Two Dimensional Quotes

Love is made up of three unconditional properties in equal measure: 1. Acceptance 2. Understanding 3. Appreciation Remove any one of the three and the triangle falls apart. Which, by the way, is something highly inadvisable. Think about it — do you really want to live in a world of only two dimensions? So, for the love of a triangle, please keep love whole.

It had become one of the defining truths of my life that, no matter how I tried to keep them flattened, two-dimensional, jailed in paper and ink, there would always be stories that refused to stay bound inside books. It was never just a story. I would know: a story had swallowed my whole life.

If a shadow is a two-dimensional projection of the three-dimensional world, then the three-dimensional world as we know it is the projection of the four-dimensional Universe.

Imagine a poem written with such enormous three-dimensional words that we had to invent a smaller word to reference each of the big ones; that we had to rewrite the whole thing in shorthand, smashing it into two dimensions, just to talk about it. Or don’t imagine it. Look outside. Human language is our attempt at navigating God’s language; it is us running between the lines of His epic, climbing on the vowels and building houses out of the consonants.

No matter how people mess with you or let you down, or how you let yourself down, a good book means that when you get in bed that night, you have a good hour. I feel like you pay all day for that hour. That's what books mean to me. I can open this two-dimensional, flat white page with squiggly little black marks on them, and someone has created this world that you're going to enter into ...

I was in love. With a two-dimensional object. A mute in love with a painting. Lovely. Just lovely.

A map is a two-dimensional representation with arbitrary symbols and incised lines that decide who is to be our enemy and who is to be our friend, who deserves our love and who deserves our hatred and who, our sheer indifference. Cartography is another name for stories told by winners. For stories told by those who have lost, there isn’t one.

In the shooter hypothesis, a good marksman shoots at a target, creating a hole every ten centimeters. Now suppose the surface of the target is inhabited by intelligent, two-dimensional creatures. Their scientists, after observing the universe, discover a great law: “There exists a hole in the universe every ten centimeters.” They have mistaken the result of the marksman’s momentary whim for an unalterable law of the universe. The farmer hypothesis, on the other hand, has the flavor of a horror story: Every morning on a turkey farm, the farmer comes to feed the turkeys. A scientist turkey, having observed this pattern to hold without change for almost a year, makes the following discovery: “Every morning at eleven, food arrives.” On the morning of Thanksgiving, the scientist announces this law to the other turkeys. But that morning at eleven, food doesn’t arrive; instead, the farmer comes and kills the entire flock.

Stop!” His voice rings out sharply, hard as a slap. He releases me and I stumble backward. “Alex is dead, do you hear me? All of that—what we felt, what it meant—that’s done now, okay? Buried. Blown away.” “Alex!” He has started to turn away; now he whirls around. The moon lights him stark white and furious, a camera image, two-dimensional, gripped by the flash. “I don’t love you, Lena. Do you hear me? I never loved you.” The air goes. Everything goes. “I don’t believe you.” I’m crying so hard, I can hardly speak. He takes one step toward me. And now I don’t recognize him at all. He has transformed entirely, turned into a stranger. “It was a lie. Okay? It was all a lie. Craziness, like they always said. Just forget about it. Forget it ever happened.

And, I think: I am but one more drop in the great sea of matter, defined, with the ability to realize my existence. Of the millions, I, too, was potentially everything at birth. I, too, was stunted, narrowed, warped, by my environment, my outcroppings of heredity. I, too, will find a set of beliefs, of standards to live by, yet the very satisfaction of finding them will be marred by the fact that I have reached the ultimate in shallow, two-dimensional living — a set of values.

If I was feeling depressed or frustrated about my lot in life, all I had to do was tap the Player One button, and my worries would instantly slip away as my mind focused itself on the relentless pixelated onslaught on the screen in front of me. There, inside the game's two-dimensional universe, life was simple: It's just you against the machine. Move with your left hand, shoot with your right, and try to stay alive as long as possible.

Since a three-dimensional object casts a two-dimensional shadow, we should be able to imagine the unknown four-dimensional object whose shadow we are. I for my part am fascinated by the search for a one-dimensional object that casts no shadow at all.

Men who read it [beauty pornography] don't do so because they want women who look like that. The attraction of what they are holding is that it is not a woman, but a two-dimensional woman-shaped blank. The appeal of the material is not the fantasy that the model will come to life; it is precisely that she will not, ever. Her coming to life would ruin the vision. It is not about life. Ideal beauty is ideal because it does not exist; The action lies in the gap between desire and gratification. Women are not perfect beauties without distance. That space, in a consumer culture, is a lucrative one. The beauty myth moves for men as a mirage, its power lies in its ever-receding nature. When the gap is closed, the lover embraces only his own disillusion.

Behold yon miserable creature. That Point is a Being like ourselves, but confined to the non-dimensional Gulf. He is himself his own World, his own Universe; of any other than himself he can form no conception; he knows not Length, nor Breadth, nor Height, for he has had no experience of them; he has no cognizance even of the number Two; nor has he a thought of Plurality, for he is himself his One and All, being really Nothing. Yet mark his perfect self-contentment, and hence learn this lesson, that to be self-contented is to be vile and ignorant, and that to aspire is better than to be blindly and impotently happy.

That is why historians surprise me. They seem to have no talent for the likeliness of any situation. They see history like a peepshow; with two-dimensional figures against a distant background.

...I am the two-dimensional one in a 3-D family.

You see, you have feelings. You can appreciate the inner me. Like right now I feel a closeness between us that Ive never felt with anyone before … anyone. Yeah, I know what you mean. Thats how I feel. I don’t know if I can put it into words, but— Thats just it, it doesnt need words. Thats the whole point. Like whats the use of all those words when the feelings arent behind them. Theyre just words. Like I can look at a painting and tell it, youre beautiful. What does it mean to the painting? But Im not a painting. Im not two dimensional. Im a person. Even a Botticelli doesnt breathe and have feelings. Its beautiful, but its still a painting. No matter how beautiful the outside may be, the inside still has feelings and needs that just words dont fulfill.

And carefully... tenderly... taking my time with every brushstroke, I sketch the curve of her neck, apply the crimson of her lips, form her face into a two-dimensional tribute to her beauty.

That means that the universe is two-dimensional. Matter, energy, time, you, me and the floor are holograms.

How much did you read?’ Sophia said. ‘Not much. I found your characters a bit two-dimensional.

Just a story. It had become one of the defining truths of my life that, no matter how I tried to keep them flattened, two-dimensional, jailed in paper and ink, there would always be stories that refused to stay bound inside books. It was never just a story. I would know: a story had swallowed my whole life.

Cheng Xin now recalled the strange feeling she had experienced each time she had looked at Van Gogh’s painting. Everything else in the painting—the trees that seemed to be on fire, and the village and mountains at night—showed perspective and depth, but the starry sky above had no three-dimensionality at all, like a painting hanging in space. Because the starry night was two-dimensional. How could Van Gogh have painted such a thing in 1889? Did he, having suffered a second breakdown, truly leap across five centuries

People are afraid of shadows. People are even more afraid of being in the shadow. But without a shadow, life will be two dimensional.

I'm also old... and my own gift for writing fantasy grows out of very literal-minded, pragmatic soil: the things I do when I'm not telling stories have always been pretty three-dimensional. I used to say that the only strong attraction reality ever had for me was horses and horseback riding, but I've also been cooking and going for long walks since I was a kid (yes, the two are related), and I'm getting even more three dimensionally biased as I get older — gardening, bell ringing... piano playing... And the stories I seem to need to write seem to need that kind of nourishment from me — how you feed your story telling varies from writer to writer. My story-telling faculty needs real-world fresh air and experiences that create calluses (and sometimes bruises).

