Irrational Numbers Quotes

Highly complex numbers like the Comma of Pythagoras, Pi and Phi (sometimes called the Golden Proportion), are known as irrational numbers. They lie deep in the structure of the physical universe, and were seen by the Egyptians as the principles controlling creation, the principles by which matter is precipitated from the cosmic mind.

Today scientists recognize the Comma of Pythagoras, Pi and the Golden Proportion as well as the closely related Fibonacci sequence are universal constants that describe complex patterns in astronomy, music and physics. ...

To the Egyptians these numbers were also the secret harmonies of the cosmos and they incorporated them as rhythms and proportions in the construction of their pyramids and temples. ~ Jonathan Black

Just as the introduction of the irrational numbers ... is a convenient myth [which] simplifies the laws of arithmetic ... so physical objects are postulated entities which round out and simplify our account of the flux of existence ... The conceptional scheme of physical objects is [likewise] a convenient myth, simpler than the literal truth and yet containing that literal truth as a scattered part. ~ Willard Van Orman Quine

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 ~ Stanisław Lem

I chose the name Pi because it's an irrational number (one with no discernable pattern). Yet scientists use this irrational number to come to a "rational" understanding of the universe. To me, religion is a bit like that, "irrational" yet with it we come together we come to a sound understanding of the universe. ~ Yann Martel

The transfinite numbers are in a certain sense themselves new irrationalities and in fact in my opinion the best method of defining the finite irrational numbers is wholly disimilar to, and I might even say in priciple the same as, my method described above of introducing trasfinite numbers. One can say unconditionally: the transfinite numbers stand or fall with the finite irrational numbers; they are like each other in their innermost being; for the former like the latter are definite delimited forms or modifications of the actual infinite. ~ Georg Cantor

It is shown that the golden ratio plays a prominent role in the dimensions of all objects which exhibit five-fold symmetry. It is also showed that among the irrational numbers, the golden ratio is the most irrational and, as a result, has unique applications in number theory, search algorithms, the minimization of functions, network theory, the atomic structure of certain materials and the growth of biological organisms. ~ Richard A. Dunlap

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. ~ Abraham Robinson

predecessor of Isaac Newton at Cambridge University, maintained that irrational numbers have no meaning independent of geometric lengths. ~ Morris Kline

The transfinite numbers are in a sense the new irrationalities [ ... they] stand or fall with the finite irrational numbers. ~ Georg Cantor

What good your beautiful proof on the transcendence of Pi: Why investigate such problems, given that irrational numbers do not even exist? ~ Leopold Kronecker

Do you know what the foundation of mathematics is?" I ask. "The foundation of
mathematics is numbers. If anyone asked me what makes me truly happy, I would
say: numbers. Snow and ice and numbers. And do you know why?"
He splits the claws with a nutcracker and pulls out the meat with curved tweezers.
"Because the number system is like human life. First you have the natural numbers.
The ones that are whole and positive. The numbers of a small child. But human
consciousness expands. The child discovers a sense of longing, and do you know
what the mathematical expression is for longing?"
He adds cream and several drops of orange juice to the soup.
"The negative numbers. The formalization of the feeling that you are missing
something. And human consciousness expands and grows even more, and the child
discovers the in between spaces. Between stones, between pieces of moss on the
stones, between people. And between numbers. And do you know what that leads
to? It leads to fractions. Whole numbers plus fractions produce rational numbers.
And human consciousness doesn't stop there. It wants to go beyond reason. It adds
an operation as absurd as the extraction of roots. And produces irrational numbers."
He warms French bread in the oven and fills the pepper mill.
"It's a form of madness.' Because the irrational numbers are infinite. They can't be
written down. They force human consciousness out bey ~ Peter Høeg

Under relentless prosecutorial grilling he sputtered that he had earlier deceived investigators "because I was an idiot," and he finally admitted that he had lied about nothing less than a treasonable overture. That lie he could not explain - but Bird and Sherwin attempt to explain it by citing a remark Oppenheimer made five years earlier to a Communist graduate student and friend of his, in which he admitted "his tendency when things get too much" to blurt out "irrational things." How difficult it must have been for an intellectual of his abilities, pride, and accomplishment to make such an admission ordinary men can only imagine. ~ Algis Valiunas

