Geometry Of Life Quotes

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.

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!

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

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.

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"!

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.

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

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!

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.

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.

Straight lines evidently belonged only to geometry, not to nature and life.

Buckminster Fuller explained to me once that because our world is constructed from geometric relations like the Golden Ratio or the Fibonacci Series, by thinking about geometry all the time, you could organize and harmonize your life with the structure of the world.

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 think all artists struggle to represent the geometry of life in their own way, just like writers deal with archetypes. There are only so many stories that you can tell, but an infinite number of storytellers.

The key to a successful education is not remembering the sequence of battles in World War I or getting an A on the geometry test. A robust education is the ability to make meaningful use of any and all information.

It is remarkable how much long-term advantage people like us have gotten by trying to be consistently not stupid, instead of trying to be very intelligent.” – Charlie Munger

No, I’m no patriot, nor was I ever allowed to be. And yet, the country of my childhood lives within me with a primacy that is a form of love. It lives within me despite my knowledge of our marginality, and its primitive, unpretty emotions. Is it blind and self-deceptive of me to hold on to its memory? I think it would be blind and self-deceptive not to. All it has given me is the world, but that is enough. It has fed me language, percep- tions, sounds, the human kind .... no geometry of landscape, no haze in the air, will live in us as intensely as the landscapes that we saw as the fi rst, and to which we gave ourselves wholly, without reservation.

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.

As her lips changed the geometry, Her smile turned to poetry.

Remember, successful investing is based more on minimizing regret than maximizing gains.

Life is geometry and chemistry, not biology.

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.

Since time immemorial, the serpent has symbolized organic vitality. Serpents move in curves and so does energy. The serpent developed from the Light created on the first cosmic day. In the firmament it manifests as the life-breath that animates souls. In the physical universe it manifests electro-magnetism, the light in substance so to speak.

Don’t forget to be specific…Details. Put in all the details. The boys appreciate all that detailed daily life sh*t they don’t get anymore. If you’ve got a teacher you’re hot for, tell ‘em what her hair looks like, what her legs look like, what she eats for lunch. If she’s teaching you geometry, tell ‘em how she draws a bloody triangle on the blackboard. If you went down the shop for a bag of sweets yesterday, did you ride your pushee? Did you go by foot? Did you see a rainbow along the way? Did you buy gobstoppers or clinkers or caramels? If you had a good meat pie last week was it steak and peas or curry or mushroom and beef? You catchin’ my drift? Details.

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

Tuna fish demonstrate a sophisticated understanding of astronomy: when the winter solstice arrives, the whole school stops precisely where it is in the water, and stays there until the following spring equinox. They know geometry and arithmetic too, for they have been observed to form themselves into a perfect cube of which all six sides are equal.

By degrees, the bitterness at my heart diffused itself to the circumference of the circle in which my life went its cheerless mechanical round.

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.

Life can have an ironic geometry. Starting from the age of thirteen or fourteen I had aspired to a bourgeois decorum, proper Italian, a good life, cultured and reflective. Naples had seemed a wave that would drown me. I didn’t think the city could contain life forms different from those I had known as a child, violent or sensually lazy, tinged with sentimental vulgarity or obtusely fortified in defense of their own wretched degradation.

The description of this proportion as Golden or Divine is fitting perhaps because it is seen by many to open the door to a deeper understanding of beauty and spirituality in life. That’s an incredible role for one number to play, but then again this one number has played an incredible role in human history and the universe at large.

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.

The afternoon had passed to a ghostly gray. She was struck by the immensity of things, so much water and sky and forest, and after a time it occurred to her that she’d lived a life almost entirely indoors. Her memories were indoor memories, fixed by ceilings and plastered white walls. Her whole life had been locked to geometries: suburban rectangles, city squares. First the house she’d grown up in, then dorms and apartments. The open air had been nothing but a medium of transit, a place for rooms to exist.

The interwoven spheres and vines ran along the bottom. I'd done some research, and I'd found this motif everywhere. These overlapping circles were ancient, tracing back to Pythagorean geometry--geometry, a measure of the world. In more mystical terms, the shape had always evoked tghe place where world overlap: dreaming with waking, death with life, the visible with the unseen. [p. 362]

Art has no immediate future because all art is collective and there is no more collective life(there are only dead collections of people), and also because of this breaking of the true pact between the body and the soul. Greek art coincided with the beginning of geometry and with athleticism, the art of the Middle Ages with the craftsmen's guilds, the art of the Renaissance with the beginning of mechanics, etc....Since 1914 there has been a complete cut. Even comedy is almost impossible. There is only room for satire (when was it easier to understand Juvenal?). Art will never be reborn except from amidst a general anarchy - it will be epic no doubt, because affliction will have simplified a great many things...It is therefore quite useless for you to envy Leonardo or Bach. Greatness in our times must take a different course. Moreover it can only be solitary, obscure and without an echo...(but without an echo, no art).

If our sides were unequal our angles might be unequal. Instead of its being sufficient to feel, or estimate by sight, a single angle in order to determine the form of an individual, it would be necessary to ascertain each angle by the experiment of Feeling. But life would be too short for such a tedious groping. The whole science and art of Sight Recognition would at once perish; Feeling, so far as it is an art, would not long survive; intercourse would become perilous or impossible; there would be an end to all confidence, all forethought; no one would be safe in making the most simple social arrangements; in a word, civilization would relapse into barbarism.

