Asymptote Quotes

You can’t ever reach perfection, but you can believe in an asymptote toward which you are ceaselessly striving.

as•ymp•tote (ˈasəm(p)ˌtōt) n. pl. -s. 1. A wish that continually approaches but never achieves fulfillment. [2015, Whittier]

Death comes for all of us. For us, for our patients: it is our fate as living, breathing, metabolizing organisms. Most lives are lived with passivity toward death -- it's something that happens to you and those around you. But Jeff and I had trained for years to actively engage with death, to grapple with it, like Jacob with the angel, and, in so doing, to confront the meaning of a life. We had assumed an onerous yoke, that of mortal responsibility. Our patients' lives and identities may be in our hands, yet death always wins. Even if you are perfect, the world isn't. The secret is to know that the deck is stacked, that you will lose, that your hands or judgment will slip, and yet still struggle to win for your patients. You can't ever reach perfection, but you can believe in an asymptote toward which you are ceaselessly striving.

If I were a function, you would be my asymptote. I always tend toward you.

Humans are immortal in their thought. Though strictly speakin’, not immortal, but endlessly, asymptotically close to immortal. That’s eternal life.

Humans may crave absolute certainty; they may aspire to it; they may pretend, as partisans of certain religions do, to have attained it. But the history of science — by far the most successful claim to knowledge accessible to humans — teaches that the most we can hope for is successive improvement in our understanding, learning from our mistakes, an asymptotic approach to the Universe, but with the proviso that absolute certainty will always elude us.

The secret is to know that the deck is stacked, that you will lose, that your hands or judgment will slip, and yet still struggle to win for your patients. You can't ever reach perfection, but you can believe in an asymptote toward which you are ceaselessly striving.

A becoming in which one never becomes, a becoming whose rule is neither evolution nor asymptote but a certain turning, a certain turning inward, turning into my own / turning on in / to my own self / at last / turning out of the / white cage, turning out of the / lady cage / turning at last.

Science asymptotically approaches reality.

Our patients’ lives and identities may be in our hands, yet death always wins. Even if you are perfect, the world isn’t. The secret is to know that the deck is stacked, that you will lose, that your hands or judgment will slip, and yet still struggle to win for your patients. You can’t ever reach perfection, but you can believe in an asymptote toward which you are ceaselessly striving.

Even if you are perfect, the world isn’t. The secret is to know that the deck is stacked, that you will lose, that your hands or judgment will slip, and yet still struggle to win for your patients. You can’t ever reach perfection, but you can believe in an asymptote toward which you are ceaselessly striving.

Though the integration into a single whole of all legitimate theologies is an eschatological desideratum, it can only be approached asymptotically in time.

The truth may be puzzling. It may take some work to grapple with. It may be counterintuitive. It may contradict deeply held prejudices. It may not be consonant with what we desperately want to be true. But our preferences do not determine what's true. We have a method, and that method helps us to reach not absolute truth, only asymptotic approaches to the truth — never there, just closer and closer, always finding vast new oceans of undiscovered possibilities. Cleverly designed experiments are the key.

The fact that there is a limit to capital does not mean that capital collapses. Rather the limit is an asymptotic curve, you get closer and closer to an absolute limit but you never reach it.

Certainly not! I didn't build a machine to solve ridiculous crossword puzzles! That's hack work, not Great Art! Just give it a topic, any topic, as difficult as you like..." Klapaucius thought, and thought some more. Finally he nodded and said: "Very well. Let's have a love poem, lyrical, pastoral, and expressed in the language of pure mathematics. Tensor algebra mainly, with a little topology and higher calculus, if need be. But with feeling, you understand, and in the cybernetic spirit." "Love and tensor algebra?" Have you taken leave of your senses?" Trurl began, but stopped, for his electronic bard was already declaiming: Come, let us hasten to a higher plane, Where dyads tread the fairy fields of Venn, Their indices bedecked from one to n, Commingled in an endless Markov chain! Come, every frustum longs to be a cone, And every vector dreams of matrices. Hark to the gentle gradient of the breeze: It whispers of a more ergodic zone. In Reimann, Hilbert or in Banach space Let superscripts and subscripts go their ways. Our asymptotes no longer out of phase, We shall encounter, counting, face to face. I'll grant thee random access to my heart, Thou'lt tell me all the constants of thy love; And so we two shall all love's lemmas prove, And in bound partition never part. For what did Cauchy know, or Christoffel, Or Fourier, or any Boole or Euler, Wielding their compasses, their pens and rulers, Of thy supernal sinusoidal spell? Cancel me not--for what then shall remain? Abscissas, some mantissas, modules, modes, A root or two, a torus and a node: The inverse of my verse, a null domain. Ellipse of bliss, converge, O lips divine! The product of our scalars is defined! Cyberiad draws nigh, and the skew mind Cuts capers like a happy haversine. I see the eigenvalue in thine eye, I hear the tender tensor in thy sigh. Bernoulli would have been content to die, Had he but known such a^2 cos 2 phi!

