William Kingdon Clifford.

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II. Selections from Letters, etc. . . . . . 44

131. Bibliographical 67


On Some of the Conditions of Mental Development . 75

On Theories of the Physical Forces 109

On the Aims and Instruments of Scientific Thought . 124

Atoms 158

The First and the Last Catastrophe . . . .191

The Unseen Universe ........ 228

The Philosophy of the Pure Sciences .... 254



It is an open secret to the few who know it, but a
mystery and a stumbling-block to the many, that
Science and Poetry are own sisters ; insomuch that in
those branches of scientific inquiry which are most
abstract, most formal, and most remote from the grasp
of the ordinary sensible imagination, a higher power of
imagination akin to the creative insight of the poet is
most needed and most fruitful of lasting work. This
living and constructive energy projects itself out into
the world at the same time that it assimilates the sur-
rounding world to itself When it is joined with quick
perception and delicate sympathies, it can work the
miracle of piercing the barrier that separates one mind
from another, and becomes a personal charm. It can
be known only in its operation, and is by its very nature
incommunicable and indescribable. Yet this faculty,
when a man is gifted with it, seems to gather up the
best of his hfe, so that the man always transcends every
work shapen and sent forth by him ; his presence is full
of it, and it hghtens the air his friends breathe ; it com-
mands not verbal assent to propositions or intellectual



acquiescence in arguments, but the conviction of being
in the sphere of a vital force for which nature must
make room. Therefore when, being happy in that we
knew and saw these things, and have received the im-
perishable gifts, we must unhappily speak of the friend
who gave them as having passed from us, it becomes
nothing less than a duty to attempt the impossible task ;
to describe that which admits of no description, and
communicate that for which words are but blundering
messengers. And perhaps it may not be in vain ; for
a voice which is in itself weak may strengthen the
kindred notes that vibrate in other memories touched
by the same power, and those we know to be very
many. For this power, when it works for fellowship
and not ambition, wins for its wearer the love of all
sorts and conditions of men, and this was marked in
Chfford by all who had to do with him even a little.
More than this, our words may peradventure strike
farther, though by no force or skill of their own, and
stir some new accord in imaginations favourably attuned
for the impulse. The discourses and writings collected
in this book will indeed testify to the intellectual grasp
and acuteness that went to the making of them. Clif-
ford's earnestness and simphcity, too, are fairly enough
presented to the reader, and the clearness of his expres-
sion is such that any comment by way of mere expla-
nation would be impertinent. But of the winning fehcity
of his manner, the varied and flexible play of his
thought, the almost boundless range of his human
interests and sympathies, his writing tells — at least, so
it seems to those who really knew him — nothing or very
little. To say a word or two in remembrance of one's


friend is but natural ; and in these days excuse is hardly-
needed for saying it in public. But here this is the
least part of the matter in hand. Personal desires and
aims are merged in the higher responsibiUty of telling
the world that it has lost a man of genius ; a responsi-
bihty which must be accepted even with the knowledge
that it cannot be adequately discharged.

Not many weeks had passed of my first year at
Trinity when it began to be noised about that among
the new minor scholars there was a young man of ex-
traordinary mathematical powers, and eccentric in ap-
pearance, habits, and opinions. He was reputed, and
at the time with truth, an ardent High Churchman. I
think it was then a more remarkable thing at Cambridge
than it would be now, the evangehcal tradition of Simeon
and his school being still prevalent. This was the first
I heard of ChfFord ; and for some two years he con-
tinued to be nothing more to me than a name and a
somewhat enigmatic person. In the course of our third
year circumstances brought us together : it is difficult
to remember the beginnings of a friendship that seems
as if it must always have been, but to the best of my
recollection there was nothing very sudden or rapid in
our closer approach. I should assign about six months
as the interval filled by the transition from acquaintance
to intimacy. At an early stage in my knowledge of him
I remember being struck by the daring versatihty of his
talk. Even then there was no subject on which he was
not ready with something in point, generally of an un-
expected kind ; and his unsurpassed power of mathe-
matical exposition was already longing to find exercise.
I shall be pardoned for giving a concrete instance which