Julia had a friend, a man named Dennys, who was as a boy a tremendously gifted artist. They had been friends since they were small, and she once showed me some of the drawings he made when he was ten or twelve: little sketches of birds pecking at the ground, of his face, round and blank, of his father, the local veterinarian, his hand smoothing the fur of a grimacing terrier. Dennys’s father didn’t see the point of drawing lessons, however, and so he was never formally schooled. But when they were older, and Julia went to university, Dennys went to art school to learn how to draw. For the first week, he said, they were allowed to draw whatever they wanted, and it was always Dennys’s sketches that the professor selected to pin up on the wall for praise and critique. But then they were made to learn how to draw: to re-draw, in essence. Week two, they only drew ellipses. Wide ellipses, fat ellipses, skinny ellipses. Week three, they drew circles: three-dimensional circles, two-dimensional circles. Then it was a flower. Then a vase. Then a hand. Then a head. Then a body. And with each week of proper training, Dennys got worse and worse. By the time the term had ended, his pictures were never displayed on the wall. He had grown too self-conscious to draw. When he saw a dog now, its long fur whisking the ground beneath it, he saw not a dog but a circle on a box, and when he tried to draw it, he worried about proportion, not about recording its doggy-ness.

Just a story. It had become one of the defining truths of my life that, no matter how I tried to keep them flattened, two-dimensional, jailed in paper and ink, there would always be stories that refused to stay bound inside books. It was never just a story.

A map is a two-dimensional representation with arbitrary symbols and incised lines that decide who is to be our enemy and who is to be our friend, who deserves our love and who deserves our hatred and who, our sheer indifference.

There, inside the game’s two-dimensional universe, life was simple: It’s just you against the machine. Move with your left hand, shoot with your right, and try to stay alive as long as possible.

He looks at me incredulously. "I think you're amazing..." Why would he think this? Bailey is amazing and Gram and Big, and of course Mom, but not me. I am the two-dimensional one in a 3-D Family

As Solomon himself had remarked, 'We can be sure of talent, we can only pray for genius.' But it was a reasonable hope that in such concentrated society some interesting reactions would take place. Few artists thrive in solitude and nothing is more stimulating than the conflict of minds with similar interests. So far, the conflict had produced worthwhile results in sculpture, music, literary criticism and film making. It was still too early to see if the group working on historical research would fulfil the hopes of its instigators, who were frankly hoping to restore mankind's pride in its own achievements. Painting still languished which supported the views of those who considered that static, two dimensional forms of art had no further possibilities. It was noticeable, though a satisfactory explanation for this had not yet been produced that time played an essential part in the colony's achievements.

beyond the tilled plain, beyond the toy roofs, there would be a low suffusion of inutile loveliness, a low sun in a platinum haze with a warm, peeled-peach tinge pervading the upper edge of a two-dimensional, dove-grey cloud fusing with the distant amorous mist. there might be a line of spaced trees silhouetted against the horizon, and hot still noons above a wilderness of clover, and claude lorrain clouds inscribed remotely into misty azure with only their cumulus part conscpicuous against the neutral swoon of the background. or again, it might be a stern el greco horizon, pregnant with inky rain, and a passing glimpse of some mummy-necked farmer, and all around alternating strips of quick-silverish water and harsh green corn, the whole arrangement opening like a fan, somewhere in kansas.

Since a three-dimensional object casts a two-dimensional shadow, we should be able to imagine the unknown four-dimensional object whose shadow we are.

The thing is you're looking for something two-dimensional and not quite real. It never lasts. But you can't expect something unreal to last anyway, can you?

Even when he seems to be interacting with someone else, the narcissist is actually engaged in a self-referential discourse. To the narcissist, all other people are cardboard cutouts, two-dimensional animated cartoon characters, or symbols. They exist only in his inner universe. He is startled when they deviate from the script and prove to be complex and autonomous.

The Matrix has its roots in primitive arcade games,' said the voice-over, 'in early graphics programs and military experimentation with cranial jacks.' On the Sony, a two-dimensional space war faded behind a forest of mathematically generated ferns, demonstrating the spatial possibilities of logarithmic spirals; cold blue military footage burned through, lab animals wired into test systems, helmets feeding into fire control circuits of tanks and war planes. 'Cyberspace. A consensual hallucination experienced daily by billions of legitimate operators, in every nation, by children being taught mathematical concepts... A graphic representation of data abstracted from the banks of every computer in the human system. Unthinkable complexity. Lines of light ranged in the nonspace of the mind, clusters and constellations of data. Like city lights, receding...

People may chuckle appreciatively at a male turkey that tries to mate with a poor rendition of a female's [suspended] head, but if you then point out that many a human male regularly gets aroused after looking at two-dimensional representations of a nude woman, they don't see the connection.

Politicians in our times feed their clichés to television, where even those who wish to disagree repeat them. Television purports to challenge political language by conveying images, but the succession from one frame to another can hinder a sense of resolution. Everything happens fast, but nothing actually happens. Each story on televised news is ”breaking” until it is displaced by the next one. So we are hit by wave upon wave but never see the ocean. The effort to define the shape and significance of events requires words and concepts that elude us when we are entranced by visual stimuli. Watching televised news is sometimes little more than looking at someone who is also looking at a picture. We take this collective trance to be normal. We have slowly fallen into it. More than half a century ago, the classic novels of totalitarianism warned of the domination of screens, the suppression of books, the narrowing of vocabularies, and the associated difficulties of thought. In Ray Bradbury’s Fahrenheit 451, published in 1953, firemen find and burn books while most citizens watch interactive television. In George Orwell’s 1984, published in 1949, books are banned and television is two-way, allowing the government to observe citizens at all times. In 1984, the language of visual media is highly constrained, to starve the public of the concepts needed to think about the present, remember the past, and consider the future. One of the regime’s projects is to limit the language further by eliminating ever more words with each edition of the official dictionary. Staring at screens is perhaps unavoidable, but the two-dimensional world makes little sense unless we can draw upon a mental armory that we have developed somewhere else. When we repeat the same words and phrases that appear in the daily media, we accept the absence of a larger framework. To have such a framework requires more concepts, and having more concepts requires reading. So get the screens out of your room and surround yourself with books. The characters in Orwell’s and Bradbury’s books could not do this—but we still can.

Just a story. It had become one of the defining truths in my life that, no matter how hard I tried to keep them flattened, two-dimensional, jailed in paper and ink, there would always be stories that refused to stay bound inside books. It was never just a story. I would know: a story had swallowed my whole life.

Don’t try to fit me in a box… My life is not one dimensional. I’m the summer breeze and the hurricane… I’m the serene lake and the raging ocean… I’m the gentle poet and the rough warrior… I can build and I can destroy... I can romance and I can ravage... I can be wise and I can be silly... I can and WILL be everything that the length, depth, and breadth of life will allow... KNOW THIS! Your labels don’t limit me… they limit your experience of me. Don’t confuse the two.

But what is passion, what are emotions? There is the source of fire, there is the fullness of energy. A man who is not on fire is nothing: he is ridiculous, he is two-dimensional. He must be on fire even if he does make a fool of himself. A flame must burn somewhere, otherwise no light shines; there is no warmth, nothing.