But the history of science—by far the most successful claim to knowledge accessible to humans—teaches that the most we can hope for is successive improvement in our understanding, learning from our mistakes, an asymptotic approach to the Universe, but with the proviso that absolute certainty will always elude us. We will always be mired in error. The most each generation can hope for is to reduce the error bars a little, and to add to the body of data to which error bars apply. The error bar is a pervasive, visible self-assessment of the reliability of our knowledge.

Somewhere between ‘I love you’ and ‘but’ is mankind, a giant loneliness strolling through an even greater loneliness. — Negar Emrani (trans. Kaveh Akbar), “Somewhere Between the World and the Mirror,” published in Asymptote (April 2017) (via bostonpoetryslam)

Growing older I descend November. The asymptotic cycle of the year plummets to now. In crystal reveries I pass beneath a fixed white line of trees where dry leaves lie for footsteps to dismember. They crackle with a muted sound like fear. That and the wind are all that I can hear. I ask cold air, “What is the word that frees?” The wind says, “Change,” and the white sun, “Remember.” —from Electra

as•ymp•tote (ˈasəm(p)ˌtōt) n. pl. -s. 1. A wish that continually approaches but never achieves fulfillment.

Quinn until he messaged me his nightly text, which had turned somewhat math-mushy recently: If I were a function, you would be my asymptote. I always tend toward you. He

This is the nature of mastery: Mastery is an asymptote. You

You can't ever reach perfection, but you can believe in an asymptote towards which you are ceaselessly striving.

You can't ever reach perfection, but you can believe in an asymptote toward which you are ceaselessly striving

You can't ever reach perfection, but you can believe in an asymptote toward which you are ceaselessly striving.

You cannot ever really go back to normal. You can approximate the axis of what your life used to be like, but as with an asymptote, all you’ll ever really do is get close and never intersect the sweet spot. It is true that the way the legal system works, once you are acquitted you are free to go home, but there’s a cognitive dissonance in the realization that the world has spun away without you.

deck is stacked, that you will lose, that your hands or judgment will slip, and yet still struggle to win for your patients. You can’t ever reach perfection, but you can believe in an asymptote toward which you are ceaselessly striving.

The beige linoleum floor turned into the ocean, crashed and crashed against Lotto's shins. He sat down. How swiftly things spun. Two minutes ago he'd been a kid, thinking about his nintendo system, worried about asymptotes and signs. Now he was, heavy, adult.

You can’t ever reach perfection, but you can believe in an asymptote toward which you are ceaselessly striving. Human knowledge is never contained in one person. It grows from the relationships we create between each other and the world, and still it is never complete.

What is it that I wish to convey?...I wish to convey something immaterial and I have to use material means for it. I have to convey something which is inexpressible and I have to use expression. I have to convey, perhaps, something unconscious and I have to use conscious means. I know in advance that I shall not succeed and cannot succeed, and therefore all I can do is to get nearer and nearer in some asymptotic approach; I do my best, but it is an agonizing struggle in which, if I am…any kind of self-conscious thinker, I am engaged for the whole of my life.

