Top 240 Differential Calculus Quotes & Sayings - Page 4

The analytical geometry of Descartes and the calculus of Newton and Leibniz have expanded into the marvelous mathematical method-more daring than anything that the history of philosophy records-of Lobachevsky and Riemann, Gauss and Sylvester. Indeed, mathematics, the indispensable tool of the sciences, defying the senses to follow its splendid flights, is demonstrating today, as it never has been demonstrated before, the supremacy of the pure reason.

With demands for special education or standardized test prep being shouted in their ears, public schools can't always hear a parent when he says: 'I want my child to be able to write contracts in Spanish,' or, 'I want my child to shake hands firmly,' or, 'I want my child to study statistics and accounting, not calculus.'

I would have I think made a bigger mistake if I had said, "Eh, chemical weapons. That doesn't really change my calculus." I think it was important for me as president of the United States to send a message that in fact there is something different about chemical weapons [in Syria].

[Mathematics] is security. Certainty. Truth. Beauty. Insight. Structure. Architecture. I see mathematics, the part of human knowledge that I call mathematics, as one thing - one great, glorious thing. Whether it is differential topology, or functional analysis, or homological algebra, it is all one thing. ... They are intimately interconnected, they are all facets of the same thing. That interconnection, that architecture, is secure truth and is beauty. That's what mathematics is to me.

Non- Euclidean calculus and quantum physics are enough to stretch any brain; and when one mixes them with folklore, and tries to trace a strange background of multi-dimensional reality behind the ghoulish hints of Gothic tales and the wild whispers of the chimney-corner, one can hardly expect to be wholly free from mental tension. (Dreams In The Witch-House)

There are certainly lots of jobs in computer coding, but coding doesn't really require advanced mathematics. And engineering jobs, they vary widely in the amount of demand that we actually need. So, you know, the number of people for whom the job description includes Newton's calculus is not perhaps that high.

Meteorologists don't use a script, and most create their own graphics and certainly put together their own forecasts. Most of us went to school to become scientists - at least I did - and studied thermodynamics, physics, and tons of calculus to take this young science to the next level. Our accuracy is amazing and will only continue to improve.

My calculus teacher would send me home every weekend with 400 problems to solve. At the time, I felt it was so strict and demanding, but now I realize that the workload instilled in me a sense of discipline, and showed me that even if I wasn't inherently skilled at something, I could be, with enough dedication and practice.

Accordingly, we find Euler and D'Alembert devoting their talent and their patience to the establishment of the laws of rotation of the solid bodies. Lagrange has incorporated his own analysis of the problem with his general treatment of mechanics, and since his time M. Poinsôt has brought the subject under the power of a more searching analysis than that of the calculus, in which ideas take the place of symbols, and intelligent propositions supersede equations.

Tell them you came, and saw, and looked into my eyes and saw the shadow of the guard receding. Thoughts in time and out of season, the hitchinker stood by the side of the road and levelled his thumb in the calm calculus of reason. [...] Why does my mind circle around you? Why do planets wonder what it would be like to be you? All your soft wild promises were words, birds, endlessly in flight.

Today I said to the calculus students, "I know, you're looking at this series and you don't see what I'm warning you about. You look and it and you think, 'I trust this series. I would take candy from this series. I would get in a car with this series.' But I'm going to warn you, this series is out to get you. Always remember: The harmonic series diverges. Never forget it."

How did Biot arrive at the partial differential equation? [the heat conduction equation] . . . Perhaps Laplace gave Biot the equation and left him to sink or swim for a few years in trying to derive it. That would have been merely an instance of the way great mathematicians since the very beginnings of mathematical research have effortlessly maintained their superiority over ordinary mortals.

The great paradox of the civil rights revolution is that instead of enforcing and expanding equality before the law, the revolution created differential rights based on race, gender and, any day now, sexual orientation. The great liberal revolution, centuries in the making, that brought forth equality in law has been overthrown. In its place we see rising a new feudal legal order of status-based rights.

I had a foretaste of another, larger kind of knowledge: one I believe human beings will be able to access in ever larger numbers in the future. But conveying that knowledge now is rather like a chimpanzee, becoming a human for a single day to experience all of the wonders of human knowledge, and then returning to one's chimp friends and trying to tell them what it was like knowing several different Romance languages, the calculus, and the immense scale of the universe.

I see with much pleasure that you are working on a large work on the integral Calculus ... The reconciliation of the methods which you are planning to make, serves to clarify them mutually, and what they have in common contains very often their true metaphysics; this is why that metaphysics is almost the last thing that one discovers. The spirit arrives at the results as if by instinct; it is only on reflecting upon the route that it and others have followed that it succeeds in generalising the methods and in discovering its metaphysics.

