Calculus Best Quotes

Everyone has their weak spot. The one thing that despite your best efforts, will always bring you to your knees, regardless of how strong you are otherwise. For some people, it's love. Others, money or alcohol. Mine was even worse: calculus.

As to the 'Left' I'll say briefly why this was the finish for me. Here is American society, attacked under open skies in broad daylight by the most reactionary and vicious force in the contemporary world, a force which treats Afghans and Algerians and Egyptians far worse than it has yet been able to treat us. The vaunted CIA and FBI are asleep, at best. The working-class heroes move, without orders and at risk to their lives, to fill the moral and political vacuum. The moral idiots, meanwhile, like Falwell and Robertson and Rabbi Lapin, announce that this clerical aggression is a punishment for our secularism. And the governments of Pakistan and Saudi Arabia, hitherto considered allies on our 'national security' calculus, prove to be the most friendly to the Taliban and Al Qaeda. Here was a time for the Left to demand a top-to-bottom house-cleaning of the state and of our covert alliances, a full inquiry into the origins of the defeat, and a resolute declaration in favor of a fight to the end for secular and humanist values: a fight which would make friends of the democratic and secular forces in the Muslim world. And instead, the near-majority of 'Left' intellectuals started sounding like Falwell, and bleating that the main problem was Bush's legitimacy. So I don't even muster a hollow laugh when this pathetic faction says that I, and not they, are in bed with the forces of reaction.

Everyone has their weak spot. The one thing that, despite your best efforts, will always bring you to your knees, regardless of how strong you are otherwise. For some people, it’s love. Others, money or alcohol. Mine was even worse: calculus.

The list of correlations to that night is as long as the Jersey coast. And so is the list of reasons I shouldn't be looking forward to seeing him at school. But I can't help it. He's already texted me three times this morning: Can I pick you up for school? and Do u want 2 have breakfast? and R u getting my texts? My thumbs want to answer "yes" to all of the above, but my dignity demands that I don't answer at all. He called my his student. He stood there alone with me on the beach and told me he thinks of me as a pupil. That our relationship is platonic. And everyone knows what platonic means-rejected. Well, I might be his student, but I'm about to school, him on a few things. The first lesson of the day is Silent Treatment 101. So when I see him in the hall, I give him a polite nod and brush right by him. The zap from the slight contact never quite fades, which mean he's following me. I make it to my locker before his hand is on my arm. "Emma." The way he whispers my name sends goose bumps all the way to my baby toes. But I'm still in control. I nod to him, dial the combination to my locker, then open it in his face. He moves back before contact. Stepping around me, he leans his hand against the locker door and turns me around to face him. "That's not very nice." I raise my best you-started-this brow. He sighs. "I guess that means you didn't miss me." There are so many things I could pop off right now. Things like, "But at least I had Toraf to keep my company" or "You were gone?" Or "Don't feel bad, I didn't miss my calculus teacher either." But the goal is to say nothing. So I turn around. I transfer books and papers between my locker and backpack. As I stab a pencil into my updo, his breath pushes against my earlobe when he chuckles. "So your phone's not broken; you just didn't respond to my texts." Since rolling my eyes doesn't make a sound, it's still within the boundaries of Silent Treatment 101. So I do this while I shut my locker. As I push past him, he grabs my arm. And I figure if stomping on his toe doesn't make a sound... "My grandmother's dying," he blurts. Commence with the catching-Emma-off-guard crap. How can I continue Silent Treatment 101 after that? He never mentioned his grandmother before, but then again, I never mentioned mine either. "I'm sorry, Galen." I put my hand on his, give it a gentle squeeze. He laughs. Complete jackass. "Conveniently, she lives in a condo in Destin and her dying request is to meet you. Rachel called your mom. We're flying out Saturday afternoon, coming back Sunday night. I already called Dr. Milligan." "Un-freaking-believable.

It is said that the best horses lose when they compete with slower ones, and win against better rivals. Undercompensation from the absence of a stressor, inverse hormesis, absence of challenge, degrades the best of the best. In Baudelaire’s poem, “The albatross’s giant wings prevent him from walking”—many do better in Calculus 103 than Calculus 101.