Once there were three tribes. The Optimists, whose patron saints were Drake and Sagan, believed in a universe crawling with gentle intelligence—spiritual brethren vaster and more enlightened than we, a great galactic siblinghood into whose ranks we would someday ascend. Surely, said the Optimists, space travel implies enlightenment, for it requires the control of great destructive energies. Any race which can't rise above its own brutal instincts will wipe itself out long before it learns to bridge the interstellar gulf. Across from the Optimists sat the Pessimists, who genuflected before graven images of Saint Fermi and a host of lesser lightweights. The Pessimists envisioned a lonely universe full of dead rocks and prokaryotic slime. The odds are just too low, they insisted. Too many rogues, too much radiation, too much eccentricity in too many orbits. It is a surpassing miracle that even one Earth exists; to hope for many is to abandon reason and embrace religious mania. After all, the universe is fourteen billion years old: if the galaxy were alive with intelligence, wouldn't it be here by now? Equidistant to the other two tribes sat the Historians. They didn't have too many thoughts on the probable prevalence of intelligent, spacefaring extraterrestrials— but if there are any, they said, they're not just going to be smart. They're going to be mean. It might seem almost too obvious a conclusion. What is Human history, if not an ongoing succession of greater technologies grinding lesser ones beneath their boots? But the subject wasn't merely Human history, or the unfair advantage that tools gave to any given side; the oppressed snatch up advanced weaponry as readily as the oppressor, given half a chance. No, the real issue was how those tools got there in the first place. The real issue was what tools are for. To the Historians, tools existed for only one reason: to force the universe into unnatural shapes. They treated nature as an enemy, they were by definition a rebellion against the way things were. Technology is a stunted thing in benign environments, it never thrived in any culture gripped by belief in natural harmony. Why invent fusion reactors if your climate is comfortable, if your food is abundant? Why build fortresses if you have no enemies? Why force change upon a world which poses no threat? Human civilization had a lot of branches, not so long ago. Even into the twenty-first century, a few isolated tribes had barely developed stone tools. Some settled down with agriculture. Others weren't content until they had ended nature itself, still others until they'd built cities in space. We all rested eventually, though. Each new technology trampled lesser ones, climbed to some complacent asymptote, and stopped—until my own mother packed herself away like a larva in honeycomb, softened by machinery, robbed of incentive by her own contentment. But history never said that everyone had to stop where we did. It only suggested that those who had stopped no longer struggled for existence. There could be other, more hellish worlds where the best Human technology would crumble, where the environment was still the enemy, where the only survivors were those who fought back with sharper tools and stronger empires. The threats contained in those environments would not be simple ones. Harsh weather and natural disasters either kill you or they don't, and once conquered—or adapted to— they lose their relevance. No, the only environmental factors that continued to matter were those that fought back, that countered new strategies with newer ones, that forced their enemies to scale ever-greater heights just to stay alive. Ultimately, the only enemy that mattered was an intelligent one. And if the best toys do end up in the hands of those who've never forgotten that life itself is an act of war against intelligent opponents, what does that say about a race whose machines travel between the stars?

Furious, the beast writhed and wriggled its iterated integrals beneath the King’s polynomial blows, collapsed into an infinite series of indeterminate terms, then got back up by raising itself to the nth power, but the King so belabored it with differentials and partial derivatives that its Fourier coefficients all canceled out (see Riemann’s Lemma), and in the ensuing confusion the constructors completely lost sight of both King and beast. So they took a break, stretched their legs, had a swig from the Leyden jug to bolster their strength, then went back to work and tried it again from the beginning, this time unleashing their entire arsenal of tensor matrices and grand canonical ensembles, attacking the problem with such fervor that the very paper began to smoke. The King rushed forward with all his cruel coordinates and mean values, stumbled into a dark forest of roots and logarithms, had to backtrack, then encountered the beast on a field of irrational numbers (F1) and smote it so grievously that it fell two decimal places and lost an epsilon, but the beast slid around an asymptote and hid in an n-dimensional orthogonal phase space, underwent expansion and came out, fuming factorially, and fell upon the King and hurt him passing sore. But the King, nothing daunted, put on his Markov chain mail and all his impervious parameters, took his increment Δk to infinity and dealt the beast a truly Boolean blow, sent it reeling through an x-axis and several brackets—but the beast, prepared for this, lowered its horns and—wham!!—the pencils flew like mad through transcendental functions and double eigentransformations, and when at last the beast closed in and the King was down and out for the count, the constructors jumped up, danced a jig, laughed and sang as they tore all their papers to shreds, much to the amazement of the spies perched in the chandelier-—perched in vain, for they were uninitiated into the niceties of higher mathematics and consequently had no idea why Trurl and Klapaucius were now shouting, over and over, “Hurrah! Victory!!

