Intersecting Lines Quotes

The desire to go home that is a desire to be whole, to know where you are, to be the point of intersection of all the lines drawn through all the stars, to be the constellation-maker and the center of the world, that center called love. To awaken from sleep, to rest from awakening, to tame the animal, to let the soul go wild, to shelter in darkness and blaze with light, to cease to speak and be perfectly understood.

No single decision you ever made has led in a straight line to where you find yourself now. You peeked down some roads and took a few steps before turning back. You followed some roads that came to a dead end and others that got lost at too many intersections. Ultimately, all roads are connected to all other roads.

When two people are in love, they are parrallel lines. That intersect. Together but seperate. Infinity.

If what's always distinguished bad writing--flat characters, a narrative world that's clichéd and not recognizably human, etc.--is also a description of today's world, then bad writing becomes an ingenious mimesis of a bad world. If readers simply believe the world is stupid and shallow and mean, then [Bret] Ellis can write a mean shallow stupid novel that becomes a mordant deadpan commentary on the badness of everything. Look man, we'd probably most of us agree that these are dark times, and stupid ones, but do we need fiction that does nothing but dramatize how dark and stupid everything is? In dark times, the definition of good art would seem to be art that locates and applies CPR to those elements of what's human and magical that still live and glow despite the times' darkness. Really good fiction could have as dark a worldview as it wished, but it'd find a way both to depict this world and to illuminate the possibilities for being alive and human in it. Postmodern irony and cynicism's become an end in itself, a measure of hip sophistication and literary savvy. Few artists dare to try to talk about ways of working toward redeeming what's wrong, because they'll look sentimental and naive to all the weary ironists. Irony's gone from liberating to enslaving. There's some great essay somewhere that has a line about irony being the song of the prisoner who's come to love his cage… The postmodern founders' patricidal work was great, but patricide produces orphans, and no amount of revelry can make up for the fact that writers my age have been literary orphans throughout our formative years. We enter a spiritual puberty where we snap to the fact that the great transcendent horror is loneliness, excluded encagement in the self. Once we’ve hit this age, we will now give or take anything, wear any mask, to fit, be part-of, not be Alone, we young. The U.S. arts are our guide to inclusion. A how-to. We are shown how to fashion masks of ennui and jaded irony at a young age where the face is fictile enough to assume the shape of whatever it wears. And then it’s stuck there, the weary cynicism that saves us from gooey sentiment and unsophisticated naïveté. Sentiment equals naïveté on this continent. You burn with hunger for food that does not exist. A U. S. of modern A. where the State is not a team or a code, but a sort of sloppy intersection of desires and fears, where the only public consensus a boy must surrender to is the acknowledged primacy of straight-line pursuing this flat and short-sighted idea of personal happiness.

If only,’ Shiroyama dreams, ‘human beings were not masks behind masks behind masks. If only this world was a clean board of lines and intersections. If only time was a sequence of considered moves and not a chaos of slippages and blunders.

If on a winter's night a traveler, outside the town of Malbork, leaning from the steep slope without fear of wind or vertigo, looks down in the gathering shadow in a network of lines that enlace, in a network of lines that intersect, on the carpet of leaves illuminated by the moon around an empty grave-What story down there awaits its end?-he asks, anxious to hear the story.

If you find the dividing line between fairy tales and reality, let me know. In my mind, the two run together, even though the intersections aren't always obvious. The girl sitting quietly in class or waiting for the bus or roaming the mall doesn't want anyone to know, or doesn't know how to tell anyone, that she is locked in a tower. Maybe she's a prisoner of a story she's heard all her life- that fairest means best, or that bruises prove she is worthy of love.

The Crone, the Reaper... She is the Dark Moon, what you don't see coming at you, what you don't get away with, the wind that whips the spark across the fire line. Chance, you could say, or, what's scarier still: the intersection of chance with choices and actions made before. The brush that is tinder dry from decades of drought, the warming of the earth's climate that sends the storms away north, the hole in the ozone layer. Not punishment, not even justice, but consequence.

A U.S. of modern A. where the State is not a team or a code, but a sort of sloppy intersection of desires and fears, where the only public consensus a boy must surrender to is the acknowledged primacy of straight-line pursuing this flat and short-sighted idea of personal happiness.

But genius, and even great talent, springs less from seeds of intellect and social refinement superior to those of other people than from the faculty of transforming and transposing them. To heat a liquid with an electric lamp requires not the strongest lamp possible, but one of which the current can cease to illuminate, can be diverted so as to give heat instead of light. To mount the skies it is not necessary to have the most powerful of motors, one must have a motor which, instead of continuing to run along the earth's surface, intersecting with a vertical line the horizontal line which it began by following, is capable of converting its speed into lifting power. Similarly, the men who produce works of genius are not those who live in the most delicate atmosphere, whose conversation is the most brilliant or their culture the most extensive, but those who have had the power, ceasing suddenly to live only for themselves, to transform their personality into a sort of mirror, in such a way that their life, however mediocre it may be socially and even, in a sense, intellectually, is reflected by it, genius consisting in reflecting power and not int he intrinsic quality of the scene reflected.

There must be some other possibility than death or lifelong penance ... some meeting, some intersection of lines; and some cowardly, hopeful geometer in my brain tells me it is the angle at which two lines prop each other up, the leaning-together from the vertical which produces the false arch. For lack of a keystone, the false arch may be as much as one can expect in this life. Only the very lucky discover the keystone.

His thoughts were hemmed in. One can only draw curved lines on the terrestrial sphere which, as they extend, forever meet with themselves. At such intersections we always encounter what we have already seen.

I was born on the boundary line between cold and hot, at the intersection of the two elements that make a clap of thunder.

In our UN-VICE world (UNknown, Volatile, Intersecting, Complex & Exponential), the lines between the present and future are becoming blurred, more liminal.

We all draw different lines. Sometimes they intersect. Sometimes they don’t. We agree on forms of evil, but judge degrees of it, saying only the worst of humanity is truly bad. And everything along the grey lines is subject to opinion.

He is only happy when he can maintain himself - mentally and spiritually - at the intersection between a vertical line and horizontal one, in a state of perfect balance. For this, he needs to know where he is located every moment, both in his relationship to the divine and to his family here on earth. If he loses that balance, he loses his power.

We were born to walk this world in intersecting lines.

What do you mean, 'Angle of Repose?' she asked me when I dreamed we were talking about Grandmother's life, and I said it was the angle at which a man or woman finally lies down. I suppose it is; and yet ... I thought when I began, and still think, that there was another angle in all those years when she was growing old and older and very old, and Grandfather was matching her year for year, a separate line that did not intersect with hers. They were vertical people, they lived by pride, and it is only by the ocular illusion of perspective that they can be said to have met. But he had not been dead two months when she lay down and died too, and that may indicate that at that absolute vanishing point they did intersect. They had intersected for years, for more than he especially would ever admit.

Such is life, imaginary or otherwise: a continuous parting of ways, a constant flux of approximation and distanciation, lines of fate intersecting at a point which is no-time, a theoretical crossroads fictitiously 'present,' an unstable ice floe forever drifting between was and will be.