Donald Saari uses a combination of stories and questions to challenge students to think critically about calculus. “When I finish this process,” he explained, “I want the students to feel like they have invented calculus and that only some accident of birth kept them from beating Newton to the punch.” In essence, he provokes them into inventing ways to find the area under the curve, breaking the process into the smallest concepts (not steps) and raising the questions that will Socratically pull them through the most difficult moments. Unlike so many in his discipline, he does not simply perform calculus in front of the students; rather, he raises the questions that will help them reason through the process, to see the nature of the questions and to think about how to answer them. “I want my students to construct their own understanding,” he explains, “so they can tell a story about how to solve the problem.

The three thousand miles in distance he put between himself and Emma tonight is nothing compared with the enormous chasm separating them when they sit next to each other in calculus. Emma's ability to overlook his existence is a gift-but not one that Poseidon handed down. Rachel insists this gift is uniquely a female trait, regardless of the species. Since their breakup, Emma seems to be the only female utilizing this particular gift. Even Rayna could learn a few lessons from Emma in the art of torturing a smitten male. Smitten? More like fanatical. He shakes his head in disgust. Why couldn't I just sift when I turned of age? Why couldn't I find a suitable mild-tempered female to mate with? Live a peaceful life, produce offspring, grow old, and watch my own fingerlings have fingerlings someday? He searches through his mind for someone he might have missed in the past. For a face he overlooked before but could now look forward to every day. For a docile female who would be honored to mate with a Triton prince-instead of a temperamental siren who mocks his title at every opportunity. He scours his memory for a sweet-natured Syrena who would take care of him, who would do whatever he asked, who would never argue with him. Not some human-raised snippet who stomps her foot when she doesn't get her way, listens to him only when it suits some secret purpose she has, or shoves a handful of chocolate mints down his throat if he lets his guard down. Not some white-haired angelfish whose eyes melt him into a puddle, whose blush is more beautiful than sunrise, and whose lips send heat ripping through him like a mine explosion. He sighs as Emma's face eclipses hundreds of mate-worthy Syrena. That's just one more quality I'll have to add to the list: someone who won't mind being second best. His just locks as he catches a glimpse of his shadow beneath him, cast by slithers of sterling moonlight. Since it's close to three a.m. here, he's comfortable walking around without the inconvenience of clothes, but sitting on the rocky shore in the raw is less than appealing. And it doesn't matter which Jersey shore he sits on, he can't escape the moon that connects them both-and reminds him of Emma's hair. Hovering in the shallows, he stares up at it in resentment, knowing the moon reminds him of something else he can' escape-his conscience. If only he could shirk his responsibilities, his loyalty to his family, his loyalty to his people. If only he could change everything about himself, he could steal Emma away and never look back-that is, if she'll ever talk to him again.

Nevertheless, Leibniz remains a great man, and his greatness is more apparent now than it was at any earlier time. Apart from his eminence as a mathematician and as the inventor of the infinitesimal calculus, he was a pioneer in mathematical logic, of which he perceived the importance when no one else did so. And his philosophical hypotheses, though fantastic, are very clear, and capable of precise expression. Even his monads can still be useful as suggesting possible ways of viewing perception, though they cannot be regarded as windowless. What I, for my part, think best in his theory of monads is his two kinds of space, one subjective, in the perceptions of each monad, and one objective, consisting of the assemblage of points of view of the various monads. This, I believe, is still useful in relating perception to physics.

The genius is apparent from page one. . . . A seamless fusion of virtuosity and insight. . . . If William Wordsworth were alive today and writing cyberpunk, this is what he might write. —David Farland New York Times Best Seller Lead judge for the world's largest genre writing competition

With the right mindset and the right teaching, people are capable of much more than expected. A teacher with a growth mindset asks: How can I teach the students? and What is the best method for them to learn?  The potential for success with this approach was proven with Jaime Escalante, a teacher who taught calculus to inner-city Hispanic students.

When physicists create a mathematical model of a physical process, they rely on the mathematical framework that can represent that process as closely as possible. When Newton developed a model of forces and motion, the appropriate mathematical framework was calculus. When Einstein developed a model of wave-particle motion, he relied on the mathematics of wave equations and eigenvalues. For many models in scientific computation, the computational framework that best aligns with our need is object orientation.

