"Riemann has shewn 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 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."

“In March 1879 Clifford died at Madeira; six years afterwards a posthumous work is for the first time placed before the public. ...The original work as planned by Clifford was to have been entitled The First Principles of the Mathematical Sciences Explained to the Non-Mathematical, and to have contained six chapters, on Number, Space, Quantity, Position, Motion, and Mass respectively. Of the projected work Clifford in the year 1875 dictated the chapters on Number and Space completely, the first portion of the chapter on Quantity, and somewhat later nearly the entire chapter on Motion. The first two chapters were afterwards seen by him in proof, but never finally revised. Shortly before his death he expressed a wish that the book should only be published after very careful revision and that its title should be changed to The Common Sense of the Exact Sciences.”

“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.”

“It is a very serious thing to consider that not only the earth itself and all that beautiful face of Nature we see, but also the living things upon it, and all the consciousness of men, and the ideas of society, which have grown up upon the surface, must come to an end. We who hold that belief must just face the fact and make the best of it; and I think we are helped in this by the words of that Jew philosopher who was himself a worthy crown to the splendid achievements of his race in the cause of progress during the middle ages, Benedict Spinoza. He said, "The freeman thinks of nothing so little as of death, and his contemplation is not of death but of life." Our interest, it seems to me, lies with so much of the past as may serve to guide our actions in the present, and to intensify our pious allegiance to the fathers who have gone before us, and the brethren who are with us; and our interest lies with so much of the future as we may hope will be appreciably affected by our good actions now. Beyond that, as it seems to me, we do not know, and we ought not to care. Do I seem to say, "Let us eat and drink, for to-morrow we die?" Far from it; on the contrary, I say, "Let us take hands and help, for this day we are alive together.”

“We have no right to believe a thing true because everybody says so unless there are good grounds for believing that some one person at least has the means of knowing what is true, and is speaking the truth so far as he knows it. However many nations and generations of men are brought into the witness-box they cannot testify to anything which they do not know. Every man who has accepted the statement from somebody else, without himself testing and verifying it, is out of court; his word is worth nothing at all. And when we get back at last to the true birth and beginning of the statement, two serious questions must be disposed of in regard to him who first made it: was he mistaken in thinking that he knew about this matter, or was he lying?”

“Joe Rooney, .pdf William Kingdon Clifford , Department of Design and Innovation, the Open University, London.”

“When a body is let fall from a higher position to lower one, it has, at the instant when it is let go, energy of motion; but it gains, in falling, as much energy of motion as it loses energy of position. 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. ...This constancy is expressed by including them in common name of Energy, and saying that energy 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.”