You might be thinking that some people are just naturally good at speaking up, and others just aren't - game over. Not true. Speaking up is a skill that you have to learn like any other, whether it's speaking Spanish or doing calculus or changing a tire.

A study of interactions between women and obstetricians offers an explanation. It described three levels of increasing power imbalance: In the first, you fight and lose; in the second you don't fight because you know you can't win. However, in the highest level of power differential, your preferences are so manipulated that you act against your own interests, but you are content. Elective [meaning requested for no medical reason, not to be confused with needed surgery planned in advance] repeat cesarean exemplifies that highest level.

One of the things that neoliberalism does is, it relies on flexible workforces who are hired and fired at will and who are basically disposable labor. You can use them. You can get rid of them. They have no rights; they have no security. Their lives and well-being are made and unmade at the whim of those who are exercising the calculus. So, instead of looking at the institution and objecting to that kind of organization, people just go, "I'm a failure;"; "I'm not working hard enough"; or, "I'm not as smart as the next person."

In the beginning no power differential existed between male and female. God empowered both with full rights and responsibility to rule outward over all creation, not over each other. As we know all too well, the fall changed everything, precipitating male rule over women and also the rule of some men over other men, a.k.a., patriarchy. Within patriarchy, women no longer derive their value from their Creator, but from men - father, husband, and sons. Within patriarchy, a woman's value is gauged by counting her sons.

The calculus was the first achievement of modern mathematics and it is difficult to overestimate its importance. I think it defines more unequivocally than anything else the inception of modern mathematics; and the system of mathematical analysis, which is its logical development, still constitutes the greatest technical advance in exact thinking.

Race is not the only differential in South Africa, in the new South Africa, where all schools are open, mother-tongue education is a very big issue. One of the main reasons why the dropout figure of black students, and the lower pass rate of black students in the present education system, and it was like that before, was that we didn't have mother-tongue education.

Ask yourself whether our language is complete--whether it was so before the symbolism of chemistry and the notation of the infinitesimal calculus were incorporated in it; for these are, so to speak, suburbs of our language. (And how many houses or streets does it take before a town begins to be a town?) Our language can be seen as an ancient city: a maze of little streets and squares, of old and new houses, and of houses with additions from various periods; and this surrounded by a multitude of new boroughs with straight regular streets and uniform houses.

For remember that in general we don't use language according to strict rules-- it hasn't been taught to us by means of strict rules, either. We, in our discussions on the other hand, constantly compare language with a calculus preceding to exact rules.

How many black holes have we been up close and personal with?" Kosta countered. "All sorts of odd things happen near the event horizon, from huge tidal forces to variations in time. Personally, I'm voting on it having to do with gravity, either a polarization of the fields themselves or else something related to the time differential." I didn't know physics had become a democracy," Hanan murmered.

It is clear that Economics, if it is to be a science at all, must be a mathematical science ... simply because it deals with quantities... As the complete theory of almost every other science involves the use of calculus, so we cannot have a true theory of Economics without its aid.

The illegitimate use of a state by economic interests for their own ends is based upon a preexisting illegitimate power of the state to enrich some persons at the expense of others. Eliminate that illegitimate power of giving differential economic benefits and you eliminate or drastically restrict the motive for wanting political influence.

Mathematics is ordinarily considered as producing precise and dependable results; but in the stock market the more elaborate and abstruse the mathematics the more uncertain and speculative are the conclusions we draw there from. Whenever calculus is brought in, or higher algebra, you could take it as a warning that the operator was trying to substitute theory for experience, and usually also to give to speculation the deceptive guise of investment.

When I was in 7th grade, we were all given an exam. It was science and math, and the boys who did well were skipped ahead so that when they got to be juniors or seniors in high school they would be able to go to the local community college and take calculus and physics there. And I wasn't skipped ahead.

Growing up in Highland Park, in high school, I had some very influential teachers: I had a math teacher who taught calculus that helped me learn to be in love with mathematics; I had a chemistry teacher who inspired us to work what was in the class and to go beyond.

In my view, there was a long period in which analytical philosophy had little to say about ethics. I think their intellectual tools did not do well with it, and analytical philosophy was above all about revolutionizing the philosophical tool box. It was more or less assumed that the Truth about ethics was some form of utilitarianism (perhaps because some consequentialist calculus looked to them like a respectable tool). Kantian ethics was then interpreted as a particularly odious version of the False - "deontology" - and treated with contempt.

There's a popular concept of 'intelligence' as book smarts, like calculus or chess, as opposed to, say, social skills. So people say that 'it takes more than intelligence to succeed in human society.' But social skills reside in the brain, not the kidneys.

