Geometry Quotes

Our civil rights have no dependence on our religious opinions any more than our opinions in physics or geometry...

If I died, would it get me out of my geometry test tomorrow? One could only hope.

Writing is the geometry of the soul.

Rachel bit her lip. "I hope you're right. I'm a little worried. What if someone asks what's on the next math test and I start spouting a prophecy in the middle of geometry class? The Pythagorean theorem shall be problem two...Gods, that would be embarrassing.

Philosophy [nature] is written in that great book which ever is before our eyes -- I mean the universe -- but we cannot understand it if we do not first learn the language and grasp the symbols in which it is written. The book is written in mathematical language, and the symbols are triangles, circles and other geometrical figures, without whose help it is impossible to comprehend a single word of it; without which one wanders in vain through a dark labyrinth.

There is geometry in the humming of the strings. There is music in the spacing of the spheres.

No story is a straight line. The geometry of a human life is too imperfect and complex, too distorted by the laughter of time and the bewildering intricacies of fate to admit the straight line into its system of laws.

What's your angle?" I asked, trying to sound more playful than demanding. "Isosceles," Jack quipped.

We are, all four of us, blood relatives, and we speak a kind of esoteric, family language, a sort of semantic geometry in which the shortest distance between any two points is a fullish circle.

Everything you invent is true: you can be sure of that. Poetry is a subject as precise as geometry.

A firm rule must be imposed upon our nation before it destroys itself. The United States needs some theology and geometry, some taste and decency. I suspect that we are teetering on the edge of the abyss.

The problem, of course, was that turning into a monster was the brighter of my two choices. Choice Number 1: I turn into a vampyre, which equals a monster in just about any human’s mind. Choice Number 2: My body rejects the Change and I die. Forever. So the good news is that I wouldn’t have to take the geometry test tomorrow.

I am the twentieth century. I am the ragtime and the tango; sans-serif, clean geometry. I am the virgin's-hair whip and the cunningly detailed shackles of decadent passion. I am every lonely railway station in every capital of Europe. I am the Street, the fanciless buildings of government. the cafe-dansant, the clockwork figure, the jazz saxophone, the tourist-lady's hairpiece, the fairy's rubber breasts, the travelling clock which always tells the wrong time and chimes in different keys. I am the dead palm tree, the Negro's dancing pumps, the dried fountain after tourist season. I am all the appurtenances of night.

Now tequila may be the favored beverage of outlaws but that doesn't mean it gives them preferential treatment. In fact, tequila probably has betrayed as many outlaws as has the central nervous system and dissatisfied wives. Tequila, scorpion honey, harsh dew of the doglands, essence of Aztec, crema de cacti; tequila, oily and thermal like the sun in solution; tequila, liquid geometry of passion; Tequila, the buzzard god who copulates in midair with the ascending souls of dying virgins; tequila, firebug in the house of good taste; O tequila, savage water of sorcery, what confusion and mischief your sly, rebellious drops do generate!

If I died, would it get me out of my geometry test tomorrow? One could only hope." - Zoey Mongomery (Redbird)

Calligraphy is a geometry of the soul which manifests itself physically.

There is no Royal Road to Geometry.

Geometry has two great treasures; one is the Theorem of Pythagoras; the other, the division of a line into extreme and mean ratio. The first we may compare to a measure of gold; the second we may name a precious jewel.

There was a wall. It did not look important. It was built of uncut rocks roughly mortared. An adult could look right over it, and even a child could climb it. Where it crossed the roadway, instead of having a gate it degenerated into mere geometry, a line, an idea of boundary. But the idea was real. It was important. For seven generations there had been nothing in the world more important than that wall. Like all walls it was ambiguous, two-faced. What was inside it and what was outside it depended upon which side of it you were on.

Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.

Possession of anything new or expensive only reflected a person's lack of theology and geometry; it could even cast doubts upon one's soul.