Almost any positive good [positive liberty] can be described in terms of freedom from something [negative liberty]. Health is freedom from disease; happiness is a life free from flaws and miseries; equality is freedom from advantage and disadvantage.. Faced with this flexibility, the theorist will need to prioritize some freedoms and discount others. At its extreme we may get the view that only some particular kind of life makes for ‘real freedom’. Real freedom might, for instance, be freedom the bondage of desire, as in Buddhism and Stoicism. Or it might be a kind of self-realization or self-perfection only possible in a community of similarly self-realized individuals, pointing us towards a communitarian, socialist, or even communist ideal. To a laissez-faire capitalist, it is freedom from more than minimal necessary political and legal interference in the pursuit of profit. But the rhetoric of freedom will typically just disguise the merits or demerits of the political order being promoted. The flexibility of the term ‘freedom’ undoubtedly plays a huge role in the rhetoric of political demands, particularly when the language of rights mingles with the language of freedom. ‘We have a right to freedom from…’ is not only a good way, but the best way to start a moral or political demand. Freedom is a dangerous word, just because it is an inspirational one. The modern emphasis on freedom is problematically associated with a particular self-image. This is the 'autonomous' or self-governing and self-driven individual. This individual has the right to make his or her own decisions. Interference or restraint is lack of respect, and everyone has a right to respect. For this individual, the ultimate irrationality would be to alienate his freedom, for instance by joining a monastery that requires unquestioning obedience to a superior, or selling himself into slavery to another. The self-image may be sustained by the thought that each individual has the same share of human reason, and an equal right to deploy this reason in the conduct of his or her own life. Yet the 'autonomous' individual, gloriously independent in his decision-making, can easily seem to be a fantasy. Not only the Grand Unifying Pessimisms, but any moderately sober reflection on human life and human societies, suggest that we are creatures easily swayed, constantly infected by the opinions of others, lacking critical self-understanding, easily gripped by fantastical hopes and ambitions. Our capacity for self-government is spasmodic, and even while we preen ourselves on our critical and independent, free and rational decisions, we are slaves of fashion and opinion and social and cultural forces of which we are ignorant. A little awareness of ethics will make us mistrustful of sound-bite-sized absolutes. Even sacred freedoms meet compromises, and take us into a world of balances. Free speech is sacred. Yet the law does not protect fraudulent speech, libellous speech, speech describing national secrets, speech inciting racial and other hatreds, speech inciting panic in crowded places, and so on. In return, though, we gain freedom from fraud, from misrepresentation of our characters and our doings, from enemy incursions, from civil unrest, from arbitrary risks of panic in crowds. For sure, there will always be difficult cases. There are websites giving people simple recipes on how to make bombs in their kitchens. Do we want a conception of free speech that protects those? What about the freedom of the rest of us to live our lives without a significant risk of being blown up by a crank? It would be nice if there were a utilitarian calculus enabling us to measure the costs and benefits of permission and suppression, but it is hard to find one.

the idea of using infinity to solve difficult geometry problems has to rank as one of the best ideas anyone ever had.