Florida's number three industry, behind tourism and skin cancer, is voter fraud. ~ Dave Barry

If naturalism were true then all thoughts whatever would be wholly the result of irrational causes ... it cuts its own throat. ~ C.S. Lewis

I must fight my demons, they are illogical and irrational, yet they seem to beat me each time they strike. ~ Sophie Glynn

Dulia is like a high but finite number; hyperdulia is like the highest number out of a finite number of finite numbers; latria is like infinity. ~ Peter Kreeft

Do you see, Harry? Do you see the flaw in my brilliant plan now? I had fallen into the trap I had foreseen, that I had told myself I could avoid, that I must avoid."
"I don't - "
"I cared about you too much," said Dumbledore simply. "I cared more for your happiness than your knowing the truth, more for your peace of mind than my plan, more for your life than the lives that might be lost if the plan failed. In other words, I acted exactly as Voldemort expects we fools who love to act.
"Is there a defense? I defy anyone who has watched you as I have - and I have watched you more closely than you can have imagined - not to want to save you more pain than you had already suffered. What did I care if numbers of nameless and faceless people and creatures were slaughtered in the vague future, if in the here and now you were alive, and well, and happy? I never dreamed that I would have such a person on my hands. ~ J.K. Rowling

the exploiter asks of a piece of land only how much and how quickly it can be made to produce, the nurturer asks a question that is much more complex and difficult: What is its carrying capacity? (That is: How much can be taken from it without diminishing it? What can it produce dependably for an indefinite time?) The exploiter wishes to earn as much as possible by as little work as possible; the nurturer expects, certainly, to have a decent living from his work, but his characteristic wish is to work as well as possible. The competence of the exploiter is in organization; that of the nurturer is in order - a human order, that is, that accommodates itself both to other order and to mystery. The exploiter typically serves an institution or organization; the nurturer serves land, household, community, place. The exploiter thinks in terms of numbers, quantities, "hard facts"; the nurturer in terms of character, condition, quality, kind. ~ Gregory Pence

The world, he now perceived, was in fact a great, flat wheel with a myriad spokes of water, trees and grass, for ever turning and turning beneath the sun and moon. At each spoke was an animal-all the animals and birds he had ever known-horses, dogs, chaffinches, mice, hedgehogs,rabbits, cows, sheep, rooks and many more which he did not recognize-a huge, striped cat, and a monstrous fish spurting water in a fountain to the sky. At the centre, on the axle itself, stood a man, who ceaselessly lashed and lashed the creatures with a whip to make them drive the wheel round. Some shrieked aloud as they bled and struggled, others silently toppled and were trodden down beneath their comrades' stumbling feet. And yet, as he himself could see, the man had misconceived his task, for in fact the wheel turned of itself and all he needed to do was to keep it balanced upon its delicate axle by adjusting, as might be necessary, the numbers of animals upon this side and that. The great fish poured blood as the man pierced it with a flying spear which exploded within its body. The striped cat melted, diminishing slowly to the size of a mouse; and a great, grey beast with a long trunk cried piteously as the man tore its white tusks out of its face. Still on towards the wheel he circled, and between him and the wheel Mr. Ephraim called him silently to fellowship with the dead. ~ Richard Adams

children not allocated their own seat do not appear in listed victim numbers in airline crash statistics. ~ Glenn Meade

Mere numbers cannot bring out ... the intimate essence of the experiment. This conviction comes naturally when one watches a subject at work ... What things can happen! What reflections, what remarks, what feelings, or, on the other hand, what blind automatism, what absence of ideas! ... The experimenter judges what may be going on in [the subject's] mind, and certainly feels difficulty in expressing all the oscillations of a thought in a simple, brutal number, which can have only a deceptive precision. How, in fact, could it sum up what would need several pages of description! ~ Alfred Binet

Numbers are a lot like people. They each have a story. They interact with one another. They entertain. They inform. They deceive. They can create happiness or inflict enormous pain. You have to know how to get them to talk. ~ Lee Goldberg

You will be remembered, in the long haul, for the quality of your work, not the quantity of your work. No one evaluates Picasso based on the number of paintings he churned out. ~ Tom Peters

Acquaintance I would have, but when it depends; not on number, but the choice of friends. ~ Abraham Cowley

The right constitutions, three in number- kingship, aristocracy, and polity- and the deviations from these, likewise three in number - tyranny from kingship, oligarchy from aristocracy, democracy from polity. ~ Aristotle.

