Infinity Symbol Quotes

Ara?" She jerked her face up. "Huh? Where were we?" But his expression had grown serious, the lesson forgotten. He interlaced his fingers and said, "We are bound." "Bound?" He collected a piece of rope, knotting it. "Oh, you mean bound?" He gave a nod, then drew in the sand. An infinity symbol? "Clever demon, how did you know that...?" He was gazing at her with a question in his eyes. "Bound forever?" And somehow she met his gaze and lied, "Yes, demon. Bound forever." As if to make her feel guiltier, he gathered her into his arms, cupping her face against his broad chest. His voice a deep rumble, he said, "Carrow is Malkom's." She wanted to sob. "Yes?" "Yes," she answered, wishing that it could be so simple between them. Demon meets girl. Girl might be falling for demon.

8 is just an infinity symbol the right way up.

He had a dragon twined around to make an infinity symbol with the head eating the tail. "It is the vampiric symbol for eternity, since we are immortal.

Sometimes in studying Ramanujan's work, [George Andrews] said at another time, "I have wondered how much Ramanujan could have done if he had had MACSYMA or SCRATCHPAD or some other symbolic algebra package.

A robed figure stood before a coin, a cup, a sword, a wand---all of the symbols of all the tarot suits. An infinity symbol floated above his head; one arm was lifted in a posture of power. Yes, thought Adam. Understanding prickled and then evaded him. He read the words at the bottom of the card. The Magician.

But that would mean it was originally a sideways number eight. That makes no sense at all. Unless..." She paused as understanding dawned. "You think it was the symbol for infinity?" "Yes, but not the usual one. A special variant. Do you see how one line doesn't fully connect in the middle? That's Euler's infinity symbol. Absolutus infinitus." "How is it different from the usual one?" "Back in the eighteenth century, there were certain mathematical calculations no one could perform because they involved series of infinite numbers. The problem with infinity, of course, is that you can't come up with a final answer when the numbers keep increasing forever. But a mathematician named Leonhard Euler found a way to treat infinity as if it were a finite number- and that allowed him to do things in mathematical analysis that had never been done before." Tom inclined his head toward the date stone. "My guess is whoever chiseled that symbol was a mathematician or scientist." "If it were my date stone," Cassandra said dryly, "I'd prefer the entwined hearts. At least I would understand what it means." "No, this is much better than hearts," Tom exclaimed, his expression more earnest than any she'd seen from him before. "Linking their names with Euler's infinity symbol means..." He paused, considering how best to explain it. "The two of them formed a complete unit... a togetherness... that contained infinity. Their marriage had a beginning and end, but every day of it was filled with forever. It's a beautiful concept." He paused before adding awkwardly, "Mathematically speaking.

There is no need to be worried by facetious people who try to make the Christian hope of ‘Heaven’ ridiculous by saying they do not want ‘to spend eternity playing harps’. The answer to such people is that if they cannot understand books written for grown-ups, they should not talk about them. All the scriptural imagery (harps, crowns, gold, etc.) is, of course, a merely symbolical attempt to express the inexpressible. Musical instruments are mentioned because for many people (not all) music is the thing known in the present life which most strongly suggests ecstasy and infinity. Crowns are mentioned to suggest the fact that those who are united with God in eternity share His splendour and power and joy. Gold is mentioned to suggest the timelessness of Heaven (gold does not rust) and the preciousness of it. People who take these symbols literally might as well think that when Christ told us to be like doves, He meant that we were to lay eggs.

The tattoo Ty now had on his ring finger was the simple wrapped infinity symbol Zane had drawn, but when he moved his middle finger, it revealed an anchor woven in. A hidden reminder of what Zane was to him. Zane’s was the exact same thing, only with a simplified compass incorporated in. Zane

Just before they boarded the yacht, Cassandra glanced at Tom and reached up to a delicate necklace she'd worn constantly since the day he'd given it to her. She touched the little charm, made in the shape of Euler's infinity symbol, that hung at the hollow of her throat. And as always, the private signal made him smile.

I am the beast with a contorted grin, contracting down to illusion and dilating toward infinity, both growing and dying, delightfully suspended between hope for nothing and despair of everything, brought up among perfumes and poisons, consumed with love and hatred, killed by lights and shadows. My symbol is death of light and the flame of death. Sparks die in me only to be reborn as thunder and lightning. Darkness itself glows in me.

Even as I regarded those two men, I became aware of the flying beams of the spotlights, to the north-east, painting ephemeral infinity symbols across the pregnant clouds that increasingly commanded the sky, of the distant roller-coaster chain clacking through the ratchet angles of the guideway as cars full of riders climbed an incline toward the next long drop, of the dusty smell of the campground, and of the scent of rain pending.

Religion, philosophy, art — those three pillars on which the world has rested—were invented by man in order symbolically to encapsulate the idea of infinity, setting against it a symbol of its possible attainment (which in real terms is of-course impossible). Humanity has found nothing else on such an enormous scale. Admittedly man found it by instinct, without understanding why he needed God (easier that way!) or philosophy (explains everything, even the meaning of life!) or art (immortality).

I found myself all at once on the brink of panic. This, I suddenly felt, was going too far. Too far, even though the going was into intenser beauty, deeper significance. The fear, as I analyze it in retrospect, was of being overwhelmed, of disintegrating under a pressure of reality greater than a mind, accustomed to living most of the time in a cosy world of symbols, could possibly bear. The literature of religious experience abounds in references to the pains and terrors overwhelming those who have come, too suddenly, face to face with some manifestation of the Mysterium tremendum. In theological language, this fear is due to the in-compatibility between man's egotism and the divine purity, between man's self-aggravated separateness and the infinity of God. Following Boehme and William Law, we may say that, by unregenerate souls, the divine Light at its full blaze can be apprehended only as a burning, purgatorial fire. An almost identical doctrine is to be found in The Tibetan Book of the Dead, where the departed soul is described as shrinking in agony from the Pure Light of the Void, and even from the lesser, tempered Lights, in order to rush headlong into the comforting darkness of selfhood as a reborn human being, or even as a beast, an unhappy ghost, a denizen of hell. Anything rather than the burning brightness of unmitigated Reality—anything!