We see that in the organic world, to the same degree that reflection gets darker and weaker, grace grows ever more radiant and dominant. But just as two lines intersect on one side of a point, and after passing through infinity, suddenly come together again on the other side; or the image in a concave mirror suddenly reappears before us after drawing away into the infinite distance, so too, does grace return once perception, as it were, has traversed the infinite--such that it simultaneously appears the purest in human bodily structures that are either devoid of consciousness or which possess an infinite consciousness, such as in the jointed manikin or the god.

If only human beings were not masks behind masks behind masks. If only this world was a clean board of lines and intersections. If only time was a sequence of considered moves and not a chaos of slippages and blunders.

A U.S. of modern A. where the State is not a team or a code, but a sort of sloppy intersection of desires and fears, where the only public consensus a boy must surrender to is the acknowledged primacy of straight-line pursuing this flat and short-sighted idea of personal happiness:

Here are the words that have brought me to a new understanding. Here are the words that will bind us forever. From this day forward, I will speak your name with gratitude, knowing it is the mantra of my soul. I will let you go, knowing we are eternal. We were born to walk this world in intersecting lines. We are circles and signposts and parallels. I have left markers for you at every turn. Look for me in everything that catches your breath. Let the simple miracle of your own presence overwhelm you. For you are beautiful, in ways that can't be described. And we are love at its most inexplicable. With these words, I am one with divinity. With these words, I am one with you.

We act as if there is a single traffic light, red or green. But sex is a road lined with intersections, which way to go, when to slow down, to yield, to stop, to speed up.

There's the imperative to keep secrets, and the imperative to have them known. How do you know that you're a person, distinct from other people? By keeping certain things to yourself. You guard them inside you, because, if you don't, there's no distinction between inside and outside. Secrets are the way you know you even have an inside. A radical exhibitionist is a person who has forfeited his identity. But identity in a vacuum is also meaningless. Sooner or later, the inside of you needs a witness. Otherwise you're just a cow, a cat, a stone, a thing in the world, trapped in your thingness. To have an identity, you have to believe that other identities equally exist. You need closeness with other people. And how is closeness built? By sharing secrets. . . . Your identity exists at the intersection of these lines of trust.

In this he was like most Midwesterners. Directions are very important to them. They have an innate need to be oriented, even in their anecdotes. Any story related by a Midwesterner will wander off at some point into a thicket of interior monologue along the lines of "We were staying at a hotel that was eight blocks northeast of the state capital building. Come to think of it, it was northwest. And I think it was probably more like nine blocks. And this woman without any clothes on, naked as the day she was born except for a coonskin cap, came running at us from the southwest... or was it the southeast?" If there are two Midwesterns present and they both witnessed the incident, you can just about write off the anecdote because they will spend the rest of the afternoon arguing points of the compass and will never get back to the original story. You can always tell a Midwestern couple in Europe because they will be standing on a traffic island in the middle of a busy intersection looking at a windblown map and arguing over which way is west. European cities, with their wandering streets and undisciplined alleys, drive Midwesterners practically insane.

Time has no meaning, space and place have no meaning, on this journey. All times can be inhabited, all places visited. In a single day the mind can make a millpond of the oceans. Some people who have never crossed the land they were born on have travelled all over the world. The journey is not linear, it is always back and forth, denying the calender, the wrinkles and lines of the body. The self is not contained in any moment or any place, but it is only in the intersection of moment and place that the self might, for a moment, be seen vanishing through a door, which disappears at once.

When rationality begins to break down, the circuits of the human brain can overload. Axons grow bright and feverish. Hallucinations turn real: the quicksilver puddle at the point where perspective makes parallel lines seem to intersect is really there; the dead walk and talk; a rose begins to sing.

Our world, seemingly global, is in reality a planet of thousands of the most varied and never intersecting provinces. A trip around the world is a journey from backwater to backwater, each of which considers itself, in its isolation, a shining star. For most people, the real world ends on the threshold of their house, at the edge of their village, or, at the very most, on the border of their valley. That, which is beyond is unreal, unimportant, and even useless, whereas that which we have at our fingertips, in our field of vision, expands until it seems an entire universe, overshadowing all else. Often, the native and the newcomer have difficulty finding a common language, because each looks at the same place through a different lens. The newcomer has a wide-angle lens, which gives him a distant diminished view, although with a long horizon line, while the local always employs a telescopic lens that magnifies the slightest detail.

I started thinking about how to draw her, how I’d capture all the things I saw in just those few moments that our lives intersected. Faces are so hard because they are more than lines and shadows. They are about light, but a light that comes from inside and shines out.

Unclaimed or abandoned bodies. There could be no stronger definition of loneliness.

The tragedy of man is the difference between what he can be, and what he is.

Truth is an illusionary ideal, a structure with a foundation of opinion, garnished by selected facts, eroded over time and rebuilt new every generation.

He pulled out a short-barreled pistol from the drawer and placed it on the desktop. It was not what he was looking for. The pistol might have been a stapler for all he noticed.

We stared at each other, bound by common experience, but each looking at the other through the steady crosshairs of inherent distrust.

Love may come more than once, but there is only one first love. The only time there is nothing to compare it to. Every subsequent love has to deal with the ghost of the first.

Civilization is diaphanous: a dazzling display, beautiful, a brilliant golden orb of order and geometric precision. But just touch it lightly and see toward you what evil things crawl.

U.S. of modern A. where the State is not a team or a code, but a sort of sloppy intersection of desires and fears, where the only public consensus a boy must surrender to is the acknowledged primacy of straight-line pursuing this flat and short-sighted idea of personal happiness:

God can turn any negative of life into a positive. If life takes us into the minus of negative experiences, heaven sends down a vertical line to intersect it and make all things positive. Let

But I can stop on any corner at the intersection of two busy streets, and before me are thousands of lives headed in all four directions, uptown downtown east and west, on foot, on bikes, on in-line skates, in buses, strollers, cars, trucks, with the subway rumble underneath my feet... and how can I not know I am momentarily part of the most spectacular phenomenon in the unnatural world? ...The city may begin from a marketplace, a trading post, the confluence of waters, but it secretly depends on the human need to walk among strangers.

A U.S. of modern A. where the State is not a team or a code, but a sort of sloppy intersection of desires and fears, where the only public consensus a boy must surrender to is the acknowledged primacy of straight-line pursuing this flat and short-sighted idea of personal happiness: The happy pleasure of the person alone, yes?

Books said nothing for a few minutes. Then, gazing out over the water, watching a sailboat heeled over, cutting across the bay, he asked, “What next?” I said evenly, “I’m going to kill the two men who murdered Carolyn.

Take a moment. What was it you saw when you were moved to pick up the camera? I'm going to pretend I didn't hear you mutter something about thinking "it looked cool." Dig deeper. Was it a thought, a feeling, a simple moment when your eyes did a double-take at the intersection of two lines? Was it a lick of light, two blocks of color?

No story, including this one, is a straight line unraveling smoothly from start to finish. Every story is a tangle of stories within stories within stories, so that a solitary life is part of the web of the world's history, where lives meet and intersect and where individual stories cross at places and times that send the whole design moving off into different directions.

