Top 174 Calculus Quotes & Sayings - Page 3

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.

...a major triumph of mathematical imagination: the use of visual imagery to condense a large quantity of information into a single comprehensible picture... Mathematicians are just beginning to understand these basic building blocks of change and to analyze how they combine. The methodology involved has a very different spirit from traditional modeling with differential equations: it is more like chemistry than calculus, requiring careful counterpoint between analysis and synthesis.

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.

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.

Throughout the 1960s and 1970s devoted Beckett readers greeted each successively shorter volume from the master with a mixture of awe and apprehensiveness; it was like watching a great mathematician wielding an infinitesimal calculus, his equations approaching nearer and still nearer to the null point.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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.

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."

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?

Nothing has afforded me so convincing a proof of the unity of the Deity as these purely mental conceptions of numerical and mathematical science which have been by slow degrees vouchsafed to man, and are still granted in these latter times by the Differential Calculus, now superseded by the Higher Algebra, all of which must have existed in that sublimely omniscient Mind from eternity.

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."

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].

There is nothing morally objectionable in stating that a country has the inalienable right to decide on the exact number of immigrants and the exact type of immigrants that it wishes to let into its borders. As part of that calculus, it is perfectly rational to exhibit preferential treatment to immigrants who share one's cultural values.

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.

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.

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.

Arithmetic starts with the integers and proceeds by successively enlarging the number system by rational and negative numbers, irrational numbers, etc... But the next quite logical step after the reals, namely the introduction of infinitesimals, has simply been omitted. I think, in coming centuries it will be considered a great oddity in the history of mathematics that the first exact theory of infinitesimals was developed 300 years after the invention of the differential calculus.

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.

I read 'On The Road' in college. I was 18 or 19, and I had a particular quarter where I was taking biology, calculus, and physics. Those were my three classes. It wasn't a well-rounded schedule at all. It was hard, hard work, all the time - hours and hours and hours of homework.

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."

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.

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.

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.

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.

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.

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.

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.

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.

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.

You'll remember Newton was furious at Leibniz, because he developed calculus at the same time. And he went to his death believing that he had copied him. And no, it's because all the elements were there, so it's almost inevitable that the next discovery - as long as people are free and allowed to experiment and try new things.

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)

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.

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 chief difficulty of modern theoretical physics resides not in the fact that it expresses itself almost exclusively in mathematical symbols, but in the psychological difficulty of supposing that complete nonsense can be seriously promulgated and transmitted by persons who have sufficient intelligence of some kind to perform operations in differential and integral calculus.

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.

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.