Once a term like "open source" entered our vocabulary, one could recast the whole public policy calculus in very different terms, so that instead of discussing the public interest, we are discussing the interests of individual software developers, while claiming that this is a discussion about "innovation" and "progress," not "accountability" or "security."

Our First Amendment expresses a far different calculus for regulating speech than for regulating nonexpressive conduct and that is as it should be. The right to swing your fist should end at the tip of my nose, but your right to express your ideas should not necessarily end at the lobes of my ears.

Looking at numbers as groups of rocks may seem unusual, but actually it's as old as math itself. The word "calculate" reflects that legacy - it comes from the Latin word calculus, meaning a pebble used for counting. To enjoy working with numbers you don't have to be Einstein (German for "one stone"), but it might help to have rocks in your head.

You always, I think, debate with yourself about whether or not you made the right decision. And you have to then give the person that you’re working for - in my instance, the president - your best judgment based on your understanding of the facts, but also the calculus you use to make a determination about what’s the best way to go forward.

Imagine a life-form whose brainpower is to ours as ours is to a chimpanzee’s. To such a species, our highest mental achievements would be trivial. Their toddlers, instead of learning their ABCs on Sesame Street, would learn multivariable calculus on Boolean Boulevard. Our most complex theorems, our deepest philosophies, the cherished works of our most creative artists, would be projects their schoolkids bring home for Mom and Dad to display on the refrigerator door.

Once you have an equalization instrument in place, as you have in Canada, there arise tremendous bureaucratic values - bureaucratic rent so to speak - in maintaining the system that you have. To shift to a system that paid the transfers directly to individuals, by having differential rates of federal income tax levied to adjust to provincial fiscal capacities, which would be my preference, you would have huge bureaucratic opposition. People would try to protect the rents they have in the current system of institutions.

The basic formulation, or bare-bones mechanics, of natural selection is a disarmingly simple argument, based on three undeniable facts (overproduction of offspring, variation, and heritability) and one syllogistic inference (natural selection, or the claim that organisms enjoying differential reproductive success will, on average, be those variants that are fortuitously better adapted to changing local environments, and that these variants will then pass their favored traits to offspring by inheritance).

Consider paint a film of light reflecting/absorbing material, and a colored paint a material which gives a particular, characteristic transmission of light via differential absorption and reflection. Call this reflected quality 'luminance' and measure it in millilamberts. This measure is as real and present as height, breadth, depth; and I find the phenomenon equally sumptuous and convincing. . . . Painted light, not color, not form, not perspective, or line, not image, or words, or equations, is painting. I make paintings which do not represent light, they are light.

Of possible quadruple algebras the one that had seemed to him by far the most beautiful and remarkable was practically identical with quaternions, and that he thought it most interesting that a calculus which so strongly appealed to the human mind by its intrinsic beauty and symmetry should prove to be especially adapted to the study of natural phenomena. The mind of man and that of Nature's God must work in the same channels.

We do not live in a time when knowledge can be extended along a pathway smooth and free from obstacles, as at the time of the discovery of the infinitesimal calculus, and in a measure also when in the development of projective geometry obstacles were suddenly removed which, having hemmed progress for a long time, permitted a stream of investigators to pour in upon virgin soil. There is no longer any browsing along the beaten paths; and into the primeval forest only those may venture who are equipped with the sharpest tools.

How can you shorten the subject? That stern struggle with the multiplication table, for many people not yet ended in victory, how can you make it less? Square root, as obdurate as a hardwood stump in a pasturenothing but years of effort can extract it. You can't hurry the process. Or pass from arithmetic to algebra; you can't shoulder your way past quadratic equations or ripple through the binomial theorem. Instead, the other way; your feet are impeded in the tangled growth, your pace slackens, you sink and fall somewhere near the binomial theorem with the calculus in sight on the horizon.

We need to raise the level of our game in terms of explaining the planetary warming by infrared absorption of CO2 etc. The missing area of understanding seems to be the actual physical mechanism. Lets target an explanation at an audience that has taken 1 year each of undergraduate physics and chemistry, plus calculus. Once we have something that is convincing at this level, we can work on how to communicate this to the interested public (i.e. those that hang out in the climate blogosphere). Willis Eschenbach’s help is needed in translating this for the WUWT crowd.

PLEASURE and pain are undoubtedly the ultimate objects of the calculus of economics. To satisfy our wants to the utmost with the least effort - to procure the greatest amount of what is desirable at the expense of the least that is undesirable - in other words, to maximize pleasure, is the problem of economics.