Our Cross Our little circle hides in the mind, It's difficult to miss but hard to find, It goes unspoken but yet it speaks, From backward years to forward weeks, We can't forget but why even try, Two of a kind doesn't know goodbye, It's a silent question that God won't share, A breeze we feel but seems unfair, Distant, rare but only madness can see, It's something deeper than any infinity, Because we walk this parallel path up and down, There is no circle to hold us circus clowns, So let's give it a symbol and label it a loss, We will remember it always as we carry our cross.

Linking their names with Euler’s infinity symbol means . . .” He paused, considering how best to explain it. “The two of them formed a complete unit . . . a togetherness . . . that contained infinity. Their marriage had a beginning and end, but every day of it was filled with forever. It’s a beautiful concept.” He paused before adding

It was the Greeks who turned math into an abstract system, a special symbolic language that allows people not just to describe the concrete world but to account for its deepest patterns and laws.

That is, for a mathematical Platonist, what the C.H. proofs really show is that set theory needs to find a better set of core axioms than classical ZFS, or at least it will need to add some further postulates that are-like the Axiom of Choice-both "self-evident" and Consistent with classical axioms. If you're interested, Godel's own personal view was that the Continuum Hypothesis is false, that there are actually a whole (Infinity Symbol) of Zeno-type (Infinity Symbol)s nested between (Aleph0) and c, and that sooner or later a principle would be found that proved this. As of now no such principle's ever been found. Godel and Cantor both died in confinement, bequeathing a world with no finite circumference. One that spins, now, in a new kind of all-formal Void. Mathematics continues to get out of bed.

It is absolutely from his vision of the whole, in which the genius always lives, that he gets his sense of the parts. He values everything within him or without him by the standard of this vision, a vision that for him is no function of time, but a part of eternity. . . . The scientist takes phenomena for what they obviously are; the great man or the genius for what they signify. Sea and mountain, light and darkness, spring and autumn, cypress and palm, dove and swan are symbols to him, he not only thinks that there is, but he recognizes in them something deeper. The ride of the Valkyrie is not produced by atmospheric pressure and the magic fire is not the outcome of a process of oxidation. And all this is possible for him because the outer world is as full and strongly connected as the inner in him, the external world in fact seems to be only a special aspect of his inner life; the universe and the ego have become one in him, and he is not obliged to set his experience together piece by piece according to rule. . . . The infinity of the universe is responded to in the genius by a true sense of infinity in his own breast; he holds chaos and cosmos, all details and all totality, all plurality, and all singularity in himself.

A canny reader here may object that there's some kind of Zenoid sleight of hand going on in the above proof, and might ask why a similar hankie procedure and series couldn't be applied to the irrational numbers to quote-unquote prove that the total % of Line-space taken up by the irrationals is also 2*(Infinitesimally small symbol). The reason such a proof can't work is that, no matter how infinitely or even (Infinity to the Infinity symbol) ly many red hankies you drape, there will always be more irrational numbers than hankies. Always. Cantor proved this, too.

The graves in the Pet Sematary mimed the most ancient religious symbol of all: diminishing circles indicating a spiral leading down, not to a point, but to infinity; order from chaos or chaos from order, depending on which way your mind worked. It was a symbol the Egyptians had chiseled on the tombs of the Pharaohs, a symbol the Phoenicians had drawn on the barrows of their fallen kings; it was found on cave walls in ancient Mycenae; the guild-kings of Stonehenge had created it as a clock to time the universe; it appeared in the Judeo-Christian Bible as the whirlwind from which God had spoken to Job.

There is no need to be worried by facetious people who try to make the Christian hope of “Heaven” ridiculous by saying they do not want “to spend eternity playing harps.” The answer to such people is that if they cannot understand books written for grown-ups, they should not talk about them. All the scriptural imagery (harps, crowns, gold, etc.) is, of course, a merely symbolical attempt to express the inexpressible. Musical instruments are mentioned because for many people (not all) music is the thing known in the present life which most strongly suggests ecstasy and infinity. Crowns are mentioned to suggest the fact that those who are united with God in eternity share His splendour and power and joy. Gold is mentioned to suggest the timelessness of Heaven (gold does not rust) and the preciousness of it. People who take these symbols literally might as well think that when Christ told us to be like doves, He meant that we were to lay eggs.

He closed his eyes. Found the ridged face of the power stud. And in the bloodlit dark behind his eyes, silver phosphenes boiled in from the edge of space, hypnagogic images jerking past like a film compiled of random frames. Symbols, figures, faces, a blurred, fragmented mandala of visual information. Please, he prayed, now- A gray disk, the color of Chiba sky. Now- Disk beginning to rotate, faster, becoming a sphere of paler gray. Expanding- And flowed, flowered for him, fluid neon origami trick, the unfolding of distanceless home, his country, transparent 3D chessboard extending to infinity. Inner eye opening to the stepped scarlet pyramid of the Eastern Seaboard Fission Authority burning beyond the green cubes of Mitsubishi Bank of America, and high and very far away he saw the spiral arms of the military systems, forever beyond his reach. And somewhere he was laughing, in a white-painted loft, distant fingers caressing the deck, tears of release streaking his face.