You don’t see something until you have the right metaphor to let you perceive it

Reading list (1972 edition)[edit] 1. Homer – Iliad, Odyssey 2. The Old Testament 3. Aeschylus – Tragedies 4. Sophocles – Tragedies 5. Herodotus – Histories 6. Euripides – Tragedies 7. Thucydides – History of the Peloponnesian War 8. Hippocrates – Medical Writings 9. Aristophanes – Comedies 10. Plato – Dialogues 11. Aristotle – Works 12. Epicurus – Letter to Herodotus; Letter to Menoecus 13. Euclid – Elements 14. Archimedes – Works 15. Apollonius of Perga – Conic Sections 16. Cicero – Works 17. Lucretius – On the Nature of Things 18. Virgil – Works 19. Horace – Works 20. Livy – History of Rome 21. Ovid – Works 22. Plutarch – Parallel Lives; Moralia 23. Tacitus – Histories; Annals; Agricola Germania 24. Nicomachus of Gerasa – Introduction to Arithmetic 25. Epictetus – Discourses; Encheiridion 26. Ptolemy – Almagest 27. Lucian – Works 28. Marcus Aurelius – Meditations 29. Galen – On the Natural Faculties 30. The New Testament 31. Plotinus – The Enneads 32. St. Augustine – On the Teacher; Confessions; City of God; On Christian Doctrine 33. The Song of Roland 34. The Nibelungenlied 35. The Saga of Burnt Njál 36. St. Thomas Aquinas – Summa Theologica 37. Dante Alighieri – The Divine Comedy;The New Life; On Monarchy 38. Geoffrey Chaucer – Troilus and Criseyde; The Canterbury Tales 39. Leonardo da Vinci – Notebooks 40. Niccolò Machiavelli – The Prince; Discourses on the First Ten Books of Livy 41. Desiderius Erasmus – The Praise of Folly 42. Nicolaus Copernicus – On the Revolutions of the Heavenly Spheres 43. Thomas More – Utopia 44. Martin Luther – Table Talk; Three Treatises 45. François Rabelais – Gargantua and Pantagruel 46. John Calvin – Institutes of the Christian Religion 47. Michel de Montaigne – Essays 48. William Gilbert – On the Loadstone and Magnetic Bodies 49. Miguel de Cervantes – Don Quixote 50. Edmund Spenser – Prothalamion; The Faerie Queene 51. Francis Bacon – Essays; Advancement of Learning; Novum Organum, New Atlantis 52. William Shakespeare – Poetry and Plays 53. Galileo Galilei – Starry Messenger; Dialogues Concerning Two New Sciences 54. Johannes Kepler – Epitome of Copernican Astronomy; Concerning the Harmonies of the World 55. William Harvey – On the Motion of the Heart and Blood in Animals; On the Circulation of the Blood; On the Generation of Animals 56. Thomas Hobbes – Leviathan 57. René Descartes – Rules for the Direction of the Mind; Discourse on the Method; Geometry; Meditations on First Philosophy 58. John Milton – Works 59. Molière – Comedies 60. Blaise Pascal – The Provincial Letters; Pensees; Scientific Treatises 61. Christiaan Huygens – Treatise on Light 62. Benedict de Spinoza – Ethics 63. John Locke – Letter Concerning Toleration; Of Civil Government; Essay Concerning Human Understanding;Thoughts Concerning Education 64. Jean Baptiste Racine – Tragedies 65. Isaac Newton – Mathematical Principles of Natural Philosophy; Optics 66. Gottfried Wilhelm Leibniz – Discourse on Metaphysics; New Essays Concerning Human Understanding;Monadology 67. Daniel Defoe – Robinson Crusoe 68. Jonathan Swift – A Tale of a Tub; Journal to Stella; Gulliver's Travels; A Modest Proposal 69. William Congreve – The Way of the World 70. George Berkeley – Principles of Human Knowledge 71. Alexander Pope – Essay on Criticism; Rape of the Lock; Essay on Man 72. Charles de Secondat, baron de Montesquieu – Persian Letters; Spirit of Laws 73. Voltaire – Letters on the English; Candide; Philosophical Dictionary 74. Henry Fielding – Joseph Andrews; Tom Jones 75. Samuel Johnson – The Vanity of Human Wishes; Dictionary; Rasselas; The Lives of the Poets

There is still a difference between something and nothing, but it is purely geometrical and there is nothing behind the geometry.

I did not know then that this is what life is - just when you master the geometry of one world, it slips away, and suddenly again, you're swarmed by strange shapes and impossible angles.

music is the arithmetic of sounds as optics is the geometry of light

The female mind is capable of understanding analytic geometry... The difficulty may just be that we have never yet discovered a way to communicate with the female mind. If it is done in the right way, you may be able to get something out of it.

It isn't a circle--it is simply a long line--as in geometry, you know, one that reaches into infinity. And because we cannot see the end--we also cannot see how it changes. And it is very odd by those who see the changes--who dream, who will not give up--are called idealists...and those who see only the circle we call them the "realists"!

Our civil rights have no dependence upon our religious opinions more than our opinions in physics or geometry.

Symmetry is only a property of dead things. Did you ever see a tree or a mountain that was symmetrical? It’s fine for buildings, but if you ever see a symmetrical human face, you will have the impression that you ought to think it beautiful, but that in fact you find it cold. The human heart likes a little disorder in its geometry, Kyria Pelagia. Look at your face in a mirror, Signorina, and you will see that one eyebrow is a little higher than the other, that the set of the lid of your left eye is such that the eye is a fraction more open that the other. It is these things that make you both attractive and beautiful, whereas…otherwise you would be a statue. Symmetry is for God, not for us.

A circle has no end.

To ride a bicycle is in itself some protection against superstitious fears, since the bicycle is the product of pure reason applied to motion. Geometry at the service of man! Give me two spheres and a straight line and I will show you how far I can take them. Voltaire himself might have invented the bicycle, since it contributes so much to man’s welfare and nothing at all to his bane. Beneficial to the health, it emits no harmful fumes and permits only the most decorous speeds. How can a bicycle ever be an implement of harm?

You must follow me carefully. I shall have to controvert one or two ideas that are almost universally accepted. The geometry, for instance, they taught you at school is founded on a misconception.

The thing about reason is that there's a geometry to it. It travels in a straight line, so that slightly different beginnings can lead you to wildly divergent endpoints.

Frost grows on the window glass, forming whorl patterns of lovely translucent geometry. Breathe on the glass, and you give frost more ammunition. Now it can build castles and cities and whole ice continents with your breath’s vapor. In a few blinks you can almost see the winter fairies moving in . . . But first, you hear the crackle of their wings.