We had assumed an onerous yoke, that of mortal responsibility. Our patients’ lives and identities may be in our hands, yet death always wins. Even if you are perfect, the world isn’t. The secret is to know that the deck is stacked, that you will lose, that your hands or judgment will slip, and yet still struggle to win for your patients. You can’t ever reach perfection, but you can believe in an asymptote toward which you are ceaselessly striving.

Humans may crave absolute certainty; they may aspire to it; they may pretend, as partisans of certain religions do, to have attained it. But the history of science—by far the most successful claim to knowledge accessible to humans—teaches that the most we can hope for is successive improvement in our understanding, learning from our mistakes, an asymptotic approach to the Universe, but with the proviso that absolute certainty will always elude us.

This is like the Six Sigma approach to quality. Six Sigma refers to the quest for continuous improvement, ultimately leading to 3.4 defects per million units. The problem is that once you’re heading down this road, there’s no room left for amazing improvements and remarkable innovations. Either you rolled ten strikes or you didn’t. Organizations that earn dramatic success always do it in markets where asymptotes don’t exist, or where they can be shattered. If you could figure out how to bowl 320, that would be amazing. Until that happens, pick a different sport if you want to be a linchpin.

Temperatures, petrol prices, the price of the dollar: the golden triangle of our summer. These are facts beyond our control and all we hope now is to see them all rising indefinitely. Sometimes the figures are mixed up in a prophetic confusion, as in 1980 in the US deserts. There, the price per gallon: 51.18, 51.20, 51 .25, varied from one place to another as an exact reflection of the temperature graphs: 100, 110 and 120 degrees Fahrenheit. With the question of confidence always lurking just beneath the surface: what price would you accept petrol rising to? What point do you think the dollar could go up to (with the implication: before causing a crash in world economies)? What record level can the heat reach (before causing a volatilization of energy and the beginnings of a worldwide insomnia)? Our artificial destiny is written in these asymptotic curves.

The virtuality of war is not, then, a metaphor. It is the literal passage from reality into fiction, or rather the immediate metamorphosis of the real into fiction. The real is now merely the asymptotic horizon of the Virtual. And it isn't just the reality of the real that's at issue in all this, but the reality of cinema. It's a little like Disneyland: the theme parks are now merely an alibi - masking the fact that the whole context of life has been disneyfied. It's the same with the cinema: the films produced today are merely the visible allegory of the cinematic form that has taken over everything - social and political life, the landscape, war, etc. - the form of life totally scripted for the screen. This is no doubt why cinema is disappearing: because it has passed into reality. Reality is disappearing at the hands of the cinema and cinema is disappearing at the hands of reality. A lethal transfusion in which each loses its specificity. If we view history as a film - which it has become in spite of us - then the truth of information consists in the postsynchronization, dubbing and sub-titling of the film of history.

So they rolled up their sleeves and sat down to experiment -- by simulation, that is mathematically and all on paper. And the mathematical models of King Krool and the beast did such fierce battle across the equation-covered table, that the constructors' pencils kept snapping. Furious, the beast writhed and wriggled its iterated integrals beneath the King's polynomial blows, collapsed into an infinite series of indeterminate terms, then got back up by raising itself to the nth power, but the King so belabored it with differentials and partial derivatives that its Fourier coefficients all canceled out (see Riemann's Lemma), and in the ensuing confusion the constructors completely lost sight of both King and beast. So they took a break, stretched their legs, had a swig from the Leyden jug to bolster their strength, then went back to work and tried it again from the beginning, this time unleashing their entire arsenal of tensor matrices and grand canonical ensembles, attacking the problem with such fervor that the very paper began to smoke. The King rushed forward with all his cruel coordinates and mean values, stumbled into a dark forest of roots and logarithms, had to backtrack, then encountered the beast on a field of irrational numbers (F_1) and smote it so grievously that it fell two decimal places and lost an epsilon, but the beast slid around an asymptote and hid in an n-dimensional orthogonal phase space, underwent expansion and came out fuming factorially, and fell upon the King and hurt him passing sore. But the King, nothing daunted, put on his Markov chain mail and all his impervious parameters, took his increment Δk to infinity and dealt the beast a truly Boolean blow, sent it reeling through an x-axis and several brackets—but the beast, prepared for this, lowered its horns and—wham!!—the pencils flew like mad through transcendental functions and double eigentransformations, and when at last the beast closed in and the King was down and out for the count, the constructors jumped up, danced a jig, laughed and sang as they tore all their papers to shreds, much to the amazement of the spies perched in the chandelier—perched in vain, for they were uninitiated into the niceties of higher mathematics and consequently had no idea why Trurl and Klapaucius were now shouting, over and over, "Hurrah! Victory!!