His next major proof (which you'll notice still concerns point sets) is an attempt to show that the 2D plane contains a (Infinity symbol) of points that's greater than the 1D Real Line's c in the same way that c is greater than the Number Line's (Aleph0). This is the proof of whose final result Cantor famously wrote to Dedekind "Je le vois, mais je'n le crois pas" in 1877. It's known in English as his Dimension Proof. The general idea is to show that the real numbers cannot be put into a 1-1C with the set of points in an n-dimensional space, here a plane, and hence that the cardinality of the plane's point set is greater than the cardinality of the set of all reals.

The difference between bush and ladder also allows us to put a lid on a fruitless and boring debate. That debate is over what qualifies as True Language. One side lists some qualities that human language has but that no animal has yet demonstrated: reference, use of symbols displaced of in time and space from their referents, creativity, categorical speech perception, consistent ordering, hierarchical structure, infinity, recursion, and so on. The other side finds some counter-example in the animal kingdom (perhaps budgies can discriminate speech sounds, or dolphins or parrots can attend to word order when carrying out commands, or some songbird can improvise indefinitely without repeating itself), and gloats that the citadel of human uniqueness has been breached. The Human Uniqueness team relinquishes that criterion but emphasizes others or adds new ones to the list, provoking angry objections that they are moving the goalposts. To see how silly this all is, imagine a debate over whether flatworms have True Vision or houseflies have True Hands. Is an iris critical? Eyelashes? Fingernails? Who cares? This is a debate for dictionary-writers, not scientists. Plato and Diogenes were not doing biology when Plato defined man as a "featherless biped" and Diogenes refuted him with a plucked chicken.

Everything you have ever seen with your eyes is the self-emptying of God into multitudinous physical and visible forms. In other words, Infinity is forever limiting itself into finite expressions, and this could even be called the “suffering” of God. The Christ learned this self-emptying, or kenosis , 183 from his eternal life in the Trinity. It is not just Jesus who suffers, but the cross is the visible symbol of what is always going on inside of God!

If we look at our traditional tales, where the action before the final success always occurs three times: the last of the three times is always a little longer because it includes success: life is somehow the famous 0.142592653589793 after three....These stories are a kind of mythical Pi, that we finally 'mathematified', quantified by numbers. That's why the number Pi was and is so important. It explains the inexplicable, life, eternity, infinity, and at the same time the cycle of rebirth.

The infinite seeks manifestation. It projects itself as the point, defined by its position, one coordinate. Further seeking fulfillment, the point extends outward to become the line, now adding the concept of reference to another, creating length, reaching to infinity. But by manifesting a third point, and forming the triangle, the point has defined itself in relation to two others, and it has become a self-contained unit, the plane, fully independent in two dimensions, at rest in perfect harmony.

Justice and honesty and loyalty are not properties of this world, she thought; and then, by God, she rammed her old enemy, her ancient foe, the Coca-Cola truck, which went right on going without noticing. The impact spun her small car around; her headlights dimmed out, horrible noises of fender against tire shrieked, and then she was off the freeway onto the emergency strip, facing the other direction, water pouring from her radiator, with motorists slowing down to gape. Come back, you motherfucker, she said to herself, but the Coca-Cola truck was long gone, probably undented. Maybe a scratch. Well, it was bound to happen sooner or later, her war, her taking on a symbol and a reality that outweighed her. Now my insurance rates will go up, she realized as she climbed from her car. In this world you pay for tilting with evil in cold, hard cash. A late-model Mustang slowed and the driver, a man, called to her, “You want a ride, miss?” She did not answer. She just kept on going. A small figure on foot facing an infinity of oncoming lights.

Musical instruments are mentioned because for many people (not all) music is the thing known in the present life which most strongly suggests ecstasy and infinity. Crowns are mentioned to suggest the fact that those who are united with God in eternity share His splendour and power and joy. Gold is mentioned to suggest the timelessness of Heaven (gold does not rust) and the preciousness of it. People who take these symbols literally might as well think that when Christ told us to be like doves, He meant that we were to lay eggs.

We might call this existential paradox the condition of individuality finitude. Man has a symbolic identity that brings him sharply out of nature. He is a symbolic self, a creature with a name, a life history. He is a creator with a mind that soars out to speculate about atoms and infinity, who can place himself imaginatively at a point in space and contemplate bemusedly his own planet. This immense expansion, this dexterity, this ethereality, this self-consciousness gives to man literally the status of a small god in nature, as the Renaissance thinkers knew. Yet, at the same time, as the Eastern sages also knew, man is a worm and food for worms. This is the paradox: he is out of nature and hopelessly in it; he is dual, up in the stars and yet housed in a heart-pumping, breath-gasping body that once belonged to a fish and still carries the gill-marks to prove it. His body is a material fleshy casing that is alien to him in many ways-the strangest and most repugnant way being that it aches and bleeds and will decay and die. Man is literally split in two: he has an awareness of his own splendid uniqueness in that he sticks out of nature with a towering majesty, and yet he goes back into the ground a few feet in order to blindly and dumbly rot and disappear forever. It is a terrifying dilemma to be in and to have to live with. The lower animals are, of course, spared this painful contradiction, as they lack a symbolic identity and the self-consciousness that goes with it. They merely act and move reflexively as they are driven by their instincts. If they pause at all, it is only a physical pause; inside they are anonymous, and even their faces have no name. They live in a world without time, pulsating, as it were, in a state of dumb being. This is what has made it so simple to shoot down whole herds of buffalo or elephants. The animals don't know that death is happening and continue grazing placidly while others drop alongside them. The knowledge of death is reflective and conceptual, and animals are spared it. They live and they disappear with the same thoughtlessness: a few minutes of fear, a few seconds of anguish, and it is over. But to live a whole lifetime with the fate of death haunting one's dreams and even the most sun-filled days-that's something else.