Tapi mencari suami memang seperti melihat toko perabot untuk setelan meja makan yang pas buat ruangan dan keuangan. Kita datang dengan sejumlah syarat geometri dan bujet. Sedangkan kekasih muncul seperti sebuah lukisan yang tiba-tiba membuat kita jatuh hati. Kita ingin mendapatkannya, dan mengubah seluruh desain kamar agar turut padanya. Laila selalu jatuh cinta pada lukisan, bukan meja makan.

Beauty is geometry.

There is geometry in the humming of the string.

His way had therefore come full circle, or rather had taken the form of an ellipse or a spiral, following as ever no straight unbroken line, for the rectilinear belongs only to Geometry and not to Nature and Life.

Today, suddenly, I reached an absurd but unerring conclusion. In a moment of enlightenment, I realized that I'm nobody, absolutely nobody. When the lightning flashed, I saw that what I had thought to be a city was in fact a deserted plain and, in the same sinister light that revealed me to myself, there seemed to be no sky above it. I was robbed of any possibility of having existed before the world. If I was ever reincarnated, I must have done so without myself, without a self to reincarnate. I am the outskirts of some non-existent town, the long-winded prologue to an unwritten book. I'm nobody, nobody. I don't know how to feel or think or love. I'm a character in a novel as yet unwritten, hovering in the air and undone before I've even existed, amongst the dreams of someone who never quite managed to breathe life into me. I'm always thinking, always feeling, but my thoughts lack all reason, my emotions all feeling. I'm falling through a trapdoor, through infinite, infinitous space, in a directionless, empty fall. My soul is a black maelstrom, a great madness spinning about a vacuum, the swirling of a vast ocean around a hole in the void, and in the waters, more like whirlwinds than waters, float images of all I ever saw or heard in the world: houses, faces, books, boxes, snatches of music and fragments of voices, all caught up in a sinister, bottomless whirlpool. And I, I myself, am the centre that exists only because the geometry of the abyss demands it; I am the nothing around which all this spins, I exist so that it can spin, I am a centre that exists only because every circle has one. I, I myself, am the well in which the walls have fallen away to leave only viscous slime. I am the centre of everything surrounded by the great nothing. And it is as if hell itself were laughing within me but, instead of the human touch of diabolical laughter, there's the mad croak of the dead universe, the circling cadaver of physical space, the end of all worlds drifting blackly in the wind, misshapen, anachronistic, without the God who created it, without God himself who spins in the dark of darks, impossible, unique, everything. If only I could think! If only I could feel!

Me, and thousands of others in this country like me, are half-baked, because we were never allowed to complete our schooling. Open our skulls, look in with a penlight, and you'll find an odd museum of ideas: sentences of history or mathematics remembered from school textbooks (no boy remembers his schooling like the one who was taken out of school, let me assure you), sentences about politics read in a newspaper while waiting for someone to come to an office, triangles and pyramids seen on the torn pages of the old geometry textbooks which every tea shop in this country uses to wrap its snacks in, bits of All India Radio news bulletins, things that drop into your mind, like lizards from the ceiling, in the half hour before falling asleep--all these ideas, half formed and half digested and half correct, mix up with other half-cooked ideas in your head, and I guess these half-formed ideas bugger one another, and make more half-formed ideas, and this is what you act on and live with.

This love triangle had reached new heights, and as much as Matt loved geometry, this was not the sort of triangle he wanted anything to do with.

The geometry of judgment is a circle. Hate is a snake that turns to consume itself from the tail, a circle that diminishes to a point, then to nothing. Pride is such a snake, and envy, and greed. Love, however, is a hoop, a wheel, that rolls on forever. We are rescued by those whom we have rescued. The saved become the saviors of their saviors.

the geometry of the place was all wrong. One could not be sure that the sea and the ground were horizontal,

Let no one destitute of Geometry enter my doors.

I guess a sock is also a geometric shape—technically—but I don't know what you'd call it. A socktagon?

At that stage of my youth, death remained as abstract a concept as non-Euclidean geometry or marriage. I didn't yet appreciate its terrible finality or the havoc it could wreak on those who'd entrusted the deceased with their hearts.

Reality never changes. Only our recollections of it do. Whenever a moment passes, we pass along with it into the realm of memory. And in that realm, geometries change. Contours shift, shades lighten, objectivities dissolve. Memory becomes what we need it to be.

Goodbyes were impossible, unless you didn't realize you were saying them.

And so will I here state just plainly and briefly that I accept God. But I must point out one thing: if God does exist and really created the world, as we well know, he created it according to the principles of Euclidean geometry and made the human brain capable of grasping only three dimensions of space. Yet there have been and still are mathematicians and philosophers-among them some of the most outstanding-who doubt that the whole universe or, to put it more generally, all existence was created to fit Euclidean geometry; they even dare to conceive that two parallel lines that, according to Euclid, never do meet on earth do, in fact, meet somewhere in infinity. And so my dear boy, I’ve decided that I am incapable of understanding of even that much, I cannot possibly understand about God.

In other words, to put it into Euclid, or old-fashioned plane geometry, a straight line is not the shortest distance between two points.

How can you study geometry and not believe in a god? A god of perfect points and planes, surrounded by angels and angles of all different degrees...