Two years, I thought. Two years living wrapped in vicious guilt, self-doubt, and rage. No truth to salve the wounds, only the steady application of alcohol. But now Books, and now this mystery man. The self-doubt vanished. The guilt and rage remained.

I climbed aboard and took it in my hand, not realizing that I would keep it and view it several thousand times over the years. I would watch the places where we intersect, and marvel at what the girl saw and how she survived. That is the best I can do- watch it fall into line with everything else I spectated during that time.

When a body is acted upon by external forces besides its weight it tips over on one side of the base if the (so-called) weight (vector) acts along a line through the so-called center-of-mass that intersects the supporting surface outside the base of the body; in the case of a stable equilibrium, the weight vector points inside the base, in the case of an unstable equilibrium it points exactly toward the tilting edge of the base, "tilting edge of the base" underlined. We always went to far, so Roithamer, so we were always pushing toward the extreme limit. But we never thrust ourselves beyond it. Once I have thrust myself beyond it, it's all over, so Roithamer, "all" underlined. We're always set toward the predetermined moment, "predetermined moment" underlined. When that moment has come, we don't know that it has come, but it is the right moment. We can exist at the heighest degree of intensity as long as we live, so Roithamer (June 7). The end is no process. Clearing.

Imagine a pulsating plane of light-that-is-not-light warping in from a direction that can’t be pointed to and finally intersecting with the horizon line of your own vision.

There are places in New York where the city's anarchic, unaccommodating spirit, its fundamental, irrepressible aimlessness and heedlessness have found especially firm footholds. Certain transfers between subway lines, passageways of almost transcendent sordidness; certain sites of torn-down buildings where parking lots have silently sprung up like fungi; certain intersections created by illogical confluences of streets--these express with particular force the city's penchant for the provisional and its resistance to permanence, order, closure.

If on a winter's night a traveler, outside the town of Malbork, leaning from the steep slope without fear of wind or vertigo, looks down in the gathering shadow in a network of lines that enlace, in a network of lines that intersect, on the carpet of leaves illuminated by the moon around an empty grave-What story down there awaits its end? - he asks, anxious to hear the story.

Almondine To her, the scent and the memory of him were one. Where it lay strongest, the distant past came to her as if that morning: Taking a dead sparrow from her jaws, before she knew to hide such things. Guiding her to the floor, bending her knee until the arthritis made it stick, his palm hotsided on her ribs to measure her breaths and know where the pain began. And to comfort her. That had been the week before he went away. He was gone, she knew this, but something of him clung to the baseboards. At times the floor quivered under his footstep. She stood then and nosed into the kitchen and the bathroom and the bedroom-especially the closet-her intention to press her ruff against his hand, run it along his thigh, feel the heat of his body through the fabric. Places, times, weather-all these drew him up inside her. Rain, especially, falling past the double doors of the kennel, where he’d waited through so many storms, each drop throwing a dozen replicas into the air as it struck the waterlogged earth. And where the rising and falling water met, something like an expectation formed, a place where he might appear and pass in long strides, silent and gestureless. For she was not without her own selfish desires: to hold things motionless, to measure herself against them and find herself present, to know that she was alive precisely because he needn’t acknowledge her in casual passing; that utter constancy might prevail if she attended the world so carefully. And if not constancy, then only those changes she desired, not those that sapped her, undefined her. And so she searched. She’d watched his casket lowered into the ground, a box, man-made, no more like him than the trees that swayed under the winter wind. To assign him an identity outside the world was not in her thinking. The fence line where he walked and the bed where he slept-that was where he lived, and they remembered him. Yet he was gone. She knew it most keenly in the diminishment of her own self. In her life, she’d been nourished and sustained by certain things, him being one of them, Trudy another, and Edgar, the third and most important, but it was really the three of them together, intersecting in her, for each of them powered her heart a different way. Each of them bore different responsibilities to her and with her and required different things from her, and her day was the fulfillment of those responsibilities. She could not imagine that portion of her would never return. With her it was not hope, or wistful thoughts-it was her sense of being alive that thinned by the proportion of her spirit devoted to him. "ory of Edgar Sawtelle" As spring came on, his scent about the place began to fade. She stopped looking for him. Whole days she slept beside his chair, as the sunlight drifted from eastern-slant to western-slant, moving only to ease the weight of her bones against the floor. And Trudy and Edgar, encapsulated in mourning, somehow forgot to care for one another, let alone her. Or if they knew, their grief and heartache overwhelmed them. Anyway, there was so little they might have done, save to bring out a shirt of his to lie on, perhaps walk with her along the fence line, where fragments of time had snagged and hung. But if they noticed her grief, they hardly knew to do those things. And she without the language to ask.

These types of magical essences tend to be drawn toward each other and then form into rivers of power, called ley lines. Sometimes these lines of power intersect, creating nodes called places of power.

It's amazing how two people can meet without really seeing each other at all, and if geometry does not recognize that two parallel lines can intersect, it's only because mathematicians do not visit enough alleys.

Though I have no kids and Hollywood doesn’t exist, I firmly believe, however, that it did exist. And like Rome, we are living amidst the fallen columns and clothes-lined courtyards, in the ruins of an empire of the self-enchanted which was once, briefly, more devastating than Caesar’s and still brings respectable families to a hot, windy intersection in August to sigh with unnoticed despondence, “…Well…here we are…Hollywood and Vine.

I can line up these moments of violence, precariously as dominoes. Sometimes I worry they will all fall; knocking each other down, knocking me down. Sometimes they do. Violence left me hollow. It left me enraged. It left me desperately needing to leave a body I couldn't trust. But most frustrating of all, violence left me too wounded to claim the space I needed in order to find fulfillment in the arms, heart, and body of a queer relationship.

There's the imperative to keep secrets, and the imperative to have them known. How do you know that you're a person, distinct from other people? By keeping certain things to yourself. You guard them inside you, because, if you don't, there's no distinction between inside and outside. Secrets are the way you know you even have an inside. A radical exhibitionist is a person who has forfeited his identity. But identity in a vacuum is also meaningless. Sooner or later, the inside of you needs a witness. Otherwise you're just a cow, a cat, a stone, a thing in the world, trapped in your thingness. To have an identity, you have to believe that other identities equally exist. You need closeness with other people. And how is closeness built? By sharing secrets. Colleen knows what you secretly think of Willow. You know what Colleen secretly thinks of Flor. Your identity exists at the intersection of these lines of trust.

If only, Shiroyama dreams, human beings were not masks behind masks behind masks. If only this world was a clean board of lines and intersections. If only time was a sequence of considered moves and not a chaos of slippages and blunders.

Anyone who comes in contact with you will have something common with you. If two lines have intersected at a point, of course they were moving towards the same direction- in the direction of the intersection point. Therefore, marrying someone just because there is something common is a wrong idea. After the intersection, the lines move more and more apart from each other. To move together after the intersection, both of you have to sacrifice things that are not common between you.

What I have observed of the pond is no less true in ethics. ... Such a rule ... draws lines through the length and breadth of the aggregate of a man's particular daily behaviors ... where they intersect will be the height or depth of his character.

She and Harriet Warner were worlds apart not only in looks, but also their place on earth–a monarch butterfly and a luna moth. Each had been dropped into lives that were polar opposites, traveling along different longitudes lines destined never to intersect.

