books and articles dealing with science, there is some hope, however,
that this particular contribution is receiving more attention. The
results of such increased attention will not be simple, but if it did
no more than add fresh æsthetic objects, the contribution would be
important.

The fourth contribution of science, both in itself and for its reaction
on other interests, is perhaps the most important of all. This
contribution is, put briefly, the light thrown by science on man’s
place in the universe. Every branch of science conspires directly to
this end. With some the emphasis is on the universe as distinct from
man; others are concerned chiefly with man himself. To the general
mind the result has been to make the universe bigger and man smaller,
and this is, perhaps, no unfair summary. It is probably difficult,
after hearing a duet sung by an astronomer and a psycho-analyst, not
to feel depressed. But, such as it is, there can be no doubt that any
conception of man’s destiny that is to command attention must conceive
that destiny as played against the background of the scientific cosmos.
Whether the vision be that of a prophet, philosopher or poet, it must
accept those postulates. The cosmos revealed by science, both in
its direct influence upon the mind and in its almost equally direct
influence upon religion, philosophy and the arts, is the most important
part of the scientific contribution to our spiritual life. So far as
philosophers and artists are concerned, this influence is recognised.
It is probably desirable that the influence upon philosophy should
increase, but in the case of the artist we are faced with a special
problem. Its discussion would be interesting, the more so in view of
the fact that artists themselves have contributed very little that is
helpful to its elucidation. We think it essential to its solution to
remember that the artist, like the scientist, starts with facts. But
the system within which the facts are related is entirely different
in the two cases. The scientific scheme must, of course, be accepted
by the artist _en bloc_ if his work is to be more than a pure
fantasy. But this is very different from identifying his own scheme
with the scientific scheme. That is to fail signally to perceive
the limitations of the scientific contribution. An interesting
particular case of this problem is to be found in the question of
the right relations of the psychological novelist to the science of
psycho-analysis. A scientific investigation is often, as we have
said, a work of art, but not necessarily a work of literary art. The
scientific contribution is very considerable, but offerings from the
older benefactors are still gratefully received.

THEORIES AND PERSONALITIES

That a scientific theory is, in some sense, a personal achievement,
becomes evident when we study a number of theories lying within the
same branch of science. The ordinary belief that science is completely
impersonal is certainly not true. And yet it is not easy to see how
a scientific theory can express the personality of its author; it is
difficult, that is to say, to understand in what way a scientific
theory can resemble a work of art. It seems that the fact that a
scientific theory must have “objective truth” renders it an altogether
different thing from a work of art. It would be more just to say that
the element of objective truth radically differentiates a scientific
theory from those works of art which are independent of all experience
of life--as certain musical compositions may be, for instance. But
it is not clear that, in general, works of art are independent of
objective truth; all those works of art which assume experience claim
assent--they do, in their intention, claim universal assent--to the
truth of their assumptions. The serious artist believes his personal
vision to be true; he will not, probably, claim “absolute” truth for
it, but neither does a scientific theory profess to be absolutely true.
And, further, works of art and scientific theories exist to serve the
same purpose--to aid _comprehension_. An artist’s chief title to
consideration is to be found in the depth and extent of his vision,
in the profundity and range, that is to say, of the comprehension he
makes possible. The value of a scientific theory is judged by the same
criteria. So far, therefore, it would appear that the chief difference
between a work of art and a scientific theory is to be found in their
subject-matter. It cannot even be said that the subject-matter is
arranged to serve different ends in the two cases, for in each case the
end which is aimed at is æsthetic satisfaction. Comprehension is one of
the elements of what is loosely termed the æsthetic emotion, and it is
the most important element. Even when we descend to particulars, and
study the quality of similes in poetry, and, indeed, “ornamentation”
generally, we shall find the criterion we employ is still the degree
of comprehension afforded by the device. But we cannot here work out
the analogy in detail. It is sufficient to show that works of art that
have a reference to experience, to an external world, in short, are, in
important respects, similar to scientific theories.

Since, then, a work of art, although conditioned by experience,
may nevertheless be a personal achievement, we need have no _a
priori_ objection to conceding personality to a scientific theory.
In each case it is the method of transformation from what we may
call the raw material to the finished product which is the personal
thing. The artist’s raw material, whether it be the Thames in a fog,
a number of incidents from Holinshed, or the lives of the inhabitants
of a Russian village, is no more and no less common property than are
the _données_ from which a scientific man constructs a theory;
the end product, also, in each case, claims universal assent and
bestows comprehension. What is personal is the law of transformation
by which the one objective thing is changed into the other objective
thing. The law of transformation is different for each individual
mind, and this is as true of scientific men as of any other sort of
men. In this sense, then, both works of art and scientific theories
are personal achievements. A history of science written from this
point of view would be instructive. It would be interesting to trace
the personal element in each great scientific achievement, to show
what kinds of personalities have dominated us, to see what meaning
_eccentricity_ can have as applied to the thought of a scientific
man. But although a detailed history of this kind has not yet been
written, certain _national_ differences have long been recognised.

There is almost as marked a difference between English and French
science as between English and French literature. The English
scientific mind is, on the whole, intuitive, mobile, illogical, and
very prone to imagery of a curiously practical kind. The French
scientific mind, on the other hand, likes to simplify the complicated
reality to as few terms as possible, and then to build up an impeccable
logical edifice. Maxwell was a very fine type of the great English
man of science, but we have Poincaré’s authority for saying that the
great _Treatise on Electricity and Magnetism_ awakens in the
French reader feelings of distrust. So far from finding an impeccable
logical structure, he finds that different parts of the book are
written from different points of view, and that these points of
view are even irreconcilable with one another. Maxwell’s liking for
immensely complicated mechanical models, designed to illustrate some
abstruse equation, is also a stumbling-block to the French reader.
What are such models supposed to prove? Surely Maxwell did not suppose
that the æther contained trains of geared wheels with “idle wheels”
in between? What mysterious satisfaction did he derive from such
unnecessary and irrelevant pictures? But this curious liking for models
is characteristic of the English school, and it is a characteristic
that Continental physicists have never been able to understand. It is
doubtless a manifestation of the English reluctance to get out of touch
with experience. The English man of science trusts logic much less
than he trusts experience. The Frenchman has much less respect for
experience. He is willing to simplify in a way which, to the English
mind, is almost outrageous--to see the Universe as a collection of
little billiard balls with forces varying inversely as the square of
the distance. And on such assumptions he is willing to proceed as far
as logic can take him. There is, indeed, a school in France which
asserts that all we can ever know of the Universe is its equations;
we can never know what they “mean” in the English sense. From the
æsthetic point of view there is no doubt that the French method is to
be preferred. We can all share Lagrange’s satisfaction when he says,
in the Avertissement to his _Mécanique Analytique_: “Je me suis
proposé de réduire la théorie de cette Science, et l’art de résoudre
les problèmes qui s’y rapportent, à des formules générales, dont le
simple développement donne toutes les équations nécessaires pour la
solution de chaque problème.” But we must remember that when the
interest is chiefly in the “développement” the assumptions may remain
uncriticised. The English way is to hold the assumptions tentatively,
and to be always open to the suggestions of experience. The German way,
which, if we are to judge by the work of Riemann and Einstein, seems
to be to concentrate an immense critical apparatus on the assumptions,
is equally interesting. The “philosophic” tendency which is supposed
to characterise German thought in other departments, is certainly
apparent in its science. The three tendencies are sufficiently marked
to constitute national differences and suggest that a detailed analysis
of individual achievements would yield equally interesting results.

THE IDEAL SCIENTIFIC MAN

Is the scientific man really a distinct kind of man, or is it merely
that science is a distinct occupation? To answer the question we
must make the elementary distinction between the scientific man and
the man who practises science, and when we do that the answer is
obvious. There is as certainly the “born” scientific man as there
is the born artist. But in saying this we are referring to ideals.
Perhaps there has never been a perfect man of science, and perhaps
there has never been a perfect artist. But in order to understand
the distinction between one kind of man and another it is helpful to
construct ideals--extreme cases which may be used as measuring rods.
What, then, are the characteristics of the ideal man of science? We may
approach the solution by trying to make precise the characteristics
which have led us, vaguely, to construct the hierarchy we already
possess. We _feel_, for instance, that Henry Cavendish, that
passionless recluse, was a much more “purely scientific” man than,
say, Thomas Henry Huxley. If we examine this conviction of ours we
make the interesting discovery that it is chiefly for his negative
characteristics that we assign this greater purity to Cavendish. Huxley
was passionately interested in the questions which concern every good
citizen, in politics, in social reform, in religion; he took sides
on these questions and fought for his side. Of Cavendish we can only
say that it is inconceivable that he would have taken sides on these
questions, and very difficult to believe that he was even remotely
interested in them. Take another point. Huxley abounded in ordinary
human affections. He was a devoted husband, a good father, a faithful
friend, a resolute opponent. Cavendish never manifested a vestige of
any of these qualities. He had no wife, no children, no friends, and
never showed the faintest dislike of anybody. Huxley was a champion of
what he thought the truth, and strained every nerve to enable it to
prevail. Cavendish, who was one of the greatest investigators, one of
the clearest and most subtle minds, in the history of science, kept
his discoveries to himself. For years Huxley bore the brunt of the
attacks on Darwin’s theory. Cavendish blandly watched the growth in
popularity of theories he had privately demonstrated to be wrong, and
never stirred a finger to rebut them. And finally, Huxley was a man who
suffered his alternations of high spirits and despondency, hope and
despair, while Cavendish, from the evidence we have, was imperturbably
serene.

