101. “You surprise me,” I said, “by these opinions, which have been contradicted by the voice of the world. You do not mean to set at naught the well-digested idea of centuries. The mathematical reason has long been regarded as the reason par excellence.”
“It may be said that every public idea, every received convention, is a piece of stupidity, for it has suited the greater number.”—Nicolas Chamfort.
102. “‘Il y a à parier,’” replied Dupin, quoting from Chamfort, “‘que toute idée publique, toute convention reçue, est une sottise, car elle a convenu au plus grand nombre.’ The mathematicians, I grant you, have done their best to promulgate the popular error to which you allude, and which is none the less an error for its promulgation as truth. With an art worthy a better cause, for example, they have insinuated the term ‘analysis’ into application to This whole section of the story triumphs notwithstanding its undue length of learned discussion and its formal diction. It must be admitted that in these respects the present-day short-story is in advance of Poe. A number of paragraphs here fail to advance the narration as fiction. algebra. The French are the originators of this practical deception; but if a term is of any importance—if words derive any value from applicability—then ‘analysis’ conveys ‘algebra,’ about as much as, in Latin, ‘ambitus’ implies ‘ambition,’ ‘religio,’ ‘religion,’ or ‘homines honesti,’ a set of honorable men.”
103. “You have a quarrel on hand, I see,” said I, “with some of the algebraists of Paris; but proceed.”
104. “I dispute the availability, and thus the value of that reason which is cultivated in any especial form other than the abstractly logical. I dispute, in particular, the reason educed by mathematical study. Unusual form. Throughout, note Poe’s unusual choice of words. The mathematics are the science of form and quantity; mathematical reasoning is merely logic applied to observation upon form and quantity. The great error lies in supposing that even the truths of what is called pure algebra are abstract or general truths. And this error is so egregious that I am confounded at the universality with which it has been received. Mathematical axioms are not axioms of general truth. What is true of relation—of form and quantity—is often grossly false in regard to morals, for example. In this latter As a piece of pure reasoning this long treatise is not without its defects, but it does bring out—though too laboriously to please—the point at which Dupin is driving. science it is very usually untrue that the aggregated parts are equal to the whole. In chemistry, also, the axiom fails. In the consideration of motive it fails; for two motives, each of a given value, have not, necessarily, a value when united equal to the sum of their values apart. There are numerous other mathematical truths which are only truths within the limits of relation. But the mathematician argues, from his finite truths, through habit, as if they were of an absolutely general applicability—as the world indeed imagines them to be. Jacob Bryant.Bryant, in his very learned ‘Mythology,’ mentions an analogous source of error, when he says that ‘although the Pagan fables are not believed, yet we forget ourselves continually, and make inferences from them as existing realities.’ He speaks figuratively. With the algebraists, however, who are Pagans themselves, the ‘Pagan fables’ are believed and the inferences are made, not so much through lapse of memory as through an unaccountable addling of the brains. In short, I never yet encountered the mere mathematician who could be trusted out of equal roots, or one who did not clandestinely hold it as a point of his faith A striking satire. that x2 + px was absolutely and unconditionally equal to q. Say to one of these gentlemen, by way of experiment, if you please, that you believe occasions may occur where x2 + px is not altogether equal to q, More satire. and, having made him understand what you mean, get out of his reach as speedily as convenient, for beyond doubt he will endeavor to knock you down.”
Note the force of “last.”
105. “I mean to say,” continued Dupin, while I merely laughed at his last observations, “that if the minister had been no more than a mathematician the Prefect would have been under no necessity of giving me this check. I knew him, however, as both mathematician and poet, and my measures were adapted to his capacity with reference to the circumstances by which he was surrounded. A return from the special argument to the practical.
Application of the foregoing principles. I knew him as courtier, too, and as a bold intriguant. Such a man, I considered, could not fail to be aware of the ordinary policial modes of action. He could not have failed to anticipate—and events have proved that he did not fail to anticipate—the waylayings to which he was subjected. He must have foreseen, I reflected, the secret investigations of his premises. A difficult point explained. His frequent absences from home at night, which were hailed by the Prefect as certain aids to his success, I regarded only as ruses, to afford opportunity for thorough search to the police, and thus the sooner to impress them with the conviction to which G——, in fact, Note the unusual use of “to,” instead of “at.” did finally arrive—the conviction that the letter was not upon the premises. I felt, also, that the whole train of thought, which I was at some pains in detailing to you just now, concerning the invariable principle of policial action in searches for articles concealed—I felt that this whole Is this probable? train of thought would necessarily pass through the mind of the minister. It would imperatively lead him to despise all the ordinary nooks of concealment. Compare [¶95].He could not, I reflected, be so weak as not to see that the most intricate and remote recess of his hotel would be as open as his commonest closets to the eyes, to the probes, to the gimlets, and to the microscopes of the Prefect. I saw, in fine, that he would be driven, as a matter of course, to simplicity, if not deliberately induced to it as a matter of choice. You will remember, perhaps, how desperately the Prefect laughed when I suggested, upon our Key. Compare [¶10]. first interview, that it was just possible this mystery troubled him so much on account of its being so very self-evident.”
106. “Yes,” said I, “I remember his merriment well. I really thought he would have fallen into convulsions.”
A return to philosophising.
107. “The material world,” continued Dupin, “abounds with very strict analogies to the immaterial; and thus some color of truth has been given to the rhetorical dogma, that metaphor, or simile, may be made to strengthen an argument, as well as to embellish a description. The principle of the vis inertiæ, Force of inertia. for example, seems to be identical in physics and metaphysics. It is not more true in the former, that a large body is with more difficulty set in motion than a smaller one, and that its subsequent momentum is commensurate with this difficulty, than it is, in the latter, that intellects of the vaster capacity, while more forcible, more constant, and more eventful in their movements than those of inferior grade, are yet the less readily moved, and more embarrassed and full of hesitation in the first few steps of their progress. This inquiry is the heart of the inference. Again: have you ever noticed which of the street signs over the shop doors are the most attractive of attention?”