The pivotal question throughout the trial was whether or not consent was issued. Yes or no. We act as if there is a single traffic light, red or green. But sex is a road lined with intersections, which way to go, when to slow down, to yield, to stop, to speed up.

Beyond the light was that distant line of horizon she had glimpsed from on high—a line like a solitary prison bar, needing no intersection with other bars to keep her jailed. And she decided then and there that she would not stay here and be mocked; she would not.

I realized with fresh horror that new doors of perception were opening up inside. New? Not so. OLD doors of perception. The perception of a child who has not yet learned to protect itself by developing the tunnel vision that keeps out ninety percent of the universe. Children see everything their eyes happen upon, hear everything in their ears' range. But if life is the rise of consciousness…, then it is also the reduction of input. Terror is the widening of perspective and perception. The horror was in knowing I was swimming down to a place most of us leave when we get out of diapers and into training pants. I could see it on Ollie's face, too. When rationality begins to break down, the circuits of the human brain can overload. Axons grow bright and feverish. Hallucinations turn real: the quicksilver puddle at the point where perspective makes parallel lines seem to intersect is really there; the dead walk and talk; a rose begins to sing.

U.S. of modern A. where the State is not a team or a code, but a sort of sloppy intersection of desires and fears, where the only public consensus a boy must surrender to is the acknowledged primacy of straight-line pursuing this flat and short-sighted idea of personal happiness: ‘The happy pleasure of the person alone, yes?

The next customer in line was a white woman who had purchased a set of baby’s pajamas for her pregnant sister. “Men,” the customer said. “Who can understand the way their minds work?” Mother knew what the lady was talking about, but she couldn’t laugh at a black man with her, even though she was only laughing at him for being a man.

Intersections of lines, for example, remain intersections, and the hole in a torus (doughnut) cannot be transformed away. Thus a doughnut may be transformed topologically into a coffee cup (the hole turning into a handle) but never into a pancake. Topology, then, is really a mathematics of relationships, of unchangeable, or “invariant,” patterns.

All pulpits must passionately declare Christ to be the eternal Son of the living God, the only Savior of sinners. All preaching must boldly announce Him as the reigning Lord of heaven and earth. He must be fearlessly announced as the One before whom every knee will bow and every tongue will confess. All preaching must assert that this Jesus is the final Judge of every human life. To fulfill this sacred duty, every preacher must proclaim the full counsel of God. Every doctrine in Scripture must be delivered. Every truth must be taught. Every sin must be exposed. Every warning must be issued. And every promise must be offered. If God is to bless our preaching, the supreme majesty of Jesus Christ Himself must be expounded in our sermons. All the lines of our preaching must intersect at this highest pinnacle—Jesus Christ and Him crucified.

Wars and chaoses and paradoxes ago, two mathematicians between them ended an age d began another for our hosts, our ghosts called Man. One was Einstein, who with his Theory of Relativity defined the limits of man's perception by expressing mathematically just how far the condition of the observer influences the thing he perceives. ... The other was Goedel, a contemporary of Eintstein, who was the first to bring back a mathematically precise statement about the vaster realm beyond the limits Einstein had defined: In any closed mathematical system--you may read 'the real world with its immutable laws of logic'--there are an infinite number of true theorems--you may read 'perceivable, measurable phenomena'--which, though contained in the original system, can not be deduced from it--read 'proven with ordinary or extraordinary logic.' Which is to say, there are more things in heaven and Earth than are dreamed of in your philosophy, Horatio. There are an infinite number of true things in the world with no way of ascertaining their truth. Einstein defined the extent of the rational. Goedel stuck a pin into the irrational and fixed it to the wall of the universe so that it held still long enough for people to know it was there. ... The visible effects of Einstein's theory leaped up on a convex curve, its production huge in the first century after its discovery, then leveling off. The production of Goedel's law crept up on a concave curve, microscopic at first, then leaping to equal the Einsteinian curve, cross it, outstrip it. At the point of intersection, humanity was able to reach the limits of the known universe... ... And when the line of Goedel's law eagled over Einstein's, its shadow fell on a dewerted Earth. The humans had gone somewhere else, to no world in this continuum. We came, took their bodies, their souls--both husks abandoned here for any wanderer's taking. The Cities, once bustling centers of interstellar commerce, were crumbled to the sands you see today.

WITH NO REPLY from Halleck to his October 26 request for a plan of operations, Grant moved forward on his own initiative on November 2. He telegraphed the general in chief that he had “commenced a movement” on Grand Junction, a sought-after prize in West Tennessee that took its name from the intersection of the east–west Memphis and Charleston and the north–south Mississippi Central railroad lines. Grant intended to assemble five divisions there and move south into Mississippi toward Holly Springs and Grenada.

I don’t want my world to be subset A such that it doesn’t intersect with any others (B, C or D), a watertight shape drawn on a slate, whole but empty. I’d rather be elsewhere, following a line that leads to places where worlds communicate with each other, overlap, where the edges are permeable, where life follows a path without breaks, where things don’t come to an end brutally for no reason, where important events come with instructions (level of risk, mains or batteries, expected duration) and the necessary equipment (airbags, GPS, ABS).

It was readily apparent that Millie was fond of geometric patterns. Today she wore double diamond checks. Her blouse in black and white, her skirt in bright teal. Around her neck she wore a scarf printed with random blocks of gray and gold. Out of sight, hanging in the tiny wardrobe of her room, were five striped blouses, two sweaters knit in intricate cables of intersecting colors. Also three tartan plaid skirts and one pair of unusual trousers, blue and yellow. She wore brown-and-white saddle shoes, which she constantly thought of decorating with fine black lines.

The rails intersect and combine in complex and convoluted ways. There are sixteen platforms in total. In addition, there are two private rail lines, the Odakyu line and the Keio line, and three subway lines plugged in, as it were, from the side. It is a total maze. During rush hour, that maze transforms into a sea of humanity, a sea that foams up, rages, and roars as it surges toward the entrances and exits. Streams of people changing trains become entangled, giving rise to dangerous, swirling whirlpools. No prophet, no matter how righteous, could part that fierce, turbulent sea.

Mind the Gap You are the kiss which manifests In the locus where heaven meets earth. You are the kiss which traverses the gap between God's and Adam's finger -- a verdant oasis on the intersection of infinite smallness and infinite greatness, the living earth in the cosmic graveyard of stars, the period beneath the scythe of the question, the period beneath the needle of exclamation, the tortoise and hare point where parallel lines meet in this universe of infinite questions without answers, in this universe of infinite wonder with exclamation, in this universe of infinite mystery where we ask 'Why is there something and not nothing?' And behold the answer in a kiss.