Now, the interesting point that emerges from this comparison is that
Cavendish, in virtue of his scientific purity, _could not_ have
exhibited those qualities which allied Huxley to the ordinary run of
men. A man’s characteristics are not disconnected. Cavendish’s cold
passion for knowledge required for its gratification qualities of the
spirit as well as of the mind. No man was ever more single in his
desire to _know_; no man ever was so little hindered by having
other interests to serve; no man, therefore, had a greater measure
of the purely scientific spirit. This is the important point for our
question; it is comparatively irrelevant that very few men have ever
had so great a mind to place at the service of their passion. That his
actual scientific standing should be so much greater than Huxley’s
is an accident; he would still have been more purely scientific than
Huxley had his ability been less than Huxley’s. Cavendish is all of
a piece. His very perfection as a recording and measuring instrument
tended to deprive him of “personality.” The less personal he was,
in fact, the more dispassionately open he could be. Other passions
were incompatible with his perfection; they would derange this
exquisite instrument. Judgments of good and evil would not have been
natural to him. His reaction to anything was exhausted in the act of
_understanding_ that thing.

So far as we have gone, it would seem that Nietzsche’s description of
what he calls the “objective man” is exactly what we mean by the ideal
man of science. “The objective man is in truth a mirror: accustomed
to prostration before everything that wants to be known, with such
desires only as knowing or ‘reflecting’ implies ...” he will regard
such personality as he has, Nietzsche goes on to say, as accidental and
arbitrary. He cannot take himself seriously and devote time to himself.
His love is constrained, his hate artificial. He is only genuine so far
as he can be objective; he is unable to say either “Yea” or “Nay” to
life; he is concerned solely to understand, to “reflect.” He says, with
Leibniz: “Je ne méprise presque rien.” This description is undoubtedly
the result of genuine psychological insight. When we try to disentangle
the purely scientific element in a man of science we find that, so far
as he is scientific, he approximates to Nietzsche’s objective man. If
this, then, is the ideal scientific man, what place does he occupy?
Where does he stand in relation to the rest of mankind? According to
Nietzsche he is merely an instrument; “he is an instrument, something
of a slave, though certainly the sublimest sort of slave, but nothing
in himself.” He is no goal, no termination, no complementary man in
whom the rest of creation justifies itself. As compared with the
_true_ philosopher, the philosopher in Nietzsche’s sense, the man
who gives a new direction to life, the ideal man of science is merely
the most costly, the most easily tarnished, the most exquisite of
instruments.

We need not quarrel with this valuation, but we would point out that
there is an omission in it. The scientific man is an instrument, but
he is an indispensable instrument. The human race has endured all the
different “new directions” given to it by the “true” philosophers of
the past without any marked increase in its spiritual stature. The
philosopher, however commanding, who would really lead us in any but a
circular direction must have _knowledge_. This knowledge, to be
valuable, must be clear and trustworthy; it must be scientific. And
if the inspirations and impulses of our leaders should prove to be
incompatible with deductions from scientific knowledge, then we may
be sure that the Promised Land does not lie their way. The scientific
man is merely an instrument. But it is this instrument alone that can
show to mankind which, of all the goals it desires, are possible goals,
and which, of all the leaders it trusts, are trustworthy leaders. The
scientific man is an instrument, but it is by this instrument that
those who would use it are first tested. Scientific knowledge is, if
you like, as dispassionate and inhuman as is the universe with which it
concerns itself--and it can as little be ignored.

PARALLEL STRAIGHT LINES

Geometry, it has been satisfactorily shown, had a purely empirical
origin. It appears that the earliest geometrical formulæ which have
been discovered belong to ancient Egypt, and that all these formulæ
served a useful purpose. The oldest of them are concerned with the
measurements of areas, a class of problem which the yearly sinking
of the Nile rendered of great importance. The formulæ obtained
by the ancient Egyptians were usually wrong, although they were
approximately correct; they evidently rested on no theoretical basis,
but were compendious statements of the results of somewhat rough
measurements, a point of view which is borne out by the fact that no
proof, nor even an attempt at a proof, is anywhere hinted at. So far
as the evidence goes, it seems to be established that geometry, as
consisting of logical deductions from stated premises, began with the
Greeks. A number of theorems of a fair degree of complexity had been
developed before they were reduced to a system; before, that is, the
assumptions on which they were based were made explicit. The task of
discovering the necessary and sufficient assumptions on which a system
of geometry rests is one of the greatest difficulty; the necessary
combination of subtlety and rigour is rare. The great systematisation
of Greek geometry was effected, of course, by Euclid, and although
his reduction of the system to its essential assumptions was not
final, his performance was such as to awaken the admiration of great
mathematicians in every succeeding century. But there is one point in
which this great reduction is notably imperfect--the so-called parallel
axiom. It says, essentially, that through a given point only one line
can be drawn parallel to a given straight line. It was felt, even
by the earliest commentators on Euclid, that this postulate did not
possess quite the same degree of self-evidence as was manifested by the
others. It was necessary, they felt, to give a proof of this postulate;
they attempted to improve on Euclid’s work in a number of minor ways,
but it was the parallel axiom which they were most concerned to revise;
the proof of this postulate should be contained, they thought, in the
other postulates. The attempts to supply this proof were all fruitless,
and the sixth century was reached with this nine-hundred-years-old
disfigurement still persisting. For some time after the sixth century
the world rested from Euclid’s parallel axiom; indeed, it rested from
geometry altogether, and the old empirical outlook of the Egyptians,
and even their formulæ, again became current. But the Greek culture
penetrated to the Arabs, and with the Greek culture came the riddle of
Euclid’s axiom. Again proofs were attempted; a famous attempt is that
of Nasir Eddin, who flourished in the thirteenth century. In 1663 John
Wallis made the important discovery that unless the parallel axiom be
assumed, similar figures of different sizes are not possible, that
is to say, that if we are to assume that _shape_ is independent
of _size_, then we must assume Euclid’s parallel axiom. Many of
these attempts brought out points of interest, but none of them were
successful. In the year 1733, however, the whole research took on a new
complexion with the publication of Girolamo Saccheri’s _Euclides ab
omni naevo vindicatus_. The importance of this work consists in the
fact that, although it was written to vindicate Euclid’s parallel axiom
once for all, it contains the first real outline of a non-Euclidean
geometry.

Saccheri was a Jesuit, and it was in 1690, while he was teaching
grammar in Milan, that he first studied the _Elements_ of Euclid.
He was a man of very great acumen, and when he, in turn, succumbed to
the spell of the parallel postulate, he brought to bear on it a more
subtle and rigorous logic than had yet been applied to it. Thirty-six
years before he published his treatise on Euclid he had published a
book on logic which gives him a high place as a logician. In it he
is particularly concerned with investigating the compatibility of
different assumptions or postulates. His method was to determine
whether a member of a group of postulates is independent of the others
by finding a particular case in which the postulate in question is not
true while all the others remain true. If such a case can be found, it
is obvious that the postulate in question cannot be deduced from the
others, else it would be true whenever they were true. This was the
method he applied to the parallel postulate of Euclid. He showed that
the parallel postulate is equivalent to saying that the three interior
angles of a triangle are equal to two right angles. He proceeds,
therefore, in accordance with his method, to develop the consequences
of supposing them less than, or greater than, two right angles. In
the latter case he succeeds in showing that we are led to impossible
conclusions, since he assumed, as everybody assumed for more than a
century after, that the straight line is of infinite length. But in the
former case, the hypothesis that the interior angles of a triangle are
together less than two right angles, Saccheri, although he struggled
very hard, did not succeed in falling into contradictions. He does not
seem to have had the boldness necessary completely to trust his own
logic, but the fact remains that, accepting the rest of Euclid’s axioms
and denying the parallel axiom, he developed a logically consistent
geometry.

There is reason to suppose that Saccheri’s work had some influence on
subsequent thought, although its full significance was certainly not
perceived. The parallel axiom continued to be investigated, and the
total effect of all these efforts was to induce a doubt concerning
the absolute _necessity_ of the Euclidean geometry. Such a doubt
was very daring; for two thousand years the postulates of Euclid had
been accepted as absolutely true; the fact of their existence had
profoundly influenced philosophy, and, indeed, theology. But the
doubt persisted and grew, until finally, early in the nineteenth
century, a perfectly logical and consistent non-Euclidean geometry,
one explicitly denying the parallel postulate, was published to the
world. As so often happens, the great step was taken by two men
independently of one another, Lobatschewski, a Russian, and Bolyai, a
Hungarian. It appeared, however, that both had been preceded by that
great mathematical genius, Gauss, although he had been too timid to
publish his conclusions. The new geometry developed the consequences of
that one of Saccheri’s alternatives which supposed the interior angles
of a triangle to be less than two right angles. The whole outlook on
geometry now assumed a new complexion. Riemann tried the effect of
denying the infinity of the straight line and of developing Saccheri’s
other alternative. He found he was led to no contradictions. But with
Riemann’s work we come to a yet further extension of geometry--the
extension to space of four, five, or any number of dimensions. And
these investigations, which seemed for some time to constitute the most
gratuitous, although the most profound and subtle, exercises of the
mind, have now received their complete justification by flowering into
the Generalised Principle of Relativity.