The greatest pleasure is not - say - sex or geometry. It is just understanding. And if you can get people to understand their own humanity - well, that's the job of the writer.

The harmony of the world is made manifest in Form and Number, and the heart and soul and all the poetry of Natural Philosophy are embodied in the concept of mathematical beauty.

Algebra is the offer made by the devil to the mathematician. The devil says: I will give you this powerful machine, it will answer any question you like. All you need to do is give me your soul: give up geometry and you will have this marvelous machine.

All its dimensions with their projected geometries are those of an unrealisible dream.

Leibniz is at the disadvantage of not having seen it. Or perhaps we should count this as an advantage, for anyone who sees it is dumbfounded by the brilliance of the geometry, and it is difficult to criticize a man’s work when you are down on your knees shielding your eyes.

She was Harrowhark alone in front of the mirror again: a nonsense, a monster, an alien geometry. A loathsome squawk of a person. She was nine, and she’d made a mistake. She was seventeen, and she’d made a mistake. Time had repeated itself. Harrow would be tripping over herself for her whole existence, a frictionless hoop of totally fucking up.

Mustardseed grinned at Bertie. "I was never any good at geometry, but you’re stuck in a love triangle, aren’t you?" "Shut up," she ordered even as Moth asked, "But what if there were four of them?" "That’s a love rectangle, and five people would be a love pentagon." "And what are six people in love?" Cobweb demanded. Mustardseed thought it over a moment. "Manslaughter, I suppose.

At that stage of my youth, death remained as abstract a concept as non-Euclidean geometry or marriage. I didn't yet appreciate its terrible finality or the havoc it could wreak on those who'd entrusted the deceased with their hearts. I was stirred by the dark mystery of mortality. I couldn't resist stealing up to the edge of doom and peering over the brink. The hint of what was concealed in those shadows terrified me, but I caught sight of something in the glimpse, some forbidden and elemental riddle that was no less compelling than the sweet, hidden petals of a woman's sex. In my case - and, I believe, in the case of Chris McCandless - that was a very different thing from wanting to die.

Give me a place to stand, a lever long enough and a fulcrum. and I can move the Earth

Keep that red-haired girl of yours in the open air all summer and don't let her read books until she gets more spring into her step." This message frightened Marilla wholesomely. She read Anne's death warrant by consumption in it unless it was scrupulously obeyed. As a result, Anne had the golden summer of her life as far as freedom and frolic went. She walked, rowed, berried, and dreamed to her heart's content; and when September came she was bright-eyed and alert, with a step that would have satisfied the Spencervale doctor and a heart full of ambition and zest once more. "I just feel like studying with might and main," she declared as she brought her books down from the attic. "Oh, you good old friends, I'm glad to see your honest face once more - yes, even you, geometry.

But then, Cap'n Crunch in a flake form would be suicidal madness; it would last about as long, when immersed in milk, as snowflakes sifting down into a deep fryer. No, the cereal engineers at General Mills had to find a shape that would minimize surface area, and, as some sort of compromise between the sphere that is dictated by Euclidean geometry and whatever sunken treasure related shapes that the cereal aestheticians were probably clamoring for, they came up with this hard -to-pin-down striated pillow formation.

I would say, if you like, that the party is like an out-moded mathematics...that is to say, the mathematics of Euclid. We need to invent a non-Euclidian mathematics with respect to political discipline.

the seven “liberal arts”: Grammar, the foundation of science; Logic, which differentiates the true from the false; Rhetoric, the source of law; Arithmetic, the foundation of order because “without numbers there is nothing”; Geometry, the science of measurement; Astronomy, the most noble of the sciences because it is connected with Divinity and Theology; and lastly Music.

The physical is inherently entropic, giving off energy in ever more disorderly ways. The metaphysical is antientropic, methodically marshalling energy. Life is antientropic. It is spontaneously inquisitive. It sorts out and endeavors to understand

Where is the library?” “Turn right, proceed thirty-four paces, turn right again, twelve paces, then through door on the right, thirty-five paces, through archway on right another eleven paces, turn right one last time, fifteen paces, enter the door on the right.” Mappo stared at Iskaral Pust. The High Priest shifted nervously. “Or,” the Trell said, eyes narrowed, “turn left, nineteen paces.” “Aye,” Iskaral muttered.

One might suppose that reality must be held to at all costs. However, though that may be the moral thing to do, it is not necessarily the most useful thing to do. The Greeks themselves chose the ideal over the real in their geometry and demonstrated very well that far more could be achieved by consideration of abstract line and form than by a study of the real lines and forms of the world; the greater understanding achieved through abstraction could be applied most usefully to the very reality that was ignored in the process of gaining knowledge.

The way your mother rolls her eyes at you, your sudden decision to stop eating red meat, the immediate unexplainable sadness you felt when you saw your father’s shirt draped over the back of a chair. You can write it all down, you can put it in your book of facts, but the truth is no one can ever really understand the tangle of experiences and passions that makes you who you are. It’s a secret collection, a private language, a pebble in your pocket that you play with when you’re anxious, hard as geometry, smooth as soap.