Our leading candidate for a theory of everything is known as M-theory. It grew from a merger of the two seemingly different approaches: 11-dimensional supergravity and 10-dimensional superstring theory. Could this be the final theory of everything?

Our eyes also fool us into thinking we can see depth. The retinas of our eyes are two-dimensional, but because we have two eyes separated by a few inches, the left and right brain merge these two images, giving us the false sense of a third dimension.

As every architect or designer knows, there is a critical step between vision and reality. Before imagination becomes three-dimensional, it usually needs to become two-dimensional. It’s as though the unseen order needs to come to life one dimension at a time.

For instance, a race of hyperintelligent pan-dimensional beings once built themselves a gigantic supercomputer called Deep Thought to calculate once and for all the Question to the Ultimate Answer of Life, the Universe and Everything. For seven and a half million years, Deep Thought computed and calculated, and in the end announced that the answer was in fact Forty-two—and so another, even bigger, computer had to be built to find out what the actual question was. And this computer, which was called the Earth, was so large that it was frequently mistaken for a planet—especially by the strange apelike beings who roamed its surface, totally unaware that they were simply part of a gigantic computer program. And this is very odd, because without that fairly simple and obvious piece of knowledge, nothing that ever happened on the Earth could possibly make the slightest bit of sense.

Oh, Martin, is that it? I seem too nice and too harmless, so I must be hiding some sinister secret, like we're nothing but two-dimensional characters in some bad novel?

Using two-dimensional lenses to perceive the multi-faceted world can limit your ability to observe the world more objectively.

I am the two-dimensional one in a 3-D family.

Behold yon miserable creature. That Point is a Being like ourselves, but confined to the non-dimensional Gulf. He is himself his own World, his own Universe; of any other than himself he can form no conception; he knows not Length, nor Breadth, nor Height, for he has had no experience of them; he has no cognizance even of the number Two; nor has he a thought of Plurality; for he is himself his One and All, being really Nothing. Yet mark his perfect self-contentment, and hence learn his lesson, that to be self-contented is to be vile and ignorant, and that to aspire is better than to be blindly and impotently happy. Now listen.

the three-dimensional world of ordinary experience—the universe filled with galaxies, stars, planets, houses, boulders, and people—is a hologram, an image of reality coded on a distant two-dimensional surface. This new law of physics, known as the Holographic Principle, asserts that everything inside a region of space can be described by bits of information restricted to the boundary.

It's like we're strands of wire intertwined in a great cable that runs through a slot . . . Most people lead two-dimensional lives. All they can see is the face of the slot, a cross section, so that the wires look like a mass of separate little circles looking bigger or smaller according to how close you are. They don't--they can't see that these 'circles' are just cross sections of wires that run backward and forward infinitely and that there is a great surge through the whole cable and that anybody who is truly into the full bare essence of the thing...

Between takeoff and landing, we are each in suspended animation, a pause between chapters of our lives. When we stare out the window into the sun's glare, the landscape is only a flat projection with mountain ranges reduced to wrinkles in the continental skin. Oblivious to our passage overhead, other stories are unfolding beneath us. Blackberries ripen in the August sun, a woman packs a suitcase and hesitates at her doorway, a letter is opened and the most surprising photograph slides from between the pages. But we are moving too fast and we are too far away; all the stories escape us, except our own. When I turn away from the window, the stories recede into the two-dimensional map of green and brown below. Like a trout disappearing into the shade of an overhanging bank, leaving you staring at the flat surface of the water and wondering if you saw it at all.

The Tears of Dark Water is not really “about” Somali piracy. It is about the multi-dimensional fallout of Somalia’s disintegration over the past two decades. Piracy offered me a narrative framework to explore not only how a hijacking and hostage crisis could end in tragedy but also how the breakdown of social order on land could inspire young Somalis to take to the ocean.

Long live transfinite mountains, the hollow earth, time machines, fractal writing, aliens, dada, telepathy, flying saucers, warped space, teleportation, artificial reality, robots, pod people, hylozoism, endless shrinking, intelligent goo, antigravity, surrealism, software highs, two-dimensional time, gnarly computation, the art of photo composition, pleasure zappers, nanomachines, mind viruses, hyperspace, monsters from the deep and, of course, always and forever, the attack of the giant ants!

In 1817 the twenty-two-year-old poet John Keats wrote a letter to his brothers in which he explained his most recent thoughts on the creative process. The world around us, he wrote, is far more complex than we can possibly imagine. With our limited senses and consciousness, we only glimpse a small portion of reality. Furthermore, everything in the universe is in a state of constant flux. Simple words and thoughts cannot capture this flux or complexity. The only solution for an enlightened person is to let the mind absorb itself in what it experiences, without having to form a judgment on what it all means. The mind must be able to feel doubt and uncertainty for as long as possible. As it remains in this state and probes deeply into the mysteries of the universe, ideas will come that are more dimensional and real than if we had jumped to conclusions and formed judgments early on. To accomplish this, he wrote, we must be capable of negating our ego. We are by nature fearful and insecure creatures. We do not like what is unfamiliar or unknown. To compensate for this, we assert ourselves with opinions and ideas that make us seem strong and certain. Many of these opinions do not come from our own deep reflection, but are instead based on what other people think. Furthermore, once we hold these ideas, to admit they are wrong is to wound our ego and vanity. Truly creative people in all fields can temporarily suspend their ego and simply experience what they are seeing, without the need to assert a judgment, for as long as possible. They are more than ready to find their most cherished opinions contradicted by reality.

In the long run, you see, none of that matters. I've seen Heaven, Dowling. And it's not a place where you exercise any power. In the long run, we are all three-dimensional side-effects of a two-dimensional universe existing in a multidimensional stack.

There’s a cellular automaton called TVC. After Turing, von Neumann and Chiang. Chiang’s version was N-dimensional. That leaves plenty of room for data within easy reach. In two dimensions, the original von Neumann machine had to reach further and further - and wait longer and longer - for each successive bit of data. In a six-dimensional TVC automaton, you can have a three-dimensional grid of computers, which keeps on growing indefinitely - each with its own three-dimensional memory, which can also grow without bound. And when the simulated TVC universe being run on the physical computer is suddenly shut down, the best explanation for what I’ve witnessed will be a continuation of that universe - an extension made out of dust. Maria could almost see it: a vast lattice of computers, a seed of order in a sea of random noise, extending itself from moment to moment by sheer force of internal logic, “accreting” the necessary building blocks from the chaos of non-space-time by the very act of defining space and time.

What we are looking for in reading the Bible is the ability to turn the two-dimensional words on paper into a three-dimensional encounter with God, so that the text takes on life and meaning and depth and perspective and gives us direction for what to do today.

Here I am, a bundle of past recollections and future dreams, knotted up in a reasonably attractive bundle of flesh. I remember what this flesh has gone through; I dream of what it may go through. I record here the actions of optical nerves, of taste buds, of sensory perception. And, I think: I am but one more drop in the great sea of matter, defined, with the ability to realize my existence. Of the millions, I, too, was potentially everything at birth. I, too, was stunted, narrowed, warped, by my environment, my outcroppings of heredity. I, too, will find a set of beliefs, of standards to live by, yet the very satisfaction of finding them will be marred by the fact that I have reached the ultimate in shallow, two-dimensional living - a set of values. This loneliness will blur and diminish, no doubt, when tomorrow I plunge again into classes, into the necessity of studying for exams. But now, that false purpose is lifted and I am spinning in a temporary vacuum. At home I rested and played, here, where I work, the routine is momentarily suspended and I am lost. There is no living being on earth at this moment except myself. I could walk down the halls, and empty rooms would yawn mockingly at me from every side. God, but life is loneliness, despite all the opiates, despite the shrill tinsel gaiety of "parties" with no purpose, despite the false grinning faces we all wear. And when at last you find someone to whom you feel you can pour out your soul, you stop in shock at the words you utter - they are so rusty, so ugly, so meaningless and feeble from being kept in the small cramped dark inside you so long. Yes, there is joy, fulfillment and companionship - but the loneliness of the soul in it's appalling self-consciousness, is horrible and overpowering.