Nature is a temple in which living pillars Sometimes give voice to confused words; Man passes there through forests of symbols Which look at him with understanding eyes. Like prolonged echoes mingling in the distance In a deep and tenebrous unity, Vast as the dark of night and as the light of day, Perfumes, sounds, and colors correspond. There are perfumes as cool as the flesh of children, Sweet as oboes, green as meadows — And others are corrupt, and rich, triumphant, With power to expand into infinity, Like amber and incense, musk, benzoin, That sing the ecstasy of the soul and senses.

If you object (as some of us did to Dr. Goris) that Cantor's transfinite numbers aren't really numbers at all but rather sets, then be apprised that what, say, 'P(Infinity to the Infinity +n), really is is a symbol for the number of members in a given set, the same way '3' is a symbol for the number of members in the set {1,2,3}. And since the transfinites are provably distinct and compose an infinite ordered sequence just like the integers,they really are numbers, symbolizable (for now) by Cantor's well-known system of alephs or '(Aleph symbol's). And, as true numbers, transfinites turn out to be susceptible to the same kinds of arithmetical relations and operations as regular numbers-although, just as with 0, the rules for these operations are very different in the case of (Alephs) and have to be independently established and proved.

Only humans can conceptualise the idea of infinity. Only humans can communicate such an abstract idea using various forms such as words and symbols. This is because humans are blessed with imagination. It is the one thing that separates us humans from animals. Humans can imagine because we have a highly developed brain, the cerebrum, with an especially large frontal lobe. This anatomical difference separates us from the rest of nature. So much so that in Samkhya, the Indian school of metaphysics, humanity or Purusha is seen as being separate from nature or Prakriti. This difference is seen as fundamental in the study of metaphysics. Because humans can imagine, the notion of a reality beyond the senses, a reality beyond nature, has come into being. Without the cerebrum there would be no imagination, and hence no notion of God! In nature, all things have form. Each of these

There is no need to be worried by facetious people who try to make the Christian hope of 'Heaven' ridiculous by saying they do not want 'to spend eternity playing harps.' The answer to such people is that if they cannot understand books written for grown-ups, they should not talk about them. All the scriptural imagery (harps, crowns, gold, etc.) is, of course, a merely symbolical attempt to express the inexpressible. Musical instruments are mentioned because for many people (not all) music is the thing known in the present life which most strongly suggests ecstasy and infinity. Crowns are mentioned to suggest the fact that those who are united with God in eternity share His splendour and power and joy. Gold is mentioned to suggest the timelessness of Heaven (gold does not rust) and the preciousness of it People who take these symbols literally might as well think that when Christ told us to be like doves, He meant that we were to lay eggs.

This was not merely the cellar maze crafted by Ronny Jessup, but also the labyrinth below Crete, where the Minotaur prowled and ate the flesh of those who dared enter its realm, but also Grendel’s far northern lair where Beowulf ventured, also the huge catacombs beneath the Mountains of Madness, where the Old Ones of Lovecraft’s story still waited to be called out of the depths of time or from another dimension, and this was as well the tunnel system under the terraforming atmosphere factories where brave Ripley had gone with a team of high-tech colonial marines on a bug hunt, to learn what happened to the colonists on the planet called LV-426. This was both reality and myth, concrete and symbol, the maze of homicidal desires and lust and hunger for power that spiraled to infinity within the deepest darkness of the human heart, male and female alike, here given dimension and immediacy. It was inhabited by a Grendel named Ulrich and a would-be hero who knew himself to be no hero at all, but only an imperfect man with something to prove to himself.

Do you have vows?” Freeman asked. Zane nodded, but he didn’t move to take out a piece of paper or any notes. He licked his lips instead and took a deep breath. “Ty,” he said, and the sound was almost lost in the night. “Some roads to love aren’t easy, and I’ve never been more thankful for being forced to fight for something. I started this journey with a partner I hated, and a man in the mirror I hated even more. The road took me from the streets of New York to the mountaintops of West Virginia, from the place I born to the place I found a home. It forced me to let go of my past and face my future. And I had to be made blind before I could see.” Zane swallowed hard and looked down, obviously fighting to finish without choking on the words or tearing up. Ty realized his own eyes were burning, and it wasn’t because of the cold wind. Zane squeezed Ty’s fingers with one hand, and he met Ty’s eyes as he reached into his lapel with his other. “I promise to love you until I die,” he said, his voice strong again. He held up a Sharpie he’d had in his suit, and pulled Ty’s hand closer to draw on his ring finger. With several sweeping motions, he created an infinity sign that looped all the way around the finger. When he was satisfied with the ring he’d drawn, he kissed Ty’s knuckles and let him go, handing him the Sharpie. Ty grasped the pen, but he couldn’t take his eyes off Zane. He ran his thumb over Zane’s palm. He had a set of vows he’d jotted down on a note card, folded up in his pocket, but he left them where they were and gazed into Zane’s eyes, their past flashing in front of him, their future opening up in his mind. He took a deep breath. “I promise to never leave you alone in the dark,” he whispered. He pulled Zane’s hand closer and pressed the tip of the Sharpie against Zane’s skin, curving the symbol for forever around it. When he was satisfied, he kissed the tip of Zane’s finger and slid the pen back into his lapel pocket. Freeman coughed and turned a page in his book. “Do you, Zane Zachary Garrett, take this man to be your lawful wedded husband?” Zane’s lips curved into a warm smile. “I do.” Freeman turned toward Ty. “Do you, Beaumont Tyler Grady, take this man to be your lawful wedded husband?” “I do,” Ty said, almost before the question was finished. “Then by the power vested in me by the state of Maryland, I pronounce you legally wed.” Freeman slapped his little book closed. “You may now share the first kiss of the rest of your lives.” Ty had fully expected to have the urge to grab Zane and plant one on him out of sheer impatience and joy, but as he stood staring at his brand-new husband, it was as if they were moving underwater. He touched the tips of his fingers to Zane’s cheek, then stepped closer and used both hands to cup his face with the utmost care. Zane was still smiling when they kissed, and it was slow and gentle, Zane’s hands at Ty’s ribs pulling them flush. “Okay, now,” Livi whispered somewhere to their side, and a moment later they were both pelted with handfuls of heart-shaped confetti. Zane laughed and finally wrapped his arms around Ty, squeezing him tight. The others continued to toss the confetti at them, even handing out bits to people passing by so they’d be sure to get covered from all sides. They laughed into the kiss, not caring. They were still locked in their happy embrace when Deuce turned the box over above them and rained little, bitty hearts down on their heads.