THE NEW SCIENTIFIC HORIZON

About current scientific speculations there is one characteristic,
subtle, perhaps, but profound and far-reaching, which distinguishes
them from the scientific speculations of the Victorian age. We can
best isolate this characteristic by considering it as a particular
manifestation of something which is met with in nearly every
phase of contemporary life--something which may fairly be called
the _Zeitgeist_ of our time. This spirit is chiefly a sense
of unlimited possibilities, a sense that the radically new and
unprecedented may be upon us; with this feeling comes a recrudescence
of the spirit of adventure; there are unknown paths leading to vague
but--probably--splendid goals. In the Victorian age the main lines of
everything were settled; the chief features of the universe were known.
There were matter and energy, and there was, of course, the æther.
The astronomical and geological scales were known in broad outline,
and a first survey of the march from amœba to man had been taken. The
work of future ages was to fill in the details. The universe of the
Victorians was a large and rather grand affair, but it was sombre.
Those emotional barometers, the poets, in so far as they were aware
of the scientific outlook, either “transcended” it or were crushed by
it. Jules Laforge furnishes an excellent example of the effect of the
Victorian scientific outlook on an intelligent and sensitive mind.
His reaction was to compose funereal dirges on the death of the earth
and the extinction of mankind. The universe of the Victorians was
objective, indifferent, tracing a purposeless pattern in obedience to
“iron” laws. It was a universe which held no great surprises.

It is obvious that a very different spirit is abroad to-day. At the
present time the general consciousness seems to hold that almost
anything is possible. In part this may be accounted for, as in other
ages, by credulity based on ignorance, but there is also a credulity
based on knowledge, and it is this aspect of the general attitude which
deserves attention. The two kinds of credulity may be observed in
different believers of the same statements. Spiritualism, for instance,
has its followers amongst those who are unfamiliar with investigations
in the subject and amongst those whose belief has been compelled by
their very knowledge of the investigations. And disbelievers form
two exactly similar classes. There is also a credulity--the most
common kind--based on neither ignorance nor knowledge, but on partial
knowledge. Thus knowledge, but incomplete knowledge, of such phenomena
as wireless telegraphy or telephony, seems to predispose many people
to believe “wonders” which have no real connection with those
phenomena, but which are merely as inexplicable by partial knowledge.
Undoubtedly the recent developments in science are responsible for much
of this kind of credulity. But the new indulgence of possibilities,
as exhibited by the man of science, is dependent on quite different
considerations. To the student of physics, at any rate, the work of
the last two or three decades has been peculiarly disturbing. He has
been called upon, not merely to revise and extend his knowledge, but to
alter his assumptions. It is in this respect that the physics of our
own day chiefly differs from Victorian physics.

The distinctively modern epoch began with the promulgation of the
Electron Theory. That “matter” could be “electrified” was easily
granted. The fact that the famous question, What is electricity? could
not be answered was no difficulty in admitting the fact that, as a
result of certain processes, matter could be made to exhibit certain
phenomena which could conveniently be referred to the fact that it
possessed an “electric charge.” And the discovery of particles very
much smaller than a hydrogen atom presented no conceptual difficulties.
The fact that the ultimate particles of matter were smaller than had
been supposed could easily be granted; the new assumption was of the
same kind as the old one. And, further, to admit that each of these
particles possessed an electric charge made no unfamiliar demands on
the imagination. But the next step, that these particles consisted
of nothing but an electric charge--that was a very different thing.
The early popularisations of the idea show something of the mental
confusion it caused. “Disembodied charges of electricity” was a
favourite descriptive phrase; many physicists fought hard to retain
even a nucleus of “ordinary matter” on which this charge could be
supposed to be lodged. That an electric charge could exist apart from
matter seemed to many people as difficult to conceive as motion without
anything which moved. But the conception speedily became familiar; that
useful entity, the æther, soon made things easier. For the disembodied
charge, the electron, could be conceived as a local distortion of
some kind in the æther, and, by endowing the æther with some sort of
substantiality, the hypothesis that matter was in some way built up
out of this primitive substance could be tolerated. But the general
effect of the theory was to give a more philosophical tinge to science.
The gross, easy assumptions of everyday thinking about “matter” had
to be revised; articles were written showing that matter was really
immaterial, and materialism was conjectured to have received a severe
set-back.

The mind had barely become accustomed to the new assumptions before it
was again profoundly disturbed by the publication of Planck’s Quantum
Theory. The theory, which was invented to explain certain radiation
phenomena, asserted, briefly, that energy was atomic. One’s most
intimate assumptions were disturbed. Men of science are not usually
accustomed to philosophic exercises, and the idea that energy, which
they regarded as necessarily continuous, had an atomic structure seemed
at first almost meaningless. If we consider, for instance, the energy
possessed by a moving body, it seems natural to suppose that this
energy can be increased or diminished in a continuous manner; the idea
that its energy can only increase or decrease by finite jumps was a
very strange idea, and led again to a scrutiny of assumptions which
had appeared fundamental in science. Here, again, objections to the
new theory were sometimes the outcome purely of mental inertia, of an
inability to examine and discard a way of thinking which seemed almost
a necessary consequence of the structure of the mind. The last great
_bouleversement_ of one’s fundamental assumptions has been, of
course, Einstein’s generalised theory of relativity. Here we are asked
to revise our most deep-rooted assumptions--so deep-rooted that we are,
for the most part, unconscious of them--our assumptions regarding space
and time.

It is this thorough overhauling of primary assumptions which
distinguishes the modern progress in physics from all the progress of
the Victorian age. Physics has not merely been extended, it has become
a radically new thing, and there are very good reasons for supposing
that it is going to change still more. A certain sense of unknown
possibilities is therefore natural, even if it be the product merely of
bewilderment. The total effect of the new ideas is to make the universe
of physics less objective; to an unsuspected extent this indifferent
universe, with its iron laws, is a product of our own minds. To some
extent this fact was always recognised, particularly by the Continental
physicists, but as a general persuasion it is comparatively recent.
We cannot escape the structure of our own minds, it is true, but we
do not yet know what that structure is; we do not know what barriers
are breakable; we do not know what thoughts are thinkable by man. A
universe in whose construction so plastic and mysterious an entity as
the mind of man collaborates, may very well hold great surprises.

THE HOPE OF SCIENCE

It is not an unfair judgment, we think, that decides, on a survey
of contemporary intellectual activities, to grant science the first
place. Whether we consider the quality of the work which is being
done, its importance to mankind, or the spirit in which the work is
done, we think science earns that place. Our age is a scientific age
to an extent which is certainly not generally realised. Contemporary
scientific work is of a quality fully comparable with that of the
greatest periods of its history; it is inevitable that our age should
emerge, in the history of the future, as an age of science. It has,
indeed, already established a perspective which leads to a revaluation
of the Victorian age. There have already been many writers who have
thought that age more memorable for its science than for its other
achievements, that its significance to humanity lay more in the work
of Darwin, Faraday, and Maxwell than in that of Tennyson and Matthew
Arnold, or even in that of Mr. Gladstone, but the perspective we have
now obtained puts the matter almost beyond doubt. With most of us our
outlook is the result of a decrepit tradition. Our orientation towards
life, so far as we are conscious of having one, is based upon the
values we attribute to the various objects of our thoughts, and these
values are determined partly by our instinctive desires and partly by
the suggestions of our education--using the term “education” to include
all converse with the minds of our fellows. Education, so defined, is
the result very largely of a long and widespread tradition, a general
tradition of European culture. It is a curious fact that, although
the history of science goes as far back as the history of the arts,
science is not an integral part of this, nevertheless, very catholic
culture. There are periods, it is true, when some scientific theory
is sufficiently dramatic, or appears sufficiently pertinent to man’s
destiny, to secure general attention; Newton’s theory of gravitation,
Darwin’s theory of evolution, and Einstein’s theory of relativity have
each given rise to such a period. Einstein’s theory, we are informed,
is now the favourite topic of enlightened conversation in Parisian
salons, as Newton’s theory once was. Some of this interest, no doubt,
is the product of disinterested curiosity, and in that respect is
vastly different from the once general interest in Darwin’s theory.
But we fear that many of those who are curious about Einstein’s theory
would, if they understood it, find it uninteresting. We dare not
interpret this curiosity as a sign that people are beginning to be
as naturally interested in science as they are in literature, for
instance.

Nevertheless, we believe that the old culture is moribund in the sense
that its particular scale of values is undergoing revision. Science
is becoming less an affair for specialists; it is acquiring a “human”
value. An increasing number of people are beginning to realise that a
great science, such as Physics, may offer objects for contemplation
which are as delicate, as subtle, as exquisitely harmonious as the
dreams of Plato--and much better founded. And in relation to man, his
present state and possible future, science alone, to those who are not
satisfied with less than verifiable knowledge, speaks with the accent
of authority. The great constructions of science are grandiose without
being chimerical; they are beautiful but not deceiving. Indeed, one
sometimes has the feeling that it is only in science, nowadays, that
one still meets with the spirit of adventure, the sense of boundless
and glorious possibilities, with an exultant hope. Our poets and
men of letters generally are extraordinarily tame and disillusioned
creatures compared with our romantic and daring men of science. It is
refreshing to turn from the lamentations of our literary men to such
a book as the _Space, Time, Matter_ of Hermann Weyl, if only for
the fervour, the immense enthusiasm with which that highly accomplished
mathematician writes. Einstein is his Columbus, with the difference
that his America has indicated the existence of yet vaster continents.
And this enthusiasm is justified by its fruits; it has inspired Herr
Weyl to make what is unquestionably the greatest advance on Einstein’s
own work which has yet been made. It is not in Physics alone that we
find this note. To the biologists, also, the world has become young
again. Should our ignorant and unimaginative politicians, and our
still more ignorant and unimaginative business men, succeed in turning
the whole heroic effort and age-long struggle which has produced our
present culture to a mockery, they will put an end to a curiously
interesting and promising transition age, to an age which is at once
_fin de siècle_ and at the morning of a glorious renaissance.
But if they do not succeed, if the ordinary man shows himself even a
little worthy of the immense travail of his species, then we prophesy
that science will become an integral part of the culture of the future.
The new physics, the new biology, the new psychology, will be too
obviously pertinent to all man’s chief preoccupations for us to be
able to pretend that the present narrowly conceived _humaniora_
furnish a liberal education. We even believe that if the old arts are
to become youthful again, it must be by a transfusion of blood. It will
not be sufficient that the philosophy and literature of the future
should “accommodate” themselves to the scientific outlook; they must be
inspired by it.

