Approximations Quotes & Sayings

Those of us who write and study history are accustomed to its approximations and ambiguities. This is why we do not take literally the tenth-hand reports of frightened and illiterate peasants who claim to have seen miracles or to have had encounters with messiahs and prophets and redeemers who were, like them, mere humans. And this is also why we will never submit to dictation from those who display a fanatical belief in certainty and revelation. — Christopher Hitchens

The conception that growth and progress are just approximations to a final unchanging goal is the last infirmity of the mind in its transition from a static to a dynamic understanding of life. — John Dewey

An entirely honest man, in the severe sense of the word, exists no more than an entirely dishonest knave; the best and the worst are only approximations to those qualities. Who are those that never contradict themselves? yet honesty never contradicts itself. Who are they that always contradict themselves? yet knavery is mere self-contradiction. Thus the knowledge of man determines not the things themselves, but their proportions, the quantum of congruities and incongruities. — Johann Kaspar Lavater

Can quantum mechanics represent the fact that an electron finds itself approximately in a given place and that it moves approximately with a given velocity, and can we make these approximations so close that they do not cause experimental difficulties? — Werner Heisenberg

Working in the digital domain, you're using approximations of things; the actual sound wave never enters the equation. You deal with sections of it, and you're able to do so much more by just reducing the information to a finite amount. — Sean Booth

Paul closed his eyes and turned his face to the sun. In spite of everything, it was hard not to take solace from the warmth flooding onto his skin. He stretched the muscles in his arms, his shoulders, his back -- and it felt like he was reaching out from the "self" in his virtual skull to all his mathematical flesh, imprinting the nebulous data with meaning; binding it all together, staking some kind of claim. He felt the stirrings of an erection. Existence was beginning to seduce him. He let himself surrender for a moment to a visceral sense of identity which drowned out all his pale mental images of optical processors, all his abstract reflections on the software's approximations and short-cuts. This body didn't want to evaporate. This body didn't want to bale out. It didn't much care that there was another -- "more real" -- version of itself elsewhere. It wanted to retain its wholeness. It wanted to endure. — Greg Egan

Truth is much too complicated to allow anything but approximations. — John Von Neumann

We're always just telling stories, and stories are always just approximations of the truth. It's never the truth exactly. — Brit Marling

Maybe this is what life is like - we try to see clearly but what we see is never clear and is never going to be. The more we strive the murkier it becomes. All we are left with are approximations, nuances, multitudes of plausible explanations. Take your pick. — William Boyd

All models are approximations. Essentially, all models are wrong, but some are useful. However, the approximate nature of the model must always be borne in mind ... — George E.P. Box

It really is appallingly difficult to do something which is complete in every respect, and I think most people are content with mere approximations. Well, my dear friend, I intend to battle on, scrape off and start again ... — Claude Monet

Science does not aim at establishing immutable truths and eternal dogmas; its aim is to approach the truth by successive approximations, without claiming that at any stage final and complete accuracy has been achieved. — Bertrand Russell

Other, more technically adroit people would soon generate closer approximations of reality. What mattered was (a) it was a rational, testable hypothesis; and (b) James made it so clear and interesting that it provoked a lot of intelligent people to join the conversation. "The — Michael Lewis

Justice based purely on laws is about as accurate as a portrait created out of large low-resolution color pixels.
If you stand back far enough it looks good.
Come any closer and the glaring approximations overtake all semblance of the original.
Justice should be viewable under the microscope, not from a telescope.
And for that it needs to be based not on law but on truth. — Vera Nazarian

Macroscopic objects, as we see them all around us, are governed by a variety of forces, derived from a variety of approximations to a variety of physical theories. In contrast, the only elements in the construction of black holes are our basic concepts of space and time. They are, thus, almost by definition, the most perfect macroscopic objects there are in the universe. — Subrahmanyan Chandrasekhar

The result of this union would be, not the fortuitous result of a series of approximations and concessions, but the harmonious synthesis of two aspects of a single thought. — Jacques Ibert