Riemann concluded that electricity, magnetism, and gravity are caused by the crumpling of our three-dimensional universe in the unseen fourth dimension. Thus a "force" has no independent life of its own; it is only the apparent effect caused by the distortion of geometry. By introducing the fourth spatial dimension, Riemann accidentally stumbled on what would become one of the dominant themes in modern theoretical physics, that the laws of nature appear simple when expressed in higher-dimensional space. He then set about developing a mathematical language in which this idea could be expressed.

In life and literature, the good guys fight for others. The bad guys fight for themselves. Heroes have context.

Taking more risk produces more return is inaccurate. Instead, taking more risk increases the range of potential outcomes

People who have more money are not necessarily happier—though some are. If anything, money alleviates sadness more than it inspires joy.

It occurred to me all of a sudden, said Amalfitano, it’s a Duchamp idea, leaving a geometry book hanging exposed to the elements to see if it learns something about real life.

And our Divine Parents have been molding God Child’s soul from stardust. And They have been breathing life-breath into its nose, and God Child’s soul has been existing as a Soul of Life.

Whenever we take the focus off ourselves and move it outward, we benefit. Life's most fortunate ironies are that what's best for the long run is best now, and selflessness serves our interests far better than selfishness. The wider our circle of considerations, the more stable we make the world—and the better the prospects for human experience and for all we might wish. The core message of each successive widening: we are one. The geometry of the human voyage is not linear; it's those ripples whose circles expand to encompass self, other, community, Life, and time.

Reverence for the natural environment, and experiencing the interconnectedness between all things has long guided me to create watercolor paintings of beauty and spirit. Life's continuing adventure has led me into an exciting exploration into the wisdom and symbolic imagery of Sacred Geometry. These paintings act as a bridge between this reality and a metaphorical world of healing, continuity, and transformation. I use multiple transparent watercolor glazes coupled with image overlapping techniques, and sacred geometry to produce visions of a multi-dimensional reality. It is my intention to create art that embodies the vibration of Universal Love and expresses the joy and gratitude I feel for the honor of being part of this earthwalk." ~Blessings, Francene~

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.

According to Thoth, because of the placement of the Great Pyramid on the Earth connecting into the Earth's huge geometrical field - specifically the octahedral field of the Earth, which is equivalent to our own fields - and because of the pyramid's mass and the geometries used in it, the white-light energy field spirals upward and becomes extremely strong, stretching all the way out to the center of the galaxy. The dark-light energy comes in from above, spirals through zero point and connects with the center of the Earth. In this way the Great Pyramid connects the center of the Earth to the center of our galaxy.

The rock I'd seen in my life looked dull because in all ignorance I'd never thought to knock it open. People have cracked ordinary New England pegmatite - big, coarse granite - and laid bare clusters of red garnets, or topaz crystals, chrysoberyl, spodumene, emerald. They held in their hands crystals that had hung in a hole in the dark for a billion years unseen. I was all for it. I would lay about me right and left with a hammer, and bash the landscape to bits. I would crack the earth's crust like a piñata and spread to the light the vivid prizes in chunks within. Rock collecting was opening the mountains. It was like diving through my own interior blank blackness to remember the startling pieces of a dream: there was a blue lake, a witch, a lighthouse, a yellow path. It was like poking about in a grimy alley and finding an old, old coin. Nothing was at it seemed. The earth was like a shut eye. Mother's not dead, dear - she's only sleeping. Pry open the thin lid and find a crystalline intelligence inside, a rayed and sidereal beauty. Crystals grew inside rock like arithmetical flowers. They lengthened and spread, adding plane to plane in awed and perfect obedience to an absolute geometry that even the stones - maybe only the stones - understood.

The mathematical order is beautiful precisely because it has no effect on the real world. Life isn't going to be easier, nor is anyone going to make a fortune, just because they know something about prime numbers. Of course, lots of mathematical discoveries have practical applications, no matter how esoteric they may seem. Research on ellipses made it possible to determine the orbits of the planets, and Einstein used non-Euclidean geometry to describe the form of the universe. Even prime numbers were used during the war to create codes—to cite a regrettable example. But those things aren't the goal of mathematics. The only goal is to discover the truth.

In short, what Brown, Enquist, and West are saying is that evolution structured our circulatory systems as fractal networks to approximate a “fourth dimension” so as to make our metabolisms more efficient. As West, Brown, and Enquist put it, “Although living things occupy a three-dimensional space, their internal physiology and anatomy operate as if they were four-dimensional … Fractal geometry has literally given life an added dimension.

On what may be the last page he wrote in his notebooks, Leonardo drew four right triangles with bases of differing lengths (fig. 143). Inside of each he fit a rectangle, and then he shaded the remaining areas of the triangle. In the center of the page he made a chart with boxes labeled with the letter of each rectangle, and below it he described what he was trying to accomplish. As he had done obsessively over the years, he was using the visualization of geometry to help him understand the transformation of shapes. Specifically, he was trying to understand the formula for keeping the area of a right triangle the same while varying the lengths of its two legs. He had fussed with this problem, explored by Euclid, repeatedly over the years. It was a puzzle that, by this point in his life, as he turned sixty-seven and his health faded, might seem unnecessary to solve. To anyone other than Leonardo, it may have been.

One consequence of losing a parent—obvious enough, although it hadn't occurred to me beforehand—is that it reconfigures the rest of your family. All my life, it had been the four of us; to the extent that had ever changed, it had only been joyfully, in the direction of more. But part of mourning my father involved acclimating to a new family geometry, a triangle instead of a square. As a unit, we were smaller, differently balanced, and, at first, unavoidably sadder.

