Infinitesimal Quotes
The success of mathematical physics led the social scientist to be jealous of its power without quite understanding the intellectual attitudes that had contributed to this power. The use of mathematical formulae had accompanied the development of the natural sciences and become the mode in the social sciences. Just as primitive peoples adopt the Western modes of denationalized clothing and of parliamentatism out of a vague feeling that these magic rites and vestments will at once put them abreast of modern culture and technique, so the economists have developed the habit of dressing up their rather imprecise ideas in the language of the infinitesimal calculus.
Norbert Wiener
From these two immediate perceptions, we gain a mediate, or inferential perception of the relation of all four instants. This mediate perception is objectively, or as to the object being represented, spread over the four instants; but subjectively, or as itself the subject of duration, it is completely embraced in the second moment. (The reader will observe that I use the word instant to mean a point in time, and moment to mean an infinitesimal duration.
Charles Sanders Peirce
Accordingly, time logically supposes a continuous range of intensity of feeling. It follows then, from the definition of continuity, that when any particular kind of feeling is present, an infinitesimal continuum of all feelings differing infinitesimally from that, is present.
Charles Sanders Peirce
Suppose a surface to be part red and part blue; so that every point on it is either red or blue, and of course, no part can be both red and blue. What then, is the color of the surface in the immediate neighborhood of the point. ...it follows that the boundary is half red and half blue. In like manner, we find it necessary to hold that consciousness essentially occupies time... Thus, the present is half past and half time to come. ...Take another case: the velocity of a particle at any instant of time is its mean velocity during an infinitesimal instant in which that time is consumed. Just so, my immediate feeling is my feeling through an infinitesimal duration containing the present instant.
Charles Sanders Peirce
As a public teacher of mere striplings, I am often amazed by the facility and absence of resistance with which the principles of the infinitesimal calculus are accepted and assimilated by the present race of learners. When I was young, a boy of sixteen or seventeen who knew his infinitesimal calculus would have been almost pointed at in the streets as a prodigy, like Dante, as a man who had seen hell. Now-a-days, our Woolwich cadets at the same age, talk with glee of tangents and asymptotes and points of contrary flexure and discuss questions of double maxima and minima, or ballistic pendulums, or motion in a resisting medium, under the familiar and ignoble name of sums.
James Joseph Sylvester
In the visible world, the Milky Way is a tiny fragment; within this fragment, the solar system is an infinitesimal speck, and of this speck our planet is a microscopic dot. On this dot, tiny lumps of impure carbon and water, of complicated structure, with somewhat unusual physical and chemical properties, crawl about for a few years, until they are dissolved again into the elements of which they are compounded. They divide their time between labour designed to postpone the moment of dissolution for themselves and frantic struggles to hasten it for others of their kind.
Bertrand Russell
...the splitting up of mankind into a multitude of infinitesimal governments, in accordance with their actual differences of dialect or their presumed differences of race, would be to undo the work of civilisation and renounce all the benefits which the slow and painful process of consolidation has procured for mankind...It is the agglomeration and not the comminution of states to which civilisation is constantly tending; it is the fusion and not the isolation of races by which the physical and moral excellence of the species is advanced. There are races, as there are trees, which cannot stand erect by themselves, and which, if their growth is not hindered by artificial constraints, are all the healthier for twining round some robuster stem.
Robert Gascoyne-Cecil, 3rd Marquess of Salisbury
When, in the slow procession of the ages, man was developed on this planet, the change worked by his appearance was at first slight. Further ages passed while he groped and struggled by infinitesimal degrees upward through the lower grades of savagery; for the general law is that life which is advanced and complex, whatever its nature, changes more quickly than simpler and less advanced forms. The life of savages changes and advances with extreme slowness, and groups of savages influence one another but little. The first rudimentary beginnings of that complex life of communities which we call civilization marked a period when man had already long been by far the most important creature on the planet. The history of the living world had become, in fact, the history of man, and therefore something totally different in kind as well as in degree from what it had been before.
Theodore Roosevelt
You will see...many very important differences between our methods of education and yours, but the main difference is that nowadays all persons equally have those opportunities of higher education which in your day only an infinitesimal portion of the population enjoyed. We should think we had gained nothing worth speaking of, in equalizing the physical comfort of men, without this educational equality....
Edward Bellamy
Descend from the infinite to the infinitesimal. Long before... observation had begun to penetrate the veil under which Nature has hidden her mysteries, the restless mind sought some principle of power strong enough and of sufficient variety to collect and bind together all parts of a world. This seemed to be found, where one might least expect it, in abstract numbers. Everywhere the exactest numerical proportion was seen to constitute the spiritual element of the highest beauty.
Benjamin Peirce
After all, of what use is it to search for a creator? The difficulty is not thus solved. You leave your creator as much in need of a creator as anything your creator is supposed to have created. The bottom of your stairs rests on nothing, and the top of your stairs leans upon nothing. You have reached no solution. The word "God” is simply born of our ignorance. We go as far as we can, and we say the rest of the way is "God.” We look as far as we can, and beyond the horizon, where there is nought so far as we know but blindness, we place our Deity. We see an infinitesimal segment of a circle, and we say the rest is "God.”.
Robert G. Ingersoll
The individual contribution, the work of any single generation, is infinitesimal; the power and glory belong to human society at large, and are the long result of selection, conservation, sacrifice, creation, and renewal - the outcome of endless brave efforts to conserve values and ideas, and to hand them on to posterity, along with physical life itself. Each person is a temporary focus of forces, vitalities, and values that carry back into an immemorial past and that reach forward into an unthinkable future.
Lewis Mumford
To prove that, until this very day, life has never been shown to man as a product of the forces that govern matter, it could be useful the spiritual doctrine which has been very neglected elsewhere, but always finds at least a glorious refuge in your groups. Perhaps you know that in this difficult question concerning the origin of the infinitesimal, I will have brought experimental rigor that has grown weary of contradiction. Referring to the merit, however, we have inherited severe rules of the method from the great experimenters: Galileo, Pascal, Newton and their followers for two centuries.
Louis Pasteur
The scientist addresses an infinitesimal audience of fellow composers. His message is not devoid of universality but it's universality is disembodied and anonymous. While the artist's communication is linked forever with it's original form, that of the scientist is modified, amplified, fused with the ideas and results of others, and melts into the stream of knowledge and ideas which forms our culture. The scientist has in common with the artist only this: that he can find no better retreat from the world than his work and also no stronger link with his world than his work.
Max Delbrück