P3 - ten minutes of that movie, or indeed of any movie whose message is similarly dystopian about a post-aging world (Blade Runner), you will see that they set it up by insinuating, with exactly no justification and also no attempt at discussion (which is how they get away with not justifying it), that the defeat of aging will self-evidently bring about some new problem that we will be unable to solve without doing more harm than good. The most common such problem, of course, is overpopulation - and I refer you to literally about 1000 interviews and hundreds of talks I have given on stage and camera over the past 20 years, of which several dozen are online, for why such a concern is misplaced. The reason there are 1000, of course, is that most people WANT to believe that aging is a blessing in disguise - they find it expedient to put aging out of their minds and get on with their miserably short lives, however irrational must be the rationalizations by which they achieve that. Aubrey has been asked on numerous occasions whether humans should use future tech to extend their lifespans. Aubrey opines, "I believe that humans should (and will) use (and, as a prerequisite, develop) future technologies to extend their healthspan, i.e. their healthy lifespan. But before fearing that I have lost my mind, let me stress that that is no more nor less than I have always believed. The reason people call me an “immortalist” and such like is only that I recognize, and am not scared to say, two other things: one, that extended lifespan is a totally certain side-effect of extended healthspan, and two, that the desire (and the legitimacy of the desire) to further extend healthspan will not suddenly cease once we achieve such-and-such a number of years." On what people can do to advance longevity research, my answer to this question has radically changed in the past year. For the previous 20 years, my answer would have been “make a lot of money and give it to the best research”, as it was indisputable that the most important research could go at least 2 or 3x times faster if not funding-limited. But in the past year, with the influx of at least a few $B, much of it non-profit (and much of it coming from tech types who did exactly the above), the calculus has changed: the rate-limiter now is personnel. It’s more or less the case now that money is no longer the main rate-limiter, talent is: we desperately need more young scientists to see longevity as the best career choice. As for how much current cryopreservation technology will advance in the next 10-20 years, and whether it enough for future reanimation? No question about the timeframe for a given amount of progress in any pioneering tech can be answered other than probabilistically. Or, to put it more simply, I don’t know - but I think there's a very good chance that within five years we will have cryo technology that inflicts only very little damage on biological tissue, such that yes, other advances in rejuvenation medicine that will repair the damage that caused the cryonaut to be pronounced dead in the first place will not be overwhelmed by cryopreservation damage, hence reanimation will indeed be possible. As of now, the people who have been cryopreserved(frozen) the best (i.e. w/ vitrification, starting very shortly immediately after cardiac arrest) may, just possibly, be capable of revival by rewarming and repair of damage - but only just possibly. Thus, the priority needs to be to improve the quality of cryopreservation - in terms of the reliability of getting people the best preservation that is technologically possible, which means all manner of things like getting hospitals more comfortable with cryonics practice and getting people to wear alarms that will alert people if they undergo cardiac arrest when alone, but even more importantly in terms of the tech itself, to reduce (greatly) the damage that is done to cells and tissues by the cryopreservation process.

we have considered games between two specific players trying to guess each other’s strategy and find a best reply. Let us now shift perspective, and consider a population of players, each with a given strategy.

A tangent that departs from the real to the imaginary: pure consciousness does and does not transcend the body, and I believe this after hearing that my mother felt suicidal after she took her medicines for weight loss and her biggest regrets in life came crushing down on her for three days in a row. This is the best of what I have learnt in my years of fascination for science and knowledge, and to make you grasp this takes fullness of life: in hydrology, the wet and the dry, and the hot and the cold always co-exist, but they are also in flux and are also stable: all depending on the reference point of analysis. Consciousness beyond matter, and consciousness tied to matter co-exist in everyplace at different scales, and sometimes even in the same scale. Tao te ching (the way and its power) that fascinated Lao Tzu; the calculus of infinitesimals; the wonderful infinity of the number line and fractals that fascinated Ramanujan and Mandelbrot; the horn of the rhinoceros that fascinated Dali, thermodynamic and hydrodynamic equilibriums that fascinate all scientists, the surety of a fading perfume smell or the permanence of a shattered mirror that is easy to understand to anyone; the concepts of anti-fragility, entropy, volatility, randomness, disorder are all intimately tied to this. Consciousness is constantly attainted and broken all around us all the time, and we rarely stop to think about this because it infinitesimally evades us. Here is where I begin to stretch this and I can't understand it and it is very discouraging -- prudence, temperance and courage -- some of the highest virtues may also be related to this. When you are prepared, it is consciousness. When we are unprepared for it, and this hits you without hurting you, it is magic and strength. Else, perhaps death.