And in between the two, in between the sky and the sea, were all the winds. And there were all the nights and all the moons. To be a castaway is to be a point perpetually at the centre of a circle. However much things may appear to change—the sea may shift from whisper to rage, the sky might go from fresh blue to blinding white to darkest black—the geometry never changes. Your gaze is always a radius. The circumference is ever great. In fact, the circles multiply. To be a castaway is to be caught in a harrowing ballet of circles.

The science of Chaos teaches us that everything is interconnected, but the contemporary developments in neuroscience, getting started with the brain neurons and their multiple connections, reveal the topology of the brain, a miniature of the universal geometry of everything.

People don’t realize how smart bees are, even smarter than dolphins. Bees know enough geometry to make row after row of perfect hexagons, angles so accurate you’d think they used rulers. They take plain flower juice and turn it into something everyone in the world loves to pour on biscuits.

Money was the blood of civilized society, its currents running through everything and everyone. Where money was insufficient, things withered. People starved, sickened and died, constructions eroded, even ideas perished. Where funds were plentiful, the same things blossomed with new life. And money was, in the end, little more than the product of collective imagination. A slip of paper or a coin had no value beyond that of the material it was fashioned of. It only took on a life of its own when people as a whole collectively agreed that certain papers and coins were worth something. Only then did people bleed and die for it. For a fantasy, a faith given form in hard, concrete numbers. Then again, much of society was built on a series of shared delusions. Clothing was little more than scraps of particular materials with particular geometries, but people clung to the idea of fashion. Style. Good and bad fashion was another belief system, one which all members of a culture were indoctrinated into. Breaking certain conventions didn’t only challenge the aesthetic sensibilities of others, but it challenged their sense of self. It reminded them, subconsciously, of the very pretendings they clung to. Only those with power could stand against society’s tides, flaunt the collective’s ‘safe’ aesthetic. When one had enough power, others couldn’t rise against them and safely say something calculated to reduce their own dissonance and remind the offending party of the unspoken rules. When one had enough power to take a life with a twitch of a finger, a thought, they earned the right to wear skin-tight clothing and call themselves Hero, or Legend. To wear a mask and name themselves something inane like ‘the Cockatoo’ and still take themselves seriously.

Sacred shape and colour are the building blocks of creation.  Your Chakras emanate Sacred Shapes – Light Language to build the energy in your Aura, which in turn, is the building block for what happens in your life.  Sacred Geometric shapes and colour are what call physical reality into existence. I

But by 1912, Einstein had come to appreciate that math could be a tool for discovering—and not merely describing—nature’s laws. Math was nature’s playbook. “The central idea of general relativity is that gravity arises from the curvature of spacetime,” says physicist James Hartle. “Gravity is geometry.

Stairs incorporate three pieces of geometry: rise, going, and pitch. The rise is the height between steps, the going is the step itself (technically, the distance between the leading edges, or nosings, of two successive steps measured horizontally), and the pitch is the overall steepness of the stairway.

Richer humans become ensnared in a “luxury trap,” in which formerly unimaginable inventions evolve from mind-blowing to luxuries to taken-for-granted to necessary. I can’t imagine living without a refrigerator or airplanes, but my great-grandparents certainly could. Over time, the amazing becomes normal.

Now suddenly he had intimations of destiny; he could see that life had a secret geometry on which his rational mind had no purchase. But even as he was overcome with a desire to subdue his reason and find happiness, he also sensed that - for the moment at least - his yearning for happiness was not yet strong enough.

The feminine mystique, elevated by Freudian theory into a scientific religion, sounded a single, overprotective, life-restricting, future-denying note for women. Girls who grew up playing baseball, baby-sitting, mastering geometry -- almost independent enough, almost resourceful enough, to meet the problems of the fission-fusion era -- were told by the most advanced thinkers of our time to go back and live their lives as if they were Noras, restricted to the doll's house by Victorian prejudice. And their own respect and awe for the authority of science -- anthropology, sociology, psychology share that authority now -- kept them from questioning the feminine mystique.

Priority one is risk management. It is to protect ourselves from the potential for loss, especially catastrophe. In the human mind, losses weigh much more heavily than gains, so elevating risk management is the right thing to do. This step is about building the proper mindset, one that values avoiding mistakes over demonstrating brilliance.

Simplification is the smart path toward effectively managing expectations. In general terms, met expectations lead to temporary happiness and unmet ones lead to temporary sadness. The human mind is wired to avoid losses more than it is to achieve gains, so minimizing regret is more important in this process than is maximizing future upside.

But in philosophy, he was closer to his contemporary Siddhartha Gautama Buddha (c. 560 – 480 B.C.). Both believed in reincarnation, possibly as an animal, so even an animal could be inhabited by what was once a human soul. Thus, both placed a high value on all life, opposing the common practice of animal sacrifice and preaching strict vegetarianism.