Millions of statements are made about the president every day on every subject and from every standpoint; threats of violence are not an integral feature of any one subject or viewpoint as distinct from others. Differential treatment of threats against the president, then, selects nothing but special risks, not special messages.

The cookbook gives a detailed description of ingredients and procedures but no proofs for its prescriptions or reasons for its recipes; the proof of the pudding is in the eating. ... Mathematics cannot be tested in exactly the same manner as a pudding; if all sorts of reasoning are debarred, a course of calculus may easily become an incoherent inventory of indigestible information.

In the moral calculus of currently prevailing state capitalism, profits and bonuses in the next quarter greatly outweigh concern for the welfare of one’s grandchildren, and since these are institutional maladies, they will not be easy to overcome. While much remains uncertain, we can assure ourselves, with fair confidence, that future generations will not forgive us our silence and apathy.

The policy that received more attention particularly in the past decade and a half or so has been the US cocaine policy, the differential treatment of crack versus powder cocaine and question is how my research impacted my view on policy. Clearly that policy is not based on the weight of the scientific evidence. That is when the policy was implemented, the concern about crack cocaine was so great that something had to be done and congress acted in the only way they knew how, they passed policy and that's what a responsible society should do.

Without doubt, matter is unlimited in extent, and, in this sense, infinite; and the forces of Nature mould it into an innumerable number of worlds. Would it be at all astonishing if, from the universal dice-box, out of an innumberable number of throws, there should be thrown out one world infinitely perfect? Nay, does not the calculus of probabilities prove to us that one such world out of an infinite number, must be produced of necessity?

Part of my job is to help other kids find books, because not everyone has a keenly organized mind. Some kids could wander the library for hours and still have no idea how to find anything. For them, the Dewey Decimal System might as well be advanced calculus.

The real issue of dealing with proliferation of weapons of mass destruction: nuclear, chemical or biological is: What is your tolerance for risk? And my tolerance for risk for WMD proliferation is pretty close to zero. Because otherwise, we and our allies are at the mercy of regimes like Ahmadinejad and the mullahs in Tehran, or Kim Jong Il and the Hitler-in-the-bunker mentality in Pyongyang, or others who don't share our calculus on the value of human life.

When I was growing up, I had lots of smart classmates that were girls, but none of us were really pushed into math or computers or anything like that. Girls took AP history and AP English and AP European history. And boys took calculus and physics.

When [Bernie] Sanders was challenged about how he would pass his visionary ideas after he became president, he talked about if lawmakers look out the window and they see a million people marching, it changes their calculus. Well, here's an opportunity to continue working to organize these million people even if he is not the one in office.

Democracy turns upon and devours itself. Universal suffrage, in theory the palladium of our liberties, becomes the assurance of our slavery. And that slavery will grow more and more abject and ignoble as the differential birth rate, the deliberate encouragement of mendicancy and the failure of popular education produce a larger and larger mass of prehensile half-wits, and so make the demagogues more and more secure.

The effects of heat are subject to constant laws which cannot be discovered without the aid of mathematical analysis. The object of the theory is to demonstrate these laws; it reduces all physical researches on the propagation of heat, to problems of the integral calculus, whose elements are given by experiment. No subject has more extensive relations with the progress of industry and the natural sciences; for the action of heat is always present, it influences the processes of the arts, and occurs in all the phenomena of the universe.

Gout produces calculus in the kidney... the patient has frequently to entertain the painful speculation as to whether gout or stone be the worst disease. Sometimes the stone, on passing, kills the patient, without waiting for the gout.

Many organizations help businesses to stay on top of what's changing or likely to change. It's important for executives and managers who focus on a company's health coverage to stay up-to-speed on what's happening, and it's important for those in the C-suite to understand the changes to factor these new variables into their strategic planning calculus.

But the indeterminate future is somehow one in which probability and statistics are the dominant modality for making sense of the world. Bell curves and random walks define what the future is going to look like. The standard pedagogical argument is that high schools should get rid of calculus and replace it with statistics, which is really important and actually useful. There has been a powerful shift toward the idea that statistical ways of thinking are going to drive the future.

With demands for special education or standardized test prep being shouted in their ears, public schools can't always hear a parent when he says: 'I want my child to be able to write contracts in Spanish,' or, 'I want my child to shake hands firmly,' or, 'I want my child to study statistics and accounting, not calculus.

The emergent terrorist threats and the spread of nuclear technology and materials have made it much more likely that terrorists will get their hands on a nuclear weapon and that just changes the whole calculus. I love the quote by Rev. Richard Cizik: "If you've never changed your mind about anything, then pinch yourself, you might be dead." The world has changed and we need to start talking about this.