The solvable systems are the ones shown in textbooks. They behave. Confronted with a nonlinear system, scientists would have to substitute linear approximations or find some other uncertain backdoor approach. Textbooks showed students only the rare non-linear systems that would give way to such techniques. They did not display sensitive dependence on initial conditions. Nonlinear systems with real chaos were rarely taught and rarely learned. When people stumbled across such things-and people did-all their training argued for dismissing them as aberrations. Only a few were able to remember that the solvable, orderly, linear systems were the aberrations. Only a few, that is, understood how nonlinear nature is in its soul. Enrico Fermi once exclaimed, "It does not say in the Bible that all laws of nature are expressible linearly!" The mathematicians Stanislaw Ulam remarked that to call the study of chaos "nonlinear science" was like calling zoology "the study of nonelephant animals. — James Gleick

Men of science have made abundant mistakes of every kind; their knowledge has improved only because of their gradual abandonment of ancient errors, poor approximations, and premature conclusions. — George Sarton

If our mental models are mere approximations of reality, then, the conclusions we draw cannot help but be prone to error. A few words uttered by someone close to us can carry enormous weight, for example, whereas the same words uttered by a stranger won't resonate at all. At our jobs, we may interpret not being invited to a meeting as a threat to us or to our projects, even when no threat is intended. But because we often don't see the flaws in our reasoning - or our biases - it's easy to be deluded while being quite convinced that we are the only sane ones around. — Ed Catmull

Escape procedures, however, were in full force. Some people, in a frenzy of antipathy and boredom, were drinking themselves into extreme approximations of longing to be together. Exchanging phone numbers, demanding to have lunch, proposing to share an apartment - the escalations of fellowship had the air of a terminal auction, a fierce adult version of slapjack, a bill-payer loan from a finance company, an attempt to buy with one grand convivial debt, to be paid in future, an exit from each other's company at that instant. — Renata Adler

Experimental science hardly ever affords us more than approximations to the truth; and whenever many agents are concerned we are in great danger of being mistaken. — Humphry Davy

I hope that I am generous and tolerant, but certainly on the intellectual side I think that there are discoverable truths, and some things that are closer approximations to the truth than others. — Edward Tufte

tackling real-world tasks requires being comfortable with chance, trading off time with accuracy, and using approximations. As — Brian Christian

And it was in the mitigated midnight of these approximations that she had discerned the promise of her dawn. — Henry James

History is a series of approximations of the final singularity. — Terence McKenna

It has been said that men carry on a kind of coasting trade with religion. In the voyage of life, they profess to be in search of heaven, but take care not to venture so far in their approximations to it, as entirely to lose sight of the earth; and should their frail vessel be in danger of shipwreck, they will gladly throw their darling vices overboard, as other mariners their treasures, only to fish them up again when the storm is over. — Charles Caleb Colton

Whatever one wishes to say, there is one noun only by which to express it, one verb only to give it life, one adjective only which will describe it. One must search until one has discovered them, this noun, this verb, this adjective, and never rest content with approximations, never resort to trickery, however happy, or to vulgarism, in order to dodge the difficulty. — Guy De Maupassant

Change the attitude toward errors. Think of an object's user as attempting to do a task, getting there by imperfect approximations. Don't think of the user as making errors; think of the actions as approximations of what is desired. — Donald A. Norman

You can't see fear or lust; you can't photograph someone's anxieties, how disappointment feels. Photographs are approximations. — Duane Michals

This is why people get obsessed with festivals, or clubs, or drugs, or football, or other temporal approximations of togetherness; these distilled vials of the elixir are craved by our starved souls. — Russell Brand

We live in a system of approximations. Every end is prospective of some other end, which is also temporary; a round and final success nowhere. We are encamped in nature, not domesticated. — Ralph Waldo Emerson

The most calamitous failures of prediction usually have a lot in common. We focus on those signals that tell a story about the world as we would like it to be, not how it really is. We ignore the risks that are hardest to measure, even when they pose the greatest threats to our well-being. We make approximations and assumptions about the world that are much cruder than we realize. We abhor uncertainty, even when it is an irreducible part of the problem we are trying to solve. — Nate Silver

Property taxes - particularly those which tax only or primarily the land and not the improvements - are the closest approximations we have today to community land contributions. For this reason, property taxes and home affordability rates - which is to say, land affordability rates - are inversely correlated.