If you are a student, be also a student of the body ... realizing that a broad chest, a muscular pair of arms, and two sinewy legs, will be just as much credit to you, and stand you in hand through your future life, equally with your geometry, your history, your classics, your law, medicine, or divinity. Let nothing divert you from your duty to your body

In the intricate and mutable space-time geometry at the black hole, in-falling matter and energy interacted with the virtualities of the vacuum in ways unknown to the flatter cosmos beyond it. Quasi-stable quantum states appeared, linked according to Schrodinger's wave functions and their own entanglement, more and more of them, intricacy compounding until it amounted to a set of codes. The uncertainty principle wrought mutations; variants perished or flourished; forms competed, cooperated, merged, divided, interacted; the patterns multiplied and diversified; at last, along one fork on a branch of the life tree, thought budded. That life was not organic, animal and vegetable and lesser kingdoms, growing, breathing, drinking, eating, breeding, hunting, hiding; it kindled no fires and wielded no tools; from the beginning, it was a kind of oneness. An original unity differentiated itself into countless avatars, like waves on a sea. They arose and lived individually, coalesced when they chose by twos or threes or multitudes, reemerged as other than they had been, gave themselves and their experiences back to the underlying whole. Evolution, history, lives eerily resembled memes in organic minds. Yet quantum life was not a series of shifting abstractions. Like the organic, it was in and of its environment. It acted to alter its quantum states and those around it: action that manifested itself as electronic, photonic, and nuclear events. Its domain was no more shadowy to it than ours is to us. It strove, it failed, it achieved. They were never sure aboardEnvoy whether they could suppose it loved, hated, yearned, mourned, rejoiced. The gap between was too wide for any language to bridge. Nevertheless they were convinced that it knew something they might as well call emotion, and that that included wondering.

Today we know that there are other solar systems only tens of light years away. Had the Golden Age continued unabated, we might by now have sent probes exploring them. We might have landed on the moon in the year 969 instead of 1969. We might have an understanding of space and life that is unimaginable to us today. Instead, events occurred that would delay the progress begun by the Greeks by a millennium.

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!

This has been my difficulty. The difficulty with my life. Those well-built trig points, those physical determinants of parents, background, school, family, birth, marriage, death, love, work, are themselves as much in motion as I am. What should be stable, shifts. What I am told is solid, slips. The sensible strong ordinary world of fixity is folklore. The earth is not flat. Geometry cedes to algebra. The Greeks were wrong.

. . .biographers tend to regard as character those elements of personality that remain constant, or nearly so, throughout. . .Like practitioners of fractal geometry, biographers seek patterns that persist as one moves from micro- to macro-levels of analysis, and back again. . . . It follows from this that the scale across which we seek similarity need not be chronological. Consider the following incidents in the life of Stalin between 1929 and 1940, arranged not by dates but in terms of ascending horror. Start with the parrot he kept in a cage in his Kremlin apartment. The dictator had the habit of pacing up and down for long periods of time, smoking his pipe, brooding, and occasionally spitting on the floor. One day the parrot tried to mimic Stalin's spitting. He immediately reached into the cage with his pipe and crushed the parrot's head. A very micro-level event, you might well say, so what? But then you learn that Stalin, while on vacation in the Crimea, was once kept awake by a barking dog. It turned out to be a seeing-eye dog that belonged to a blind peasant. The dog wound up being shot, and the peasant wound up in the Gulag. And then you learn that Stalin drove his independently minded second wife, who tried to talk back to him, into committing suicide. And that he arranged for Trotsky, who also talked back, to be assassinated halfway around the world. And that he arranged as well the deaths of as many of Trotsky's associates that he could reach, as well as the deaths of hundred of thousands of other people who never had anything to do with Trotsky. And that when his own people began to talk back by resisting the collectivization of agriculture, he allowed some fourteen million of them to die from the resulting starvation, exile, or imprisonment. Again, there's self-similarity across scale, except that the scale this time is a body count. It's a fractal geometry of terror. Stalin's character extended across time and space, to be sure, but what's most striking about it is its extension across scale: the fact that his behavior seemed much the same in large matters, small matters, and most of those that lay in between.

Do you remember, Meir, that epigram quoted in the name of Rabbi Johanan ben Zaccai: 'There is no truth unless there be a faith on which it may rest'? Ironically enough the only sure principle I have achieved is this which I have known almost all my life. And it is so. For all truths rest ultimately on some act of faith, geometry on axioms, the sciences on the assumptions of the objective existence and orderliness of the world of nature. In every realm one must lay down postulates or he shall have nothing at all. So with morality and religion. Faith and reason are not antagonists. On the contrary, salvation is through the commingling of the two, the former to establish first premises, the latter to purify them of confusion and to draw the fullness of their implications. It is not certainty which one acquires so, only plausibility, but that is the best we can hope for.

Mrs. Reilly looked at her son slyly and asked, “Ignatius, you sure you not a communiss?” “Oh, my God!” Ignatius bellowed. “Every day I am subjected to a McCarthyite witch-hunt in this crumbling building. No! I told you before. I am not a fellow traveler. What in the world has put that into your head?” “I read someplace in the paper where they got plenty communiss at college.” “Well, fortunately I didn’t meet them. Had they crossed my path, they would have been beaten to within an inch of their lives. 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’ve come to believe that there are four enduring sources of a joyful life. I call these Connection, Control, Competence, and Context. Connection is the need to belong. Control is the need to direct one’s own destiny. Competence is the need to be good at something worthwhile. Context is the need for a purpose outside of one’s self. At the nexus of money and meaning the “Four C’s” are what is being underwritten. They sit at the heart of funded contentment. Let’s look at each of these in turn.

