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Updated: June 25, 2025
"Taking arsenic is followed by death" is a good empirical generalization; it may have exceptions, but they will be rare. As against the professedly exact laws of physics, such empirical generalizations have the advantage that they deal with observable phenomena. We cannot observe infinitesimals, whether in time or space; we do not even know whether time and space are infinitely divisible.
We have made a step, indeed, but perhaps only towards acquaintance with a new order of infinitesimals. Once the distances of our Solar System seemed almost infinite quantities; compare them with the intervals between the fixed stars, and they become no quantities at all.
Arriving at infinitesimals, mathematics, the most exact of sciences, abandons the process of analysis and enters on the new process of the integration of unknown, infinitely small, quantities. Abandoning the conception of cause, mathematics seeks law, that is, the property common to all unknown, infinitely small, elements.
He gave good measure, not prodigal, for he was loyal to his employer, but putting a very moderate strain on the ribbon, and letting the thumb-nail slide with a contempt of infinitesimals which betokened a large soul in its genial mood.
This war has eaten its way backward through all the technicalities of lawyers learned in the infinitesimals of ordinances and statutes; through all the casuistries of divines, experts in the differential calculus of conscience and duty; until it stands revealed to all men as the natural and inevitable conflict of two incompatible forms of civilization, one or the other of which must dominate the central zone of the continent, and eventually claim the hemisphere for its development.
Vashti has lost her veil!" When I see a woman of comely features, and of adroitness of intellect, and endowed with all that the schools can do for one, and of high social position, yet moving in society with superciliousness and hauteur, as though she would have people know their place, and with an undefined combination of giggle and strut and rhodomontade, endowed with allopathic quantities of talk, but only homeopathic infinitesimals of sense, the terror of dry-goods clerks and railroad conductors, discoverers of significant meanings in plain conversation, prodigies of badinage and innuendo I say: "Vashti has lost her veil."
This war has eaten its way backward through all the technicalities of lawyers learned in the infinitesimals of ordinances and statutes; through all the casuistries of divines, experts in the differential calculus of conscience and duty; until it stands revealed to all men as the natural and inevitable conflict of two incompatible forms of civilization, one or the other of which must dominate the central zone of the continent, and eventually claim the hemisphere for its development.
I see infinitesimals which ride on dogs and pigs, and I see others which are fat and naked, with breasts like leather bottles, bellies in great folds, and thighs of enormous size." "Is it possible," said the vicar, "that you can see as distinctly as that? But if your faults are such as you say, it would be better not to describe them and to be content to detest them in your own mind."
I forgot the smoke and jabber of the club altogether; I became a lonely spirit flung aloft by some queer accident, a stone upon a ledge in some high and rocky wilderness, and below as far as the eye could reach stretched the swarming infinitesimals of humanity, like grass upon the field, like pebbles upon unbounded beaches.
It subjected credulous mankind to the last of indignities, in forcing it to listen to that doctrine of infinitesimals and potencies which is at once the most epigrammatic of paradoxes, and the crowning exploit of pseudo-scientific audacity.
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