Perfect hexagonal tubes in a packed array. Bees are hard-wired to lay them down, but how does an insect know enough geometry to lay down a precise hexagon? It doesn't. It's programmed to chew up wax and spit it out while turning on its axis, and that generates a circle. Put a bunch of bees on the same surface, chewing side-by-side, and the circles abut against each other - deform each other into hexagons, which just happen to be more efficient for close packing anyway.

The Fibonacci Sequence turns out to be the key to understanding how nature designs... and is... a part of the same ubiquitous music of the spheres that builds harmony into atoms, molecules, crystals, shells, suns and galaxies and makes the Universe sing.

He deals the cards to find the answer The sacred geometry of chance The hidden law of a probable outcome The numbers lead a dance I know that the spades Are the swords of a soldier I know that the clubs are weapons of war I know that diamonds Mean money for this art But that's not the shape of my heart

Be honest: did you actually read [the above geometric proof]? Of course not. Who would want to? The effect of such a production being made over something so simple is to make people doubt their own intuition. Calling into question the obvious by insisting that it be 'rigorously proved' ... is to say to a student 'Your feelings and ideas are suspect. You need to think and speak our way.

Of all the possible pathways of disorder, nature favors just a few.

What music is to the heart, mathematics is to the mind.

Why is geometry often described as ""cold" and ""dry?" One reason lies in its inability to describe the shape of a cloud, a mountain, a coastline, or a tree. Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line.

For me the camera is a sketch book, an instrument of intuition and spontaneity, the master of the instant which, in visual terms, questions and decides simultaneously. In order to "give a meaning" to the world, one has to feel oneself involved in what one frames through the viewfinder. This attitude requires concentration, a discipline of the mind, sensitivity, and a sense of geometry.

My faith is what they bury when they force me to expose it.

Do you think that I want to live in a communal society with people like that Battaglia acquaintance of yours, sweeping streets and breaking up rocks or whatever it is people are always doing in those blighted countries? What I want is a good, strong monarchy with a tasteful and decent king who has some knowledge of theology and geometry and to cultivate a Rich Inner Life.

I am convinced that everything has come down to us from the banks of the Ganges, - astronomy, astrology, metempsychosis, etc... It is very important to note that some 2,500 years ago at the least Pythagoras went from Samos to the Ganges to learn geometry...But he would certainly not have undertaken such a strange journey had the reputation of the Brahmins' science not been long established in Europe

Scientists say every action initiates an equal and opposite reaction. I say that's just the start. I say every action initiates a most unequal and upredictable chain reaction, that every filament of living becomes part of a larger weave, while remaining identifiable. That every line of latitude requires several stripes of longitude to obtain meaning. That every universe is part of a bigger heaven, a heaven of rhythm and geometry, where a heartbeat is the apex of a triangle.

A green hunting cap squeezed the top of the fleshy balloon of a head. The green earflaps, full of large ears and uncut hair and the fine bristles that grew in the ears themselves, stuck out on either side like turn signals indicating two directions at once. Full, pursed lips protruded beneath the bushy black moustache and, at their corners, sank into little folds filled with disapproval and potato chip crumbs. In the shadow under the green visor of the cap Ignatius J. Reilly’s supercilious blue and yellow eyes looked down upon the other people waiting under the clock at the D.H. Holmes department store, studying the crowd of people for signs of bad taste in dress. Several of the outfits, Ignatius noticed, were new enough and expensive enough to be properly considered offenses against taste and decency. Possession of anything new or expensive only reflected a person’s lack of theology and geometry; it could even cast doubts upon one’s soul.

Why did you do all that, Frankie?" asked Porter. "I mean, it was brilliant, what you did, what you made us do - but why would you bother? That's what I can't figure out." Frankie sighed. "Have you ever heard of the panopticon?" she asked him. Porter shook his head. "Have you ever been in love?" He shook his head again. "Then I can't explain it," Frankie said. They went inside and took the geometry test.

He could not believe that any of them might actually hit somebody. If one did, what a nowhere way to go: killed by accident; slain not as an individual but by sheer statistical probability, by the calculated chance of searching fire, even as he himself might be at any moment. Mathematics! Mathematics! Algebra! Geometry! When 1st and 3d Squads came diving and tumbling back over the tiny crest, Bell was content to throw himself prone, press his cheek to the earth, shut his eyes, and lie there. God, oh, God! Why am I here? Why am I here? After a moment's thought, he decided he better change it to: why are we here. That way, no agency of retribution could exact payment from him for being selfish.

... I succeeded at math, at least by the usual evaluation criteria: grades. Yet while I might have earned top marks in geometry and algebra, I was merely following memorized rules, plugging in numbers and dutifully crunching out answers by rote, with no real grasp of the significance of what I was doing or its usefulness in solving real-world problems. Worse, I knew the depth of my own ignorance, and I lived in fear that my lack of comprehension would be discovered and I would be exposed as an academic fraud -- psychologists call this "imposter syndrome".