Hockey is a club that holds its members tightly, the bond forged by shared hardship and mutual passion, by every trip to the pond, where your feet hurt and your face is cold and you might get a stick in the ribs or a puck in the mouth, and you still can’t wait to get back out there because you are smitten with the sound of blades scraping against ice and pucks clacking off sticks, and with the game’s speed and ever-changing geometry. It has a way of becoming the center of your life even when you’re not on the ice.

Let us wonder, Carole, at the genius of hyperbolic geometry, where the sum of the angles adds up to tales than 180 degrees Let us wonder at how the ancient Egyptians worked out how to measure an irregularly-shaped field Let us wonder how X was just a rare letter until algebra came along and made it something special that can be unraveled to reveal its inner value You see, maths is a process of discovery, Carole, it is like the exploration of space, the planets were always there, it just took us a long time to find them

With this, in a powerful sense, our Question has been answered. The world, insofar as we speak of the world of Chemistry, biology, astrophysics, engineering, and everyday life, does embody beautiful ideas. The Core, which governs those domains, is profoundly rooted in concepts of symmetry and geometry, as we have seen. And it works its will, in quantum theory, through music-like rules. Symmetry really does determine structure. A pure and perfect Music of the Spheres really does animate the soul of reality. Plato and Pythagoras: We salute you!

Grossmann went home to think about the question. After consulting the literature, he came back to Einstein and recommended the non-Euclidean geometry that had been devised by Bernhard Riemann.11 Riemann (1826–1866) was a child prodigy who invented a perpetual calendar at age 14 as a gift for his parents and went on to study in the great math center of Göttingen, Germany, under Carl Friedrich Gauss, who had been pioneering the geometry of curved surfaces. This was the topic Gauss assigned to Riemann for a thesis, and the result would transform not only geometry but physics.

Books. More books than I had ever seen in my life. I gasped and crawled to my knees. I couldn’t breathe. Books galore. Music books, philosophy books. Math books. Geometry. Opera scores, logic. I sobbed and cradled the books. I hugged them to my naked chest and I cried. I smelled them and touched their spines. I remember how violently my fingers shook. I buried my nose in their pages and wept. Never had I ever held so many books in my life. And they were mine. All my very own. The orgasm still riddled my body. It had barely begun to fade. One orgasm ended, but the euphoria was just beginning.

I try to tell the teacher, you know. I don't give a fuck about geometry or English. Like I'm probably going to drive a truck or something when I get out of school. Join the army or something simple. I'm sure in the army they're all going to be wondering what an acute angle is. I'm sure I'll make lots of friends driving my truck because I can diagram some lousy goddamn sentence. And then after school I'm free, right? What's that mean? I go down to the bowling alley or the shopping mall with my friends. We scope the grils, smoke a little doobidge, maybe a tab of acid every now and then. But that's not really living, is it? I mean, if that's living, then excuse me right now. I'll go out and put a bullet in the old brainpan. But if that's not all there is, right, well, maybe there's something I could do a little less radical, like, you know. I don't mind life or anything--I'm perfectly willing to give it a try. So what the hell, I figured. I'm sick of school, drugs, this goddamn oppressive house of Ethel's and all. Maybe it's time I experimented a little more with my life, took a few more chances. So that's when I decided to become a warlock. To master the satanic arts of black magic. Devil worshiping, for you laymen. I want to master what they call the black arts.

A maze is a puzzle to be solved, with twists and turns and dead ends. It requires logical, analytical thinking and usually has a different way out than the way in. The maze could be a metaphor of struggling through life, going one way and then another until the exit takes your by surprise. A maze signifies entrapment, while the labyrinth, with its unicursal path leading into the center and out again the same way, provides enlightenment. It's the process, the journey into your deepest self, your soul, the part where God abides. It's a passive path, a surrender even, to an order and design repeated through creation. A sacred geometry.

Nevertheless he cherished throughout his life the hope of discovering a kind of generalized mathematics, which he called Characteristica Universalis, by means of which thinking could be replaced by calculation. 'If we had it,' he says, 'we should be able to reason in metaphysics and morals in much the same way as in geometry and analysis.' 'If controversies were to arise, there would be no more need of disputation between two philosophers than between two accountants. For it would suffice to take their pencils in their hands, to sit down to their slates, and to say to each other (with a friend as witness, if they liked): Let us calculate.

It is hard to believe that the myths told about Pythagoras did not influence the creation of some of the later stories about Christ. Pythagoras, for instance, was believed by many to be the son of God, in this case, Apollo. His mother was called Parthenis, which means “virgin.” Before traveling to Egypt, Pythagoras lived the life of a hermit on Mount Carmel, like Christ's solitary vigil on the mountain. A Jewish sect, the Essenes, appropriated this myth and is said to have later had a connection to John the Baptist. There is also a myth that Pythagoras returned from the dead, although, according to the story, Pythagoras faked this by hiding in a secret underground chamber.

To do so he used something called a tensor. In Euclidean geometry, a vector is a quantity (such as of velocity or force) that has both a magnitude and a direction and thus needs more than a single simple number to describe it. In non-Euclidean geometry, where space is curved, we need something more generalized—sort of a vector on steroids—in order to incorporate, in a mathematically orderly way, more components. These are called tensors. A metric tensor is a mathematical tool that tells us how to calculate the distance between points in a given space. For two-dimensional maps, a metric tensor has three components. For three-dimensional space, it has six independent components. And once you get to that glorious four-dimensional entity known as spacetime, the metric tensor needs ten independent components.

