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 RiemannRelated topics
absence boundary case comparison counting definite division form general less magnitude manifoldness mark measure measuring position quantity quantum regard science standard superposition unit using means regionsRelated quotes
A digital computer can usually be regarded as consisting of three parts: (i) Store. (ii) Executive unit. (iii) Control. ...The executive unit is the part which carries out the various individual operations involved in a calculation. ...It is the duty of the control to see that...[the table of] instructions are obeyed correctly and in the right order. ...A typical instruction might say-"Add the number stored in position 6809 to that in 4302 and put the result back into the latter storage position." Needless to say it would not occur in the machine expressed in English. It would more likely be coded in a form such as 6809430217. Here 17 says which of various possible operations [add] is to be performed on the two numbers. ...It will be noticed that the instruction takes up 10 digits and so forms one packet of information...
Alan Turing
I have already accepted the policy of Imperial preference...to the effect that a preference will be given on existing duties and on any duties which may subsequently be imposed. On this subject I think there is no difference of opinion between us. ... I am prepared to say that the key industries on which the life of the nation depends must be preserved. I am prepared to say also that, in order to keep up the present standard of production and develop it to the utmost extent possible, it is necessary that security should be give against the unfair competition to which our industries have been in the past subjected by the dumping of goods below the actual cost of production. ... I shall look at every problem simply from the point of view of what is the best method of securing the objects at which we are aiming without any regard to theoretical opinions about Free Trade or Tariff Reform.
David Lloyd George
The Chancellor of the Exchequer should boldly uphold economy in detail; and it is the mark of a chicken-hearted Chancellor when he shrinks from upholding economy in detail, when because it is a question of only two or three thousand pounds, he says it is no matter. He is ridiculed, no doubt, for what is called candle-ends and cheese-parings, but he is not worth his salt if he is not ready to save what are meant by candle-ends and cheese-parings in the cause of the country. No Chancellor of the Exchequer is worth his salt who makes his own popularity either his consideration, or any consideration at all, in administering the public purse. In my opinion, the Chancellor of the Exchequer is the trusted and confidential steward of the public. He is under a sacred obligation with regard to all that he consents to spend.
William Ewart Gladstone
Though acts of reception and of understanding are in some measure fictions of ordered intuition, myths of reason, this truth does not justify the denial of intentional conduct. It is as absurd to discard as mendacious, as anarchically opaque, the bearing of contextual probability and suggestion, as it is to invest in such probability any blind trust. The negations of post-structuralism and of certain varieties of deconstruction are precisely as dogmatic, as political as were the positivist equations of archival historicism. The "emptiness of meaning" postulate is no less a priori, no less a case of despotic reductionism than were, say, the axioms of economic and psycho-sociological causality in regard to the generation of meaning in literature and the arts in turn-of-the-century pragmatism and scientism.
George Steiner
The chief distinction in the intellectual powers of the two sexes is shewn by man attaining to a higher eminence, in whatever he takes up, than woman can attain - whether requiring deep thought, reason, or imagination, or merely the use of the senses and hands. If two lists were made of the most eminent men and women in poetry, painting, sculpture, music, - comprising composition and performance, history, science, and philosophy, with half-a-dozen names under each subject, the two lists would not bear comparison. We may also infer, from the law of the deviation of averages, so well illustrated by Mr. Galton, in his work on 'Hereditary Genius,' that if men are capable of decided eminence over women in many subjects, the average standard of mental power in man must be above that of woman. ... Thus man has ultimately become superior to woman.
Charles Darwin