Actresses talking about characters they’ve played often use the phrase “strong woman”, which kind of irks me. Firstly, the description appears to be reserved for two kinds of female: the gun-toting chick in tiny-vest-and-shorts combo, or the tough-talking businesswoman who secretly longs for a man to bring out her softer side. So obviously, our idea of strength is pretty narrow and one-dimensional. Secondly, why isn’t Brad Pitt ever asked about how much he enjoys playing a “strong man”? Is it automatically assumed that men’s roles will be complex and interesting?

We have one real candidate for changing the rules; this is string theory. In string theory the one-dimensional trajectory of a particle in spacetime is replaced by a two-dimensional orbit of a string. Such strings can be of any size, but under ordinary circumstances they are quite tiny, ... a value determined by comparing the predictions of the theory for Newton's constant and the fine structure constant to experimental values.

One of my great wishes is that people of the present will see those of the past as friendly (or irritating) acquaintances they can look to for advice. It’s easy to forget that people from the past weren’t the two-dimensional black-and-white photos or line drawings you might encounter in some dry textbooks. They weren’t just gray-faced guys in top hats. They were living, breathing, joking, burping people, who could be happy or sad, funny or boring, cool or the lamest people you ever met in your life. They had no idea they were living in the past. They all thought they were living in the present. Accordingly, like any person, past or present, could be, some of them were smart and kind and geniuses about medicine and also completely dull on a personal level. (I’m trying to come to terms with loving John Snow’s deductive brilliance and being absolutely certain I would never want to spend more than ten minutes talking to him.)

I kept thinking, as I was telling Didi, that somehow what was in my head--in my memory, in my thoughts--was not being translated fully into the world. I felt as though three-dimensional people and events were becoming two-dimensional in the telling, and as though they were smaller as well as flatter, that they were just less for being spoken. What was missing was the intense emotion that I felt, which, like water or youth itself, buoyed these small insignificant encounters into all that they meant to me. There they were, shrinking before my eyes, shrinking into my words. Anything that can be said, can be said clearly. Anything that cannot be said clearly, cannot be said.

The learning principle is to plunge into the detailed mystery of the micro in order to understand what makes the macro tick. Our obstacle is that we live in an attention-deficit culture. We are bombarded with more and more information on television, radio, cell phones, video games, the Internet. The constant supply of stimulus has the potential to turn us into addicts, always hungering for something new and prefabricated to keep us entertained. When nothing exciting is going on, we might get bored, distracted, separated from the moment. So we look for new entertainment, surf channels, flip through magazines. If caught in these rhythms, we are like tiny current-bound surface fish, floating along a two-dimensional world without any sense for the gorgeous abyss below. When these societally induced tendencies translate into the learning process, they have devastating effect.

Staring at screens is perhaps unavoidable, but the two-dimensional world makes little sense unless we can draw upon a mental armoury that we have developed somewhere else. When we repeat the same words and phrases that appear in the daily media, we accept the absence of a larger framework. To have such a framework requires more concepts, and having more concepts requires reading. So get the screens out of your room and surround yourself with books. The characters in Orwell's and Bradbury's books could not do this - but we still can.

We are the Western World. We read, see, think. Left. To. Right. We can't help it. ..The problem with Top to Bottom is that it's unAmerican. We want to begin in the depths and climb our way upward. But our typographic system argues against this and wins, and images follow suit. ..What you have to be careful to remember about Big and Small, is that they can extend to infinity in either direction. Consider: Big can always be bigger and Small smaller. The atom is the Universe and vice versa. And they're both identical. ..Left to Right, Top to Bottom, Big and Small; on a two-dimensional plane, all of these tools rely on a relative truth. Now we come to In Front Of and In Back of, which for us are big, fat lies. Very useful though, and the first of many at your disposal.

When The Matrix debuted in 1999, it was a huge box-office success. It was also well received by critics, most of whom focused on one of two qualities—the technological (it mainstreamed the digital technique of three-dimensional “bullet time,” where the on-screen action would freeze while the camera continued to revolve around the participants) or the philosophical (it served as a trippy entry point for the notion that we already live in a simulated world, directly quoting philosopher Jean Baudrillard’s 1981 reality-rejecting book Simulacra and Simulation). If you talk about The Matrix right now, these are still the two things you likely discuss. But what will still be interesting about this film once the technology becomes ancient and the philosophy becomes standard? I suspect it might be this: The Matrix was written and directed by “the Wachowski siblings.” In 1999, this designation meant two brothers; as I write today, it means two sisters. In the years following the release of The Matrix, the older Wachowski (Larry, now Lana) completed her transition from male to female. The younger Wachowski (Andy, now Lilly) publicly announced her transition in the spring of 2016. These events occurred during a period when the social view of transgender issues radically evolved, more rapidly than any other component of modern society. In 1999, it was almost impossible to find any example of a trans person within any realm of popular culture; by 2014, a TV series devoted exclusively to the notion won the Golden Globe for Best Television Series. In the fifteen-year window from 1999 to 2014, no aspect of interpersonal civilization changed more, to the point where Caitlyn (formerly Bruce) Jenner attracted more Twitter followers than the president (and the importance of this shift will amplify as the decades pass—soon, the notion of a transgender US president will not seem remotely implausible). So think how this might alter the memory of The Matrix: In some protracted reality, film historians will reinvestigate an extremely commercial action movie made by people who (unbeknownst to the audience) would eventually transition from male to female. Suddenly, the symbolic meaning of a universe with two worlds—one false and constructed, the other genuine and hidden—takes on an entirely new meaning. The idea of a character choosing between swallowing a blue pill that allows him to remain a false placeholder and a red pill that forces him to confront who he truly is becomes a much different metaphor. Considered from this speculative vantage point, The Matrix may seem like a breakthrough of a far different kind. It would feel more reflective than entertaining, which is precisely why certain things get remembered while certain others get lost.

with you, the sense i have lost my place in a book or simply lost — misplaced the memory which isn't in the last place where I looked. a thought that the clouds don't move — that it is we who thunder past — there it is! an old vacation, a train ride — sense of immobility. as sky and forest scroll past in relation, we are not moved, pretend to love the view, resort at length to scripted conversation by a poet-turned-screenwriter who didn't want this job, career gone grossly wrong and now drafts action film scripts wholly two- dimensional unless you choose to don the 3d glasses that do not stay on —

She was so beautiful, you see. Not in any two-dimensional sense: she wasn’t young, she wasn’t innocent, she didn’t have that pristine symmetry so favored by ad-men and photographers. Her face was plainly that of a woman in her early forties: it had been used to laugh and cry, and usage leaves its marks. But she had a power to transform herself, in the subtlest way, making that face as various as the sky.

