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Updated: May 13, 2025
Some persons will immediately cry out, 'How CAN a reality resemble a feeling? Here we find how wise we were to name the quality of the feeling by an algebraic letter Q. We flank the whole difficulty of resemblance between an inner state and an outward reality, by leaving it free to any one to postulate as the reality whatever sort of thing he thinks CAN resemble a feeling, if not an outward thing, then another feeling like the first one, the mere feeling Q in the critic's mind for example.
And if I may change the metaphor, an algebraic formula is like a magnificent diamond, cutting its way through the thick and opaque glass, which represents the unknown! I long for the end of the war for many reasons, but chief among them is the fact that I may return to the romantic and illimitable fields of the mathematical problem!"
In reply to No. 1, I ask whether, in the nature of the mind, illustration and explanation must not of necessity proceed from the lower to the higher? or whether a boy is to be taught his addition, subtraction, multiplication, and division, by the highest branches of algebraic analysis?
But passing over all ingenious mechanism, making no mention here of astronomical discoveries, some of them surprising enough, it is especially for the Algebraic analysis that we must thank the Moors. A strange fascination, doubtless, these crafty men found in the cabalistic characters and hidden processes of reasoning peculiar to this science.
Fiction becomes less interesting than affairs, and poetry turns into a sort of incompetent whimper, a childish fore-shortening of the outspread world. On the other hand, prose has a great defect, which is abstractness. It drops the volume of experience in finding bodiless algebraic symbols by which to express it.
Our images of all sorts, down to our geometrical diagrams, and even our ciphers and algebraic symbols, should always be figured to ourselves as written in space, and not on paper or any other material substance. M. Comte adds that they should be conceived as green on a white ground. We cannot go on any longer with this.
But this variation is not that of the economists, who place in their list of the causes of the variation of values, not only the means of production, but taste, caprice, fashion, and opinion. In short, the true value of a thing is invariable in its algebraic expression, although it may vary in its monetary expression.
In resolving an algebraic equation, by what rules do we proceed? By applying at each step to a, b, and x the proposition that equals added to equals make equals; that equals taken from equals leave equals; and other propositions founded on these two. These are not properties of language, or of signs as such, but of magnitudes, which is as much as to say, of all things.
"Do you think they would complain if they became colonists of X Island?" But where was this X? It was an island lost in the immensity of the Pacific Ocean between the Equator and the Tropic of Cancer an island most appropriately named by Robur in this algebraic fashion. It was in the north of the South Pacific, a long way out of the route of inter-oceanic communication.
And in ether, just as in water, the motion of every particle is the algebraic sum of all the separate motions imparted to it. One motion does not blot out the other; or, if extinction occur at one point, it is strictly atoned for, by augmented motion, at some other point. Every star declares by its light its undamaged individuality, as if it alone had sent its thrills through space.
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