While the akashic records are an occultist concept, the laws of physics demand that they must exist; and there are numerous ways to prove this beyond such methods involving geology, astronomy, archaeology, and anthropology. Take the case of reverberation. Every sound that has ever been uttered gets fainter and fainter and fainter. But does it ever completely disappear? Physicists would say that the sound diminishes asymptotically. It never totally goes away. Just because we cannot retrieve Napoleon’s voice does not mean that it does not exist as some extremely faint vibration embedded in the atmosphere and the walls around where he lived. Our modern technology has numerous ways to capture the past, such as on newsreel footage, audio-and videotapes, and photo archives. But nature also provides a record through tree rings, carbon dating, fossils, petrifaction, and sediment layers that record major celestial and Earth changes, such as floods, droughts, and en masse extinctions, as when major asteroids have collided with the planet and left their mark as craters.

• God is man squared. That is to say, God is man raised to a higher power. • Man is the root, the square root, of God. • We believe in the ideal (truth, wisdom, justice, honor, integrity, selflessness, sacrifice, compassion, goodness) and God is the name we give to that ideal. • What else is God but a heuristic for what we want to do with our lives? • The worship of God is the worship of perfection. The perfection of space: infinity. The perfection of time: eternity. The perfection of power: omnipotence. The perfection of knowledge: omniscience. The perfection of behavior: virtue. • Since the Fall, falling is what we've learned to do. • We are blemished perfections. • Man is the asymptote of what he predicates God to be. from "Getting Godless" in The Lice of Christ (MadHat Press 2014).

One of the reasons for its success is that science has built-in, error-correcting machinery at its very heart. Some may consider this an overbroad characterization, but to me every time we exercise self-criticism, every time we test our ideas against the outside world, we are doing science. When we are self-indulgent and uncritical, when we confuse hopes and facts, we slide into pseudoscience and superstition. Every time a scientific paper presents a bit of data, it's accompanied by an error bar - a quiet but insistent reminder that no knowledge is complete or perfect. It's a calibration of how much we trust what we think we know. If the error bars are small, the accuracy of our empirical knowledge is high; if the error bars are large, then so is the uncertainty in our knowledge. Except in pure mathematics nothing is known for certain (although much is certainly false). Moreover, scientists are usually careful to characterize the veridical status of.their attempts to understand the world - ranging from conjectures and hypotheses, which are highly tentative, all the way up to laws of Nature which are repeatedly and systemati­cally confirmed through many interrogations of how the world works. But even laws of Nature are not absolutely certain. There may be new circumstances never before examined - inside black holes, say, or within the electron, or close to the speed of light -where even our vaunted laws of Nature break down and, however valid they may be in ordinary circumstances, need correction. Humans may crave absolute certainty; they may aspire to it; they may pretend, as partisans of certain religions do, to have attained it. But the history of science - by far the most successful claim to knowledge accessible to humans - teaches that the most we can hope for is successive improvement in our understanding, learning from our mistakes, an asymptotic approach to the Universe, but with the proviso that absolute certainty will always elude us. We will always be mired in error. The most each generation can hope for is to reduce the error bars a little, and to add to the body of data to which error bars apply. The error bar is a pervasive, visible self-assessment of the reliability of our knowledge.

asymptote,

And, mastery is an asymptote: It's impossible to fully realize, which makes it simultaneously frustrating and alluring

However, when we step back and take a longer-term perspective, bitcoin’s supply trajectory looks anything but linear (see Figure 4.2). In fact, by the end of the 2020s it will approach a horizontal asymptote, with annual supply inflation less than 0.5 percent. In other words, Satoshi rewarded early adopters with the most new bitcoin to get sufficient support, and in so doing created a big enough base of monetary liquidity for the network to use. He understood that if bitcoin was a success over time its dollar value would increase, and therefore he could decrease the rate of issuance while still rewarding its supporters.

