The Press., 1893-08-10

opponent depends, if T understand you aright, upon the accuracy with which the opponents intellect is measuredY' "For it's practical value it depends upon this," replied Dupin. ''and the pre- feet and his cohort fail so frequently, first, by default of 1; his identification, and, secondly, by i'll admeasuremento or rather through nonadmeasurment off, the intellect with which: they are engaged. They consider only:their own ideas of ingenuity, and in searching for anything hidden advert only to the modes in which they would have hidden it. They l are right in this much-that their own ingenuity is faithful representative of 1 that of the mass, but when the cunning of the individual felon is diverse in char acter from their own the felon foils them, of course.
 "This always happens when it is above their own, and very usually when it is below. They have no variation of principle in their Investigations. Atbest, when urged by some unusual emer- gency, by some extraordinary reward, they extend or exaggerate their old modes of practice, without touching their principles. What, for example, in this case of D. has been done to vary the principle of action? What is all this probing and boring and sounding and scrutinizing with the microscope and dividing the surface of the building into registered square inches-what is it all but an exaggeration of the application of the one principle or set of principles of search, which are based upon the one set of notions regarding human inge- nuity to which the prefect, in the long routine of his duty. has been accns- 1 toned?
 | "Do you not see he has taken it for granted that all men proceed to conceal a letter not exactly in 0 gimlet hole bored in chair leg. but at least in some out of the way hole or corner suggested by the same tenor of thought which would urge q man to secrete letter in g gimlet hole bored in a chair leg? And do you not see also that such recherche hooks for concealment are adapted only for ordinary occasions and would be adopted only by ordinary intellects. for in all cases of concealment disposal of the article concealed-a disposal of it ill this recherche manner-is, in the very first instance, presun1able and presumed, and thus it's discovery depends not at all upon the acumen but altogether upon the mere care, patience and determina- ton of the seekers. And where the case is of fimportance-or what amounts to the same thing in the policial eyes, when the reward is of magnitude-the qualities ill | Iax l., L. e,s
 "You will now understand what meant in suggesting. that had the pur- Joined letter been hidden anywhere with in the limits of the projects examination lin other words, had the principle of its concealment been comprehended within the principles of the prefect-its discov- cry would have been 8 matter altogether beyond question. This functionary however, has been thoroughly mystified and the remote source of his defeat lies in the supposition that the minister is g fool because he has, acquired renown as a poet. All fools are poets. This the pre-. feet feels, and he is merely guilty of 8 non distributio medii in thence inferrine that all poets are fools"
 But is this really the poetY' asked ''There are two brothers, know, and both have attained reputation in letters EThe minister, | believe. has written learnedly on the "Differential Calculus. He is mathematician and no poet"
 "You are mistaken. know him we'll He is both. As poet and mathematician he would reason we'll. As mere mathe- matician he could not have reasoned al \ a1 nd Inns hox la mercy of the prefect," ..
 "You surprise me-" said, ''by these opinions, which have been contradicted by the voice of the world. You do not mean to set at naught the we'll digested |idea of centuries. The mathematical reason has long been rega1 ded as there son par excellence" .,
 ''The mathematicians, l grant you, Ireplied Dupin, "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 8 better cause, for example, they have insinuated the term analysis into application to algebra. particular deception. But if 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 're- ligio' religion or shomines honesti,' a set of honorable men,"
 "You have quarrel on hand, see, said I, with some of the algebraists of Paris But proceed"
 'I dispute the availability, and thus the value, of that reason which is culti- vated in any especial form other than the abstractly logical. dispute in par ticular the reason educed by mathemat ical study. The mathematics are tn. science of form and quantity; mathe matical reasoning is merely logic applied to observation upon form and quantity The great error lies in supposing tha even the truths of what is called pure al zebra are abstract or general truths, ani this error is so egregious that 1 am con founded at the universally with whicl 1t has been received. Mathematical xxi oms are not axioms of general truth What is true of relation-of form ani quantity-is often grossly false in regard to morals, for example. In this latter sci ence it is very usually untrue that thu aggregated parts are equal to the whole
 "In chemistry also the axiom fails. II the consideration of motive it fails, fol two motives, each of a given value, hay, not necessarily value when unitet equal to the sum of their values apart There are numerous other mathematica truths which are only truths within tn, limits of relation. But the mathema tician argues from his finite truth through habit, as if they were of an ab solutely general applicability-as tn world indeed imagines them to be. Bry ant, in his very learned Mythology, mentions an analogous source of erro when he says that although the pagan fables are not believed, yet we forge ourselves continually and make infer ences from them as existing realities
 "With the algebraists, however, wh'