Meanwhile, scientific men must be charitable; they must believe the
best. If science is to become an integral part of culture, scientific
men must help to make this possible. We believe that much of the
present interest in science is genuine; that it springs from a serious
attempt on the part of many people to find out what science can tell
them about themselves and the Universe they live in. Science is not
hunted purely for its dividend-earning capacities or for its power of
providing new thrills. Einstein, we understand, is suspicious of the
popular interest his theory has evoked; “a mere fashion,” he says. And
doubtless his suspicion is largely justified. But we believe there is
more in it than that--that there are many who, besides valuing the
delightful dreams of the poets and philosophers, have an affection for
_knowledge_. And when they find that the constructions of science
are not one whit less delightful than the dreams of the poets, this
affection may give rise to a permanent attachment. And with these new
objects of interest will come a change in values. Men will learn to
differentiate in their beliefs between those which are mere indulgences
of emotion and those which correspond to objective truth. This is the
path by which the mind becomes mature. It may not be, in all stages,
a pleasant process, but it leads to increased freedom and increased
power. The impossible will no longer be attempted, but the region of
the possible will be seen to be vastly greater. Man will see in what
directions he can shape his destiny, and he will be able to enter on
the task with a rational hope. All his courage and endurance will have
a chance of victorious achievement; he will know that he is not engaged
in a forlorn hope; the world will become young again.

THE RETURN OF MYSTERY

“It is a universal condition of the enjoyable that the mind must
believe in the existence of a law and yet have a mystery to move about
in.”--JAMES CLERK MAXWELL.

That our thinking, and with it our feeling, is largely conditioned
by assumptions which have no logical necessity, is a commonplace of
philosophy, and is indeed apparent to the slightest introspection.
Characteristic of any age is a body of beliefs, resting on more or less
good evidence, and a group of feelings associated with those beliefs.
The German language, so rich in indefinite but valuable general terms,
afforded the word _Zeitgeist_ for this complex, a word we have
directly translated into the Spirit of the Age. The name is a good
one; it indicates that we are dealing with something which is widely
diffused and also subject to change. It is subject to change, but it
plays a dominating rôle in the age to which it belongs. The Spirit of
the Age is something that practically all the intellectual life of the
age has in common. It is not manifested only in philosophical treatises
or in works of art; it is often manifested even more strikingly in
statesmen’s speeches and a country’s domestic and foreign policy. It is
a kind of intellectual and emotional atmosphere of which everybody is
aware, but which probably nobody could define. We see, however, that
a very important part of it consists of a sense of probability, of a
tendency to accept certain kinds of explanation and to reject others.

For the last few decades, at any rate, Science has been the chief
factor in forming this omnipresent sense of probability. As a matter
of fact, it is probable that the influence of Science in forming
the Spirit of the Age can be traced a very long way back, as far
back as Copernicus. Not that we assert the existence of a close
connection between the Science and the other intellectual activities
of Copernicus’s own age. The influence of which we speak is likely to
manifest itself gradually; in particular, it may take a long time to
affect the arts. And by the time it has percolated so far its origin
may be forgotten; it may appear as a subconscious rather than as a
conscious group of assumptions. By the time a scientific discovery
becomes part of the mental furniture of an age, many of what were
originally its possible implications will have become an integral part
of it. The original discovery will then be merely the nucleus of a rich
intellectual and, possibly, emotional complex, of which the parts are
no longer envisaged separately. The work of Newton, for example, and
the great body of exact investigations he made possible, influenced the
outlook of the nineteenth century chiefly in the direction of making
determinism plausible. Such lecturers as Tyndall could confidently
appeal to this mental predisposition on the part of their audience,
although they had no need to postulate any direct acquaintance with the
work of Newton and of his successors. The fact that Newton successfully
formulated exact laws for the description of natural phenomena is
the important aspect of his work from our present point of view. The
influence of Copernicus was rather different. From the point of view of
the history of Science his importance is that he made Newton possible;
from our present point of view his importance is that he made Darwin
possible. Copernicus’ destruction of the isolated position of man’s
planet in the solar system prepares the mind for Darwin’s destruction
of the isolated position of man in the animal kingdom. They each
shocked the same set of prepossessions.

The “materialistic philosophy” which was so marked a feature of the
latter part of the nineteenth century, and which still forms, we
believe, the prevalent intellectual complexion, owed the whole of its
plausibility to its supposed scientific backing. Its basis was not
merely biological; physics played quite as great a part as biology.
The notion of determinism derived its strength, as we have said,
chiefly from physics; biology was not in a position to demonstrate the
exact correspondences required. The ultimate grandiose vision of the
purely natural and inevitable march of evolution from the atoms of
the primitive nebula to the British Association for the Advancement
of Science, as outlined by Tyndall in his Belfast Address, assumed
the results of physics and astronomy as much as Darwin’s _Origin
of Species_. It was because biology was not the only science
involved that it was possible to found a “materialistic” philosophy
on Darwinism. One primary assumption of that philosophy, that life
arises from “dead” matter, not only had no biological support, but had
been decisively refuted by the experiments of Pasteur. But, as related
to the general movement of Science, the hypothesis had the necessary
plausibility. Considering the then existing evidence, this hypothesis,
together with the hypothesis that mental states are produced by atomic
movements in a strictly determinist manner, are, indeed, striking
instances of the way in which the _Zeitgeist_, as much as the
evidence, determines the direction of our thinking.

The importance of such conceptions cannot be over-estimated. Directly
or indirectly they influence the whole life, if not of their time, then
of an age which succeeds them. The philosophy in question had existed
for centuries, of course; what made it influential was the scientific
backing it received, for, in these matters, Science has for some time
past played the dominant rôle. Neither religion nor philosophy has been
able successfully to oppose it; nowadays, indeed, they seem concerned
only to agree with it. And if, here and there, a few artists have
felt themselves outraged by what were supposed to be the teachings
of Science, their influence has not been sufficient to deflect the
stream. Such isolated protestants have had nothing but their feelings
to oppose to what were considered to be facts, and the world, with what
may have been a stupid honesty, has followed after the supposed facts.
But the influence of Science on the arts would require a separate
investigation. A certain stability is given to some serious art by
its own tradition, and this may lessen its sensitiveness regarded
merely as an indication of the spirit of its age. It is, nevertheless,
very sensitive. In a history of modern literature, for example, it
is impossible to exclude direct references to Darwin; it is usual,
indeed, to devote some space to such “influences.” And the artist who
is not at home in his age may be reduced to impotence by it. Dostoevsky
is a magnificent example of a writer who, extremely sensitive to the
spirit of his age, and profoundly understanding it, strove to transcend
it. A smaller Dostoevsky might well have been nothing. And is a
post-Darwinian Beethoven, or a post-Darwinian Dante, really conceivable?

Now it is unfortunate that, so far as scientific discoveries form
the Spirit of the Age, they do so at second-hand. The _Origin of
Species_ happens to be easy to read, but even so that body of
thought known as “Darwinism” owes its influence chiefly to such
expositors as Huxley and Tyndall. The thing becomes set; it assumes
hard, bold outlines; the issue has to be presented with something of
the simplicity of an election cry. The universe of Science becomes
finally a universe from which all mystery is banished and where the
only ultimates are small, incompressible spheres whose movements and
combinations produce--everything. The chasm separating this conclusion
from the actual scientific evidence is not realised. Very tentative and
almost fantastic hypotheses become dogmas, and it is as dogmas that
they become influences. As a matter of fact the scientific evidence,
even of Darwin’s day, suggested quite other possibilities than those
popularised as a “materialistic” philosophy. James Clerk Maxwell,
who had a profounder insight into physical reality than any other
man of his time, in a very little known essay, draws attention to
the “singularities” characteristic of certain natural phenomena, and
suggests that there are more singular points the higher the rank of the
existence. “At these points, influences whose physical magnitude is too
small to be taken account of by a finite being, may produce results
of the greatest importance,” and he warns his readers against “that
prejudice in favour of determinism which seems to arise from assuming
that the physical science of the future is a mere magnified image of
that of the past.”