Hindutava's nationalism ignores the rationalist traditions of India, a country in which some of the earliest steps in algebra, geometry, and astronomy were taken, where the decimal system emerged, where early philosophy — secular as well as religious — achieved exceptional sophistication, where people invented games like chess, pioneered sex education, and began the first systematic study of political economy. The Hindu militant chooses instead to present India — explicitly or implicitly — as a country of unquestioning idolaters, delirious fanatics, belligerent devotees, and religious murderers

My task is to explain to you as quickly as possible my essence, that is, what sort of man I am, what I believe in, and what I hope for, is that right? And therefore I declare that I accept God pure and simple. But this, however, needs to be noted: if God exists and if he indeed created the earth, then, as we know perfectly well, he created it in accordance with Euclidean geometry, and he created human reason with a conception of only three dimensions of space. At the same time there were and are even now geometers and philosophers, even some of the most outstanding among them, who doubt that the whole universe, or, even more broadly, the whole of being, was created purely in accordance with Euclidean geometry; they even dare to dream that two parallel lines, which according to Euclid cannot possibly meet on earth, may perhaps meet somewhere in infinity. I, my dear, have come to the conclusion that if I cannot understand even that, then it is not for me to understand about God. I humbly confess that I do not have any ability to resolve such questions, I have a Euclidean mind, an earthly mind, and therefore it is not for us to resolve things that are not of this world. And I advise you never to think about it, Alyosha my friend, and most especially about whether God exists or not. All such questions are completely unsuitable to a mind created with a concept of only three dimensions. And so, I accept God, not only willingly, but moreover I also accept his wisdom and his purpose, which are completely unknown to us; I believe in order, in the meaning of life, I believe in eternal harmony, in which we are all supposed to merge, I believe in the Word for whom the universe is yearning, and who himself was 'with God,' who himself is God, and so on and so forth, to infinity. Many words have been invented on the subject. It seems I'm already on a good path, eh? And now imagine that in the final outcome I do not accept this world of God's, created by God, that I do not accept and cannot agree to accept. With one reservation: I have a childlike conviction that the sufferings will be healed and smoothed over, that the whole offensive comedy of human contradictions will disappear like a pitiful mirage, a vile concoction of man's Euclidean mind, feeble and puny as an atom, and that ultimately, at the world's finale, in the moment of eternal harmony, there will occur and be revealed something so precious that it will suffice for all hearts, to allay all indignation, to redeem all human villainy, all bloodshed; it will suffice not only to make forgiveness possible, but also to justify everything that has happened with men--let this, let all of this come true and be revealed, but I do not accept it and do not want to accept it! Let the parallel lines even meet before my own eyes: I shall look and say, yes, they meet, and still I will not accept it.

Before Jeremiah knew God, God knew Jeremiah: “Before I shaped you in the womb, I knew all about you.” This turns everything we ever thought about God around. We think that God is an object about which we have questions. We are curious about God. We make inquiries about God. We read books about God. We get into late-night bull sessions about God. We drop into church from time to time to see what is going on with God. We indulge in an occasional sunset or symphony to cultivate a feeling of reverence for God. But that is not the reality of our lives with God. Long before we ever got around to asking questions about God, God had been questioning us. Long before we got interested in the subject of God, God subjected us to the most intensive and searching knowledge. Before it ever crossed our minds that God might be important, God singled us out as important. Before we were formed in the womb, God knew us. We are known before we know. This realization has a practical result: no longer do we run here and there, panicked and anxious, searching for the answers to life. Our lives are not puzzles to be figured out. Rather, we come to God, who knows us and reveals to us the truth of our lives. The fundamental mistake is to begin with ourselves and not God. God is the center from which all life develops. If we use our ego as the center from which to plot the geometry of our lives, we will live eccentrically.

...there's something about telling other people what to ignore that just doesn't work for me. Especially things we shouldn't be ignoring. Kid bullying you at school? Ignore him. Girl passing rumors? Ignore her. Eighth-grade teacher pinch your friend's ass? Ignore it. Sexist geometry teacher says girls shouldn't go to college because they will only ever pop out babies and get fat? Ignore him. Hear that a girl in your class is being abused by her stepfather and had to go to the clinic? Hear she's bringing her mother's pills to school and selling them to pay for it? Ignore. Ignore. Ignore. Mind your own business. Don't make waves. Fly under the radar. It's just one of those things, Vera. I'm sorry, but I don't get it. If we're supposed to ignore everything that's wrong with our lives, then I can't see how we'll ever make things right.

A philosophical thought is not supposed to be impervious to all criticism; this is the error Whitehead describes of turning philosophy into geometry, and it is useful primarily as a way of gaining short-term triumphs in personal arguments that no one else cares (or even knows) about anyway. A good philosophical thought will always be subject to criticisms (as Heidegger’s or Whitehead’s best insights all are) but they are of such elegance and depth that they change the terms of debate, and function as a sort of “obligatory passage point” (Latour’s term) in the discussions that follow. Or in other words, the reason Being and Time is still such a classic, with hundreds of thousands or millions of readers almost a century later, is not because Heidegger made “fewer mistakes” than others of his generation. Mistakes need to be cleaned up, but that is not the primary engine of personal or collective intellectual progress.