The paper comes in plastic, a little thinner each week, a few more ads. Pretty soon there'll be no news. We'll be underwhelmed, over-bored & all storied out. The clouds ready to burst with our blue-skinned memories. Everyone with a blog, a website, an online store, dedicated server & two-dimensional quick-response-coded documentary made about their precious life. Our brains at maximum capacity, running optimization programs to recover what's left of our sanity. Still, we hope. We go see the latest blockbuster, buy the latest iPhone, zone out in front of our schizo-screens drinking jugs of moonshine corn syrup with our latent mutant meals. Facebook keeps us chained to our pasts, our posts, screwed in our seats... Scarecrows surrounded by night soil & spirits. Your acid shield may protect you from outside threat, but it'll never protect you from yourself.

Of course, I’ve only brought up two examples. Other universal laws of physics have been used as weapons as well, though we don’t know all of them. It’s very possible that every law of physics has been weaponized. It’s possible that in some parts of the universe, even … Forget it, I don’t even believe that.” “What were you going to say?” “The foundation of mathematics.” Cheng Xin tried to imagine it, but it was simply impossible. “That’s … madness.” Then she asked, “Will the universe turn into a war ruin? Or, maybe it’s more accurate to ask: Will the laws of physics turn into war ruins?” “Maybe they already are.… The physicists and cosmologists of the new world are focused on trying to recover the original appearance of the universe before the wars more than ten billion years ago. They’ve already constructed a fairly clear theoretical model describing the pre-war universe. That was a really lovely time, when the universe itself was a Garden of Eden. Of course, the beauty could only be described mathematically. We can’t picture it: Our brains don’t have enough dimensions.” Cheng Xin thought back to the conversation with the Ring again. Did you build this four-dimensional fragment? You told me that you came from the sea. Did you build the sea? “You are saying that the universe of the Edenic Age was four-dimensional, and that the speed of light was much higher?” “No, not at all. The universe of the Edenic Age was ten-dimensional. The speed of light back then wasn’t only much higher—rather, it was close to infinity. Light back then was capable of action at a distance, and could go from one end of the cosmos to the other within a Planck time.… If you had been to four-dimensional space, you would have some vague hint of how beautiful that ten-dimensional Garden must have been.” “You’re saying—” “I’m not saying anything.” Yifan seemed to have awakened from a dream. “We’ve only seen small hints; everything else is just guessing. You should treat it as a guess, just a dark myth we’ve made up.” But Cheng Xin continued to follow the course of the discussion taken so far. “—that during the wars after the Edenic Age, one dimension after another was imprisoned from the macroscopic into the microscopic, and the speed of light was reduced again and again.…” “As I said, I’m not saying anything, just guessing.” Yifan’s voice grew softer. “But no one knows if the truth is even darker than our guesses.… We are certain of only one thing: The universe is dying.” The

Imagine fish swimming in a shallow pond, just below the lily pads, thinking that their “universe” is only two-dimensional. Our three-dimensional world may be beyond their ken. But there is a way in which they can detect the presence of the third dimension. If it rains, they can clearly see the shadows of ripples traveling along the surface of the pond. Similarly, we cannot see the fifth dimension, but ripples in the fifth dimension appear to us as light.

It is extremely interesting, then, to think about the meaning of the word ‘form’ as it applies to constructions of arbitrarily complex shapes. For instance, what is it that we respond to when we look at a painting and feel its beauty? Is if the ‘form’ of the lines and dots on our retina? Evidently it must be, for that is how it gets passed along to the analyzing mechanisms in our heads–but the complexity of the processing makes us feel that we are not merely looking at a two-dimensional surface; we are responding to some sort of inner meaning inside the picture, a multidimensional aspect trapped somehow inside those two dimensions. It is the word ‘meaning’ which is important here. Our minds contain interpreters which accept two-dimensional patterns and then ‘pull’ from them high-dimensional notions which are so complex that we cannot consciously describe them. The same can be said about how we respond to music, incidentally.

It doesn't get any easier. No matter what they say, time doesn't heal the wound. Time just unravels and shows you new and more painful ways to miss someone. The longer they've been gone, the worse it is. You start to forget their smile or the way they tilted their head when they were confused or the way they looked at you and knew exactly what you were thinking. You can look at them in photos, but it's not even close to the real thing, and pretty soon you feel like your real memories are being replaced by the photo memories - like the only way you can picture them anymore is in one of those photographs. They become two-dimensional, and it rips your heart out whenever you think about it so you really try not to.

A quantum atom with two electrons is a much more complicated object to visualize, and I'm not aware that it's ever been done very well. The challenge is that for each possible position of one electron, the wave function of the other is a different three-dimensional object. So really, the natural home of the total wave function, for the two-electron system, is a space of 3 + 3 = 6 dimensions. It is quite a challenge to present such an object in a way that human brains find meaningful.

Equally important was the fact that the interpretation provided the model for how Tianming had hidden his message in the three stories. He employed two basic methods: dual-layer metaphors and two-dimensional metaphors. The dual-layer metaphors in the stories did not directly point to the real meaning, but to something far simpler. The tenor of this first metaphor became the vehicle for a second metaphor, which pointed to the real intelligence. In the current example, the princess’s boat, the He’ershingenmosiken soap, and the Glutton’s Sea formed a metaphor for a paper boat driven by soap. The paper boat, in turn, pointed to curvature propulsion. Previous attempts at decipherment had failed largely due to people’s habitual belief that the stories only involved a single layer of metaphors to hide the real message. The two-dimensional metaphors were a technique used to resolve the ambiguities introduced by literary devices employed in conveying strategic intelligence. After a dual-layer metaphor, a single-layer supporting metaphor was added to confirm the meaning of the dual-layer metaphor. In the current example, the curved snow-wave paper and the ironing required to flatten it served as a metaphor for curved space, confirming the interpretation of the soap-driven boat. If one viewed the stories as a two-dimensional plane, the dual-layer metaphor only provided one coordinate; the supporting single-layer metaphor provided a second coordinate that fixed the interpretation on the plane. Thus, this single-layer metaphor was also called the bearing coordinate. Viewed by itself, the bearing coordinate seemed meaningless, but once combined with the dual-layer metaphor, it resolved the inherent ambiguities in literary language. “A subtle and sophisticated system,” a PIA specialist said admiringly. All the committee members congratulated Cheng Xin and AA. AA, who had always been looked down on, saw her status greatly elevated among the committee members. Cheng

The shadows on the flat screen of a shadow play are projections from more complex objects. Our three-dimensional hands can cast a variety of two-dimensional shadows to delight the audience. In the same way there are fabulous beasts that swim in the seas of mathematics. Multidimensional behemoths of incredible beauty that even the best of minds struggle to glimpse. The equations we battle with, the proofs that we use to nibble at the edges of such wonders: these are the shadows cast by those we hunt.

I know you can’t. Because you’re too kind. It’s very simple. The attacker must first transform themselves into life forms that can survive in a low-dimensional universe. For instance, a four-dimensional species can transform itself into three-dimensional creatures, or a three-dimensional species can transform itself into two-dimensional life. After the entire civilization has entered a lower dimension, they can initiate a dimensional strike against the enemy without concern for the consequences.” Cheng

Relativity theory applies to macroscopic bodies, such as stars. The event of coincidence, that is, in ultimate analysis of collision, is the primitive event in the theory of relativity and defines a point in space-time, or at least would define a point if the colliding panicles were infinitely small. Quantum theory has its roots in the microscopic world and, from its point of view, the event of coincidence, or of collision, even if it takes place between particles of no spatial extent, is not primitive and not at all sharply isolated in space-time. The two theories operate with different mathematical conceptsãthe four dimensional Riemann space and the infinite dimensional Hilbert space, respectively. So far, the two theories could not be united, that is, no mathematical formulation exists to which both of these theories are approximations. All physicists believe that a union of the two theories is inherently possible and that we shall find it. Nevertheless, it is possible also to imagine that no union of the two theories can be found. This example illustrates the two possibilities, of union and of conflict, mentioned before, both of which are conceivable.

