William Kingdon Clifford Quotes (1845-1879)

“No mathematician can give any meaning to the language about matter, force, inertia used in current text-books of mechanics.”

“Remember, then, that [scientific thought] is the guide of action; that the truth which it arrives at is not that which we can ideally contemplate without error, but that which we may act upon without fear; and you cannot fail to see that scientific thought is not an accompaniment or condition of human progress, but human progress itself. And for this reason the question what its characters are...is the question of all questions for the human race.”

“The harm which is done by credulity in a man is not confined to the fostering of a credulous character in others, and consequent support of false beliefs.”

“Inquiry into the evidence of a doctrine is not to be made once for all, and then taken as finally settled. It is never lawful to stifle a doubt; for either it can be honestly answered by means of the inquiry already made, or else it proves that the inquiry was not complete.”

“[E]nergy is conserved, or is indestructible. This form of speech might be applied to other cases of alternate immortality, where one of two things comes into existence on disappearance of the other.”

“Causation is defined by some modern philosophers as unconditional uniformity of succession, e.g., existence of fire follows from putting a lighted match to the fuel. This idea must be got rid of to understand force. All universally true laws of nature are laws of co-existence, not succession.”

“[T]here is every reason to believe that we were gregarious animals before we became men... And a belief in the eject—some sort of recognition of a kindred consciousness in one's fellow beings—is clearly a condition of gregarious action among animals so highly developed as to be called conscious at all.”

“It is found that the sum of energy of motion and energy of position is always constant. ...Energy is a quantity which can be greater or less but has no direction. ...[E]nergy is conserved, or is indestructible. This form of speech might be applied to other cases of alternate immortality, where one of two things comes into existence on disappearance of the other.”

“The name philosopher, which meant originally 'lover of wisdom,' has come in some strange way to mean a man who thinks it is his business to explain everything in a certain number of large books. It will be found, I think, that in proportion to his colossal ignorance is the perfection and symmetry of the system which he sets up; because it is so much easier to put an empty room tidy than a full one.”

“If a man, holding a belief which he was taught in childhood or persuaded of afterwards, keeps down and pushes away any doubts which arise about it in his mind, purposely avoids the reading of books and the company of men that call into question or discuss it, and regards as impious those questions which cannot easily be asked without disturbing it—the life of that man is one long sin against mankind.”

“Riemann has shown that as there are different kinds of lines and surfaces, so there are different kinds of space of three dimensions; and that we can only find out by experience to which of these kinds the space in which we live belongs. In particular, the axioms of plane geometry are true within the limits of experiment on the surface of a sheet of paper, and yet we know that the sheet is really covered with a number of small ridges and furrows, upon which (the total curvature not being zero) these axioms are not true. Similarly, he says although the axioms of solid geometry are true within the limits of experiment for finite portions of our space, yet we have no reason to conclude that they are true for very small portions; and if any help can be got thereby for the explanation of physical phenomena, we may have reason to conclude that they are not true for very small portions of space.”

“Pearson's enthusiasm for W. K. Clifford's intuitive dynamics and physics, also for Clifford's violent hostility to traditional beliefs, influenced at least his earlier thinking. Both Clifford and Pearson were creative mathematicians; neither fitted the milk-and-water, namby-pamby 'great man' ideal of the 'great mathematician' which seems to be the accepted norm in historical accounts of mathematicians; and at least one of them would have hooted at the idea that he was, or was to become, an object of reverence for generations of students.”