Land contributions are necessary for the vitality of every community and city. For example, urban sprawl is a consequence of not capturing sufficient land contributions and thus enabling inefficient land use.

Community land contributions lead to a more intensive use of land and encourage the greening of a city's surroundings, as the existing population will tend to cluster closer together. Land contributions also encourage the restoration of blighted areas. — Martin Adams

Free men are aware of the imperfection inherent in human affairs, and they are willing to fight and die for that which is not perfect. They know that basic human problems can have no final solutions, that our freedom, justice, equality, etc. are far from absolute, and that the good life is compounded of half measures, compromises, lesser evils, and gropings toward the perfect. The rejection of approximations and the insistence on absolutes are the manifestation of a nihilism that loathes freedom, tolerance, and equity. — Eric Hoffer

Not sunflowers, not roses, but rocks in patterned sand grow here. And bloom. - ROBERT HAYDEN, Approximations — Taiye Selasi

Stereotypes are valid first-order approximations.' The — Dennis E. Taylor

According to the anthropic principle proponents, if the universal constants (e.g. gravitation, the strong force, etc.) were just a nose-hair off, the universe as we know it would not exist; stars wouldn't form and there would be no life and no us. That supposedly makes our universe truly special. To demonstrate just how ridiculous this fine-tuning argument is, consider the fact that no measurement in physics is perfect. All of them are approximations and have margins of error. That means the universal constants, that make our universe what it is, have some wiggle room. Within that wiggle room are an infinite quantity of real numbers. Each of those real numbers could represent constants that could make a universe like ours. Since there are an infinite number of potential constants within that wiggle room, there are an infinite number of potential universes, like ours, that could have existed in lieu of ours. Thus, there is really nothing special about our universe. — G.M. Jackson

Awkward approximations, dull stammerings which cannot convey my sense of exhilaration as I seem to burst impediments, to exceed bounds of the possible, to experience, in the ruins of the human, the birth of something utterly new. — Steven Millhauser

There is a clear acknowledgement all over the world that we should not teach people to read and then to leave them without literature. For they would then relapse into a dreary and ultimately dangerous state of half-education, in which they would be easily satisfied by crude semi-pictorial approximations of the strip cartoon and by the abundant supply of degenerate literature which destroys, rather than promotes, a capacity to face the problems of the world with skill and courage — A. D. Patel

I take aliens very seriously and don't appreciate light entertainment or weak approximations being made of them. — Helen Oyeyemi

[The theory of universal gravitation] is not cast-iron. No theory is, and there is always room for improvement. Isn't that so? Science is constructed out of approximations that gradually approach the truth ... Well, that means all theories are subject to constant testing and modification, doesn't it? And if it eventually turns out that they're not quite close enough to the truth, they need to be replaced by something that's closer. Right? — Isaac Asimov

It takes a fearless, unflinching love and deep humility to accept the universe as it is. The most effective way he knew to accomplish that, the most powerful tool at his disposal, was the scientific method, which over time winnows out deception. It can't give you absolute truth because science is a permanent revolution, always subject to revision, but it can give you successive approximations of reality. — Ann Druyan

I think I am most fond of the unseen part. I mean that the various cultural experiences that I go through, and the behavioral aspects of getting the work done, are just as important as the installation and the photograph. So, for me, the relationship between the two is more about hybridism and the search for an ideal form that I'm never going to arrive at. The installation and the photograph are mere approximations of this ideal. — Sandy Skoglund

The various approximations that constitute our current physics theories are successful because simple mathematical structures can provide good approximations of how a self-aware substructure will perceive more complex mathematical structures. In other words, our successful theories are not mathematics approximating physics, but mathematics approximating mathematics! — Max Tegmark

The effect your readers want is for what they read to trigger in them the sights and sounds and smells of what's happening in the story. They don't want approximations, they don't want a report, they want to experience the story's reality. — Ray Rhamey