The solution which I am urging is to eradicate the fatal disconnection of subjects which kills the vitality of our modern curriculum. There is only one subject-matter for education, and that is LIfe in all its manifestations. Instead of this single unity, we offer children--Algebra, from which nothing follows; Geometry, from which nothing follows; Science, from which nothing follows; History, from which nothing follows; a Couple of Languages, never mastered; and lastly, most dreary of all, Literature, represented by plays of Shakespeare, with philological notes and short analyses of plot and character to be in substance committed to memory. Can such a list be said to represent Life, as it is known in the midst of living it? The best that can be said of it is, that it is a rapid table of contents which a deity might run over in his mind while he was thinking of creating a world, and has not yet determined how to put it together

The human mind is only capable of absorbing a few things at a time. We see what is taking place in front of us in the here and now, and cannot envisage simultaneously a succession of processes, no matter how integrated and complementary. Our faculties of perception are consequently limited even as regards fairly simple phenomena. The fate of a single man can be rich with significance, that of a few hundred less so, but the history of thousands and millions of men does not mean anything at all, in any adequate sense of the word. The symmetriad is a million—a billion, rather—raised to the power of N: it is incomprehensible. We pass through vast halls, each with a capacity of ten Kronecker units, and creep like so many ants clinging to the folds of breathing vaults and craning to watch the flight of soaring girders, opalescent in the glare of searchlights, and elastic domes which criss-cross and balance each other unerringly, the perfection of a moment, since everything here passes and fades. The essence of this architecture is movement synchronized towards a precise objective. We observe a fraction of the process, like hearing the vibration of a single string in an orchestra of supergiants. We know, but cannot grasp, that above and below, beyond the limits of perception or imagination, thousands and millions of simultaneous transformations are at work, interlinked like a musical score by mathematical counterpoint. It has been described as a symphony in geometry, but we lack the ears to hear it.

Magnolias don't look like that," Ignatius said, thrusting his cutlass at the offending pastel magnolia. "You ladies need a course in botany. And perhaps geometry, too." "You don't have to look at our work," an offended voice said from the group, the voice of the lady who had drawn the magnolia in question. "Yes, I do!" Ignatius screamed. "You ladies need a critic with some taste and decency. Good heavens! Which one of you did this camellia? Speak up. The water in this bowl looks like motor oil." "Let us alone," a shrill voice said. "You women had better stop giving teas and brunches and settle down to the bustiness of learning how to draw," Ignatius thundered. "First, you must learn how to handle a brush. I would suggest that you all get together and paint someone's house for a start." "Go away." "Had you 'artists' had a part in the decoration of the Sistine Chapel, it would have ended up looking like a particularly vulgar train terminal," Ignatius snorted.

I am trying to explain as quickly as possible my essential nature, that is, what manner of man I am, what I believe in, and for what I hope, that's it, isn't it? And therefore I tell you that I accept God honestly and simply. But you must note this: If God exists and if He really did create the world, then, as we all know, He created it according to the geometry of only three dimensions in space. Yet there have been some very distinguished ones, who doubt whether the whole universe, or to speak more generally the whole of being, was only created in Euclid's geometry; they even dare to dream that two parallel lines, which according to Euclid can never meet on earth, may meet somewhere in infinity. I have come to the conclusion that, since I can't understand even that, I can't expect to understand about God. I acknowledge humbly that I have no faculty for settling such questions, I have a Euclidian earthly mind, and how could I solve problems that are not of this world? And I advise you never to think about it either, my dear Alyosha, especially about God, whether He exists or not. All such questions are utterly inappropriate for a mind created with a conception of only three dimensions. And so I accept God and am glad to, and what's more I accept His wisdom, His purpose - which are utterly beyond our ken; I believe in the underlying order and the meaning of life; I believe in the eternal harmony in which they say we shall one day be blended. I believe in the Word to Which the universe is striving, and Which Itself was "with God", and Which Itself is God and so on, and so on, to infinity.

Sadhana Look around. Among your family, coworkers, and friends, can you see how everyone has different levels of perception? Just observe this closely. If you know a few people who seem to have a greater clarity of perception than others, watch how they conduct their body. They often have a certain poise without practice. But just a little practice can make an enormous difference. If you sit for just a few hours a day with your spine erect, you will see that it will have an unmistakable effect on your life. You will now begin to understand what I mean by the geometry of your existence. Just the way you hold your body determines almost everything about you. Another way of listening to life is paying attention to it experientially, not intellectually or emotionally. Choose any one thing about yourself: your breath, your heartbeat, your pulse, your little finger. Just pay attention to it for eleven minutes at a time. Do this at least three times a day. Keep your attention on any sensation, but feel free to continue doing whatever you are doing. If you lose attention, it doesn’t matter. Simply refocus your attention. This practice will allow you to move from mental alertness to awareness. You will find the quality of your life experience will begin to change.

Is everyone with one face called a Milo?" "Oh no," Milo replied; "some are called Henry or George or Robert or John or lots of other things." "How terribly confusing," he cried. "Everything here is called exactly what it is. The triangles are called triangles, the circles are called circles, and even the same numbers have the same name. Why, can you imagine what would happen if we named all the twos Henry or George or Robert or John or lots of other things? You'd have to say Robert plus John equals four, and if the four's name were Albert, things would be hopeless." "I never thought of it that way," Milo admitted. "Then I suggest you begin at once," admonished the Dodecahedron from his admonishing face, "for here in Digitopolis everything is quite precise.

