Infinitesimal Quotes - page 2
The fact is that seven per cent of the global population emits 50 per cent of greenhouse gas emissions, and the proportions are the same for the use of energy and raw materials, meat, wood, etc. Simply put, an infinitesimal minority consumes the most and imposes damage on the overwhelming majority, while asking it to change.
Yann Arthus-Bertrand
Rapidly going over what I could recall of Jim Bursley's information about pathological curves confirmed the conjecture. The snowball curve, derived from an equilateral triangle, is a perimeter of infinite length enclosing a finite area. The angles or points of the perimeter are uncountable. An equilateral triangle projected integrally in the third dimension is a triangular pyramid of equal surfaces. The three-dimensional snowflake derived from this pyramid--hence its diamantine appearance--is a finite volume enclosed in a surface of infinite area. The convolutions of such a surface, to be gathered around its defined content extrude a number of discrete angles or points beyond all possibility of computation. The pressure on each point is infinitesimal, unmeasurably small; the total external pressure exerted on any part of the surface is an aggregate of infinitesimal values, itself infinitesimal.
William Grey Walter
The method applied by Newton to the grounding of the Infinitesimal Calculus, and which since the beginning of this century has been recognised by the best mathematicians as the only one that furnishes sure results, is the method of limits. The method consists in this, viz., instead of considering a continuous transition from one value of a quantity to another, from one position to another, or, speaking generally, from one determination of a concept to another, one considers in the first place a transition through a finite number of intervals and then allows the number of these intervals to increase so that the distances of two successive points of division all decrease infinitely.
Bernhard Riemann
The statement is so frequently made that the differential calculus deals with continuous magnitude, and yet an explanation of this continuity is nowhere given; even the most rigorous expositions of the differential calculus do not base their proofs upon continuity but, with more or less consciousness of the fact, they either appeal to geometric notions or those suggested by geometry, or depend upon theorems which are never established in a purely arithmetic manner. Among these, for example, belongs the above mentioned theorem, and a more careful investigation convinced me that this theorem, or any one equivalent to it, can be regarded in some way as a sufficient basis for infinitesimal analysis. It then only remained to discover its true origin in the elements of arithmetic and thus at the same time to secure a real definition of the essence of continuity. I succeeded Nov. 24, 1858.
Richard Dedekind
Clearly, many branches of science need an exquisite precision of timekeeping and the infinitesimal decimals of calibration, so space launches, for example, are not scheduled for leap-second dates. But society as a whole neither needs that obsessive time measurement nor is well served by it.
Jay Griffiths
I do have faith. I don't have faith that a God exists, nor do I have faith that one does not; I have absolute faith that I do not know, cannot know, am only human, am an infinitesimal creature packed onto a cramped planet crowded with seven billion bodies, and as many yearning hearts, and as many questioning minds.
Marya Hornbacher
To be so closely caught up in the teeth of things that they kill you, no matter how infinitesimally kill you, is, truly, to be a poet: and to be a poet in fact it is additionally necessary that you should possess the tongues and instruments with which to record this series of infinitesimal deaths.
George Barker (poet)
The saying that a little knowledge is a dangerous thing is, to my mind, a very dangerous adage. If knowledge is real and genuine, I do not believe that it is other than a very valuable posession, however infinitesimal its quantity may be. Indeed, if a little knowledge is dangerous, where is a man who has so much as to be out of danger?
Thomas Henry Huxley
At the time the book of Marquis de l'Hôpital had appeared, and almost all mathematicians began to turn to the new geometry of the infinite [that is, the new infinitesimal calculus], until then little known. The surprising universality of the methods, the elegant brevity of the proofs, the neatness and speed of the most difficult solutions, a singular and unexpected novelty, all attracted the mind and there was in the mathematical world a well marked revolution [une révolution bien marquée.
Bernard Le Bovier de Fontenelle
Our public life depends primarily not upon the men who occupy public positions for the moment, because they are but an infinitesimal fraction of the whole. Our public life depends upon men who take an active interest in that public life; who are bound to see public affairs honestly and competently managed; but who have the good sense to know what honesty and competency actually mean.
Theodore Roosevelt
I cannot tell you of what infinitesimal importance I regard this incident as compared with the great issues at stake in this campaign, and I ask it not for my sake, not the least in the world, but for the sake of common country, that they make up their minds to speak only the truth, and not use that kind of slander and mendacity which if taken seriously must incite weak and violent natures to crimes of violence.
Theodore Roosevelt