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 LandRelated topics
calculus change duration establishing formal idealization indistinguishable intelligence line mathematics natural number obstruction principia pure real science way things IsaacRelated quotes
Do I worship modern medicine? Is science my religion? Not at all; there is no aspect of modern medicine or science that I would exempt from the most rigorous scrutiny, and I can readily identify a host of serious problems that still need to be fixed. That's easy to do, of course, because the worlds of medicine and science are already engaged in the most obsessive, intensive, and humble self-assessments yet known to human institutions, and they regularly make public the results of their self-examinations. Moreover, this open-ended rational criticism, imperfect as it is, is the secret of the astounding success of these human enterprises. There are measurable improvements every day.
Daniel Dennett
These Peripatetics accordingly made careful investigations into the nature of all things, so as to determine which I should be avoided as evil, discounted as useless, sought after as good, or preferred as better, and finally which are called "good" or "bad" according to circumstances. There thus developed two branches of philosophy, natural and moral, which are also called ethics and physics. But, through lack of scientific skill in argumentative reasoning, many absurdities were concluded. Thus Epicurus would have the world originate from atoms and a void, and would dispense with God as its author; whereas the Stoics asserted that matter is coeternal with God, and held that all sins are equally grave. p. 76.
John of Salisbury
Einstein is the only figure in the physical sciences with a stature that can be compared with Newton. Newton is reported to have said "If I have seen further than other men, it is because I stood on the shoulders of giants." This remark is even more true of Einstein who stood on the shoulders of Newton. Both Newton and Einstein put forward a theory of mechanics and a theory of gravity but Einstein was able to base General Relativity on the mathematical theory of curved spaces that had been constructed by Riemann while Newton had to develop his own mathematical machinery. It is therefore appropriate to acclaim Newton as the greatest figure in mathematical physics and the Principia is his greatest achievement.
Stephen Hawking
Comprehension is neither an arbitrary act nor a passive experience, but a responsible act claiming universal validity. Such knowing is indeed objective in the sense of establishing contact with a hidden reality; a contact that is defined as the condition for anticipating an indeterminate range of yet unknown (and perhaps yet inconceivable) true implications. It seems reasonable to describe this fusion of the personal and the objective as Personal Knowledge. Personal knowledge is an intellectual commitment, and as such inherently hazardous. Only affirmations that could be false can be said to convey objective knowledge of this kind.
Michael Polanyi
The definition of random in terms of a physical operation is notoriously without effect on the mathematical operations of statistical theory because so far as these mathematical operations are concerned random is purely and simply an undefined term. The formal and abstract mathematical theory has an independent and sometimes lonely existence of its own. But when an undefined mathematical term such as random is given a definite operational meaning in physical terms, it takes on empirical and practical significance. Every mathematical theorem involving this mathematically undefined concept can then be given the following predictive form: If you do so and so, then such and such will happen.
Walter A. Shewhart