When K & I returned to the gingerbread house after taking Nana home, I was beyond exhausted. But I couldn't sleep, not for a long time. I stayed awake. Thinking of boys, of myself, & of all the intersections in between. ... Regardless, there were times when I was at least part boy. A femme boy deep down. Shy sweater fag, my cardigan on hand to comfort me in the cold world. Bookworm queer boy at heart, K told me on more than one occasion. Certain moods & I was the most enviable of drag princesses, eyelashes all a-flutter & my fingers tickling the air with each gesture. Sometimes I was full of flirtatious swagger, but that playful swag could turn fierce snarl for defense, if need be. Never, I promised myself one line I wouldn't cross, never would I be the mean kind of boy that laughed me back inside the store's red doors when I did no good at hot afternoon sour pissing contests. Of course, there were plenty of times I was such a fairy lady that I ceased to be even part boy. Yes, Rob would have accused me of bringing the communal growl down for saying I'm part boy. And pre-Stonewall dykes would have wanted to call my game. What kind of dyke was I, anyway? Good question. Simple & complicated all at once, I wasn't a pigeon to be tucked away neatly into a hole. I didn't wear a fixed category without feeling pain. I was more, or less, or something different entirely.

Preferring confusion to order is not limited to waiting lines but spills over into other sectors of life, at least in Rome and other more southern regions of the country. One of these is driving, an area where stereotypes about Italians, or at least about Romans, tend to be confirmed. Gridlock, here caused by a willful invasion of the intersection, is a daily occurrence. Red lights and stop signs often are viewed as optional. Using la freccia (directional lights) to signal an intention to turn right or left is infrequent, to say the least, or else left to the last minute, that is when the driver has already begun his turn, frequently from the farthest lane on the opposite side of the roadway.

Lucy gripped her chilled glass of orange and raspberry juice. When Rebecca talked about Austen, she’d mostly mentioned Mr. Darcy or Mr. Knightley. She hadn’t really thought of the doe-eyed, pale-skinned heroines. On the screen, Anne Elliot walked down a long hallway, glancing just once at covered paintings, her mouth a grim line. Lucy thought Jane Austen would start the story with the romance, or the loss of it, but instead the tale seemed to begin with Anne’s home, and having to make difficult decisions. Maybe this writer from over two hundred years ago knew how everything important met at the intersection of family, home, love, and loss. This was something Lucy understood with every fiber of her being.

I reach out and trace the dragon relic on his back, my fingers lingering on the raised silver scars, and he stiffens. They're all short, thin lines, too precise to be a whip, no rhyme or reason to their pattern but never intersecting. 'What happened?' I whisper, holding my breath. 'You really don't want to know.' He's tense, but doesn't move away from my touch. 'I do.' They don't look accidental. Someone hurt him deliberately maliciously, and it makes me want to hunt the person down and do the same to them. His jaw flexes as he looks over his shoulder, and his eyes meet mine. I bite my lip, knowing this moment can go either way. He can shut me out like always or he can actually let me in. 'There's a lot of them,' I murmur, dragging my fingers down his spine. 'A hundred and seven.' He looks away. The number makes my stomach lurch, and then my hand pauses. A hundred and seven. That's the number Liam mentioned. 'That's how many kids under the age of majority carry the rebellion relic.' 'Yeah.' I shift so I can see his face. 'What happened, Xaden?' He brushes my hair back, and the look that passes is over his face is so close to tender that it makes my heart stutter. 'I saw the opportunity to make a deal,' he says softly. 'And I took it.' 'What kind of deal leaves you with scars like that?' Conflict rages in his eyes, but then he sighs. 'The kind where I take personal responsibility for the loyalty of the hundred and seven kids the rebellion's leaders left behind, and in return, we're allowed to fight for our lives in the Riders Quadrant instead of being put to death like our parents.' He averts his gaze. 'I chose the chance of death over the certainty.' The cruelty of the offer and the sacrifice he made to save the others hits like a physical blow. I cradle his cheek and guide his face back to mine. 'So if any of them betray Navarre...' I lift my brows. 'Then my life is forfeit. The scars are a reminder.' It's why Liam says he owes him everything. 'I'm so sorry that happened to you.' Especially when he wasn't the one who led the rebellion. He looks at me like he sees into the very depths of who I am. 'You have nothing to apologise for.

The fanatic loathes an open-ended situation. Perhaps he does not acknowledge such situation. He always has an urgent need to know what the 'bottom line' is, what the inevitable conclusion is, when we will finally 'come full circle.' Yet history, including the private history of each of us, is usually not a circle but a line: a winding line with retreats and bends, which sometimes changes course and intersects with itself and occasionally draws loops, but nevertheless, a line and not a circle. Being immune to fanaticism entails, among other things, a willingness to exist inside open-ended situations that do not come full circle and cannot be unequivocally settled. A readiness to live with questions and choices whose resolutions hide far beyond the hazy horizon.

There seems little or no hope for the adult writer who produces sentences like these: "Her cheeks were thick and smooth and held a healthy natural red color. The heavy lines under them, her jowls, extended to the intersection of her lips and gave her a thick-lipped frown most of the time." The phrase "Her cheeks were thick and smooth" is normal English, but "[Her cheeks] held a healthy natural red color" is elevated, pseudo-poetic. The word "held" faintly hints at personification of "cheeks," and "healthy natural red color" is clunky, stilted, slightly bookish. The second sentence contains similar mistakes. The diction level of "extended to the intersection of her lips" is high and formal, in ferocious conflict with the end of the sentence, which plunges to the colloquial "most of the time.

progress—like those cartoons that begin with an ape and end with a man sitting at a computer—now gets lost in a hundred detours and false starts, intersecting paths and dead ends. It is difficult to find the story line in a tangled bush. Evolutionary theory is not threatened by the disappearance of the main highway. On the contrary, from the beginning Darwin insisted on the randomness of mutations, followed by the editing of natural selection, that lead to the emergence of new species. Still, it is disquieting to look around and see a wilderness of discontinuous and crisscrossing tracks. David Pilbeam once published a book called The Ascent of Man. It is not at all clear that he would do so today. Nonetheless, most of us, including evolutionary biologists, continue to search for and construct stories

To mount the skies it is not necessary to have the most powerful of motors, one must have a motor which, instead of continuing to run along the earth's surface, intersecting with a vertical line the horizontal which it began by following, is capable of converting its speed into lifting power. Similarly, the men who produce works of genius are not those who live in the most delicate atmosphere, whose conversation is the most brilliant or their culture the most extensive, but those who have had the power, ceasing suddenly to live only for themselves, to transform their personality into a sort of mirror, in such a way that their life, however mediocre it may be socially and even, in a sense, intellectually, is reflected by it, genius consisting in reflecting power and not the intrinsic quality of the scene reflected.

When I saw them on the beach, perfectly tanned, or when I watched them twirling in the waves, I grasped the transcendental element in surf music. It was all about freedom from the rules of life, the whole of your being concentrated in the act of shooting the tube. For several years after that trip to L.A. I subscribed to Surfer magazine, and I practiced the Atlantic Ocean version of the sport, though only with my body and on rather tame waves. With my voice muffled by the water I would shout a line from “Surf City.” To me, this was the ultimate fantasy of plenty: “two girls for every boy,” except I sang it as “Two girls for every goy.” Fortunately, Brian has survived the schizoid tendencies that seemed close to the surface when I met him. He’s still performing and writing songs. But it was his emotional battle and the intersection of that struggle with the acid-dosed aesthetic of the sixties that produced his most astonishing music.