Maxwell’s remark is now seen to have been prophetic. The
extraordinarily profound and far-reaching philosophical implications
of the theory of relativity have hardly yet begun to be investigated,
but we have already a general sense of their direction. Hermann
Weyl’s _Raum, Zeit, Materie_, for instance, the most thorough
mathematical exposition of the whole theory which has yet appeared,
hints not obscurely at the philosophical bearing of the new
investigations. Now that, by Weyl’s own work, Maxwell’s electromagnetic
equations are included by the theory, it seems to be scientifically
complete. It presents us with a picture of the universe which is wholly
unlike the picture of the early physics. In particular, an altogether
different rôle is assigned to the human mind. So far as the exterior
universe and the laws of nature are concerned, we see that the primary
entity is the mind itself. It is the mind which has created, not only
space and time, but the matter it has put within that framework. The
mind has not created the universe out of nothing, it is true. But it
is almost impossible to say anything intelligible in the old sense
about the fundamental entities to which Einstein’s theory leads us.
Professor Eddington suggests that they may be “the very stuff of our
consciousness,” a somewhat mystical remark which nevertheless shows
the trend of the new speculations. And, as a striking confirmation of
Maxwell’s view of the possible development of physical science, we may
quote one of the last sentences of Weyl’s profound discussion: “It
must be emphatically stated that the present state of physics lends no
support whatever to the belief that there is a causality of physical
nature which is founded on rigorously exact laws.” Unfortunately not
all men are mathematicians. The great and wonderful vista now opened
up by Science--greater and more significant, we believe, than has
existed at any previous time in the history of thought--is at present
a consequence of highly abstruse investigations. The sheer technical
difficulty of these inquiries will long hinder them from exerting their
due influence on philosophy and, through philosophy, on the whole of
the intellectual life of the age. But the new conceptions exist, and
they derive their unshakable strength from the fact that they are the
result of the severest Science. And surely no one can fail to see
that they promise not only fascinating regions for thought, but a new
liberation of the human spirit. Mystery, but more wonderful and full of
promise than ever, has been restored to the universe.

MATHEMATICS AND MUSIC

It is possible that the old heading “Arts and Sciences” has been
responsible for some of the barrenness which is so conspicuous a
feature of æsthetic theory. For the heading seems usually to have
suggested, not only that there is a difference between the arts and the
sciences, but that the difference is of a fundamental kind. For the
purposes of æsthetic theory the various arts are assumed to have more
in common than any one of them has with any of the sciences. We find
the writer on æsthetics expounding his principles in chapters headed
Painting, Sculpture, Poetry, Music; but it is rare indeed to find the
argument extended to mathematics and physics. Yet there is no evidence
that such omissions are due to deliberate reflection; the philosopher
has not decided, after examination, that the sciences are unæsthetic
objects; we must assume that accidents of taste and education have
prevented him from paying attention to what may conceivably be useful
data for the formulation of a theory of æsthetic. Within the last two
or three generations scientific men have been thinking and writing
a good deal about the philosophic basis and implications of their
study, and it is significant that this inquiry has led many of them
to insist on the æsthetic character of the satisfactions that science
affords. The late Henri Poincaré, in particular, has shown that
scientific theories are akin to works of art, and in this country, Dr.
Norman Campbell has asserted his belief that great men of science are
essentially great artists. The point of view is an interesting one,
and suggests that fresh light may be thrown upon æsthetic problems by
a new grouping of their subject-matter. Instead of putting the arts
and the sciences on opposite sides of the fence, it may be helpful to
see whether certain members of these two groups have not a natural
affinity with one another, and so gain hints for a different and more
comprehensive classification.

It is noteworthy, in this respect, that music has always occupied an
exceptional position among the arts. Pater tried to relate it to other
arts by saying it was the art to which all others aspire:

The arts may be represented as continually struggling after the law
or principle of music, to a condition which music alone completely
realises; and one of the chief functions of æsthetic criticism,
dealing with the products of art, new or old, is to estimate the
degree in which each of these products approaches, in this sense, to
musical law.

It is characteristic of Pater’s criticism, and of much of the criticism
of his school, that it exists, as it were, within a world of its own.
The meanings to be attached to his most important terms are always
suggested or insinuated; they are never defined. The method is useful,
perhaps even necessary, in dealing with a complex and elusive object,
and where appeal is made to perceptions which lie on the fringe of
consciousness. But it runs the grave danger of becoming altogether
too tenuous to be intelligible when we make direct reference to the
object it is supposed to illuminate. When, for instance, Pater says
of the best music, “the end is not distinct from the means, the form
from the matter, the subject from the expression,” we become acutely
aware of the absence of definition in each of these primary terms
directly we think of any actual composition. We feel, indeed, that the
terminology is not natural; in contemplating a poem the mind may be
naturally impelled to distinguish between subject and expression as a
kind of first effort in analysis; it is doubtful whether, in listening
to music, this direction for analysis ever presents itself. So that
to say that in music subject and expression are identical is not to
say anything useful about music, but merely to declare that that kind
of analysis is irrelevant. It is very probable that nothing is to be
gained by first making distinctions which have a meaning for other arts
and then bringing music into the scheme by saying that for music such
distinctions become meaningless.

But if we are to maintain that this kind of criticism is irrelevant,
then music becomes not only an isolated art but the art of which we
know least. If it cannot be accommodated as an example within the
general body of æsthetic criticism, the criticism that uses such terms
as Pater uses, then whatever general conclusions the multifarious
writings of the last two centuries on the “beautiful” may be considered
to have reached are not applicable to music. In this extremity it is
natural, nowadays, to become “scientific.” Comparative studies are
undertaken: the music of Java is compared with the music of Bach: the
evolution of musical devices is made clear; the psychological condition
of the patient under music is examined: the time taken for the right
degree of hypnosis to be induced is determined. That such methods may
one day stumble upon important facts it would be rash to deny, but
nothing has yet been reached which illuminates the particular problem
that music presents. We are frankly of the opinion that, so far, the
difficult utterances of certain mystical or semi-mystical writers throw
more light on the real nature of music than do those of common sense.

Among such writers on music Schopenhauer is notorious; and it is worth
while to dwell a little on his speculations, fantastic as they may
seem, since they contain an element common to all such interpretations,
which does serve to isolate the essential problem of music. In
Schopenhauer’s æsthetic the object of all arts, except music, is to
lead, by the description of objects, to the recognition of the Ideas
(Platonic) whose appearance in multiplicity constitutes the world.
All arts, therefore, have a transcendental function; their aim is to
reveal to us the Platonic world of eternal essences or Ideas. But they
have to raise us to this region _via_ the objects of experience;
in that sense they are also, therefore, concerned with the world of
appearance and are dependent upon it. The case is different with music.
Music is not concerned with the external world either as a symbol or as
a reality. It is not even, in Schopenhauer’s language, concerned with
the Ideas, but refers directly to that “Will” which, in Schopenhauer’s
philosophy, underlies the Ideas themselves. The essence of his theory
is given in the following passage:

... so ist die Musik, da sie die Ideen übergeht, auch von der
erscheinenden Welt ganz unabhängig, ignoriert sie schlechthin, könnte
gewissermaassen, auch wenn die Welt gar nicht wäre, doch bestehen:
was von den anderen Künsten sich nicht sagen lässt. Die Musik ist
nämlich eine so unmittelbare Objektivation und Abbild des ganzen
Willens, wie die Welt selbst es ist, ja wie die Ideen es sind, deren
vervielfältigte Erscheinung die Welt der einzelnen Dinge ausmacht.

Or, as he says a little later on, the world may be regarded as embodied
music.

It is not likely that anyone will take Schopenhauer’s philosophy of
music seriously; and even those who are sympathetic to his general
view are not likely to find their sense of the ludicrous undisturbed
by his identification of bass notes with the planets, tenor notes with
the vegetable world, and so on. The intensity of his response to music
and his humourless courage have led him to what are perhaps the most
fantastic statements in all his writings. But what is worth noting is
that so imaginative and fertile a speculator, because he was genuinely
sensitive to music, had to give it a profoundly isolated position in
his æsthetic. In so doing we think he recognised one very important
difference between music and the other arts. It is true that music is
independent of the world of experience in a way that other arts are
not. It is true that there is a sense in which Schopenhauer is right
when he says that music would exist even if the world did not. We
can see what is meant if we compare the development of a “dramatic”
piece of music, such as the first movement of Beethoven’s C minor
Symphony, with a great tragedy. The tragedy, as a condition of success,
must make reference to our experience of life. The ostensible matter
of the tragedy, the characters and incidents, must not violate our
conception of reality if they are to be accepted. The tragedy must be
plausible. Such considerations obviously do not apply to music. It is
meaningless to say that the development of a composition must satisfy
our sense of probability. Yet there is a meaning in saying that its
development seems either arbitrary or inevitable. The analogy that
immediately presents itself is a chain of logical reasoning, as in
the sustained development of a mathematical theorem. Such development
is independent of all experience; the mind is obeying none but its
own laws, and is paying no attention to any alien elements. And it is
this characteristic of mathematics which seems responsible for the
fascination the study possesses for its devotees.

Remote from human passions, remote even from the pitiful facts of
nature, the generations have gradually created an ordered cosmos,
where pure thought can dwell as in its natural home, and where one, at
least, of our nobler impulses can escape from the dreary exile of the
actual world,

says Mr. Bertrand Russell in a typical passage. A strain of romantic
eloquence seems, indeed, to be inseparable from the writings of
mathematicians on their subject. But the analogy can be pressed more
closely. There are elegant and inelegant mathematical demonstrations,
those which merely “command assent,” as Lord Rayleigh said, and those
which provide a very high degree of æsthetic satisfaction. In these
latter demonstrations the mind seems to be moving with more swiftness
and freedom; the whole demonstration seems to flower in a natural
and spontaneous way; we have the impression of _inevitability_.
Mathematical elegance, as Poincaré has put it, “n’est autre chose que
la satisfaction due à je ne sais quelle adaptation entre la solution
que l’on vient de découvrir et les besoins de notre esprit.” It is
as if there were a mode of living natural to the human spirit, an
_unadapted_ life, a life free from the necessity of accommodating
itself to the elements, so largely alien, of the actual world.
Mathematics is the expression of this life so far as the intellect is
concerned. Is it too much to say that music is a fuller embodiment of
this free life?