Twin studies of adult individuals have found a heritability of IQ between 57% and 73%[6] with the most recent studies showing heritability for IQ as high as 80%.[7] IQ goes from being weakly correlated with genetics, for children, to being strongly correlated with genetics for late teens and adults. The heritability of IQ increases with age and reaches an asymptote at 18–20 years of age and continues at that level well into adulthood. This phenomenon is known as the Wilson Effect

Here’s the painful irony: The big-picture economy, which is largely out of any president’s control, is the real source of this president’s political strength with voters who like him. The SSRN poll for CNN in June 2019 had a striking finding. Of those who approve of Trump, a plurality of 26 percent said they do so because of the economy, more than twice the next most-frequent answer. In the same economic issue basket, 8 percent cited jobs as a reason for liking him. On immigration, 4 percent said that’s the reason they like him. When it comes to other aspects of Trump’s persona, support falls to the single digits. Just 1 percent said they approve of him because he’s draining the proverbial D.C. swamp. A whopping 1 percent said they like him because he’s honest, which proves you can fool 1 percent of the people all the time. All of this is a sign of trouble ahead for Donald Trump, because his economic record is a rickety construction prone to collapse from external forces at any moment. A BUBBLE, READY TO POP The long, sweet climb in economic prosperity we’ve enjoyed for a decade comes down to the decisions of two men and one institution: George W. Bush in taking the vastly unpopular step of bailing out Wall Street in the 2009 economic crisis, and Barack Obama for flooding the economy with economic stimulus in his first term. The Federal Reserve enabled both of these decisions by issuing an ocean of low- or zero-interest credit for ten years. Sure, the bill will come due someday, but the party is still going. While Trump took short-term political advantage of it, every bubble gets pricked by the old invisible hand. In the current economic case, the blizzard of Trumpian bullshit will inevitably hit the fan. We’re awash in trillion-dollar deficits, the national debt is asymptotically approaching infinity, and we have a president who’s never hesitated to borrow and spend well beyond his means, or to simply throw up his hands and declare bankruptcy when it suits him. We never did—and most likely never will—tackle entitlement reform. Nations don’t get to go bankrupt; they collapse. The GOP passed a tax bill that is performing exactly as expected and predicted: A handful of hedge funds, America’s top corporations, and a few dozen billionaires were given a trillion-dollar-plus tax benefit. Even the tax cut’s most fervent proponents know that its effects were short-lived, the bill is coming due, and in 2022 or thereabouts it’s going to lead to annual deficits of close to $2 trillion.

Mastery is a mindset: It requires the capacity to see your abilities not as finite, but as infinitely improvable. Mastery is a pain: It demands effort, grit, and deliberate practice. And mastery is asymptote: It's impossible to fully realize, which makes it simultaneously frustrating and alluring.

We’re hitting an asymptote, a natural ceiling for how cheaply and how fast we can deliver uninspired work. Becoming more average, more quick, and more cheap is not as productive as it used to be.

As you mature in your profession, your error rate should rapidly decrease towards the asymptote of zero.

Death is only ever that free future we dream of when we put off everything and consign all things to their future occurrence. Objectively, the world is an illusion: it can only appear to us. Subjectively, it is the opposite: we regard it spontaneously as real. But one may propose the opposite: subjectively, the world is an illusion of our senses. Objectively, it has force of reality. Asymptote, clinamen, parallax, metalepsis - these are dance patterns, this is a whole non-linear geometry of theoretical space. Patterns of near-contact and reversal, of approaching the truth without ever succumbing to it.

I have begun to imagine human knowledge and ignorance as tracing a curve of asymptotic divergence, such that with every increase in knowledge, there occurs a greater increase in ignorance, the result being that our ignorance always exceeds our knowledge, and the gap between the two grows infinitely greater, not smaller, as infinite time passes.

Later, there was a more moderate and localized proposal for taking advantage of curved space for navigation. Supposing a spaceship could somehow iron flat the space behind it and decrease its curvature, the more curved space in front of it would pull it forward. This was the idea of curvature propulsion. Unlike folding space, curvature propulsion couldn’t get a spaceship to its destination instantaneously, but it would be possible to drive it asymptotically to the speed of light. Until Yun Tianming’s message had been correctly interpreted, curvature propulsion remained a dream, like hundreds of other proposals for lightspeed spaceflight. No one knew whether it was possible at either a theory or practice level.