“With the new views advocated by Riemann... the texture, structure or geometry of space is defined by the metrical field, itself produced by the distribution of matter. Any non-homogeneous distribution of matter would then entail a variable structure of geometry for space from place to place. ... Riemann's exceedingly speculative ideas on the subject of the metrical field were practically ignored in his day, save by the English mathematician Clifford, who translated Riemann's works, prefacing them to his own discovery of the non-Euclidean Clifford space. Clifford realised the potential importance of the new ideas and suggested that matter itself might be accounted for in terms of these local variations of the non-Euclidean space, thus inverting in a certain sense Riemann's ideas. But in Clifford's day this belief was mathematically untenable. Furthermore, the physical exploration of space seemed to yield unvarying Euclideanism. ...it was reserved for the theoretical investigator Einstein, by a stupendous effort of rational thought, based on a few flimsy empirical clues, to unravel the mystery and to lead Riemann's ideas to victory. (In all fairness to Einstein... he does not appear to have been influenced directly by Riemann.) Nor were Clifford's hopes disappointed, for the varying non-Euclideanism of the continuum was to reveal the mysterious secret of gravitation, and perhaps also of matter, motion, and electricity. ... Einstein had been led to recognize that space of itself was not fundamental. The fundamental continuum whose non-Euclideanism was fundamental was... one of Space-Time... possessing a four-dimensional metrical field governed by the matter distribution. Einstein accordingly applied Riemann's ideas to space-time instead of to space... He discovered that the moment we substitute space-time for space (and not otherwise), and assume that free bodies and rays of light follow geodesics no longer in space but in space-time, the long-sought-for local variations in geometry become apparent. They are all around us, in our immediate vicinity... We had called their effects gravitational effects... never suspecting that they were the result of those very local variations in the geometry for which our search had been in vain....the theory of relativity is the theory of the space-time metrical field.”

“But even the distant reader must allow that Clifford's mental personality belonged to the highest possible type to say no more. The union of the mathematician with the poet, fervor with measure, passion with correctness, this surely is the ideal. And if in these modern days we are to look for any prophet or saviour who shall influence our feelings towards the universe as the founders and renewers of past religions have influenced the minds of our fathers, that prophet, if he ever come, must, like Clifford, be no mere sentimental worshipper of science, but an expert in her ways. And he must have what Clifford had in so extraordinary a degree—that lavishly generous confidence in the worthiness of average human nature to be told all truth, the lack of which in Goethe made him an inspiration to the few but a cold riddle to the many.”

“Students of Spinoza will easily trace the connection between his theory of mind and matter and the doctrine set forth in Clifford's essays on "Body and Mind," and "The Nature of Things-in themselves. … Briefly put, the conception is that mind is the one ultimate reality; not mind as we know it in the complex forms of conscious feeling and thought, but the simpler elements out of which thought and feeling are built up. The hypothetical ultimate element of mind, or atom of mind-stuff, precisely corresponds to the hypothetical atom of matter, being the ultimate fact of which the material atom is the phenomenon. Matter and the sensible universe are the relations between particular organisms, that is, mind organized into consciousness, and the rest of the world. This leads to results which would in a loose and popular sense be called materialist. But the theory must, as a metaphysical theory, be reckoned on the idealist side. To speak technically, it is an idealist monism. Indeed it is a very subtle form of idealism, and by no means easy of apprehension at first sight. Nevertheless there are distinct signs of a convergence towards it on the part of recent inquirers who have handled philosophical problems in a scientific spirit, and particularly those who have studied psychology on the physiological side. Perhaps we shall be told that this proves the doctrine to be materialism in disguise; but it is hardly worth while to dispute about names while more serious things remain for discussion. And the idea does require much more working out; involving, as it does, extensive restatement and rearrangement of metaphysical problems. It raises not only several questions, but preliminary (and really fundamental) problems as to what questions are reasonable.”

“The models of Einstein and de Sitter are static solutions of Einstein's modified gravitational equations for a world-wide homogeneous system. They both involve a positive cosmological constant λ, determining the curvature of space. If this constant is zero, we obtain a third model in classical infinite Euclidean space. This model is empty, the space-time being that of Special Relativity. It has been shown that these are the only possible static world models based on Einstein's theory. In 1922, Friedmann... broke new ground by investigating non-static solutions to Einstein's field equations, in which the radius of curvature of space varies with time. This possibility had already been envisaged, in a general sense, by Clifford in the eighties.”