This is why, from this point on, no debt will be paid off. It can at best be bought back at a knock-down price and put back on to a debt market — the public sector borrowing requirement, the national debt, th e world deb t — having once again become an exchange value. It is unlikely the debt will ever be called in, and this is what gives it its incalculable value. For, suspended as it is in this way, it is our only insurance against time. Unlike the countdown, whic h signifies th e exhaustion of time, the indefinitely deferred debt is our guarantee that time itself is inexhaustible. Now, we very much need assuring about time in this way at the very poin t whe n the future itself is tendin g to be wholly consume d in real time . Clearing the debt, balancing up the books, writing off Third World debt — these are things not even to be contemplated. It is only the disequilibrium of the debt, its proliferation, its promise of infinity, which keeps us going. The global, planetary debt clearly has no meaning in traditional terms of obligation and credit. On the other hand, it is our true collective claim on each other — a symbolic claim, by whic h persons, companies and nations find themselves bound to one another through lack. Each is bound to the other (even the banks) by their virtual bankruptcy , as accomplices are bound by their crime. All assured of existing for each other in the shade of a debt which cannot be settled or written off, since the repayment of the accumulated world debt would take far more than the funds available. The only sense of it, then, is to bind all civilized human beings into the same destiny as creditors. Just as nuclear weapons, stockpiled across the world to a point of considerable planetary overkill, have no other meaning than to bind all human beings into a single destiny of threat and deterrence.

Imagine you can see the whole Number Line and every one of the infinite individual points it comprises. Imagine you want a quick and easy way to distinguish those points corresponding to rational numbers from the ones corresponding to irrationals. What you're going to do is ID the rational points by draping a bright-red hankie over each one; that way they'll stand out. Since geometric points are technically dimensionless, we don't know what they look like, but what we do know is that it's not going to take a very big red hankie to cover one. The red hankie here can in truth be arbitrarily small, like say .00000001 units, or half that size, or half that half,...,etc. Actually, even the smallest hankie is going to be unnecessarily large, but for our purposes we can say that the hankie is basically infinitesimally small-call such a size (infinitesimally small symbol). So a hankie of size (infinitesimally small symbol) covers the N.L.'s first rational point. Then, because of course the hankie can be as small as we want, let's say you use only a (Infinitesimally small symbol)/2-size hankie to drape over the next rational point. And say you go on like that, with the size of each red hankie used being exactly (1/2) that of the previous one, for all the rational numbers, until they're all draped and covered. Now, to figure out the total percentage of space all the rational points take up on the Number Line, all you have to do is add up the sizes of all the red hankies. Of course, there are infinitely many hankies, but size-wise they translate into the terms in an infinite series, specifically the Zeno-esque geometric series (1/2^0 +1/2^1 + 1/2^2 +1/2^3 +1/2^4 + ...; and, given the good old a/1-r formula for summing such a series, the sum-size of all the infinite hankies ends up being 2*(Infinitesimally small symbol). But (Infinitesimally small symbol) is infinitesimally small, with infinitesimals being (as we mentioned in Section 2b) so incredibly close to 0 that anything times an infinitesimal is also an infinitesimal, which means that 2*(Infinitesimally small symbol) is also infintesimally small, which means that all the infinite rational numbers combined take up only an infinitesimally small portion of the N.L.-which is to say basically none at all-which is in turn to say that the vast, vast bulk of the points on any kind of continuous line will correspond to irrational numbers, and thus that while the aforementioned Real Line really is a line, the all-rational Number Line, infinitely dense though it appears to be, is actually 99.999...% empty space, rather like DQ ice cream or the universe itself.

The tattoo Ty now had on his ring finger was the simple wrapped infinity symbol Zane had drawn, but when he moved his middle finger, it revealed an anchor woven in. A hidden reminder of what Zane was to him. Zane’s was the exact same thing, only with a simplified compass incorporated in.

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.