Democracy is nothing but the Tyranny of Majorities, the most abominable tyranny of all, for it is not based on the authority of a religion, not upon the nobility of a race, not on the merits of talents and of riches. It merely rests upon numbers and hides behind the name of the people. ~ Pierre-Joseph Proudhon

I've got nothing against selling out, but just let me do it for something that matters. Not so I can be Number One With a Bullet, as it were, but so I can leave this world feeling like I made a difference. ~ Harry Chapin

They do not know what they say. If it came to a conflict of arms, the war will last at least four years. Northern politicians will not appreciate the determination and pluck of the South, and Southern politicians do not appreciate the numbers, resources, and patient perseverance of the North. Both sides forget that we are all Americans. I foresee that our country will pass through a terrible ordeal, a necessary expiation, perhaps, for our national sins. ~ Robert E.Lee

Then little Gerda said the Lord's Prayer; the cold was so intense that she could see her own breath; it came out of her mouth like smoke. Her breath became thicker and thicker, and took the form of little angels who grew larger and larger as soon as they touched the ground. All had helmets on their heads, and lances and shields in their hands; their numbers increased, and when Gerda had finished her prayer a whole legion stood around her. They trust their lances against the horrible snow-flakes, so that the latter flew into a hundred pieces; and little Gerda went forward safely and cheerfully. The angels stroked her hands and feet, so that she felt the cold less, and she hastened on to the Snow Queen's castle. ~ Hans Christian Andersen

The value is in the worth, not in the number. ~ Aesop

The defect of power in the existing confederacy, to regulate the commerce between its several members is in the number of those which have been clearly pointed out by experience ... A very material object of this power was the relief of the States which import and export through other States from the improper contributions levied on them by the latter. ~ James Madison

The happiest life has the greatest number of points of contact with the world, and it has the deepest feeling and sympathy with everything that is. ~ Liberty Hyde Bailey

By this time the Vietnam War was such a confusing issue to most Americans that Nixon could take as many positions as he liked and find support somewhere for them all. Roughly equal numbers wanted to expand the war as negotiate a peace. ~ Nancy Gibbs; Michael Duffy

My father says that if I hit 2,500 balls each day, I'll hit 17,500 balls each week, and at the end of one year I'll have hit nearly one million balls. He believes in math. Numbers, he says, don't lie. A child who hits one million balls each year will be unbeatable. ~ Andre Agassi

Small is the number of people who see with their eyes and think with their minds. ~ Albert Einstein

Topology and number theory are my faves. ~ Janna Levin

I had a number of teachers who hated me. I didn't do well in school. ~ Francis Ford Coppola

There are a number of World War II historians I admire: Cornelius Ryan, Mark Stoler, Antony Beevor, to name a few. As for generals, there are those I admire as combat leaders and others I admire because they're great fun to write about. ~ Rick Atkinson

Of all many-sided subjects, [education] is the one which has the greatest number of sides. ~ John Stuart Mill

Make use of life while you have it. Whether you have lived enough depends upon yourself, not on the number of your years. ~ Michel De Montaigne

The window counter considered numbers often. How many tons of air did the universe contain, for instance. She wanted to know the average number of thoughts projected on an object in its life, to measure the silences in a dream, to calculate the ideal amount of light a window should emit. But the most pressing question of all was the number of windows the world contained. How many worlds could a person view from within or without? ~ Meia Geddes

When you look at the actual numbers, the number of people who died after 9/11 was greater than the number of people who died in 9/11, even if you are talking Americans. But you know, I don't like to talk Americans. I want to talk everybody. More innocent people died after 9/11 because of 9/11 than died in 9/11. ~ Penn Jillette

The reason that truth is stranger than fiction is that fiction has to have a rational thread running through it in order to be believable, whereas reality may be totally irrational. ~ Sydney J. Harris

It never ceases to amaze me how prosaic, pedestrian, unimaginative people can persistently pontificate about classical grammatical structure as though it's fucking rocket science. These must be the same people who hate Picasso, because he couldn't keep the paint inside the lines and the colors never matched the numbers. ~ Abbe Diaz