B 2


may be in itself trivial. In the analytical treatment of
statics there occurs a proposition called Ivory's Theorem
concerning the attractions of an elhpsoid. The text-books
demonstrate it by a formidable apparatus of co-ordinates
and integrals, such as we were wont to call a grind.
On a certain day in the Long Vacation of 1866, which
Clifford and I spent at Cambridge, I was not a little
exercised by the theorem in question, as I suppose many
students have been before and since. The chain of
symbolic proof seemed artificial and dead ; it compelled
the understanding but failed to satisfy the reason.
After reading and learning the proposition one still
failed to see what it was all about. Being out for a
walk with Clifford, I opened my perplexities to him ; I
think I can recall the very spot. What he said I do
not remember in detail, which is not surprising, as I
have had no occasion to remember anything about
Ivory's Theorem th^ese twelve years. But I know that
as he spoke he appeared not to be working out a
question, but simply telhng what he saw. Without
any diagram or symbolic aid he described the geome-
trical conditions on which the solution depended, and
they seemed to stand out visibly in space. There were
no longer consequences to be deduced, but real and
evident facts which only required to be seen. And
this one instance, fixed in my memory as the first that
came to my knowledge, represents both Clifford's theory
of what teaching ought to be, and his constant way of
carrying it out in his discourses and conversation on
mathematical and scientific subjects. So whole and
complete was the vision that for the time the only strange
thing was that anybody should fail to see it in the same


way. When one endeavoured to call it up again, and
not till then, it became clear that the magic of genius
had been at work, and that the common sight had been
raised to that higher perception by the power which
makes and transforms ideas, the conquering and
masterful quahty of the human mind which Goethe
called in one word das Ddmonische.

A soul eager for new mastery and ever looking
forward cares httle to dwell upon the past ; and
CUfford was not much apt' to speak of his own earher
hfe, or indeed of himself at all. Hence I am indebted
to his wife and to other friends for what little I am
able to say of the time before I knew him. Wilham
Kingdon Clifford was born at Exeter on May 4, 1845 ;
his father was a well-known and active citizen, and filled
the office of justice of the peace. His mother he lost
^arly in hfe ; he inherited from her probably some of
his genius, and almost certainly the deep-seated constitu-
tional weakness, ill paired with restless activity of nerve
and brain, which was the cause of his premature loss.
He was educated at Exeter till 1860, when he was sent
to King's College, London, not without distinction
already won in the University Local Examinations. At
school he showed little taste for the ordinary games, but
made himself proficient in gymnastics ; a pursuit which
at Cambridge he carried out, in fellowship with a few
hke-minded companions, not only into the performance
of the most difficult feats habitual to the gymnasium,
but into the invention of other new and adventurous
ones. But (as he once said himself of Dr. Whewell) his
nature was to touch nothing without leaving some
stamp of invention upon it. His accomplishments of


this kind were the only ones in which he ever mani-
fested pride. When he took his degree there was a
paragraph in ' Bell's Life ' pointing out, for the rebuke
of those who might suppose manly exercises incom-
patible with intellectual distinction, that the Second
Wrangler, Mr. Clifford, was also one of the most daring
athletes of the University. This paragraph gave him
far more hvely pleasure than any of the more serious
and academical marks of approval which he had
earned. In 1869 he wrote from Cambridge : — ' I am at
present in a very heaven of joy because my corkscrew
was encored last night at the assault of arms : it consists
in running at a fixed upright pole which you seize with
both hands and spin round and round descending in a
corkscrew fashion.' In after years he did not keep up
his gymnastic practice with anything like regularity ;
but he was with great difficulty induced to accept the
necessity of completely abandoning it when it was known
to be positively injurious to his health. A friend who
was his companion in gymnastics writes to me : — ' His
neatness and dexterity were unusually great, but the
most remarkable thing was his great strength as com-
pared with his weight, as shown in some exercises. At
one time he could pull up on the bar with either hand,
which is well known to be one of the greatest feats of
strength. His nerve at dangerous heights was extra-
ordinary. I am appalled now to think that he climbed
up and sat on the cross bars of the weathercock on a
church tower, and when by way of doing something
worse I went up and hung by my toes to the bars he
did the same.'

At King's College Clifford's peculiar mathematical


abilities came to the front, but not so as to exclude at-
tention to other subjects. He was at various times and
in various ways marked out for honourable mention in
classics, modern history, and Enghsh literature. His
knowledge of the classics, though he did not cultivate
the niceties of scholarship, was certainly as sound and
extensive as that of many professedly classical students ;
and, hke all his knowledge, it was vital. If he made
use of it for quotation or otherwise, it was not because
the passage or circumstance was classical, but because
it was the thing he wanted to illustrate his own
thought. Of history he knew a good deal ; he was
fond of historical reading throughout his life, and had
a ready command of parallels and analogies between
widely remote times and countries, sometimes too in-
genious to bear criticism. I doubt if he studied
historical works critically ; it seems to me that he
regarded history in a poetical rather than a scientific
spirit, seeing events in a series of vivid pictures which
had the force of present reahties as each came in turn
before the mind's eye. Thus he threw himself into
the past with a dramatic interest, and looked on the
civihzed world as a field where the destinies of man are
fought out in a secular contest between the powers of
good and evil, rather than as a scene of the develop-
ment and interaction of infinite and infinitely complex
motives. This indeed, in a meagre and far cruder form,
is essentially the popular view ; the sort of history upon
which most people are still brought up divides men,
actions, and institutions into good and bad according to
the writer's present notions of what might and ought to
be, and distributes blessing and cursing without more