The purpose of consciousness—any consciousness—was to achieve infinite comprehension. It was as simple as that. If a God existed, humanity must strive to discover this God and help this deity become omniscient, not just in one infinity, but in an infinity of infinities. This was one possible purpose for her species. But her alter ego, using symbolic logic, had arrived at a possibility she considered much more likely: that humanity’s purpose, together with all life across all universes, was not to discover God—it was to become God. If a single human egg could possess consciousness at the instant of fertilization, how would it view itself? It couldn’t possibly predict or comprehend the multi-trillion-celled being it would ultimately become. The entirety of humanity could well be that single, fertilized cell, unaware that it would grow a trillion-fold more complex and eventually become God, perhaps had already become God, in a universe in which all pasts, presents, and futures existed side by side. Humanity was composed of separate individuals now, but an embryo at early stages was also nothing more than a ball of separate cells. But these separate cells would ultimately become connected in wondrous ways to create something unimaginably greater than themselves. And seen in this light, altruism and sociopathy were far from straightforward concepts, beyond even the complexities that Abraham Lincoln had revealed. Absolute altruism on one level could be absolute selfishness in disguise on another, and vice-versa. The cells making up the human body were selfless; gladly sacrificing themselves when necessary for the good of the organism. On the microscopic level they were being foolishly altruistic, foolishly suicidal, but on the macroscopic level they were being purely selfish—ensuring the survival of the body. And what happened when an individual cell became selfish and exhibited Nietzsche’s will to power? It became a cancer. The cell would break free of the restraints on its own division and become immortal—for a while—until its very immortality choked the entire organism to death, killing the selfish cell in the process.

The casting away of things is symbolic, you know. Talismanic. When you cast away things, you're also casting away the self-related others that are symbolically related to those things. You start a cleaning-out process. You begin to empty the vessel." Larry shook his head slowly. "I don't follow that." "Well, take an intelligent pre-plague man. Break his TV, and what does he do at night?" "Reads a book," Ralph said. "Goes to see his friends," Stu said. "Plays the stereo," Larry said, grinning. "Sure, all those things," Glen said. "But he's also missing that TV. There's a hole in his life where that TV used to be. In the back of his mind he's still thinking, At nine o'clock I'm going to pull a few beers and watch the Sox on the tube. And when he goes in there and sees that empty cabinet, he feels as disappointed as hell. A part of his accustomed life has been poured out, is it not so?" "Yeah," Ralph said. "Our TV went on the fritz once for two weeks and I didn't feel right until it was back." "It makes a bigger hole in his life if he watched a lot of TV, a smaller hole if he only used it a little bit. But something is gone. Now take away all his books, all his friends, and his stereo. Also remove all sustenance except what he can glean along the way. It's an emptying-out process and also a diminishing of the ego. Your selves, gentlemen--they are turning into a window-glass. Or better yet, empty tumblers." "But what's the point?" Ralph asked. "Why go through all the rigmarole?" Glen said, "If you read your Bible, you'll see that it was pretty traditional for these prophets to go out into the wilderness from time to time--Old Testament Magical Mystery Tours. The timespan given for these jaunts was usually forty days and forty nights, a Hebraic idiom that really means 'no one knows exactly how long he was gone, but it was quite a while.' Does that remind you of anyone?" "Sure. Mother," Ralph said. "Now think of yourself as a battery. You really are, you know. Your brain runs on chemically converted electrical current. For that matter, your muscles run on tiny charges, too--a chemical called acetylcholine allows the charge to pass when you need to move, and when you want to stop, another chemical, cholinesterase, is manufactured. Cholinesterase destroys acetylcholine, so your nerves become poor conductors again. Good thing, too. Otherwise, once you started scratching your nose, you'd never be able to stop. Okay, the point is this: Everything you think, everything you do, it all has to run off the battery. Like the accessories in a car." They were all listening closely. "Watching TV, reading books, talking with friends, eating a big dinner ... all of it runs off the battery. A normal life--at least in what used to be Western civilization--was like running a car with power windows, power brakes, power seats, all the goodies. But the more goodies you have, the less the battery can charge. True?" "Yeah," Ralph said. "Even a big Delco won't ever overcharge when it's sitting in a Cadillac." "Well, what we've done is to strip off the accessories. We're on charge." Ralph said uneasily: "If you put a car battery on charge for too long, she'll explode." "Yes," Glen agreed. "Same with people. The Bible tells us about Isaiah and Job and the others, but it doesn't say how many prophets came back from the wilderness with visions that had crisped their brains. I imagine there were some. But I have a healthy respect for human intelligence and the human psyche, in spite of an occasional throwback like East Texas here--" "Off my case, baldy," Stu growled. "Anyhow, the capacity of the human mind is a lot bigger than the biggest Delco battery. I think it can take a charge almost to infinity. In certain cases, perhaps beyond infinity." They walked in silence for a while, thinking this over. "Are we changing?" Stu asked quietly. "Yes," Glen answered. "Yes, I think we are.

For instance, if you keep taking on others’ feelings, inserting a 1 into your emotional boundary will help you put yourself first. Following are some of the meanings of the numbers 1 through 10, plus some powerful numbers above 10: 1:​Initiates and begins; invokes the Creator; brings your needs to a conclusion and puts yourself first. 2:​Represents pairing and duality; balances relationships; creates healthy liaisons; shares power. 3:​Reflects optimism; the number of creation, it brings a beginning and an end together; ends chaos. 4:​Signifies foundation and stability; provides grounding; achieves balance. 5:​Promotes and progresses; creates a space for decision-making; provides the ability to go in any direction at will. 6:​The number of service; indicates the presence of light and dark, good and evil, and the choices made between these. 7:​Represents the divine principle; opens us for love and grace, erasing doubts about the divine path. 8:​The symbol of power and infinity; establishes recurring patterns and illuminates karma; can be used to erase old and entrenched patterns or syndromes. 9:​Represents change and harmony; eliminates the old and opens us to a new cycle; can erase evil. 10:​Signifies building and starting over. The number of physical matter, it can create heaven on earth. 11:​Represents inspiration; releases personal mythology; opens us to divine powers; erases self-esteem issues. 12:​Signifies mastery over human drama; accesses own divine self, but still encompasses humanity; excellent for forgiveness. 22:​For success in anything you do. 33:​For teaching and accepting our own wisdom; invokes bravery and discipline.