We associate two different terms with this phenomenon: asymptotic freedom and infrared slavery. At one end of the scale, the short distances, the quarks barely affect one another; rather, they act like free particles. At the other end of the scale, the strength of the color interaction sees to it that the quarks remain enclosed inside their particles-the neutrons or protons for which they act as building blocks. This is what we call infrared slavery. When we try to separate one quark from another, the force with which they hold together increases. The energy expended for their separation will then be transformed into the creation of added particles according to Einstein's formula E=mc^2. What this means, in short, is that it is impossible to set a quark free.

Death and pleasure we experience asymptotically. We spend much time working upward on the slope, and most people only sometimes approach the lines of pure pleasure or death, close enough to touch. Maybe once or twice in a lifetime, for each

Can growth be sustained into the indefinite future? We first briefly address the general worry that since the world’s resources are finite, growth must be unsustainable in the very long term. If all resources were non-renewable, all economic activity, whether growing or static in magnitude, might eventually become unsustainable. But even this is not quite certain since a finite stock of non-renewable resources can last infinitely if the usage declines asymptotically over time—a not impossible achievement in a technologically dynamic society with a constant population. Fortunately, many resources are not of the non-renewable type. Furthermore, the law of conservation of mass energy shows that one does not destroy mass energy but merely transforms it into other forms. Also, the world is not a closed system, receiving a continuous flow of new energy from the sun. So there seems little substance in the general worry that over many centuries all forms of growth are unsustainable because of ultimate resource limitations.

Asymptotes - Nasadia Sukta - only infinity and there is no zero - "0

Asymptotes - Nasadia Sukta - only infinity and there is no zero - "0” - up above and so below reach near zero but there is not absolute zero - "0

the production curve of any given species of fossil fuel will rise, pass through one or several maxima, and then decline asymptotically to zero.” Decline asymptotically to zero! The potential consequences were vast. Hubbert believed that the fossil-fuel explosion had created the population explosion—that consuming coal, oil, and gas had provided the impetus to drive our species up Gause’s S-shaped curve. Because the amount of the world’s oil was by definition finite, the supply would fall to zero after too much use. As a result, we were bound, so to speak, to hit the edge of the petri dish.

Any possibility of a future between us was an asymptote of a curve, approaching zero reaching to infinity but never touching the axis. I was clear on all of that.

The point is not that there is no reality outside our mind, the point is rather that there is no mind outside reality. The distortion of reality occurs precisely because our mind is part of reality. So when Lenin claims that we can only arrive at objective reality in an endless asymptotic process of approximation, what he overlooks is that our distortions of reality occur precisely because we are part of reality and therefore do not have a neutral view of it: our perception distorts reality because the observer is part of the observed. It is this universalized perspectivism which, I think, contains a radically materialist position.

The theory posits that in the early stages of a technology, the rate of progress in performance will be relatively slow. As the technology becomes better understood, controlled, and diffused, the rate of technological improvement will accelerate. 12 But in its mature stages, the technology will asymptotically approach a natural or physical limit such that ever greater periods of time or inputs of engineering effort will be required to achieve improvements. Figure 2.5 illustrates the resulting pattern.

We are all gastropods, soft, sticky creatures pulling ourselves along the earth from which we came and leaving a trail of silvery drool behind. But the snail, a worm that eternally slides along the horizon, lifts into the air, from its soft bivalve back, the geometrical wonder of its spiral shell, seemingly unrelated to the body that produced it in fear and loneliness. We secrete our shell in the sweat and mucous of our skin, in the transparent, scaly flesh of the foot we use to drag ourselves along. Through an alchemical transmutation, our drool turns to ivory and the spasms of our flesh into an undisturbed stillness. We curl around our central pilaster of rose-colored kaolin, we add, in our desperate drive to persist, spiral after spiral, each one wider, asymptotic, and translucid, until the miracle comes to pass: the revolting worm—existing in the life it lives, fermenting in its sins, irrigated by hormones and blood and sperm and lymph—rots and dies, leaving behind the ceramic filigree of its shell, a triumph of symmetry, the deathless icon in the platonic world of the mind. We all secrete, as we live, poems and pictures, ideas and hope, glistening palaces of music and faith, shells which begin by protecting our soft abdomen but after our disappearance live in the golden air of pure forms. Geometry always appears out of the amorphous, serenity out of pain and torture, just as dry tears leave behind the most wondrous crystals of salt.