Calculus Quotes - page 4
Our problem is that we do not fully understand Putin's calculus, just as he does not understand ours. In Putin's view, the United States, the European Union and NATO have launched an economic and proxy war in Ukraine to weaken Russia and push it into a corner. As Valery Gerasimov, chief of staff of the Russian armed forces, has underscored, this is a hybrid, 21st-century conflict, in which financial sanctions, support for oppositional political movements and propaganda have all been transformed from diplomatic tools to instruments of war. Putin likely believes that any concession or compromise he makes will encourage the West to push further.
Fiona Hill (presidential advisor)
The calculus is to mathematics no more than what experiment is to physics, and all the truths produced solely by the calculus can be treated as truths of experiment. The sciences must proceed to first causes, above all mathematics where one cannot assume, as in physics, principles that are unknown to us. For there is in mathematics, so to speak, only what we have placed there... If, however, mathematics always has some essential obscurity that one cannot dissipate, it will lie, uniquely, I think, in the direction of the infinite; it is in that direction that mathematics touches on physics, on the innermost nature of bodies about which we know little.
Bernard Le Bovier de Fontenelle
At the time the book of Marquis de l'Hôpital had appeared, and almost all mathematicians began to turn to the new geometry of the infinite [that is, the new infinitesimal calculus], until then little known. The surprising universality of the methods, the elegant brevity of the proofs, the neatness and speed of the most difficult solutions, a singular and unexpected novelty, all attracted the mind and there was in the mathematical world a well marked revolution [une révolution bien marquée.
Bernard Le Bovier de Fontenelle
Indeed, most bright, intellectually curious college students suffer through Econ 101, are happy to pass, and then wave goodbye to the subject forever. Economics is filed away with calculus and chemistry-rigorous subjects that required a lot of memorization and have little to do with anything that will come later in life. And, of course, a lot of bright students avoid the course in the first place. This is a shame on two levels.
First, many intellectually curious people are missing a subject that is provocative, powerful, and highly relevant to almost every aspect of our lives....Second, many of our brightest citizens are economically illiterate.
Charles Wheelan
Donald Trump's political rivals look at the price exacted by a Muslim like Syed Farouk and his bride in the aggregate. To a politician, 14 lives in 322 million is a small price to pay for 'our freedoms.' Fourteen dead in San Bernardino is not a steep price to pay for unfettered immigration from Islamic countries, peddled politically as 'our values,' 'our tolerance,' 'our greatness.' This callous calculus is second nature to neoconservative politicians like Lindsey Graham or Darth Vader Cheney. Not to Trump.
Ilana Mercer
So intimate is the union between Mathematics and Physics that probably by far the larger part of the accessions to our mathematical knowledge have been obtained by the efforts of mathematicians to solve the problems set to them by experiment, and to create for each successive class phenomena a new calculus or a new geometry, as the case might be, which might prove not wholly inadequate to the subtlety of nature. Sometimes the mathematician has been before the physicist, and it has happened that when some great and new question has occurred to the experimentalist or the observer, he has found in the armory of the mathematician the weapons which he needed ready made to his hand. But much oftener, the questions proposed by the physicist have transcended the utmost powers of the mathematics of the time, and a fresh mathematical creation has been needed to supply the logical instrument requisite to interpret the new enigma.
Henry John Stephen Smith
The minimum principle that unified the knowledge of light, gravitation, and electricity of Hamilton's time no longer suffices to relate these fundamental branches of physics. Within fifty years of its creation, the belief that Hamilton's principle would outlive all other physical laws of physics was shattered. Minimum principles have since been created for separate branches of physics... but these are not only restricted... but seem to be contrived...
A single minimum principle, a universal law governing all processes in nature, is still the direction in which the search for simplicity is headed, with the price of simplicity now raised from a mastery of differential equations to a mastery of the calculus of variations.
William Rowan Hamilton
To sum up: we have seen that of the three notions of 'partial interpretation' discussed, each is either unsuitable for Carnap's purposes (starting with observation terms), or incompatible with a rather minimal scientific realism; and, in addition, the second notion depends upon gross and misleading changes in our use of language. Thus in none of these senses is 'a partially interpreted calculus in which only the observation terms are directly interpreted' an acceptable model for a scientific theory.
Hilary Putnam
If you put it as "complex nervous systems” it sounds pretty deflationary. What's so special about a complex nervous system? But of course, that complex nervous system allows you to do calculus. It allows you to do astrophysics... to write poetry... to fall in love. Put under that description, when asked "What's so special about humans...?”, I'm at a loss to know how to answer that question. If you don't see why we'd be special... because we can do poetry [and] think philosophical thoughts [and] we can think about the morality of our behavior, I'm not sure what kind of answer could possibly satisfy you at that point.
...I could pose the same kinds of questions of you... So God says, "You are guys are really, really special.” How does his saying it make us special? "But you see, he gave us a soul.” How does our having a soul make us special? Whatever answer you give, you could always say... "What's so special about that?”.
Shelly Kagan
Kepler's achievements in mathematics would alone have been sufficient to win for him enduring fame; he first enunciated clearly the principle of continuity in mathematics, treating the parabola as at once the limiting case of the ellipse and the hyperbola, and showing that parallel lines can be regarded as meeting at infinity; he introduced the word 'focus' into geometry; while in his Stereometria Dolorum, published 1615, he applied the conception to the solution of certain volumes and areas by the use of infinitesimals, thus preparing the way for Desargues, Cavalieri, Barrow, and the developed calculus of Newton and Leibniz.
Johannes Kepler
