It is not true, out of geometry, that the mathematical sciences are, in all their parts those models of finished accuracy which many suppose. The extreme boundaries of analysis have always been as imperfectly understood as the tract beyond the boundaries was absolutely unknown. But the way to enlarge the settled country has not been by keeping within it, but by making voyages of discovery, and I am perfectly convinced that the student should be exercised in this manner; that is, that he should be taught how to examine the boundary, as well as how to cultivate the interior. ...allowing all students whose capacity will let them read on the higher branches of applied mathematics, to have each his chance of being led to the cultivation of those parts of analysis on which rather depends its future progress than its present use in the sciences of matter.
Augustus De MorganRelated topics
accuracy analysis beyond boundary capacity chance country cultivation discovery examine extreme future geometry interior keeping led making manner mathematics matter present progress read should student suppose teach tract unknown use way well higher parts sciencesRelated quotes
[T]he rapid march of scientific discovery...made me feel that it was quite within the realm of possibility that one day there might be an invention which would neutralise our [naval] superiority, and reduce us to equality with, if not inferiority to, our neighbours. ... In such an event our position would be one of complete helplessness in the face of an invader with a powerful army. ... We had two fundamental weaknesses in such a contingency. The first was that our army was too insignificant to stand up against the gigantic forces on the Continent. The second was that we were so overwhelmingly dependent upon overseas supplies for our food, that if these were cut off we should, within a few months, be brought to the very verge of starvation. It was this consideration amongst others that always led me to urge that we ought to devote more thought to the development of the resources of British soil.
David Lloyd George
I used to be a hide-bound Tory simply for traditional and antiquarian reasons-and because I had never done any real thinking on civics and industry and the future. The depression-and its concomitant publicisation of industrial, financial, and governmental problems-jolted me out of my lethargy and led me to reëxamine the facts of history in the light of unsentimental scientific analysis; and it was not long before I realised what an ass I had been. The liberals at whom I used to laugh were the ones who were right-for they were living in the present while I had been living in the past. They had been using science while I had been using romantic antiquarianism. At last I began to recognise something of the way in which capitalism works-always piling up concentrated wealth and impoverishing the bulk of the population until the strain becomes so intolerable as to force artificial reform.
H. P. Lovecraft
I came to understand why animals have horns. It was the incomprehensibility that could not be contained within their lives, a wild and obsessive caprice, their ill-judged and blind obstinacy. Some idée fixe-grown beyond the borders of their being and high above their heads, suddenly brought into the light-had solidified into palpable, hard matter. There, it had assumed its wild, incalculable, and incredible shape, twisted into a fantastical arabesque, invisible to their eyes, but dreadful nonetheless, the unknown numeral under whose menace they lived. I understood why those animals were disposed to ill-judged and wild panic, to startled frenzy. Herded into their mania, they could not extricate themselves from the knot of those horns, and so, lowering their heads, they looked out sadly and wildly from between them as if trying to find a pathway through their branches.
Bruno Schulz
Much has been said in the present debate about conciliation and the value of conciliatory measures to Ireland...Conciliatory legislation is infinitely superior; but it depends for its efficacy on the circumstances under which it is used, and on the manner in which it is applied. Deterrent legislation, if vigorous and strong, at least deters, whatever the value of that process may be. But conciliatory legislation only conciliates where there is a full belief on the part of those with whom you are dealing that you are acting on a principle of justice, and not that you are acting on motives of fear. Where there is a suspicion or a strong belief that your conciliatory measures have been extorted from you by the violence which they are meant to put a stop to, all the value of that conciliation is taken away.
Robert Gascoyne-Cecil, 3rd Marquess of Salisbury
As for New England as a seat of weirdness-a little historic reflection will show why it is more naturally redolent of the bizarre & the sinister than any other part of America. It was here that the most gloomy-minded of all the colonists settled; & here that the dark moods & cryptic hills pressed closest. An abnormal Puritan psychology led to all kinds of repression, furtiveness, & grotesque hidden crime, while the long winters & backwoods isolation fostered monstrous secrets which never came to light. To me there is nothing more fraught with mystery & terror than a remote Massachusetts farmhouse against a lonely hill. Where else could an outbreak like the Salem witchcraft have occurred? Rhode Island does not share these tenedencies-its history & settlement being different from those of other parts of New England-but just across the line in the old Bay State the macabre broods at its strongest.
H. P. Lovecraft