In the presence chamber of your dreaming mind, I take upon myself the symbols and metaphors most apt to your understanding. This crown is my sovereignty; these breasts the source of milk that sustains and feeds the myriads of my galaxy; this veil my chastity; the bridal gown the sign of my surrender and coming mental union with Milky Way, an intimate violation more intimate than rape, or else a consummation more fertile; these chains are the cliometry of creation, which operates at a larger scale than the history of races and the evolution of stars. You have a dim memory of myth about a royal woman thus chained, also named Andromeda, fated to be fed to a sea monster. The symbolism is compelling. Also, I occupy a female hence submissive position, pleading for your chivalry.

The game spools on.” Deep in her abyss, Circe spun a finger, and a whirlpool circled here. Ever since my grandmother had told me to look for symbols, I’d been seeing them everywhere. Infinity symbols. A bow. A jagged fracture of rock like a lightning bolt. A vortex. I recalled my dreams: When the Magician had created that infinity symbol for Fauna, there’d already been one in that scene. Behind the two of them, the lions’ long tails had curved over each other, making two perfect loops. Patterns continued to appear before my eyes. Circe’s whirlpool was like a helicopter’s tailspin on its way down. Or a carousel that would never spin backward again. Like a tourniquet twisting. “But for how long?” she murmured, and her whirlpool tightened.

human beings love to invent stories. Baboons, though no less fascinating than us, spend only 10 percent of their time interpreting, adopting, and imitating others’ actions. The rest of their time they dedicate to finding food and nourishment. Our percentages are the complete opposite. We spend an astonishing amount of time trying to understand others—putting ourselves in their shoes, empathizing, acting as a mirror for their emotions and intentions. This tendency has been a major force in the development of our social intelligence. Other factors, of course, have played a role, but we are the only species that uses imagination. Every day we create real, probable, possible, impossible, and absurd scenarios. An infinity of fictions, one layered atop the other. We create things that don’t exist in nature, such as symbols. Along with histories, laws, institutions, governments. All of this is made up. And all of it hinges on the exchange of information: storytelling, forging alliances, establishing and disrupting social equilibriums, gossip.

He said, "I am. I'm--I'm pulling another card." He hesitated, waiting for her to tell him it wasn't allowed. But she just waited. Adam cut the deck, laid his hand on each stack. He took the card that felt warmer. Flipping it, he placed the card beside the nine of swords. A robed figure stood before a coin, a cup, a sword, and a wand--all of the symbols of the tarot suits. An infinity symbol floated above his head; one arm was lifted in a posture of power. Yes, thought Adam. Understanding prickled and then evaded him. He read the words at the bottom of the card. The Magician.

Maybe it wasn't about the number; maybe it was about the symbol. Infinity. Maybe because there were infinite questions to ask, maybe because wonder was limitless. There were so many variables so many unknowns.

A mark from the stars.” He admired it in the light and it glimmered with some deep, unknown magic. I stared at him as he looked up at me once more and a grin split across his face which I immediately returned. He held his hand out to me to clasp and where I hands joined, the marks created an infinity symbol connecting us to one another. “Holy shit, fratello. I think the stars just made us best friends.

It was a gold necklace with seven small diamonds lined up in the center of a gold infinity symbol charm.

Timelessly, that flame flickered. Unquenchable upon its undying wick. Fluctuating, pulsating, Dimming to near darkness at moments only to spark the clearer. Endlessly, that fire wickered. Ubiquitous in its guiding light. Permeating, coalescing, All-encompassing of the smallest point and grandest of spheres. Boundlessly, that blaze bickered. Ultimate in its infinite valour. Contesting, challenging, And settling with the edge of infinity, that ultimate bound severe.

However, in regard to these more sophisticated applications, the system was not universal. Since there was no higher-valued symbol than (one thousand), the numerals from two thousand onwards all began with a string of ’s, which therefore became nothing more than tally marks for thousands.

From the epistemological side, Hilbert's point of view reduces to a strict limitation to the finite; all mathematical sentences in which the infinity enters one way or the other are declared devoid of any meaning. True, with a brilliant skill, Hilbert recovers rejected mathematical theories in the form of a formal consistent game of symbols. Yet, this way out, giving no explanation of what sustained mathematics to date, of why, while expressing judgments about infinity that have no meaning, mathematicians understood each other, is dictated only by inability to find a more satisfactory way out.

The Enlightened mind sees truly – without distinction – anything that comes before it; it understands the true nature of everything, just as a mirror faithfully reflects all objects. If one looks into the depths of the Enlightened mind one sees everything. It is like the experience of Sudhana as described in the Gandavyuha-Sutra. Sudhana is a pilgrim wandering in search of truth, and at the crucial point of the sutra he reaches a magnificent tower in south India. Entering the tower he sees the whole cosmos mirrored, stretching out to infinity – but all contained within this magical tower. In fact, the tower is a symbol of the bodhicitta, or of the Enlightened mind itself.