Ours was the marsh country, down by the river, within, as the river wound, twenty miles of the sea. My first most vivid and broad impression of the identity of things seems to me to have been gained on a memorable raw afternoon towards evening. At such a time I found out for certain that this bleak place overgrown with nettles was the churchyard; and that Philip Pirrip, late of this parish, and also Georgiana wife of the above, were dead and buried; and that Alexander, Bartholomew, Abraham, Tobias, and Roger, infant children of the aforesaid, were also dead and buried; and that the dark flat wilderness beyond the churchyard, intersected with dikes and mounds and gates, with scattered cattle feeding on it, was the marshes; and that the low leaden line beyond was the river; and that the distant savage lair from which the wind was rushing was the sea; and that the small bundle of shivers growing afraid of it all and beginning to cry, was Pip. "Hold

some 1,500 people set out from Sproul Plaza to downtown Berkeley to demonstrate peaceably. But the troops and police were waiting for them, ready to spring a trap identified in Cable Splicer records as “Operation Box.” As the professors leading the march reached the intersection of Shattuck Avenue and Center Street, police ordered them to disperse but did not try to enforce the order. Instead, the guard and police diverted their path. Then, at Allston Way, the march was stopped by a tight line of National Guardsmen. Many people who did try to leave found their path blocked by a second line of soldiers, who had come up behind them. Troop transport trucks roared up with more soldiers, who closed all other exits and boxed them in. A combined force of police, deputies, and highway patrolmen herded the marchers—and everyone else—into a parking lot by the Bank of America. There Captain Charles Plummer of the Berkeley Police announced that they were all under arrest for unlawful assembly.

INTRODUCTION TO GENDER AND SOCIETY The Second Sex by Simone de Beauvoir A classic analysis of the Western conception of the woman. Feminism Is for Everybody by bell hooks A primer about the power and potential of feminist action. We Should All Be Feminists by Chimamanda Ngozi Adichie Feminism redefined for the twenty-first century. QUEER THEORY AND INTERSECTIONAL FEMINISM Gender Trouble by Judith Butler A classic, and groundbreaking, text about gender and the boundaries of identity. Gender Outlaw by Kate Bornstein A 1990s-era memoir of transition and nonbinary identity. This Bridge Called My Back ed. Cherríe Moraga and Gloria Anzaldúa A collection of essays about the intersections between gender, class, sexuality, and race. Sister Outsider by Audre Lorde A landmark collection of essays and speeches by a lauded black lesbian feminist. The Woman Warrior by Maxine Hong Kingston A memoir of growing up as a Chinese American woman. MODERN HISTORY How We Get Free: Black Feminism and the Combahee River Collective ed. Keeanga-Yamahtta Taylor A history of the Combahee River Collective, a group of radical black feminists operating in the 1960s and 1970s. And the Band Played On by Randy Shilts Investigative reportage about the beginning of the AIDS crisis. A Queer History of the United States by Michael Bronski An LGBT history of the United States, from 1492 to the present. CONTEMPORARY QUESTIONS Blurred Lines: Rethinking Sex, Power, and Consent on Campus by Vanessa Grigoriadis An exploration of the effects of the sexual revolution in American colleges. The End of Men: And the Rise of Women by Hanna Rosin A book about the shifting power dynamics between men and women. Bad Feminist by Roxane Gay Essays about the author’s experiences as a woman and our cultural understanding of womanhood. All the Single Ladies by Rebecca Traister An investigation into the lives of twenty-first-century unmarried women. GENDER AND SEXUALITY IN FICTION Rubyfruit Jungle by Rita Mae Brown A groundbreaking lesbian coming-of-age novel, originally published in 1973. Giovanni’s Room by James Baldwin A classic of morality and desire, set in 1950s Paris, about an American man and his relationship with an Italian bartender. Angels in America by Tony Kushner A Pulitzer Prize–winning play about the Reagan-era AIDS epidemic. Oranges Are Not the Only Fruit by Jeanette Winterson A coming-of-age and coming-out novel about a woman growing up in an evangelical household.

What I have observed of the pond is no less true in ethics. Such a rule of the two diameters not only guides us toward the sun in the system and the heart in man, but draws lines through the length and breadth of the aggregate of a man’s particular daily behaviors and waves of life into his coves and inlets, and where they intersect will be the height and depth of his character. Perhaps we only need to know how his shores trend, and his adjacent country or circumstances, to infer his depth and concealed bottom. If he is surrounded by mountainous circumstances, an Achillean shore, whose peaks overshadow and are reflected in his bosom, they suggest a corresponding depth to him. But a low and smooth shore proves him shallow on that side. Also there is a bar across the entrance of our every cove, or particular inclination; each is a harbor for a season, in which we are detained and partially landlocked. These inclinations are not whimsical usually, but their form, size, and direction are determined by the promontories of the shore, the ancient axes of elevation. When this bar is gradually increased by storms, tides, or currents, or there is a subsidence of waters…It becomes an individual lake, cut off from the ocean, wherein the thought secures its own conditions, changes, perhaps, from salt to fresh, becomes a sweet sea, dead sea, or a marsh.

I was most pleasantly surprised, with this chart, to see a Yod pointing at the Moon. After all, what other planet influences changeable behaviour and creates a strong magnetic pull? I am tempted to say that the problem of the Bermuda Triangle has been solved: it was the Moon all along! But it is obviously more complicated than that. For one thing, there is a theory that there is an energy vortex operating through the earth, with a corresponding ‘problem’ area on the other side of the world, based near the west coast of Australia in the Indian Ocean. I noticed when I was looking at my Atlas that these trouble spots are on, or near, the Tropic of Cancer in the north, and the Tropic of Capricorn in the south. Being that these circles are the northern-most and southern-most positions of the Sun as it passes over the earth at the summer and winter solstices, there must be a residue of magnetic energy along those lines. To create a vortex, another energy line must be intersecting each tropical line at a right angle (90°). We can see this energy line on the chart: the Pluto-Midheaven opposition would be operating at full strength, as the critical degree is within 45’ of true (meaning, that the difference between the position of Pluto and the Midheaven, directly overhead, is almost exactly 180°). Because Mars is conjunct to Pluto, also opposite to the Midheaven, stormy weather, previously noted in this book, was raging: a potent combination.

On April 1, 1865, in Virginia, Pickett was defending an intersection known as Five Forks, six miles south of the Appomattox River and a good bit closer to the Southside Railroad, the last remaining supply line to Richmond. While thirty thousand Union troops led by Little Phil Sheridan approached from the southeast, Pickett’s twelve thousand, spread two miles wide behind fences and in ditches, braced to meet them. Pickett’s supreme commander, Robert E. Lee, was headquartered ten miles away, near Petersburg. Should Pickett fall to Sheridan, Lee would be forced from Petersburg, the Federals would capture Richmond, and the Confederate cause would be lost. Someone mentioned shad. The spring spawning run was in full penetration of the continent. The fish were in the rivers. Tom Rosser, another Confederate general, had caught some, and on the morning of April 1st ordered them baked for his midday dinner, near Hatcher’s Run, several miles from Five Forks. He invited Pickett and Major General Fitzhugh Lee, nephew of Robert E. Lee, to join him. Pickett readily accepted, and rode off from his battle station with Lee. The historian Shelby Foote continues the narrative (“The Civil War,” vol. 3, p. 870): “Neither told any subordinate where he was going or why, perhaps to keep from dividing the succulent fish too many ways; with the result that when the attack exploded—damped from their hearing, as it was, by a heavy stand of pines along Hatcher’s Run—no one knew where to find them. Pickett only made it back to his division after half its members had been shot or captured, a sad last act for a man who gave his name to the most famous charge in a war whose end was hastened by his threehour absence at a shad bake.