ado. Only Clifiord, accepting to some extent the
popular or pictorial way of looking at history, took on
most questions the unpopular side, and so found him-
self in colhsion with current opinions. He had a fair
general knowledge of English Hterature (by which I
mean considerably more than is yet supposed necessary
for an Enghshman's education), with a preference for
modern poetry, and especially for such as gave ex-
pression to his own ideas. Milton's prose had also a
special attraction for him. I do not think he cared
much for the use of language as a fine art, though he
had a great appreciation of arrangement and composi-
tion. His own style, always admirably clear and often
eloquent, was never elaborate ; for we cannot fairly
count the studied ornament of his College declamations,
which were not only produced while he was an under-
graduate, but for an occasion which justified some
special aiming at rhetorical effect. Much of his best
work was actually spoken before it was written. He
gave most of his pubhc lectures with no visible prepa-
ration beyond very short notes, and the outline seemed
to be filled in without effort or hesitation. Afterwards
he would revise the lecture from a shorthand-writer's
report, or sometimes write down from memory almost
exactly what he had said. It fell out now and then,
however, that neither of these things was done ; and in
such cases there is now no record of the lecture at all.
Once or twice he tried writing part of the lecture
beforehand, but found it only an embarrassment in the
delivery. I beheve the only one wholly put in writing
in the first instance was Ethics of Religion, which he


was unable to deliver himself. I cannot find anything
showing early aptitude for acquiring languages ; but
that he had it and was fond of exercising it in later life
is certain. One practical reason for it was the desire of
being able to read mathematical papers in foreign
journals ; but this would not account for his taking up
Spanish, of which he acquired a competent knowledge
in the course of a tour to the Pyrenees. When he was
at Algiers in 1876 he began Arabic, and made progress
enough to follow in a general way a course of lessons
given in that language. He read modern Greek
fluently, and at one time he was curious about Sanskrit.
He even spent some time on hieroglyphics. A new
language is a riddle before it is conquered, a power in
the hand afterwards : to Clifford every riddle was a
challenge, and every chance of new power a divine
opportunity to be seized. Hence he was hkewise
interested in the various modes of conveying and ex-
pressing language invented for special purposes, such as
the Morse alphabet and shorthand. One of his ideas
about education was that children might learn these
things at an early age, perhaps in play, so as to grow
up no less famihar with them than with common print-
ing and writing. I have forgotten to mention his
command of French and German, the former of which
he knew very well, and the latter quite sufficiently ; I
think his German reading was mostly in the direction
of philosophy and mathematics.

In 1863 Chfford came up with a minor scholarship to
Trinity College, Cambridge ; in his third year (to continue
for the present on the hue of his literary accomplish-


ments) he won the College declamation prize ^ with a
very brilHant discourse on Sir W. Ealeigh, partly cast
in the form of quasi-dramatic dialogues, and accordingly
had to dehver the annual oration at the Commemoration
of Benefactors in December. His subject was a pane-
gyric of the late Master of the College, Dr. Whewell,
whose death was then recent. It was treated in an
original and unexpected manner. Dr. Whewell's claim to
admiration and emulation being put on the ground of
his intellectual life exemplifying in an eminent degree
the active and creating faculty. ' Thought is powerless
except it make something outside of itself : the thought
which conquers the world is not contemplative but
active. And it is this that I am asking you to worship
to-day.' Taking this oration as a whole, it must be
considered as a tour de force, giving ghmpses and un-
determined promises of speculative power. But there
occurred in it an apologue which caught the attention
of some good judges at the time, and so well illustrates
the fanciful and sportive side of Clifford's mind that I
shall here transcribe it.

' Once upon a time — much longer than six thousand
years ago — the Trilobites were the only people that had
eyes ; and they were only just beginning to have them,
and some even of the Trilobites had as yet no signs of
coming sight. So that the utmost they could know
was that they were living in darkness, and that perhaps
there was such a thing as light. But at last one of
them got so far advanced that when he happened to

^ He was bracketed with Mr. 0. A. Elliott for the first prize : but (I
now forget for what reason) the office of delivering the Oration fell to
Clifford alone.


come to the top of the water in the daytime he saw the
sun. So he went down and told the others that in
general the world was light, but there was one great
light which caused it all. Then they killed him for
disturbing the commonwealth ; but they considered it
impious to doubt that in general the world was Hght,
and that there was one great light which caused it all.
And they had great disputes about the manner in which
they had come to know this. Afterwards another of
them got so far advanced that when he happened to
come to the top of the water in the night-time he saw
the stars. So he went down and told the others that in
general the world was dark, but that nevertheless there
was a great number of little lights in it. Then they
killed him for maintaining false doctrines : but from
that time there was a division amongst them, and all
the Trilobites were split into two parties, some main-
taining one thing and some the other, until such time
as so many of them had learned to see that there could
be no doubt about the matter.'