The point becomes not to understand the other’s reasons, perspectives, and beliefs, or to honor them as fellow believers and come to a deeper understanding and perhaps resolution of differences. The point, rather, is to remain on guard from being contaminated by the out-group or allowing them to grow in influence. And in that process the other is very easily turned into an impersonal, two-dimensional caricature. Out-groups are reduced to an abstract “them” whose beliefs are abridged into a few bullet points of greatest disagreement, which need not actually be taken seriously on their own terms but rather simply need to be refuted and discredited as a means to validate the views of one’s own group. In this way, differences between Christian groups cease to be existentially troubling facts that divide Christians. Instead they become dismissible ideas of people far away, ideas already known to be wrong.

There must always remain, however, from the standpoint of normal waking consciousness, a certain baffling inconsistency between the wisdom brought forth from the deep, and the prudence usually found to be effective in the light world. Hence the common divorce of opportunism from virtue and the resultant degeneration of human existence. Martyrdom is for saints, but the common people have their institutions, and these cannot be left to grow like lilies of the field; Peter keeps drawing his sword, as in the garden, to defend the creator and sustainer of the world. The boon brought from the transcendent deep becomes quickly rationalized into nonentity, and the need becomes great for another hero to refresh the word. How teach again, however, what has been taught correctly and incorrectly learned a thousand thousand times, throughout the millenniums of mankind’s prudent folly? That is the hero’s ultimate difficult task. How render back into light-world language the speech-defying pronouncements of the dark? How represent on a two-dimensional surface a three-dimensional form, or in a three-dimensional image a multi-dimensional meaning? How translate into terms of “yes” and “no” revelations that shatter into meaninglessness every attempt to define the pairs of opposites? How communicate to people who insist on the exclusive evidence of their senses the message of the all-generating void?

Alex, please.” He balls his fists. “Stop saying my name. You don’t know me anymore.” “I do know you.” I’m still crying, swallowing back spasms in my throat, struggling to breathe. This is a nightmare and I will wake up. This is a monster-story, and he has come back to me a terror-creation, patched together, broken and hateful, and I will wake up and he will be here, and whole, and mine again. I find his hands, lace my fingers through his even as he tries to pull away. “It’s me, Alex. Lena. Your Lena. Remember? Remember 37 Brooks, and the blanket we used to keep in the backyard—” “Don’t,” he says. His voice breaks on the word. “And I always beat you in Scrabble,” I say. I have to keep talking, and keep him here, and make him remember. “Because you always let me win. And remember how we had a picnic one time, and the only thing we could find from the store was canned spaghetti and some green beans? And you said to mix them—” “Don’t.” “And we did, and it wasn’t bad. We ate the whole stupid can, we were so hungry. And when it started to get dark you pointed to the sky, and told me there was a star for every thing you loved about me.” I’m gasping, feeling as though I am about to drown; I’m reaching for him blindly, grabbing at his collar. “Stop.” He grabs my shoulders. His face is an inch from mine but unrecognizable: a gross, contorted mask. “Just stop. No more. It’s done, okay? That’s all done now.” “Alex, please—” “Stop!” His voice rings out sharply, hard as a slap. He releases me and I stumble backward. “Alex is dead, do you hear me? All of that—what we felt, what it meant—that’s done now, okay? Buried. Blown away.” “Alex!” He has started to turn away; now he whirls around. The moon lights him stark white and furious, a camera image, two-dimensional, gripped by the flash. “I don’t love you, Lena. Do you hear me? I never loved you.” The air goes. Everything goes. “I don’t believe you.” I’m crying so hard, I can hardly speak. He takes one step toward me. And now I don’t recognize him at all. He has transformed entirely, turned into a stranger. “It was a lie. Okay? It was all a lie. Craziness, like they always said. Just forget about it. Forget it ever happened.” “Please.” I don’t know how I stay on my feet, why I don’t shatter into dust right there, why my heart keeps beating when I want it so badly to stop. “Please don’t do this, Alex.” “Stop saying my name.

I am only slightly less astonished by the egotism of the assassins, the inflated self-esteem it requires to kill a president, than I am astonished by the men who run for president. These are people who have the gall to believe they can fix us--us and our deficit, our fossil fuels, our racism, poverty, our potholes and public schools. The egomania required to be president or a presidential assassin makes the two types brothers of sorts. Presidents and presidential assassins are like Las Vegas and Salt Lake City in that way. Even though one city is all about sin and the other is all about salvation, they are identical, one-dimensional company towns built up out of the desert by the sheer will of true believers. The assassins and the presidents invite the same basic question: Just who do you think you are?

Kaluza also gave an answer as to where the fifth dimension was. Since we see no evidence of a fifth dimension, it must have "curled up" so small that it cannot be observed. (Imagine taking a two-dimensional sheet of paper and rolling it up tightly into a cylinder. From a distance, the cylinder looks like a one-dimensional line. In this way, a two-dimensional object has been turned into a one-dimensional object by curling it up.) Kaluza's paper initially created a sensation. But in the coming years, objections were found to his theory. What was the size of this new fifth dimension? How did it curl up? No answers could be found. For decades Einstein would work on this theory in fits and starts. After he passed away in 1955, the theory was soon forgotten, becoming just a strange footnote to the evolution of physics.

Furious, the beast writhed and wriggled its iterated integrals beneath the King’s polynomial blows, collapsed into an infinite series of indeterminate terms, then got back up by raising itself to the nth power, but the King so belabored it with differentials and partial derivatives that its Fourier coefficients all canceled out (see Riemann’s Lemma), and in the ensuing confusion the constructors completely lost sight of both King and beast. So they took a break, stretched their legs, had a swig from the Leyden jug to bolster their strength, then went back to work and tried it again from the beginning, this time unleashing their entire arsenal of tensor matrices and grand canonical ensembles, attacking the problem with such fervor that the very paper began to smoke. The King rushed forward with all his cruel coordinates and mean values, stumbled into a dark forest of roots and logarithms, had to backtrack, then encountered the beast on a field of irrational numbers (F1) and smote it so grievously that it fell two decimal places and lost an epsilon, but the beast slid around an asymptote and hid in an n-dimensional orthogonal phase space, underwent expansion and came out, fuming factorially, and fell upon the King and hurt him passing sore. But the King, nothing daunted, put on his Markov chain mail and all his impervious parameters, took his increment Δk to infinity and dealt the beast a truly Boolean blow, sent it reeling through an x-axis and several brackets—but the beast, prepared for this, lowered its horns and—wham!!—the pencils flew like mad through transcendental functions and double eigentransformations, and when at last the beast closed in and the King was down and out for the count, the constructors jumped up, danced a jig, laughed and sang as they tore all their papers to shreds, much to the amazement of the spies perched in the chandelier-—perched in vain, for they were uninitiated into the niceties of higher mathematics and consequently had no idea why Trurl and Klapaucius were now shouting, over and over, “Hurrah! Victory!!