Kant distinguished between two types of truths: (1) analytic propositions, which derive from logic and “reason itself” rather than from observing the world; for example, all bachelors are unmarried, two plus two equals four, and the angles of a triangle always add up to 180 degrees; and (2) synthetic propositions, which are based on experience and observations; for example, Munich is bigger than Bern, all swans are white. Synthetic propositions could be revised by new empirical evidence, but not analytic ones. We may discover a black swan but not a married bachelor or (at least so Kant thought) a triangle with 181 degrees. As Einstein said of Kant’s first category of truths: “This is held to be the case, for example, in the propositions of geometry and in the principle of causality. These and certain other types of knowledge… do not previously have to be gained from sense data, in other words they are a priori knowledge.” Einstein

One method that Einstein employed to help people visualize this notion was to begin by imagining two-dimensional explorers on a two-dimensional universe, like a flat surface. These “flatlanders” can wander in any direction on this flat surface, but the concept of going up or down has no meaning to them. Now, imagine this variation: What if these flatlanders’ two dimensions were still on a surface, but this surface was (in a way very subtle to them) gently curved? What if they and their world were still confined to two dimensions, but their flat surface was like the surface of a globe? As Einstein put it, “Let us consider now a two-dimensional existence, but this time on a spherical surface instead of on a plane.” An arrow shot by these flatlanders would still seem to travel in a straight line, but eventually it would curve around and come back—just as a sailor on the surface of our planet heading straight off over the seas would eventually return from the other horizon. The curvature of the flatlanders’ two-dimensional space makes their surface finite, and yet they can find no boundaries. No matter what direction they travel, they reach no end or edge of their universe, but they eventually get back to the same place. As Einstein put it, “The great charm resulting from this consideration lies in the recognition that the universe of these beings is finite and yet has no limits.” And if the flatlanders’ surface was like that of an inflating balloon, their whole universe could be expanding, yet there would still be no boundaries to it.10 By extension, we can try to imagine, as Einstein has us do, how three-dimensional space can be similarly curved to create a closed and finite system that has no edge. It’s not easy for us three-dimensional creatures to visualize, but it is easily described mathematically by the non-Euclidean geometries pioneered by Gauss and Riemann. It can work for four dimensions of spacetime as well. In such a curved universe, a beam of light starting out in any direction could travel what seems to be a straight line and yet still curve back on itself. “This suggestion of a finite but unbounded space is one of the greatest ideas about the nature of the world which has ever been conceived,” the physicist Max Born has declared.

Rμv– 1/2 gμv R = 8πTμv The left side of the equation starts with the term Rμv, which is the Ricci tensor he had embraced earlier. The term gμv is the all-important metric tensor, and the term R is the trace of the Ricci tensor called the Ricci scalar. Together, this left side of the equation—which is now known as the Einstein tensor and can be written simply as Gμv—compresses together all of the information about how the geometry of spacetime is warped and curved by objects. The right side describes the movement of matter in the gravitational field. The interplay between the two sides shows how objects curve spacetime and how, in turn, this curvature affects the motion of objects. As the physicist John Wheeler has put it, “Matter tells spacetime how to curve, and curved space tells matter how to move.”83 Thus is staged a cosmic tango, as captured by another physicist, Brian Greene: Space and time become players in the evolving cosmos. They come alive. Matter here causes space to warp there, which causes matter over here to move, which causes space way over there to warp even more, and so on. General relativity provides the choreography for an entwined cosmic dance of space, time, matter, and energy.84 At

One solution might be to liken the path of the light beam through a changing gravitational field to that of a line drawn on a sphere or on a surface that is warped. In such cases, the shortest line between two points is curved, a geodesic like a great arc or a great circle route on our globe. Perhaps the bending of light meant that the fabric of space, through which the light beam traveled, was curved by gravity. The shortest path through a region of space that is curved by gravity might seem quite different from the straight lines of Euclidean geometry. There was another clue that a new form of geometry might be needed. It became apparent to Einstein when he considered the case of a rotating disk. As a disk whirled around, its circumference would be contracted in the direction of its motion when observed from the reference frame of a person not rotating with it. The diameter of the circle, however, would not undergo any contraction. Thus, the ratio of the disk’s circumference to its diameter would no longer be given by pi. Euclidean geometry wouldn’t apply to such cases. Rotating motion is a form of acceleration, because at every moment a point on the rim is undergoing a change in direction, which means that its velocity (a combination of speed and direction) is undergoing a change. Because non-Euclidean geometry would be necessary to describe this type of acceleration, according to the equivalence principle, it would be needed for gravitation as well.

Goodness and Reality being timeless, the best State will be the one which most nearly copies the heavenly model, by having a minimum of change and a maximum of static perfection, and its rulers should be those who best understand the eternal Good. In the second place: Plato, like all mystics, has, in his beliefs, a core of certainty which is essentially incommunicable except by a way of life. The Pythagoreans had endeavoured to set up a rule of the initiate, and this is, at bottom, what Plato desires. If a man is to be a good statesman, he must know the Good; this he can only do by a combination of intellectual and moral discipline. If those who have not gone through this discipline are allowed a share in the government, they will inevitably corrupt it. In the third place: much education is needed to make a good ruler on Plato's principles. It seems to us unwise to have insisted on teaching geometry to the younger Dionysius, tyrant of Syracuse, in order to make him a good king, but from Plato's point of view it was essential. He was sufficiently Pythagorean to think that without mathematics no true wisdom is possible. This view implies an oligarchy. In the fourth place: Plato, in common with most Greek philosophers, took the view that leisure is essential to wisdom, which will therefore not be found among those who have to work for their living, but only among those who have independent means or who are relieved by the State from anxieties as to their subsistence. This point of view is essentially aristocratic.

