Magnitude Quotes - page 6
By this lux as the first corporeal form Grosseteste did not, of course, mean simply visible light. As an emanation or propagation of substance and power lux was the basis of all bodily magnitude and of all natural operations, of which the manifestation of visible light was only one. One of the most important functions of lux was to be the intermediary between spirit and matter. It was the instrument by which God produced the macrocosm of the universe, and the instrument by which the soul made contact with the physical body and the things of sense in the microcosm of man.
Alistair Cameron Crombie
If for the entire universe we conceive the same magnitude to be determined, consistently and with due regard to all circumstances, which for a single body I have called entropy, and if at the same time we introduce the other and simpler conception of energy, we may express in the following manner the fundamental laws of the universe which correspond to the two fundamental theorems of the mechanical theory of heat.
1. The energy of the universe is constant.
2. The entropy of the universe tends to a maximum.
Rudolf Clausius
Never before in the history of war had there been a more convincing example of the effectiveness of sea power than when a well-armed, highly efficient and undefeated army of over a million men surrendered their homeland unconditionally to the invader without even token resistance. True, the devastation already wrought by past bombings, as well as the terrible demonstration of power by the first atomic bombs, augured nothing less for the Japanese than total extinction; yet without sea power there would have been no possession of Saipan, Iwo Jima, and Okinawa from which to launch these bombings. True, the Japanese homeland might have been taken by assault in one final amphibious operation of tremendous magnitude, yet without sea power such an assault could not have been attempted.
Ernest King
The concept-systems of antithesis are concepts that are indeed thoroughly determined by negative predicates but are not positively representable.
Just because a precise and complete representation of these concept-systems is impossible, they are inaccessible to direct investigation and elaboration by our reflection. They may, however, be regarded as lying at the limit of the representable, i. e., we can form a concept-system lying within the representable, which passes over into the given system by simple change of magnitude ratio. By abstracting from the ratios of the quantities, the concept-system remains unchanged in case of transition to the limit. At the limit itself, however, some of the correlative concepts of the system lose their susceptibility of being represented, and those, indeed, that mediate the relation between other concepts.
Bernhard Riemann
Definite portions of a manifoldness, distinguished by a mark or by a boundary, are called Quanta. Their comparison with regard to quantity is accomplished in the case of discrete magnitudes by counting, in the case of continuous magnitudes by measuring. Measure consists in the superposition of the magnitudes to be compared; it therefore requires a means of using one magnitude as the standard for another. In the absence of this, two magnitudes can only be compared when one is a part of the other; in which case also we can only determine the more or less and not the how much. The researches which can in this case be instituted about them form a general division of the science of magnitude in which magnitudes are regarded not as existing independently of position and not as expressible in terms of a unit, but as regions in a manifoldness.
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