The little Hexagon meditated on this a while and then said to me; "But you have been teaching me to raise numbers to the third power: I suppose three-to-the-third must mean something in Geometry; what does it mean?" "Nothing at all," replied I, "not at least in Geometry; for Geometry has only Two Dimensions." And then I began to shew the boy how a Point by moving through a length of three inches makes a Line of three inches, which may be represented by three; and how a Line of three inches, moving parallel to itself through a length of three inches, makes a Square of three inches every way, which may be represented by three-to-the-second. xxx Upon this, my Grandson, again returning to his former suggestion, took me up rather suddenly and exclaimed, "Well, then, if a Point by moving three inches, makes a Line of three inches represented by three; and if a straight Line of three inches, moving parallel to itself, makes a Square of three inches every way, represented by three-to-the-second; it must be that a Square of three inches every way, moving somehow parallel to itself (but I don't see how) must make Something else (but I don't see what) of three inches every way—and this must be represented by three-to-the-third." "Go to bed," said I, a little ruffled by this interruption: "if you would talk less nonsense, you would remember more sense.

The water beneath the Temple was both actual and metaphorical, existing as springs and streams, as spiritual energy, and as a symbol of the receptive or lunar aspect of nature. The meaning of that principle is too wide and elusive for it to be given any one name, so in the terminology of ancient science it was given a number, 1,080. Its polar opposite, the positive, solar force in the universe, was also referred to as a number 666. These two numbers, which have an approximate golden-section relationship of 1:1.62, were at the root of the alchemical formula that expressed the supreme purpose of the Temple. Its polar opposite, the positive, solar force in the universe, was also referred to as a number 666. Not merely was it used to generate energy from fusion of atmospheric and terrestrial currents, but it also served to combine in harmony all the correspondences of those forces on every level of creation.

unsolicited advice to adolescent girls with crooked teeth and pink hair When your mother hits you, do not strike back. When the boys call asking your cup size, say A, hang up. When he says you gave him blue balls, say you’re welcome. When a girl with thick black curls who smells like bubble gum stops you in a stairwell to ask if you’re a boy, explain that you keep your hair short so she won’t have anything to grab when you head-butt her. Then head-butt her. When a guidance counselor teases you for handed-down jeans, do not turn red. When you have sex for the second time and there is no condom, do not convince yourself that screwing between layers of underwear will soak up the semen. When your geometry teacher posts a banner reading: “Learn math or go home and learn how to be a Momma,” do not take your first feminist stand by leaving the classroom. When the boy you have a crush on is sent to detention, go home. When your mother hits you, do not strike back. When the boy with the blue mohawk swallows your heart and opens his wrists, hide the knives, bleach the bathtub, pour out the vodka. Every time. When the skinhead girls jump you in a bathroom stall, swing, curse, kick, do not turn red. When a boy you think you love delivers the first black eye, use a screw driver, a beer bottle, your two good hands. When your father locks the door, break the window. When a college professor writes you poetry and whispers about your tight little ass, do not take it as a compliment, do not wait, call the Dean, call his wife. When a boy with good manners and a thirst for Budweiser proposes, say no. When your mother hits you, do not strike back. When the boys tell you how good you smell, do not doubt them, do not turn red. When your brother tells you he is gay, pretend you already know. When the girl on the subway curses you because your tee shirt reads: “I fucked your boyfriend,” assure her that it is not true. When your dog pees the rug, kiss her, apologize for being late. When he refuses to stay the night because you live in Jersey City, do not move. When he refuses to stay the night because you live in Harlem, do not move. When he refuses to stay the night because your air conditioner is broken, leave him. When he refuses to keep a toothbrush at your apartment, leave him. When you find the toothbrush you keep at his apartment hidden in the closet, leave him. Do not regret this. Do not turn red. When your mother hits you, do not strike back.

I am in doubt as to the propriety of making my first meditations in the place above mentioned matter of discourse; for these are so metaphysical, and so uncommon, as not, perhaps, to be acceptable to every one. And yet, that it may be determined whether the foundations that I have laid are sufficiently secure, I find myself in a measure constrained to advert to them. I had long before remarked that, in relation to practice, it is sometimes necessary to adopt, as if above doubt, opinions which we discern to be highly uncertain, as has been already said; but as I then desired to give my attention solely to the search after truth, I thought that a procedure exactly the opposite was called for, and that I ought to reject as absolutely false all opinions in regard to which I could suppose the least ground for doubt, in order to ascertain whether after that there remained aught in my belief that was wholly indubitable. Accordingly, seeing that our senses sometimes deceive us, I was willing to suppose that there existed nothing really such as they presented to us; and because some men err in reasoning, and fall into paralogisms, even on the simplest matters of geometry, I, convinced that I was as open to error as any other, rejected as false all the reasonings I had hitherto taken for demonstrations; and finally, when I considered that the very same thoughts (presentations) which we experience when awake may also be experienced when we are asleep, while there is at that time not one of them true, I supposed that all the objects (presentations) that had ever entered into my mind when awake, had in them no more truth than the illusions of my dreams. But immediately upon this I observed that, whilst I thus wished to think that all was false, it was absolutely necessary that I, who thus thought, should be somewhat; and as I observed that this truth, I think, therefore I am ["cogito ergo sum"], was so certain and of such evidence that no ground of doubt, however extravagant, could be alleged by the sceptics capable of shaking it, I concluded that I might, without scruple, accept it as the first principle of the philosophy of which I was in search