If we are to say this we must acknowledge that more than the intellect
is capable of this free life, that there is a logic of the emotions as
well as of the mind. This assumption is not difficult to make; indeed,
if we reflect on our experience of some compositions, such as, to take
the same example, the first movement of the C minor Symphony, it is
difficult to avoid making it. And, in considering the matter from this
point of view, we may gain some results useful for musical criticism
in general. The theme of the movement in question is characteristic
of many of Beethoven’s themes in that it does not serve merely as a
kind of structural skeleton on which a composition is to be built. In
this respect it differs from, for instance, many of Bach’s themes.
The theme immediately, in its ominous and arresting quality, throws
the mind into a certain state of expectancy, a state where a large
number of happenings, but only the happenings belonging to a certain
class, can logically follow. As an analogous vague yet restricted
initial preparation we may instance the entry of the witches at the
beginning of _Macbeth_. As the music proceeds this rich, but more
or less definite, state in the hearer becomes more and more precise,
more and more subtle. It is, as it were, explored and shown in all
its height and depth. What was pregnant in the theme is exhibited
to us in all its extent, its definiteness, and its force. The theme
was the entrance to a world. And we have the consciousness of logic,
of _inevitability_, because at no point are we constrained. We
exult because we are free; this is how we, too, would move but for
our fetters, our alien, arbitrary fetters from which, for this time,
we have been freed. And in none of this, unless we have incurably
literary minds, are we ever reminded of experience. This life is no
life that we have lived or that, on this planet, we could live. Music
is as independent of the world as mathematics, but it cannot, like a
system of geometry, even be applied to the real world as an hypothesis.
It is even doubtful how far the emotions it expresses, when it is
merely expressing emotion, correspond to those of real life. The
sorrow of the bereaved father is not the same thing as the sorrow
of the bereaved lover, but music can express sorrow with thousands
of _nuances_. It is customary to say that the emotions of music
are generalised emotions; that its sorrow, for instance, is a kind of
common denominator of all sorrows. But the exact opposite seems to be
the case. The situations of real life, like the resources of language,
are probably too limited to afford correspondences to the immense
variety of emotions expressible in music. The musician is as free as
the non-Euclidean geometer to create worlds which have no objective
counterpart.

It is natural, therefore, in comparing the arts, that we should class
mathematics and music together, since they resemble one another by
their most intimate characteristics and differ, in these respects,
from all other arts. It is worth noting, in this connection, that it
is only in mathematics and music that we have the creative infant
prodigy. Experience and learning, compared with what we vaguely call
“instinct” or “gift,” play a comparatively insignificant rôle; the
boy mathematician or musician, unlike other artists, is not utilising
a store of impressions, emotional or other, drawn from experience or
learning; he is utilising inner resources so obviously independent of
experience that, like Plato’s slave, he seems to have brought them
with him from some anterior life. And the artistic progress of a
musician, if it be a true progress, means primarily that he is making
ever more accessible the riches of this inner life. It is difficult
to avoid mysticism, or at least Platonism, at this point. But here
again it seems to us that Schopenhauer understood something essential.
When he says that music, like the Platonic ideas, is an embodiment
of the “Will” that underlies all things, he does at least say that
what is revealed to us by a composition is something other than the
“personality” of the composer. The function of music is not, like
that of literature, to illuminate this world, but there is a world it
illuminates--a world at least as vast and independent of this one as
that mathematical “cosmos” described by Mr. Bertrand Russell.

There is much music, of course, which suggests no such mystical
fancies. With most of Wagner’s music, for instance, there is no hint
of other worlds, but rather a gorgeous colouring of this one--or of
those aspects of this one which excite romantic poets with strong
bodily appetites who can assume the background of the vigorous
material prosperity of the nineteenth century. Such music is fully
comparable with a certain kind of literature; all it lacks is the
definiteness of statement, and hence the intellectual clarity, which
the use of language affords. It may be even more powerful and subtle
than literature can be--_Tristan und Isolde_ expresses certain
emotions with immense adequacy. But it is not doing something which
music alone can do; and, for that reason, it throws very little light
on the peculiar problem of music. For the peculiar problem of music
consists in its independence, in its power of transporting us to a
world which is not otherwise revealed. To Schopenhauer, to whom both
the world and music were embodiments of the same Will, there was a
musical equivalent for every experience; and, it would seem to follow,
for every musical utterance there is a corresponding experience.
The two worlds are independent, but there exists between them, as a
mathematician would say, a one-to-one correspondence. Yet he very
strangely goes on to accept the theory that a musical utterance is a
kind of generalisation of a number of distinct experiences. He points
out that the musical setting of a poem, for instance, will serve for a
number of similar poems. It is the “kernal” of all these poems which
is given directly by the music. But it is equally true that the same
poem will serve for several musical settings. When Beethoven, as one
of sixty-three composers, composed his setting of Carpani’s poem “In
questa tomba oscura,” he probably composed the best setting, since it
is the only one that has survived; but among the other sixty-two there
must have been many which, in Schopenhauer’s phrase, were expressions
of the “kernal” of the poem. The fact seems to be that, unless music
is deliberately illustrative, it is not concerned with what is
otherwise expressible. That is why musicians are always dissatisfied
with “literary” descriptions of music. However good in their own kind
they may be, they are always felt to be irrelevant and even, in some
way, a degradation of the actual musical utterance. It is felt that
they exhibit a certain insensitiveness or lack of taste, as in that
curiously popular image which likens twin hills to a woman’s breasts.

As compared with literature, music is abstract. It is independent, as
literature is not, of the facts of life. But just as there is some
music which approaches to the condition of literature, so there is some
literature which approaches to the condition of music. Such literature,
while it is concerned with the world of experience, as literature must
be, is concerned with that world as symbol and not as reality. Such
literature, we might say, is not concerned to illuminate the world
of what we here call experience, but to reveal something about the
soul of man itself--or, if we prefer scientific jargon to mystical,
to deal with the normally subconscious rather than with the normally
conscious. Both kinds of literature have been called realistic, but
they are realistic from entirely different points of view. Dostoevsky,
for instance, regarded the realism of such writers as Zola as trivial.
And can _Macbeth_ be regarded as a realistic work, on the basis of
the French conception of realism? _Macbeth_ is, indeed, a striking
example of the extent to which literature can approach the condition
of music. The whole apparatus of the play, the witches, the characters,
the incidents, are so obviously not presented for their own sakes, but
as symbols through which an overwhelming perception was to be conveyed.
Here the fact that the literary artist must accommodate himself to the
laws of the real world, that he must satisfy our sense of probability,
seems hardly a hindrance. Our sense of probability is, indeed,
purposely lulled by the entrance of the witches at the beginning. We
are made aware that not the real world alone is concerned. In this
respect the supernatural “machinery” of _Macbeth_ performs an
altogether different function from that in _Hamlet_. The whole of
_Hamlet_ is perfectly realistic in the tight sense. But the fact
that literature must always use symbols differentiates it utterly from
music. And just as we have seen that real life may present no analogies
to what is revealed in music, so it may happen that the literary artist
who has access to a wide and deep inner life may find no symbols, such
as are essential to literary art, to convey his perceptions. Mr. T.
S. Eliot has stated that _Hamlet_ is an artistic failure because
the whole play, considered as presentation in terms of symbols, does
not adequately convey the emotions or perceptions we confusedly feel
Shakespeare is trying to express. Whether or not Mr. Eliot is correct
in his instance, his general thesis is perfectly sound. Even if
_Hamlet_ could be re-written so as to satisfy Mr. Eliot, it is
still true that there are some perceptions, states of mind, emotions,
or whatever one likes to call them, which it is very difficult to
believe are expressible in literature at all. Santayana gives a neat
but somewhat trivial instance in one of his essays where he says that
there is no human incident or group of incidents which can serve as a
fitting symbol for pure radiant joy--a sort of prolonged, exultant,
celestial state of joy. A shadow, to the mature mind, lies over the
brightest and most delightful of life’s happenings. He suggests that a
poet who should try to imitate music in this respect could do little
but write the word “Joy!” with exclamation marks. He could write
nothing else that was unambiguous. And, indeed, a symbol is always
ambiguous unless, like the symbols of the mathematician, its meaning is
completely exhausted by its symbolic intent. The symbol distracts; it
brings with it a crowd of irrelevant associations, and for that reason,
even when the symbols are most superbly handled, as in _Macbeth_,
the resultant communication is less definite than with music. But the
very great, the immense, importance of literature lies in the fact that
it can, partially at least, shape the facts of life so as to make them
consonant with the nature of man. If experience can furnish symbols
which express the deepest needs and aspirations of the soul, then life
can be, at least partially, illuminated. For man can understand nothing
which is not consonant with his own nature. The literature which truly
illuminates life is the literature which interprets life most fully
in terms of our own emotions and aspirations. In this sense not only
all literature, but all science, is anthropomorphic. Science is only
possible in so far as it is logical. That is to say, the universe can
only be understood in so far as its happenings are obedient to the laws
of man’s own mind. In its relation to mathematics, where the mind pays
no attention to the arbitrary conditions of experience, physics plays
something of the same part as is played by literature in its relation
to music. Both physics and literature, in their universal function,
are concerned with a world which _need_ not obey the laws native
to the spirit of man. Such illumination as they can give is dependent
upon, as it were, what correspondences they can find. The revelation of
life afforded by _The Brothers Karamazov_, for instance, consists
in relating the phenomena of life to the deepest impulses of the spirit
of man. Only so does life become in any measure truly comprehended;
and it is in this respect that such works differ from those reports
on life where we may recognise and assent to everything, but where
our comprehension of anything is not deepened. Such works as _The
Brothers Karamazov_ may be called philosophic, if we use the word to
include something other than purely intellectual understanding.