And yet, being surveilled with the intention of assault or rape is practically mundane, it happens so often. It’s such an ingrained part of the female experience that it doesn’t register as unusual. The danger of it, then, is in its routine, in how normalized it is for a woman to feel monitored, so much so that she might not know she’s in trouble until that invisible line is crossed from “typical patriarchy” to “you should run.” So now, when I drink, I’m far more cautious. I don’t like ordering draft beers from taps hidden from view. I don’t like pouring bottles into pint glasses. I don’t leave my drink with strangers, I don’t let people I don’t know order drinks for me without watching them do it, and I don’t drink excessively with people I don’t think I can trust with my sleepy body. I don’t turn my back on a cocktail, not just because I like drinking but because I can’t trust what happens to it when I’m not looking. The intersection of rape culture and surveillance culture means that being a guarded drinker is not only my responsibility, it is my sole responsibility. Any lapse in judgment could not only result in clear and present danger, but also set me up for a chorus of “Well, she should’ve known better.” The mistake we make is in thinking rape isn’t premeditated, that it happens by accident somehow, that you’re drunk and you run into a girl who’s also drunk and half-asleep on a bench and you sidle up to her and things get out of hand and before you know it, you’re being accused of something you’d never do. But men who rape are men who watch for the signs of who they believe they can rape. Rape culture isn’t a natural occurrence; it thrives thanks to the dedicated attention given to women in order to take away their security. Rapists exist on a spectrum, and maybe this attentive version is the most dangerous type: women are so used to being watched that we don’t notice when someone’s watching us for the worst reason imaginable. They have a plan long before we even get to the bar to order our first drink.

CHANGING YOUR LIFE TO ACCOMMODATE THE SIXTH SECRET The sixth secret is about the choiceless life. Since we all take our choices very seriously, adopting this new attitude requires a major shift. Today, you can begin with a simple exercise. Sit down for a few minutes and reassess some of the important choices you’ve made over the years. Take a piece of paper and make two columns labeled “Good Choice” and “Bad Choice.” Under each column, list at least five choices relating to those moments you consider the most memorable and decisive in your life so far—you’ll probably start with turning points shared by most people (the serious relationship that collapsed, the job you turned down or didn’t get, the decision to pick one profession or another), but be sure to include private choices that no one knows about except you (the fight you walked away from, the person you were too afraid to confront, the courageous moment when you overcame a deep fear). Once you have your list, think of at least one good thing that came out of the bad choices and one bad thing that came out of the good choices. This is an exercise in breaking down labels, getting more in touch with how flexible reality really is. If you pay attention, you may be able to see that not one but many good things came from your bad decisions while many bad ones are tangled up in your good decisions. For example, you might have a wonderful job but wound up in a terrible relationship at work or crashed your car while commuting. You might love being a mother but know that it has drastically curtailed your personal freedom. You may be single and very happy at how much you’ve grown on your own, yet you have also missed the growth that comes from being married to someone you deeply love. No single decision you ever made has led in a straight line to where you find yourself now. You peeked down some roads and took a few steps before turning back. You followed some roads that came to a dead end and others that got lost at too many intersections. Ultimately, all roads are connected to all other roads. So break out of the mindset that your life consists of good and bad choices that set your destiny on an unswerving course. Your life is the product of your awareness. Every choice follows from that, and so does every step of growth.

In the past, the states best able to manage events beyond their borders have been those best able to avoid the temptation to overreach. Great powers remain great in large measure because they posses wisdom to temper active involvement in foreign interventions - to remain within the limits of a national strategy that balances ambition with military resources. The first principle of the strategic art states simply that the greatest weight of resources be devoted to safeguarding the most vital interests of the state. If a vital interest is threatened, the survival of the state is threatened. Generally, the most vital interest of a liberal democracy include, first and foremost, preservation of the territorial integrity of the state. The example of the attacks on New York and Washington should send a message to those of similar ambitions that the surest way to focus the wrath of the American people against them would be to strike this country within its borders again. The second strategic priority is the protection of the national economic welfare by ensuring free and open access to markets for vital materials and finished goods. Other important but less vital interests should be defended by the threat of force only as military resources permit. Outside the limits of U.S. territory, the strategic problem defining the geographic limits of U.S. vital interests becomes complex. While the United States may have some interests in every corner of the world, there are certain regions where its strategic interests, both economic and cultural, are concentrated and potentially threatened. These vital strategic "centers of gravity" encompass in the first instance those geographic areas essential to maintaining access to open markets and sources of raw material, principally oil. Fortunately, many of these economically vital centers are secure from serious threat. But a few happen to be located astride regions that have witnessed generations of cultural and ethnic strife. Four regions overshadow all others in being both vital to continued domestic prosperity and continually under the threat of state-supported violence. These regions are defined generally by an arc of territories along the periphery of Eurasia: Europe, the Middle East, South Asia, and north East Asia. For the past several centuries, these regions have been the areanas of the world's most serious and intractable conflicts. Points of collision begin with the intersection of Western and Eastern Christianity and continue southward to mark Islam's incursion into southeastern Europe in the Balkans. The cultural divide countries without interruption across the Levant in an unbroken line of unrest and warring states from the crescent of the Middle East to the subcontinent of South Asia. The fault-line concludes with the divide between China and all the traditional cultural competitors along its land and sea borders. Other countries outside the periphery of Eurasia might, in extreme cases, demand the presence of U.S. forces for peacekeeping or humanitarian operations. But it is unlikely that in the years to come the United States will risk a major conflict that will involve the calculated commitment of forces in a shooting war in regions outside this "periphery of Eurasia," which circumscribes and defines America's global security.

One human characteristic that exacerbates such bad decision making is adaptation: the uneven process by which we get used to things. The satisfaction finish line is actually more like a snake than a line. Some parts of it move away as we approach, and some do not. Some things we adapt to quickly and some things we just never get used to. Daniel Gilbert, Harvard psychologist and author of Stumbling on Happiness, explained the commuting paradox to me this way: “Most good and bad things become less good and bad over time as we adapt to them. However, it is much easier to adapt to things that stay constant than to things that change. So we adapt quickly to the joy of a larger house because the house is exactly the same size every time we come in the front door. But we find it difficult to adapt to commuting by car, because every day is a slightly new form of misery, with different people honking at us, different intersections jammed with accidents, different problems with weather, and so on.

