The history of human knowledge has so uninterruptedly shown that to collateral, or incidental, or accidental events we are indebted for the most numerous and most valuable discoveries, that it has at length become necessary, in any prospective view of improvement, to make not only large, but the largest allowances for inventions that shall arise by chance, and quite out of the range of ordinary expectation. It is no longer philosophical to base, upon what has been, a vision of what is to be. Accident is admitted as a portion of the substructure. We make chance a matter of absolute calculation. We subject the unlooked for and unimagined, to the mathematical formulae of the schools.
Edgar Allan PoeRelated topics
absolute accident accidental arise base calculation chance collateral expectation formula history human improvement knowledge large length longer matter necessary ordinary portion prospective quite range show subject substructure valuable view vision incidentalRelated quotes
Isaac Newton's Philosophae Naturalis Principia Mathematica abstracted time from events, establishing its tractability to scientific calculation. Conceived as pure, absolute duration, without qualities, it conforms perfectly to its mathematical idealization (as the real number line). Since time is already pure, its reality indistinguishable from its formalization, a pure mathematics of change – the calculus – can be applied to physical reality without obstruction. The calculus can exactly describe things as they occur in themselves, without straying, even infinitesimally, from the rigorous dictates of formal intelligence. In this way natural philosophy becomes modern science.
Nick Land
Being, in whose name Heidegger's philosophy increasingly concentrates itself, is for him-as a pure self-presentation to passive consciousness-just as immediate, just as independent of the mediations of the subject as the facts and the sensory data are for the positivists. In both philosophical movements thinking becomes a necessary evil and is broadly discredited. Thinking loses its element of independence. The autonomy of reason vanishes: the part of reason that exceeds the subordinate reflection upon and adjustment to pre-given data. With it, however, goes the conception of freedom and, potentially, the self-determination of human society.
Theodor Adorno
One of the most important axioms is, that as the quantity of any commodity, for instance, plain food, which a man has to consume, increases, so the utility or benefit derived from the last portion used decreases in degree. The decrease in enjoyment between the beginning and the end of a meal may be taken as an example. And I assume that on an average, the ratio of utility is some continuous mathematical function of the quantity of commodity. This law of utility has, in fact, always been assumed by political economists under the more complex form and name of the Law of Supply and Demand. But once fairly stated in its simple form, it opens up the whole of the subject.
William Stanley Jevons
As if the butterfly, like the artist, were conscious of something not entirely congenial in the child's nature, it alternately sparkled and grew dim. At length it arose from the small hand of the infant with an airy motion that seemed to bear it upward without an effort, as if the ethereal instincts with which its master's spirit had endowed it impelled this fair vision involuntarily to a higher sphere. Had there been no obstruction, it might have soared into the sky and grown immortal. But its lustre gleamed upon the ceiling; the exquisite texture of its wings brushed against that earthly medium; and a sparkle or two, as of stardust, floated downward and lay glimmering on the carpet.
Nathaniel Hawthorne
Bohr had... discovered that the frequencies corresponding to very large integers could be calculated accurately from the classical mechanics; they were simply the number of times that an ordinary electron would complete the circuit of its orbit in one second when it was at a very great distance from the nucleus of the atom to which it belonged. This could only mean that when an electron receded to a great distance from the nucleus of its atom, it not only assumed the properties of an ordinary electron, but also behaved as directed by the classical mechanics. Yet the classical mechanics failed completely for the calculation of frequencies corresponding to small orbits.
James Jeans