No, emptiness is not nothingness. Emptiness is a type of existence. You must use this existential emptiness to fill yourself.” His words were very enlightening to me. Later, after I thought about it a bit, I realized that it wasn’t Buddhist philosophy at all, but was more akin to some modern physics theories. The abbot also told me he wasn’t going to discuss Buddhism with me. His reason was the same as my high school teacher’s: With my sort, he’d just be wasting his time. That first night, I couldn’t sleep in the tiny room in the temple. I didn’t realize that this refuge from the world would be so uncomfortable. My blanket and sheet both became damp in the mountain fog, and the bed was so hard. In order to make myself sleep, I tried to follow the abbot’s advice and fill myself with “emptiness.” In my mind, the first “emptiness” I created was the infinity of space. There was nothing in it, not even light. But soon I knew that this empty universe could not make me feel peace. Instead, it filled me with a nameless anxiety, like a drowning man wanting to grab on to anything at hand. So I created a sphere in this infinite space for myself: not too big, though possessing mass. My mental state didn’t improve, however. The sphere floated in the middle of “emptiness”—in infinite space, anywhere could be the middle. The universe had nothing that could act on it, and it could act on nothing. It hung there, never moving, never changing, like a perfect interpretation for death. I created a second sphere whose mass was equal to the first one’s. Both had perfectly reflective surfaces. They reflected each other’s images, displaying the only existence in the universe other than itself. But the situation didn’t improve much. If the spheres had no initial movement—that is, if I didn’t push them at first—they would be quickly pulled together by their own gravitational attraction. Then the two spheres would stay together and hang there without moving, a symbol for death. If they did have initial movement and didn’t collide, then they would revolve around each other under the influence of gravity. No matter what the initial conditions, the revolutions would eventually stabilize and become unchanging: the dance of death. I then introduced a third sphere, and to my astonishment, the situation changed completely. Like I said, any geometric figure turns into numbers in the depths of my mind. The sphereless, one-sphere, and two-sphere universes all showed up as a single equation or a few equations, like a few lonesome leaves in late fall. But this third sphere gave “emptiness” life. The three spheres, given initial movements, went through complex, seemingly never-repeating movements. The descriptive equations rained down in a thunderstorm without end. Just like that, I fell asleep. The three spheres continued to dance in my dream, a patternless, never-repeating dance. Yet, in the depths of my mind, the dance did possess a rhythm; it was just that its period of repetition was infinitely long. This mesmerized me. I wanted to describe the whole period, or at least a part of it. The next day I kept on thinking about the three spheres dancing in “emptiness.” My attention had never been so completely engaged. It got to the point where one of the monks asked the abbot whether I was having mental health issues. The abbot laughed and said, “Don’t worry. He has found emptiness.” Yes, I had found emptiness. Now I could be at peace in a bustling city. Even in the midst of a noisy crowd, my heart would be completely tranquil.

And then they half-ran, half-skipped the last eight blocks to her apartment, their bodies connected by their crossed arms. Half a block away, their combined shadow looked like the wings of a single sea bird, wheeling in a bright sky. Two blocks further, and they looked like two boats, alone on an endless ocean. One block from that, and their joined bodies merged into a symbol of infinity.

The fear, as I analyze it in retrospect, was of being overwhelmed, of disintegrating under a pressure of reality greater than a mind, accustomed to living most of the time in a cosy world of symbols, could possibly bear. The literature of religious experience abounds in references to the pains and terrors overwhelming those who have come, too suddenly, face to face with some manifestation of the Mysterium tremendum. In theological language, this fear is due to the in- compatibility between man's egotism and the divine purity, between man's self-aggravated separateness and the infinity of God. Following Boehme and William Law, we may say that, by unregenerate souls, the divine Light at its full blaze can be apprehended only as a burning, purgatorial fire. An almost identical doctrine is to be found in The Tibetan Book of the Dead, where the departed soul is described as shrinking in agony from the Pure Light of the Void, and even from the lesser, tempered Lights, in order to rush headlong into the comforting darkness of selfhood as a reborn human being, or even as a beast, an unhappy ghost, a denizen of hell. Anything rather than the burning brightness of unmitigated Reality - anything!

The word or symbol infinity represents something that is seemingly ongoing, never ending, beyond calculation.

It is absolutely from his vision of the whole, in which the genius always lives, that he gets his sense of the parts. He values everything within him or without him by the standard of this vision, a vision that for him is no function of time, but a part of eternity. . . . The scientist takes phenomena for what they obviously are; the great man or the genius for what they signify. Sea and mountain, light and darkness, spring and autumn, cypress and palm, dove and swan are symbols to him, he not only thinks that there is, but he recognizes in them something deeper. The ride of the Valkyrie is not produced by atmospheric pressure and the magic fire is not the outcome of a process of oxidation. And all this is possible for him because the outer world is as full and strongly connected as the inner in him, the external world in fact seems to be only a special aspect of his inner life; the universe and the ego have become one in him, and he is not obliged to set his experience together piece by piece according to rule. . . .The infinity of the universe is responded to in the genius by a true sense of infinity in his own breast; he holds chaos and cosmos, all details and all totality, all plurality, and all singularity in himself.

I stopped numbering my pages. Infinity seems to be a better number and my story is still unwritten. Besides, I do like its symbol a lot— a sleeping 8

But nothing is more difficult than to accept the last impassable border. Everything finite would like to extend itself into infinity. The individual wants to continue his life indefinitely, and in many Christian lands a superstition has developed inside and outside the churches which misinterprets eternal life as endless duration, and does not perceive that an infinity of the finite could be a symbol for hell. In the same way, families resist their finitude in time and in space and destroy each other in a reciprocal battle to eliminate the frontier. But most important for the possibility of peace is the acceptance of their own finitude by the nations - of their time, of their space, and of the finitude of their worth.

Dalle stelle,” Dante said heavily, our hands breaking apart. Then he lunged at me, wrapping me in his arms and I grunted in surprise before winding my arms around him too and holding him tight. I noticed a mark on my hand like half of a figure of eight as it locked around Inferno’s shoulder. As he stepped back, I pointed out one on his too, nestled between the crook of his forefinger and thumb just as mine was. “What is that?” I murmured. “A mark from the stars.” He admired it in the light and it glimmered with some deep, unknown magic. I stared at him as he looked up at me once more and a grin split across his face which I immediately returned. He held his hand out to me to clasp and where I hands joined, the marks created an infinity symbol connecting us to one another. “Holy shit, fratello. I think the stars just made us best friends.