The interpretation was barely indicated on this
occasion ; but it is worked out in another Cambridge
MS. which must have been written shortly afterwards,
and in which the apologue stands first as a kind of text.
It was nothing less than a theory of the intellectual
growth of mankind ; and the position was that, as the
physical senses have been gradually developed out of
confused and uncertain impressions, so a set of in-
tellectual senses or insights are still in course of develop-
ment, the operation of which may ultimately be expected
to be as certain and immediate as our ordinary sense-


This theory may be traced in the discourse ' On
some of the Conditions of Mental Development,' dehvered
in March, 1868, which stands first in the present collec-
tion; and for that reason I make special mention of it.
Otherwise it was only one inventive experiment among
many. I should far exceed my limits if I were to
attempt any account of the various forms of speculation,
physical, metaphysical, social, and ethical, through
which Clifford ranged in the first few years after his
degree. Not that he was constantly changing his
opinions, as a superficial observer might have thought ;
he was seeking for definite principles, and of set purpose
made his search various and wide-spread. He had a
singular power of taking up any theory that seemed to
him at all worth investigating, reahzing it, working it
out, and making it completely his own for the time
being, and yet all the while consciously holding it as an
experiment, and being perfectly ready to give it up
when found wanting.

Chfford's mathematical course at Cambridge was a
struggle between the exigencies of the Tripos and his
native bent for independent reading and research going
far beyond the subjects of the examination ; and the
Tripos had very much the worst of it. If there was
any faculty in which he was entirely wanting, it was
the examination-faculty. On this subject I am not
competent to speak with certainty, but it is my belief
that, from the point of view to which the class-fist is an
end in itself, Chfford omitted most of the things he ought
to have read, and read everything he ought not to have
read. Nevertheless his powers of original work carried
him so far that he came out Second Wrangler in the


Tripos of 1867, and was also Second Smith's Prizeman.
I am fortunately able to quote on this head the state-
ment of one of our first hving analysts, Professor
Sylvester : —

' Like the late Dr. Whewell, Professor Clerk Max-
well, and Sir William Thomson, Mr. Chfford was Second
Wrangler at the University of Cambridge. I beheve
there is httle doubt that he might easily have been first
of his year had he chosen to devote himself exclusively
to the University curriculum instead of pursuing his
studies, while still an undergraduate, in a more extended
field, and with a view rather to self-culture than to the
acquisition of immediate honour or emolument.'

This pursuit of knowledge for its own sake, and
without even such regard to collateral interests as most
people would think a matter of common prudence, was
the leading character of CHfford's work throughout his
life. The discovery of truth was for him an end in
itself, and the proclamation of it, or of whatever seemed
to lead to it, a duty of primary and paramount obhga-
tion. This had something to do with the fascination of
his teaching ; he never seemed to be imposing dogmas
on his hearers, but to be leading them into the enjoy-
ment of a common possession. He did not tell them
that knowledge was priceless and truth beautiful; he
made them feel it. He gave them not formulas, but
ideas. Again I can appeal to a witness of undoubted
authority. The following words were written in 1871
by a man in no way given to unmeasured expression of
his mind, and as eminent in mathematical physics as
the author of the statement I have already cited is in
pure mathematics, I mean Professor Clerk Maxwell : —


' The peculiarity of Mr. Cliflford's researches, which
in my opinion points him out as the right man for a
chair of mathematical science, is that they tend not to
the elaboration of abstruse theorems by ingenious calcu-
lations, but to the elucidation of scientific ideas by the
concentration upon them of clear and steady thought.
The pupils of such a teacher not only obtain clearer
views of the subjects taught, but are encouraged to
cultivate in themselves that power of thought which is so
liable to be neglected amidst the appliances of education.'

I shall not attempt to enter in more detail on the
amount and character of Clifford's subsequent contribu-
tions to mathematical science, having reason to hope
that this task will shortly be undertaken by competent
hands and in a more appropriate connexion. But in an
introduction to his philosophical writings it is fitting to
call attention to the manner in which he brought
mathematical conceptions to bear upon philosophy.
He took much pleasure in the speculative constructions
of imaginary or non-Euchdean systems of space-rela-
tions which have been achieved by Continental geo-
meters, partly because they afforded a congenial field
for the combined exercise of scientific intuition and un-
bridled fancy. He liked talking about imaginary geo-
metry, as a matter of pure amusement, to anyone in-
terested in it. But at the same time he attached a
serious import to it. He was the first in this country,
as Helmholtz in Germany, to call attention to the philo-
sophical importance of these new ideas with regard to
the question of the nature and origin of geometrical

Online LibraryWilliam Kingdon CliffordLectures and essays (Volume v. 1) → online text (page 1 of 24)