Imagine that a tribe of ignorant natives find a motor-car, and decide that it makes an ideal storage room for food. So when they set out on a journey, they load it with food, attach ropes to it, and pull it through the jungle as if it was a cart. One of them fiddling about inside it, discovers the hand brake and releases it. Immediately, they find the car much easier to pull. They congratulate the discoverer, tell him he is a genius, and convince themselves that they now know the purpose and use of the car. This is how I feel with my body. Occasionally, as I am dragging it along, it accidentally gets into gear; there is a roar, and the engine starts for a moment. Then, just as quickly, it cuts out. But I know that this body is not merely designed for this boring, irritating, two-dimensional life that so easily becomes a burden to me.

In summary, the rather obscure laws of the weather are easy to understand once we view the earth from space. Thus the solution to the problem is to go up into space, into the third dimension. Facts that were impossible to understand in a flat world suddenly become obvious when viewing a three-dimensional earth. Similarly, the laws of gravity and light seem totally dissimilar. They obey different physical assumptions and different mathematics. Attempts to splice these two forces have always failed. However, if we add one more dimension, a fifth dimension, to the previous four dimensions of space and time, then the equations governing light and gravity appear to merge together like two pieces of a jigsaw puzzle. Light, in fact, can be explained as vibrations in the fifth dimension. In this way, we see that the laws of light and gravity become simpler in five dimensions.

Avoid extremes. Don’t make a distinction between outer and inner and don’t become one of Jung’s types, either extrovert or introvert. Sosan says: Be flowing, balancing. Outer and inner are just like the right and left leg. Why choose one? If you choose one, all movement stops. They are like two eyes: if you choose one then you will be able to see but your vision is no more three dimensional, the depth is lost. You have two ears: you can use one, you can be addicted to the idea that you are a left ear type or a right ear type, but then you lose. Then half the world is closed to you. The inner and outer are just two eyes, two ears, two legs – why choose? Why not use both choicelessly? And why divide? Because you are one! The left leg and the right leg only appear two. You flow within both – the same energy, the same being. You look through both your eyes. Why not use inner and outer and give them a balance? Why move to the extreme?

A city finds its life through the humans who inhabit it. When they go, what is truly left? Just silent stones, witnesses to the history but mute in its telling, remaining thus while slowly turning to rubble. It saddens me that life’s moments are thus lost, that one cannot experience the past in the same rich vibrancy as the present. You live the moments and then relegate them to memory, now just two-dimensional shadows, pictures without depth, stripped of their purest emotion, their tactile connections no longer accessible. You try to recall, but can bring back only a fraction of the event lived. The rest is gone, never to be as full and complete as it was in that one place at that one time. That was what I thought as I studied these stone remains; that all the tangible things experienced here abide somewhere in time, but can never again be wholly re-animated, now just ghosts imbedded in the crumbling walls and in the fading memories of those who once lived here.

The Pyrenean ibex, an extinct form of wild mountain goat, was brought back to life in 2009 through cloning of dna taken from skin samples. This was followed in June of 2010 by researchers at Jeju National University in Korea cloning a bull that had been dead for two years. Cloning methods are also being studied for use in bringing back Tasmanian tigers, woolly mammoths, and other extinct creatures, and in the March/April 2010 edition of the respected Archaeology magazine, a feature article by Zah Zorich (“Should We Clone Neanderthals?”) called for the resurrection via cloning of what some consider to be man’s closest extinct relative, the Neanderthals. National Geographic confirmed this possibility in its May 2009 special report, “Recipe for a Resurrection,” quoting Hendrik Poinar of McMaster University, an authority on ancient dna who served as a scientific consultant for the movie Jurassic Park, saying: “I laughed when Steven Spielberg said that cloning extinct animals was inevitable. But I’m not laughing anymore.… This is going to happen.

space-time is not flat, as had been previously assumed: it is curved, or ‘warped,’ by the distribution of mass and energy in it. Bodies like the earth are not made to move on curved orbits by a force called gravity; instead, they follow the nearest thing to a straight path in a curved space, which is called a geodesic. A geodesic is the shortest (or longest) path between two nearby points. For example, the surface of the earth is a two-dimensional curved space. A geodesic on the earth is called a great circle, and is the shortest route between two points (Fig. 2.7). As the geodesic is the shortest path between any two airports, this is the route an airline navigator will tell the pilot to fly along. In general relativity, bodies always follow straight lines in four-dimensional space-time, but they nevertheless appear to us to move along curved paths in our three-dimensional space. (This is rather like watching an airplane flying over hilly ground. Although it follows a straight line in three-dimensional space, its shadow follows a curved path on the two-dimensional ground.)

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

When the members of the Frontiers of Science discussed physics, they often used the abbreviation “SF.” They didn’t mean “science fiction,” but the two words “shooter” and “farmer.” This was a reference to two hypotheses, both involving the fundamental nature of the laws of the universe. In the shooter hypothesis, a good marksman shoots at a target, creating a hole every ten centimeters. Now suppose the surface of the target is inhabited by intelligent, two-dimensional creatures. Their scientists, after observing the universe, discover a great law: “There exists a hole in the universe every ten centimeters.” They have mistaken the result of the marksman’s momentary whim for an unalterable law of the universe. The farmer hypothesis, on the other hand, has the flavor of a horror story: Every morning on a turkey farm, the farmer comes to feed the turkeys. A scientist turkey, having observed this pattern to hold without change for almost a year, makes the following discovery: “Every morning at eleven, food arrives.” On the morning of Thanksgiving, the scientist announces this law to the other turkeys. But that morning at eleven, food doesn’t arrive; instead, the farmer comes and kills the entire flock. Wang

I, too, will find a set of beliefs, of standards to live by, yet the very satisfaction of finding them will be marred by the fact that I have reached the ultimate in shallow, two-dimensional living- a set of values. This loneliness will blur and diminish, no doubt, when tomorrow I plunge again into classes, into the necessity of studying for exams. But now, that false purpose is lifted and I am spinning in a temporary vacuum. At home I rested and played, here, where I work, the routine is momentarily suspended and I am lost. There is no living being on earth at this moment except myself. I could walk down the halls, and empty rooms would yawn mockingly at me from every side. God, but life is loneliness, despite all the opiates, despite the shrill tinsel gaiety of "parties" with no purpose, despite the false grinning faces we all wear. And when at last you find someone to whom you feel you can pour out your soul, you stop in shock at the words you utter- they are so rusty, so ugly, so meaningless and feeble from being kept in the small cramped dark inside you so long. Yes, there is joy, fulfillment and companionship- but the loneliness of the would in its appalling self-consciousness, is horrible and overpowering-

But historically the fourth dimension has been considered a mere curiosity by physicists. No evidence has ever been found for higher dimensions. This began to change in 1919 when physicist Theodor Kaluza wrote a highly controversial paper that hinted at the presence of higher dimensions. He started with Einstein's theory of general relativity, but placed it in five dimensions (one dimension of time and four dimensions of space; since time is the fourth space-time dimension, physicists now refer to the fourth spatial dimension as the fifth dimension). If the fifth dimension were made smaller and smaller, the equations magically split into two pieces. One piece describes Einstein's standard theory of relativity, but the other piece becomes Maxwell's theory of light! This was a stunning revelation. Perhaps the secret of light lies in the fifth dimension! Einstein himself was shocked by this solution, which seemed to provide an elegant unification of light and gravity. (Einstein was so shaken by Kaluza's proposal that he mulled it over for two years before finally agreeing to have this paper published.) Einstein wrote to Kaluza, "The idea of achieving [a unified theory] by means of a five-dimensional cylinder world never dawned on me...At first glance, I like your idea enormously...The formal unity of your theory is startling.