Braid groups have many important practical applications. For example, they are used to construct efficient and robust public key encryption algorithms.7 Another promising direction is designing quantum computers based on creating complex braids of quantum particles known as anyons. Their trajectories weave around each other, and their overlaps are used to build “logic gates” of the quantum computer.8 There are also applications in biology. Given a braid with n threads, we can number the nails on the two plates from 1 to n from left to right. Then, connect the ends of the threads attached to the nails with the same number on the two plates. This will create what mathematicians call a “link”: a union of loops weaving around each other. In the example shown on this picture, there is only one loop. Mathematicians’ name for it is “knot.” In general, there will be several closed threads. The mathematical theory of links and knots is used in biology: for example, to study bindings of DNA and enzymes.9 We view a DNA molecule as one thread, and the enzyme molecule as another thread. It turns out that when they bind together, highly non-trivial knotting between them may occur, which may alter the DNA. The way they entangle is therefore of great importance. It turns out that the mathematical study of the resulting links sheds new light on the mechanisms of recombination of DNA. In mathematics, braids are also important because of their geometric interpretation. To explain it, consider all possible collections of n points on the plane. We will assume that the points are distinct; that is, for any two points, their positions on the plane must be different. Let’s choose one such collection; namely, n points arranged on a straight line, with the same distance between neighboring points. Think of each point as a little bug. As we turn on the music, these bugs come alive and start moving on the plane. If we view the time as the vertical direction, then the trajectory of each bug will look like a thread. If the positions of the bugs on the plane are distinct at all times – that is, if we assume that the bugs don’t collide – then these threads will never intersect. While the music is playing, they can move around each other, just like the threads of a braid. However, we demand that when we stop the music after a fixed period of time, the bugs must align on a straight line in the same way as at the beginning, but each bug is allowed to end up in a position initially occupied by another bug. Then their collective path will look like a braid with n threads. Thus, braids with n threads may be viewed as paths in the space of collections of n distinct points on the plane.10

The intersecting point of diagonals on the GPG's base area marks the tip of the line joining the apex of a cone to the center of its base on the same course of the two shafts' ends. Half of the vertex angle of this cone equals to 32.5.

Intermission. Mare Internum. We will have a brief pause now. If this novel were a theater, you could go out into the lobby, wait in line for a drink, or for the bathroom. Give people a chance to admire your clothes, hair, or jewels. Step outside for some air or a smoke. Backstage the crew would be busy transforming the scenery, actors would change their costumes and redo their makeup, Some would be done until final curtain, others awaiting their first entrance. But we're not in the theater, and I am not letting you go outside this story, not really. Where we are is more like a pause between breaths. Whether you're inhaling or exhaling, there's a pause just before, like the pause you can feel more than hear before the tide reverses. Where we are is the point of intersection in the figure eight. Turned on its side the eight becomes the symbol of infinity. You can make this figure with your hips when you dance. Over and over you will return to that moment of balance before your weight shifts from one hip to the other. The balance of this story is about to shift. The scenery is changing, as we make our slow way across Mare Internum. A journey I am not going to describe. When the story begins again, some of the people you have come to know and love, or not, Dido, Bertha, Paulina, Reginus, and Joseph will appear less frequently... I don't like it when characters fade form the story, so I am apologizing in advance, but life is like that. We leave people and places and times behind. We encounter new ones. Sometimes we can't see the patterns or connections, but they are there, between one breath and the next. In the ebb and flow of tides. In the rhythm of the dance.

On a June afternoon in 1791, George Washington, Andrew Ellicott, and Peter Charles L’Enfant rode east from Georgetown “to take,” so Washington recorded in his diary, “a more perfect view of the ground” of the new federal city. From David Burnes’s fields they surveyed the prospect of the Potomac River, and then, continuing east across the Tiber Creek, they climbed to the crest of Jenkins Hill. With the confluence of the Eastern Branch and the Potomac, the cities of Alexandria and Georgetown, and the hills of Maryland and Virginia spread majestically before them, the time had come, the president wrote, “to decide finally on the spots on which to place the public buildings.” From their vantage point on Jenkins Hill, L’Enfant presented his vision of a city worthy of the new republic. He began by siting the two principal buildings: the “Congress House,” as he called it, would command Jenkins Hill, “a pedestal waiting for a superstructure”; the “President’s Palace,” L’Enfant’s name for today’s White House, would rise about a mile away on the land partially belonging to David Burnes. A star of avenues each named for a state would radiate from the center of each house. Pennsylvania Avenue—the name would honor the state’s importance in the nation’s creation—would connect the two buildings. It would be “a direct and large avenue,” 180 feet wide and lined with a double row of trees. These radiating avenues would intersect at circles and squares, to be named for heroes, and they would overlay a grid of streets similar to that of Philadelphia.

Why might there not be as many real worlds as imaginary ones? Why a single real world? Why such an exception? Truth to tell, the real world, among all the other possible ones, is unthinkable, except as dangerous superstition. We must break with it as critical thought once broke (in the name of the real!) with religious superstition. Thinkers, one more effort! In any case, the two orders of thought are irreconcilable. They each follow their course without merging; at best they slide over each other like tectonic plates, and occasionally their collision or subduction creates fault lines into which reality rushes. Fate is always at the intersection of these two lines of force. Similarly, radical thought is at the violent intersection of meaning and non-meaning, of truth and non-truth, of the continuity of the world and the continuity of the nothing.

Saddle horses lined the hitching-rails as far as Brite could see. Canvas-covered wagons, chuck-wagons, buckboards, vehicles of all Western types, stood outside the saddle horses. And up one side and down the other a procession ambled in the dust. On the wide sidewalk a throng of booted, belted, spurred men wended their way up or down. The saloons roared. Black-sombreroed, pale-faced, tight-lipped men stood beside the wide portals of the gaming-dens. Beautiful wrecks of womanhood, girls with havoc in their faces and the look of birds of prey in their eyes, waited in bare-armed splendor to be accosted. Laughter without mirth ran down the walk. The stores were full. Cowboys in twos and threes and sixes trooped by, young, lithe, keen of eye, bold of aspect, gay and reckless. Hundreds of cowboys passed Brite in that long block from the hotel to the intersecting street. And every boy gave him a pang. These were the toll of the trail and of Dodge. It might have been the march of empire, the tragedy of progress, but it was heinous to Brite. He would never send another boy to his death.

The grid derives from the golden ratio and the simpler rule of thirds: it divides your photograph into three segments both horizontally and vertically. The idea of the grid is that you should position your main motif (for example, the person you are photographing) on one of the points where the lines intersect rather than in the middle of the grid, which will improve the composition of the photograph.

The rate at which we can adapt is increasing,” said Teller. “A thousand years ago, it probably would have taken two or three generations to adapt to something new.” By 1900, the time it took to adapt got down to one generation. “We might be so adaptable now,” said Teller, “that it only takes ten to fifteen years to get used to something new.” Alas, though, that may not be good enough. Today, said Teller, the accelerating speed of scientific and technological innovations (and, I would add, new ideas, such as gay marriage) can outpace the capacity of the average human being and our societal structures to adapt and absorb them. With that thought in mind, Teller added one more thing to the graph—a big dot. He drew that dot on the rapidly sloping technology curve just above the place where it intersected with the adaptability line. He labeled it: “We are here.” The graph, as redrawn for this book, can be seen on the next page. That dot, Teller explained, illustrates an important fact: even though human beings and societies have steadily adapted to change, on average, the rate of technological change is now accelerating so fast that it has risen above the average rate at which most people can absorb all these changes. Many of us cannot keep pace anymore.