We have suggested that, if mathematics may be taken as the intellectual
analogue of music, then it is not perhaps too far-fetched to say that
such a science as physics may be taken as the intellectual analogue
of literature, since both are concerned to interpret what we call the
real in terms of what we call the ideal, while the two former arts
are not concerned with the real. And the question arises whether the
arts, mathematics, and music, which are not concerned to illuminate
experience, are worthy of serious attention. In the case of mathematics
the answer is not doubtful, since it has repeatedly shown itself
applicable to real happenings, however little notions of utility may
have played a part, or need have played a part, in its creation. Even
the most remote mathematical theorems are not certainly immune from
practical application. But no such claim can be made for music, and
it is for that reason that to some philosophers music is a pleasing
but essentially trivial art. To such philosophers music, while it may
suggest spiritual profundities, is, after all, saying nothing of any
possible significance. The adventures of the soul that it depicts are
less significant even than a stage fight. Its one justification is the
pleasure it affords; it takes us out of ourselves in a way no other art
can do, and after this refreshing interregnum we return to the things
that matter. It may be so; we can give no proof that it is not so; we
can only say we find the point of view incredible. On this point,
again, we certainly find the mystical view of Schopenhauer, if less
intelligible, at least more convincing than that of common sense.

HUMAN TESTIMONY

Everybody normally acts on the assumption that the value of human
testimony is an extremely variable quantity. The rules by which we
assess the value of testimony, in the ordinary affairs of life, are of
that thoroughly habitual kind that hardly involve conscious processes;
they repose on two judgments, which we are always making. Our belief in
direct testimony to an event is conditioned by the nature of the event
and by our estimate of the “personal equation” of the witness. These
two factors are not quite independent; it is very seldom, for instance,
that we attribute “general untrustworthiness” to anybody who is known
to us. Our experience usually teaches us that there are certain classes
of statements--e.g. his breaks at billiards, the number of miles
his motor-car runs on a gallon of petrol--for which that particular
witness’s credibility is at a minimum. For some other classes of
statements we may have learnt to take his word without hesitation. What
the mathematicians call the “credibility” of a witness is not, in the
case of any witness of whom we have personal knowledge, a constant
figure. It varies with the event, often in an extremely complicated
way. When Brown is listening to Jones talking about the enormities of
Smith the extremely delicate and rapid weighing of probabilities being
performed by Brown beggars any mathematical description. When the
witness is personally unknown to us the matter becomes simpler. Our
conclusions, one way or another, will be held with less confidence, but
they will be more simply arrived at. We may, on the evidence supplied
by the testimony itself--the tone of the letter, the man’s manner in
the dock--class the witness as a man of a certain type. Corresponding
to each type we have a rough scale of credibility for different types
of events. In cases where we know nothing of the witness beyond his
bare statement that he witnessed the occurrence of the event our
estimate of his credibility is based on very general and usually
rather vague considerations. We are guided by two things: the initial
credibility of the event and our estimate of the general value of human
testimony. Both of these criteria, and in particular the second, are
excessively ill-defined.

In the first place, what do we mean by the initial credibility
of an event? There are very few cases where this notion can be
precisely defined. The simple instances dealt with in the elements of
mathematical probability do, it is true, permit of precise definition.
The chance that a white ball will be drawn from an urn containing
five black balls and one white ball can be exactly estimated, for we
are in possession of all the very simple relevant factors. But the
probability that Romulus founded Rome obviously belongs to a very
different category. And what is the initial credibility of a miracle?
Hume, as is well known, thought that the _a priori_ incredibility
of a miracle was so great that its occurrence could not be established
by human testimony. He is here trying to establish a ratio between the
initial credibility of a class of events and the initial credibility
of human testimony to such events. He is taking some kind of average
in both cases, but it is difficult to see how such an average can
be arrived at. Vague considerations of this kind are of no value in
forming conclusions on matters of real interest to us, although they
may be sufficient to warrant a lazy scepticism regarding what William
James calls “dead hypotheses,” or may form the basis for amusing and
ingenious mathematical exercises. But we have no notion of an average
initial credibility which is of any use in practice; each case must
be judged on its own merits. And if, to take the second point, we
reached some average for the value of human testimony in general, we
should never, in practice, apply it. The utmost we can hope to do is
to establish a more or less constant relation between the testimony
of classes of witnesses and classes of events. We have to divide
witnesses into types, and for each given type estimate the value of
its testimony to different classes of events. We must investigate the
difference it makes when the witness is taken as isolated and when he
is taken as a member of a group of witnesses. In this way we may hope
to reach results which are of value in judicial procedure, in the study
of history, and in various particular investigations, including those
modern substitutes for miracles, the phenomena of spiritualism. We
are, in fact, to investigate man in his capacity as a truth-recording
instrument.

The result of such researches as have been made may be said, briefly,
to show that human testimony has much less value than is normally
assigned to it and, in particular, much less value than it is held to
possess in a Court of Law. The experimental results obtained in this
field are, indeed, often startling. It is hardly too much to say that
one’s first impulse, on becoming acquainted with the results hitherto
reached, is to fall back on a general and dismayed scepticism regarding
the value of human testimony to anything whatever. But a closer
examination of the results show us that this attitude is unwarranted,
and reinforces the common-sense assumption that the value of human
testimony is a matter of degree, varying from complete worthlessness
to a very fair presumption that the event occurred as stated. The
investigation is useful chiefly in showing us what factors influence
this value.

It is convenient to separate out these factors according to the scheme
recently employed by Dr. Edmond Locard, in his analysis of police
records over a number of years. The statements made by a witness
repose, in the first place, on sensations which he has experienced. It
might be thought too obvious to be worth mentioning that we require
the witness who heard a sound, for instance, to have reasonably
good hearing, and yet there are many cases where simple preliminary
considerations of this kind are not taken into account. Professor
Zöllner’s famous book _Transcendental Physics_, for instance,
alleged marvels that occurred in the presence of Slade, the medium;
and these alleged marvels, of great influence in spreading a belief
in spiritualism, were witnessed to by four professors, Zöllner,
Fechner, Scheibner and Weber. But a member of the Seybert Commission,
Mr. George S. Fullerton, as a result of personal interviews, found
that two of these professors, Fechner and Scheibner, were partially
blind at the time. Their sensations, therefore, in this respect, were
untrustworthy. But defects of this kind may usually be determined and
this factor conditioning the witnesses’ credibility allowed for. Where
a witness makes appeal to a sensation which may be checked the check
should always be imposed. Thus Dr. Locard gives an instance where a
witness stated that an event occurred in a mill at a certain hour.
How did he know the hour? By hearing a clock strike at the time the
event occurred. A test was made, and it was found that the noise of
the mill made the striking of the clock quite inaudible. The witness
then remembered that he did not hear the clock strike until he had
left the mill. Similarly, witnesses have testified that they saw a man
leave a doorway, their post of observation being one from which the
doorway could not be seen. Sensations may often be checked, however,
and, to a careful inquirer, they need not be a grave source of error.
But the next stage is concerned with the witness’s perceptions. Of his
sensations he will single some out for attention and neglect the rest.
He singles out those which, for some reason or another, interest him
most. It may quite easily happen, therefore, that the sensations most
relevant to the inquiry in hand have been neglected. They have been
filtered, as it were, through the medium of the witness’s interest;
and it is often the case that his interest has not been excited by the
sensations most pertinent to the subsequent inquiry. It is on this fact
that conjurers very largely depend for their success. The attention
of the audience is distracted; they are invited to dismiss certain
sensations as being of no importance, and, in general, it is remarkably
easy to ensure this distraction of attention. Dr. Hodgson’s case of the
English officer and the Hindu juggler well illustrates this point:

Referring to the movements of the coins, he said that he had taken a
coin from his own pocket and placed it on the ground himself, yet
that this coin had indulged in the same freaks as the other coins.
His wife ventured to suggest that the juggler had taken the coin and
placed it on the ground, but the officer was emphatic in repeating
his statement, and appealed to me for confirmation. He was, however,
mistaken. I had watched the transaction with special curiosity, as I
knew what was necessary for the performance of the trick. The officer
had apparently intended to place the coin upon the ground himself, but
as he was doing so the juggler leant slightly forward, dexterously and
in a most unobtrusive manner received the coin from the fingers of the
officer, as the latter was stooping down, and laid it close to the
others. If the juggler had not thus taken the coin, but had allowed
the officer himself to place it on the ground, the trick, as actually
performed, would have been frustrated.

Now I think it highly improbable that the movement of the juggler
entirely escaped the perception of the officer; highly improbable,
that is to say, that the officer was absolutely unaware of the
juggler’s action at the moment of its happening; but I suppose that,
although an impression was made on his consciousness, it was so slight
as to be speedily effaced by the officer’s _imagination_ of
himself as stooping and placing the coin upon the ground.