The result was not nearly as vivid to the layman as, say, E=mc2. Yet using the condensed notations of tensors, in which sprawling complexities can be compressed into little subscripts, the crux of the final Einstein field equations is compact enough to be emblazoned, as it indeed often has been, on T-shirts designed for proud physics students. In one of its many variations,82 it can be written as: Rμv– 1/2 gμv R = 8πTμv The left side of the equation starts with the term Rμv, which is the Ricci tensor he had embraced earlier. The term gμv is the all-important metric tensor, and the term R is the trace of the Ricci tensor called the Ricci scalar. Together, this left side of the equation—which is now known as the Einstein tensor and can be written simply as Gμv—compresses together all of the information about how the geometry of spacetime is warped and curved by objects. The right side describes the movement of matter in the gravitational field. The interplay between the two sides shows how objects curve spacetime and how, in turn, this curvature affects the motion of objects. As the physicist John Wheeler has put it, “Matter tells spacetime how to curve, and curved space tells matter how to move.”83 Thus is staged a cosmic tango, as captured by another physicist, Brian Greene: Space and time become players in the evolving cosmos. They come alive. Matter here causes space to warp there, which causes matter over here to move, which causes space way over there to warp even more, and so on. General relativity provides the choreography for an entwined cosmic dance of space, time, matter, and energy.

Schools, gymnasiums, arithmetic, geometry, history, rhetoric, physics, biology, anatomy, hygiene, therapy, cosmetics, poetry, music, tragedy, comedy, philosophy, theology, agnosticism, skepticism, stoicism, epicureanism, ethics, politics, idealism, philanthropy, cynicism, tyranny, plutocracy, democracy: these are all Greek words for cultural forms seldom originated, but in many cases first matured for good or evil by the abounding energy of the Greeks. All the problems that disturb us today—the cutting down of forests and the erosion of the soil; the emancipation of woman and the limitation of the family; the conservatism of the established, and the experimentalism of the unplaced, in morals, music, and government; the corruptions of politics and the perversions of conduct; the conflict of religion and science, and the weakening of the supernatural supports of morality; the war of the classes, the nations, and the continents; the revolutions of the poor against the economically powerful rich, and of the rich against the politically powerful poor; the struggle between democracy and dictatorship, between individualism and communism, between the East and the West—all these agitated, as if for our instruction, the brilliant and turbulent life of ancient Hellas. There is nothing in Greek civilization that does not illuminate our own. We shall try to see the life of Greece both in the mutual interplay of its cultural elements, and in the immense five-act drama of its rise and fall. We shall begin with Crete and its lately resurrected civilization, because apparently from Crete, as well as from Asia, came that prehistoric culture of Mycenae

My bedroom is separated from the main body of my house so that I have to go outside and cross some pseudo-Japanese stepping stones in order to go to sleep at night. Often I get rained on a little bit on my way to bed. It’s a benediction. A good night kiss. Romantic? Absolutely. And nothing to be ashamed of. If reality is a matter of perspective, then the romantic view of the world is as valid as any other - and a great deal more rewarding. It makes of life and unpredictable adventure rather that a problematic equation. Rain is the natural element for romanticism. A dripping fir is a hundred times more sexy than a sunburnt palm tree, and more primal and contemplative, too. A steady, wind-driven rain composed music for the psyche. It not only nurtures and renews, it consecrates and sanctifies. It whispers in secret languages about the primordial essence of things. Obviously, then, the Pacific Northwest's customary climate is perfect for a writer. It's cozy and intimate. Reducing temptation (how can you possibly play on the beach or work in the yard?), it turns a person inward, connecting them with what Jung called "the bottom below the bottom," those areas of the deep unconscious into which every serious writer must spelunk. Directly above my writing desk there is a skylight. This is the window, rain-drummed and bough-brushed, through which my Muse arrives, bringing with her the rhythms and cadences of cloud and water, not to mention the latest catalog from Victoria's Secret and the twenty-three auxiliary verbs. Oddly enough, not every local author shares my proclivity for precipitation. Unaware of the poetry they're missing, many malign the mist as malevolently as they non-literary heliotropes do. They wring their damp mitts and fret about rot, cursing the prolonged spillage, claiming they're too dejected to write, that their feet itch (athlete's foot), the roof leaks, they can't stop coughing, and they feel as if they're slowly being digested by an oyster. Yet the next sunny day, though it may be weeks away, will trot out such a mountainous array of pagodas, vanilla sundaes, hero chins and god fingers; such a sunset palette of Jell-O, carrot oil, Vegas strip, and Kool-Aid; such a sea-vista display of broad waters, firred islands, whale spouts, and boat sails thicker than triangles in a geometry book, that any and all memories of dankness will fizz and implode in a blaze of bedazzled amnesia. "Paradise!" you'll hear them proclaim as they call United Van Lines to cancel their move to Arizona.

In any event, Socrates’ proof of prenatal immortality is that one of Meno’s uneducated slave boys actually comes up with the Pythagorean theorem without ever having studied geometry! Therefore, he must be remembering it. You recall that theorem: in a right triangle, the square of the hypotenuse is equal to the sum of the squares of the other two sides. Huh? We can barely remember that from tenth grade, let alone from before we were born.

