1. The human mind is so constructed that it must see every perception in a time-relation-in an order-and every perception of an object in a space-relation-as outside or beside our perceiving selves. 2. These necessary time-relations are reducible to Number, and they are studied in the theory of number, arithmetic and algebra. 3. These necessary space-relations are reducible to Position and Form, and they are studied in geometry. Mathematics, therefore, studies an aspect of all knowing, and reveals to us the universe as it presents itself, in one form, to mind. To apprehend this and to be conversant with the higher developments of mathematical reasoning, are to have at hand the means of vitalizing all teaching of elementary mathematics.
Nicholas Murray ButlerRelated topics
algebra arithmetic aspect beside conversant elementary form geometry human knowing mathematics mind necessary number outside perception position see study teaching means higher presentsRelated quotes
That the universe, as was once thought, expands and contracts indefinitely, one Big Bang collapsing into another one, seemed reasonable enough. But in both models of the universe, what caused the first Big Bang? Or was there a first Big Bang, any more than a last number? If there was a first cause, was there a first causer? Did Big Bangs just happen to happen? Can we name the first causer "God”? We can name it anything we want. I can name it after myself. It is utterly insignificant what it is called, because we would be giving a name to something that falls outside all categories of thought and must be unknowable and irrelevant to knowledge. So naming it is a futile enterprise. The word "God” is unhelpful because it implies it has a knowable definition.
Roger Ebert
This idea is that laws which purport to be statements of what actually occurs are statistical in character as distinct from so-called dynamic laws that are abstract and mathematical, and disguised definitions. Recognition of the statistical nature of physical laws was first effected in the case of gases when it became evident that generalizations regarding the behavior of swarms of molecules were not descriptions or predictions of the behavior of any individual particle. A single molecule is not and cannot be a gas. It is consequently absurd to suppose that a scientific law is about the elementary constituents of a gas. It is a statement of what happens when a large number of such constituents interact with one another under certain conditions.
John Dewey
[Y]ou have expressed my inward conviction, though far more vividly and clearly than I could have done, that the Universe is not the result of chance. ... Lastly, I could show fight on natural selection having done and doing more for the progress of civilization than you seem inclined to admit. Remember what risk the nations of Europe ran, not so many centuries ago of being overwhelmed by the Turks, and how ridiculous such an idea now is! The more civilized so-called Caucasian races have beaten the Turkish hollow in the struggle for existence. Looking to the world at no very distant date, what an endless number of the lower races will have been eliminated by the higher civilized races throughout the world.
Charles Darwin
Writers after Coase have referred to the authority structure of the firm as a "visible hand" that works in combination with Smith's invisible hand. The everyday fact that employers exercise power over their employees - not news to most employees - had been a central theme in Marx's economics, but it was (and generally continues to be) overlooked by most neoclassical economists. Early in his studies Coase noted the similarity between the hierarchical organization of capitalist firms, with their reliance on command relations, and the then-existing system of centralized economic planning in the Communist countries, where production was carried out in accordance with orders from higher authorities and where market competition played little role.
Samuel Bowles
The professional administrators - especially those at higher levels - serve key roles at the boundary of the organization, between the professionals inside and interested parties - governments, client associations, and so on - on the outside. On the one hand, the administrators are expected to protect the professionals' autonomy, to "buffer" them from external pressures. On the other hand, the administrators are expected to woo these outsiders to support the organization, both morally and financially. Thus, the external roles of the manager-maintaining liaison contacts, acting as figurehead and spokesman in a public relations capacity, negotiating with outside agencies-emerge as primary ones in professional administration.
Henry Mintzberg