And Ella starts rapping: Straight A's, good grades, that's the plan Study hard, top of the class Doing the best you can You won't need it but you're studying algebra Won't use Japanese, world history or calculus You follow the path they tell you to Go straight to college when you finish school If there's no scholarship take out a loan Clock up a debt kid, you're on your own Take all your stuff, you're leaving home The big wide world is yours to roam The crowd roars. She is seriously so good! Damon picks up his guitar and starts singing: But life can give us lemons and not ice cream And the path we take is not what it seems But we can't give up and cry and scream We have to turn up and change our dream Ella raps again: Science, physics and chemistry Make sure you ace your SATs Gotta get into an Ivy League Make my parents proud of me The say the road is straight and clear No need to wait, choose a career Doctor, lawyer, engineer Need to make a hundred grand a year And Damon sings: But life can give you lemons and not ice cream Find yourself against the current going upstream And all you wanna do is cry and scream Because you realize this ain't your dream You realize you have to change your dream Ella raps: Sat in class reading Romeo and Juliet But never understanding a word of it It's so old fashioned, it just doesn't fit You hate it so much, you wanna quit That's the stuff they think you need to learn But what happens when you crash and burn What happens when life deals you a blow What happens when you sink so low? And Damon sings: When life gives you lemons and not ice cream When you find yourself without a team When it throws you things that are too extreme When you can no longer chase your dream Then know it's time to change your dream And together they sing: When life gives you lemons and not ice cream When you wanna cry and shout and scream When you've fallen off your balance beam Then you know it's time to change your dream And you can do it You Can Change Your Dream

Some teachers refer to this as the 2-3-1 tool of emphasis, where the most emphatic words or images go at the end, the next most emphatic at the beginning, and the least emphatic in the middle, but that’s too much calculus for my brain. Here’s my simplified version: put your best stuff near the beginning and at the end; hide weaker stuff in the middle. Amy

Because Aristotle’s was the accepted lens on the universe, centuries of medieval scientists and thinkers went to great lengths to make epicycles work. It wasn’t until the sixteenth century, with one simple but profound observation, that Renaissance astronomer Nicolaus Copernicus reframed our view of the universe. The planets revolved not around the earth, but around the sun. Finally, understanding that provided a foundation for some of the most important advances in history and the foundation for modern astronomy and calculus. Of course, it took eighteen centuries for someone like Copernicus to see and articulate the flaws in Aristotle’s logic. And even he died without knowing that the world would accept he was right. Changing a well-established view of the world rarely happens overnight—and even when it happens, it still takes time to refine and perfect the right new perspective. In the world of innovation, many companies are stuck in a world of creating “epicycles”: elaborate approximations, estimations, and extrapolations. Because we gather, fine-tune, and cross-reference all manner of data, it seems like we should be getting better and better at predicting success. But if we fail to understand why customers make the choices they make, we’re just getting better and better at a fundamentally flawed process. Without the right understanding of the causal mechanism at the center of the innovation universe, companies are trying to make sense of the universe revolving around the earth. They’re forced to rely on an array of borrowed best practices, probabilistic tools, and tips and tricks that have worked for other companies, but which can’t guarantee success. As you look at innovation through the lenses of the Jobs Theory, what you see is not the customer at the center of the innovation universe, but the customer’s Job to Be Done. It may seem like a small distinction—just a few minutes of arc—but it matters a great deal. In fact, it changes everything.

These results were obtained by making up tables in which were listed the volumes for given sets of values of the dimensions, and from these selecting the best proportions.

The Singaporean study also identified three specific conditions that promoted productive failure. First, failure is best when it promotes a sense of challenge and engagement versus frustration. Frustration, of course, is the feeling that you are going nowhere at top speed, so there has to be a sense of progress and achievement. You can’t just hand a child a calculus equation and expect productive failure. It has to be within their capabilities and they have to be able to see improvement.  Second, failure is best when learners have the opportunity to elaborate on what they are doing and thinking, as was done in a group setting during the study. When you can narrate what you’re doing, instead of toiling away in silence, it can help shed light on your efforts because you’re actively thinking about what you’re doing and analyzing it. Often, thinking out loud leads to solutions that wouldn’t have appeared otherwise. Third, failure is best when learners have the chance to compare solutions that work, and solutions that don’t. This is what happens when you aren’t shown the exact path every single time. You recognize the red flags of failure and gain intuition when something seems right or wrong.

IT IS BEST TO THINK OF DEDEKIND AS A GREAT DIAGNOSTICIAN, A DOCTOR of discovery.