Andrew’s kissing Amanda again, her back pinned against the door frame, his hands working through a geometry problem where the goal is to find the point of intersection where two legs bisect. People would like math so much more if it involved real life like that.

However, the answer can be inferred from the WMAP data, by measuring the sizes of the temperature fluctuations—the hot and cold (light and dark) splotches in Figure 3 ([>]). Before WMAP was launched, theorists had already worked out how big the physical sizes of the strongest fluctuations should be. Converting that into apparent angular size in the sky depends on the geometry of space: if the universe is positively curved, it would make the angles appear larger, while negative curvature would make them smaller. If the universe is geometrically flat (that is, has Euclidean geometry), the angular size of the strongest hot and cold fluctuations should be about 1° across. The results that flowed back from the satellite were definitive.14 The fluctuations were very close to 1° in size, a result confirmed by ground-based and balloon-based experiments. Cosmologists then declared that to within observational accuracy of about 2 percent, space is flat.15

No, I'm no patriot, nor was I ever allowed to be. And yet, the country of my childhood lives within me with a primacy that is a form of love. It lives within me despite my knowledge of our marginality, and its primitive, unpretty emotions. Is it blind and self-deceptive of me to hold on to its memory? I think it would be blind and self-deceptive not to. All it has given me is the world, but that is enough. It has fed me language, perceptions, sounds, the human kind. It has given me the colors and the furrows of reality, my first loves. The absoluteness of those loves can never be recaptured: no geometry of the landscape, no haze in the air, will live in us as intensely as the landscapes that we saw as the first, and to which we gave ourselves wholly, without reservations. Later, of course, we learn how to be more parsimonious; how to parse ourselves into constituent elements, how to be less indiscriminate and foolish in our enthusiasms. But if we're not to risk falling into that other absurd, in which we come unpeeled from all the objects of the world, and they all seem equally two-dimensional and stale, we must somehow preserve the memory and possibility of our childish, absurd affections. Insofar as we retain the capacity for our attachment, the energy of desire that draws us toward the world and makes us want to live within it, we're always returning. All we have to draw on is that first potent furnace, the uncomparing, ignorant love, the original heat and hunger for the forms of the world, for the here and now.

Chris Argyris, professor emeritus at Harvard Business School, wrote a lovely article in 1977,191 in which he looked at the performance of Harvard Business School graduates ten years after graduation. By and large, they got stuck in middle management, when they had all hoped to become CEOs and captains of industry. What happened? Argyris found that when they inevitably hit a roadblock, their ability to learn collapsed: What’s more, those members of the organization that many assume to be the best at learning are, in fact, not very good at it. I am talking about the well-educated, high-powered, high-commitment professionals who occupy key leadership positions in the modern corporation.… Put simply, because many professionals are almost always successful at what they do, they rarely experience failure. And because they have rarely failed, they have never learned how to learn from failure.… [T]hey become defensive, screen out criticism, and put the “blame” on anyone and everyone but themselves. In short, their ability to learn shuts down precisely at the moment they need it the most.192 [italics mine] A year or two after Wave, Jeff Huber was running our Ads engineering team. He had a policy that any notable bug or mistake would be discussed at his team meeting in a “What did we learn?” session. He wanted to make sure that bad news was shared as openly as good news, so that he and his leaders were never blind to what was really happening and to reinforce the importance of learning from mistakes. In one session, a mortified engineer confessed, “Jeff, I screwed up a line of code and it cost us a million dollars in revenue.” After leading the team through the postmortem and fixes, Jeff concluded, “Did we get more than a million dollars in learning out of this?” “Yes.” “Then get back to work.”193 And it works in other settings too. A Bay Area public school, the Bullis Charter School in Los Altos, takes this approach to middle school math. If a child misses a question on a math test, they can try the question again for half credit. As their principal, Wanny Hersey, told me, “These are smart kids, but in life they are going to hit walls once in a while. It’s vital they master geometry, algebra one, and algebra two, but it’s just as important that they respond to failure by trying again instead of giving up.” In the 2012–2013 academic year, Bullis was the third-highest-ranked middle school in California.194

Beautiful Things always come with Simple Equations.

Much of our intellectual development is the story of how we learn to sort impressions: self or environment, rocks, trees, clouds, books, cats. It is a story of how we learn to judge and recognize colors, numbers, shapes, and abstract concepts. When we learn a new category, our internal model of the world rotates - often slightly, occasionally more.... Some shifts are emotional: holding a newborn in your hands and understanding just what a rich and varied life will come to this tiny seed of an individual, looking into the eyes of an animal and recognizing a kinship despite having traveled very different evolutionary paths. Some shifts are abstract: learning the crystalline pure beauty of a geometric proof's logic. Fractal geometry also represents a shift, both emotional and abstract...

Here’s a summary of our predicaments: We have more responsibility for our financial lives than ever before. We are uncomfortable talking and learning about money. We are living considerably longer, prolonging all of these problems. Our brains are hardwired to make lousy financial decisions. An unprecedented amount of information and choice makes decision-making harder. Many people are financially fragile. Our earnings and savings potential is less than it once was. Outsized investment returns are unlikely, so the market will not save us. This is not a good state of affairs. But as so many of us like to say when confronted with a tough situation: It is what it is. We carry on. Let’s now see what we can do about it. 1

Kahneman’s terms, “what you see is all there is.” One of the ironies of our brain wiring is that the need to make the world feel safe and sensible can lead to poor decision-making.