We have here an instance of erroneous testimony by a witness to his own
actions; testimony to the actions of other people is usually much less
trustworthy. In this matter of direct perception we may discriminate
still further. Tactile perceptions are of almost no value whatever. If
a witness be blindfolded and asked to determine, by touch alone, the
nature, the volume and the material of an object, it will be found that
the responses are very inaccurate. Experience of tactile sensations is
relatively small and deductions therefrom are practically valueless.
Thus the shock of a bullet entering the body may be interpreted as a
slight blow, several dagger thrusts in the back as one thrust, and so
on. A piece of ice drawn across the neck of a blindfolded man and warm
water simultaneously poured on his chest have been stated to cause
death by fright, the man having previously been informed that he was
going to have his throat cut. Perceptions of odour or of taste are even
less trustworthy; and here the difficulty of expression in precise
terms, in the lack of a precise vocabulary, is complicated by the fact
that the witness primarily perceives odours and tastes as pleasant or
unpleasant, and pays attention only to that aspect of them. In cases of
poisoning, therefore, evidence of this kind should be given very little
value.

It is only when we come to the senses of hearing and of sight that
we enter the region where perceptions may have evidential value. In
the case of hearing, however, we must still proceed very warily.
Experiment has shown that estimates of direction, for example, are
quite valueless, since the different estimates made by different
observers obey the laws of pure chance. Training can do a little, but
very little, to render these perceptions more trustworthy; in general,
however, evidence as to the direction of a sound may be neglected.
Estimates of the distance of a sound, also, are of very small value.
The intensity of a heard sound depends on the intensity of the source,
and also on its distance; and these two factors may be apportioned
by the observer in the most arbitrary manner. In the case where the
sound is articulate, as in overhearing a conversation, we are in the
presence of still other sources of error, due to illegitimate inference
and the association of ideas. For words which are not heard will be
supplied by the witness in all good faith. He will have a theory of
the purport of the conversation, and will arrange the sounds he heard
to fit it. Edgar Allen Poe’s example, in _The Murders in the Rue
Morgue_, of the cries of an ape which were interpreted as remarks
in different languages by different observers, is judged by Dr. Locard
to be not at all fantastic. The same general source of error applies
to visual perceptions. Not everything is observed, and the lacunæ
are filled in by the witness in what seems to him the most probable
manner. Oversights in proof-reading furnish a familiar example of this
kind of error. But psychological experiments have produced much more
striking examples. Claparède arranged for a man, wearing the mask of
a clown, to enter his lecture room while a lecture was in progress.
The students were afterwards asked to pick out this mask from a series
of ten, and out of twenty-three who attempted the task five only
were successful--and even these successes were probably due, largely
or wholly, to chance. The appreciation of distances, measured by the
eye, is also very likely to be erroneous, the rule being that large
distances are under-estimated and small ones over-estimated. A similar
rule holds good of estimations of intervals of time. Errors of this
kind are not pure errors of perception; they are due chiefly to lack
of experience. A carpenter or builder would usually make a much more
accurate estimate of the dimensions of, say, the side of a house than
would the ordinary person; and astronomers who work with transit
instruments have, as a class, very accurate perceptions of small
intervals of time. It is chiefly lack of experience, also, which is
responsible for the absurdly different estimates different observers
will make of the number of people in a crowd. Dr. Locard states that,
on questioning the policemen employed to keep order during a procession
as to the number of people they estimated to be taking part in the
procession, he obtained the figures five thousand, ten thousand,
twenty-four thousand. The actual number, he states, was three thousand.
And during another procession two middle-aged, intelligent, educated
Paris journalists gave as their estimates for the number of people
engaged, the one thirty thousand and the other three hundred thousand.

But now let us suppose that our witness, through the medium of his
imperfect senses and his partial attention, has received a certain
image. What deformations may it suffer before it is produced as his
evidence? If his memory of the incident has “lapsed” the image will
undergo comparatively little alteration, but if it has often been
called to mind it will probably suffer a very considerable change.
Each time the image is recalled it will suggest others; the creative
imagination gets to work, altering the emphasis, adding particulars,
obliterating others, and the result will be as much a work of art
as the reproduction of a fact. This tendency is particularly to be
noticed with women, and with certain “excitable” types; it may be
almost a national characteristic, as with Gascons and Sicilians. But
all witnesses are prone to this kind of inaccuracy. Where the event has
often been narrated by the witness the deformations become even more
serious. For he is here exposed not only to the suggestions of his own
creative imagination, but to the suggestions of other people. Every one
wishes to make a success of the story he is telling, and the perception
of what points to stress and what details to add is wonderfully ready
and alert. It has often happened that a witness of perfect good faith
has changed from the simple spectator of a drama to a prominent actor
in it under the influence of repeated narration. Finally, we reach
the point when the witness has to bear his formal testimony. His
observations were imperfect, he has imperfectly remembered them, his
imagination has distorted them, and he is now to express them. A very
considerable additional source of inaccuracy is likely to enter here.
The witness probably cannot express his complete image--words may not
be sufficiently precise to render the fine shades of his remembered
perceptions. The nature of a sound, the kind of emotion expressed by
a voice,--he may have no words for such things. And, in any case,
the witness will not express his complete image. He will select--in
accordance with his own estimate of what is pertinent and what trivial.
He will do this even if he be allowed to talk to his heart’s content;
but the method of question and answer as pursued in our Law Courts
leads to even more imperfect expression. For he is forced to be precise
where his recollection is vague, and he will either give a false
precision to his answer or else profess complete ignorance. More often
still the witness sins by exaggeration, and these exaggerations, in a
thousand subtle ways, usually tend to add to his own importance. And
it is important to notice that, besides tending to import fictitious
details, the witness will tend to exaggerate his degree of conviction.
Where he was originally doubtful he is now perfectly sure.

So far we have been considering the witness in isolation, and we have
not considered the reaction upon his testimony of the emotional state
produced in him by the event. Yet the emotions accompanying the event
have a great bearing upon the value of the witness’s testimony. During
the war it was noticed that the evidence of soldiers freshly wounded
was often of the most fantastic description. They would testify to
the details of catastrophes which had never occurred; they would
assert that so-and-so had been decapitated in front of their eyes, and
so-and-so buried by an explosion, when, as a matter of fact, nothing
remotely resembling these events had taken place. And, under the
influence of the comparatively slighter emotions of a spiritualistic
séance, people will identify the same “materialised” mask as the
features of their husbands, wives, sons, daughters. Under the influence
of such emotions it may be taken as a general rule that perceptions
deteriorate, and illegitimate inference, “unconscious reasoning,”
becomes more marked. Unconscious reasoning, indeed, plays a very great
part in nearly all cases of mal-observation. It is well exemplified
in the statement of the man sitting in a dark wood: “That dog’s bark
is not really a grasshopper, it is the squeaking of a cart.” And Dr.
Locard tells of one experiment he made, while in the Army, with a
barometer which bore a remote resemblance to a clock. His suggestion
that it was a clock was invariably accepted, even by the most eminent
people, and several of them acquired their knowledge of the time of
day from its indications, even when the hour so indicated was highly
improbable. The testimony of great and commanding figures, even to
the time of day, may therefore be open to suspicion. But the immense
part played by unconscious reasoning is best seen in the psychology
of conjuring, under which head it is fair to group the great majority
of alleged spiritualistic phenomena. In this latter case we have
further to recognise what Freud calls the “pleasure-pain principle,”
as distinguished from the “reality-principle.” In other words, the
witnesses are seldom disinterested; they strongly desire to witness
certain events rather than others, and in such cases the slightest
suggestion is sufficient to produce conviction.

When the witness is not isolated, but is a member of a group, the
defects we have before noted, due to the creative imagination, are
likely to be accentuated. The event will have been discussed and a
uniform version gradually prepared. It is almost impossible, from
the unanimous testimony of a number of witnesses who have been in
consultation, to extract the original perceptions. The phenomenon of
_mimétisme testimonial_ makes its appearance, and may assume
abnormal dimensions. A kind of collective hysteria may be induced, and
there can be little doubt that some of the collective denunciations of
witches which took place in the Middle Ages were manifestations of this
form of mimicry.

Such are some of the results that have been reached by the modern
investigations of the value of human testimony. They tell us little
we did not know before, for mankind has had an immense experience of
human testimony; but they make our knowledge more precise and enable us
to see what kinds of testimony are most open to suspicion. The effect
of these researches on judicial procedure should be considerable, and
their influence on the study of history not less marked. On this latter
subject their influence can only be indirect, and in the direction,
probably, of throwing still more doubt on the accuracy of historical
records. The “credibility” of a witness still remains a vague quantity,
but the chances are that it is something less than the value hitherto
assigned to it. The investigation can claim no such precise results
as those enunciated by Craig in 1699 in his _Theologiæ Christianæ
Principia mathematica_, where, after proving that the suspicions of
any history vary in the duplicate ratio of the times taken from the
beginning of the history, he shows that faith in the Gospel, so far as
it depended on oral tradition, expired about the year 880, and, so far
as it depended on written tradition, would expire in the year 3150. The
new investigations of the value of human testimony start from humbler,
but surer, foundations.

_Printed in Great Britain by_ Butler & Tanner, _Frome and
London_

=TRANSCRIBER’S NOTES=

Simple typographical errors have been silently corrected; unbalanced
quotation marks were remedied when the change was obvious, and
otherwise left unbalanced.

Punctuation, hyphenation, and spelling were made consistent when a
predominant preference was found in the original book; otherwise they
were not changed.

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