Introducing higher dimensions may be essential for prying loose the secrets of Creation. According to this theory, before the Big Bang, our cosmos was actually a perfect ten-dimensional universe, a world where interdimensional travel was possible. However, this ten-dimensional world was unstable, and eventually it "cracked" in two, creating two separate universes: a four-and a six dimensional universe. The universe in which we live was born in that cosmic cataclysm. Our four-dimensional universe expanded explosively, while our twin six-dimensional universe contracted violently, until it shrank to almost infinitesimal size. This would explain the origin of the Big Bang. If correct, this theory demonstrates that the rapid expansion of the universe was just a rather minor aftershock of a much greater cataclysmic event, the cracking of space and time itself. The energy that drives the observed expansion of the universe is then found in the collapse of ten-dimensional space and time. According to the theory, the distant stars and galaxies are receding from us at astronomical speeds because of the original collapse of ten-dimensional space and time. This theory predicts that our universe still has a dwarf twin, a companion universe that has curled up into a small six-dimensional ball that is too small to be observed. This six-dimensional universe, far from being a useless appendage to our world, may ultimately be our salvation.

So they rolled up their sleeves and sat down to experiment -- by simulation, that is mathematically and all on paper. And the mathematical models of King Krool and the beast did such fierce battle across the equation-covered table, that the constructors' pencils kept snapping. Furious, the beast writhed and wriggled its iterated integrals beneath the King's polynomial blows, collapsed into an infinite series of indeterminate terms, then got back up by raising itself to the nth power, but the King so belabored it with differentials and partial derivatives that its Fourier coefficients all canceled out (see Riemann's Lemma), and in the ensuing confusion the constructors completely lost sight of both King and beast. So they took a break, stretched their legs, had a swig from the Leyden jug to bolster their strength, then went back to work and tried it again from the beginning, this time unleashing their entire arsenal of tensor matrices and grand canonical ensembles, attacking the problem with such fervor that the very paper began to smoke. The King rushed forward with all his cruel coordinates and mean values, stumbled into a dark forest of roots and logarithms, had to backtrack, then encountered the beast on a field of irrational numbers (F_1) and smote it so grievously that it fell two decimal places and lost an epsilon, but the beast slid around an asymptote and hid in an n-dimensional orthogonal phase space, underwent expansion and came out fuming factorially, and fell upon the King and hurt him passing sore. But the King, nothing daunted, put on his Markov chain mail and all his impervious parameters, took his increment Δk to infinity and dealt the beast a truly Boolean blow, sent it reeling through an x-axis and several brackets—but the beast, prepared for this, lowered its horns and—wham!!—the pencils flew like mad through transcendental functions and double eigentransformations, and when at last the beast closed in and the King was down and out for the count, the constructors jumped up, danced a jig, laughed and sang as they tore all their papers to shreds, much to the amazement of the spies perched in the chandelier—perched in vain, for they were uninitiated into the niceties of higher mathematics and consequently had no idea why Trurl and Klapaucius were now shouting, over and over, "Hurrah! Victory!!

If these avatars were real people in a real street, Hiro wouldn't be able to reach the entrance. It's way too crowded. But the computer system that operates the Street has better things to do than to monitor every single one of the millions of people there, trying to prevent them from running into each other. It doesn't bother trying to solve this incredibly difficult problem. On the Street, avatars just walk right through each other. So when Hiro cuts through the crowd, headed for the entrance, he really is cutting through the crowd. When things get this jammed together, the computer simplifies things by drawing all of the avatars ghostly and translucent so you can see where you're going. Hiro appears solid to himself, but everyone else looks like a ghost. He walks through the crowd as if it's a fogbank, clearly seeing The Black Sun in front of him. He steps over the property line, and he's in the doorway. And in that instant he becomes solid and visible to all the avatars milling outside. As one, they all begin screaming. Not that they have any idea who the hell he is -- Hiro is just a starving CIC stringer who lives in a U-Stor-It by the airport. But in the entire world there are only a couple of thousand people who can step over the line into The Black Sun. He turns and looks back at ten thousand shrieking groupies. Now that he's all by himself in the entryway, no longer immersed in a flood of avatars, he can see all of the people in the front row of the crowd with perfect clarity. They are all done up in their wildest and fanciest avatars, hoping that Da5id -- The Black Sun's owner and hacker-in-chief -- will invite them inside. They flick and merge together into a hysterical wall. Stunningly beautiful women, computer-airbrushed and retouched at seventy-two frames a second, like Playboy pinups turned three-dimensional -- these are would-be actresses hoping to be discovered. Wild-looking abstracts, tornadoes of gyrating light-hackers who are hoping that Da5id will notice their talent, invite them inside, give them a job. A liberal sprinkling of black-and-white people -- persons who are accessing the Metaverse through cheap public terminals, and who are rendered in jerky, grainy black and white. A lot of these are run-of-the-mill psycho fans, devoted to the fantasy of stabbing some particular actress to death; they can't even get close in Reality, so they goggle into the Metaverse to stalk their prey. There are would-be rock stars done up in laser light, as though they just stepped off the concert stage, and the avatars of Nipponese businessmen, exquisitely rendered by their fancy equipment, but utterly reserved and boring in their suits.

You may not recognize the name Steven Schussler, CEO of Schussler Creative Inc., but you are probably familiar with his very popular theme restaurant Rainforest Café. Steve is one of the scrappiest people I know, with countless scrappy stories. He is open and honest about his wins and losses. This story about how he launched Rainforest Café is one of my favorites: Steve first envisioned a tropical-themed family restaurant back in the 1980s, but unfortunately, he couldn’t persuade anyone else to buy into the idea at the time. Not willing to give up easily, he decided to get scrappy and be “all in.” To sell his vision, he transformed his own split-level suburban home into a living, mist-enshrouded rain forest to convince potential investors that the concept was viable. Yes, you read that correctly—he converted his own house into a jungle dwelling complete with rock outcroppings, waterfalls, rivers, and layers of fog and mist that rose from the ground. The jungle included a life-size replica of an elephant near the front door, forty tropical birds in cages, and a live baby baboon named Charlie. Steve shared the following details: Every room, every closet, every hallway of my house was set up as a three-dimensional vignette: an attempt to present my idea of what a rain forest restaurant would look like in actual operation. . . . [I]t took me three years and almost $400,000 to get the house developed to the point where I felt comfortable showing it to potential investors. . . . [S]everal of my neighbors weren’t exactly thrilled to be living near a jungle habitat. . . . On one occasion, Steve received a visit from the Drug Enforcement Administration. They wanted to search the premises for drugs, presuming he may have had an illegal drug lab in his home because of his huge residential electric bill. I imagine they were astonished when they discovered the tropical rain forest filled with jungle creatures. Steve’s plan was beautiful, creative, fun, and scrappy, but the results weren’t coming as quickly as he would have liked. It took all of his resources, and he was running out of time and money to make something happen. (It’s important to note that your scrappy efforts may not generate results immediately.) I asked Steve if he ever thought about quitting, how tight was the money really, and if there was a time factor, and he said, “Yes to all three! Of course I thought about quitting. I was running out of money and time.” Ultimately, Steve’s plan succeeded. After many visits and more than two years later, gaming executive and venture capitalist Lyle Berman bought into the concept and raised the funds necessary to get the Rainforest Café up and running. The Rainforest Café chain became one of the most successful themed restaurants ever created, and continues that way under Landry’s Restaurants and Tilman Fertitta’s leadership. Today, Steve creates restaurant concepts in fantastic warehouses far from his residential neighborhood!

Gadgetry will continue to relieve mankind of tedious jobs. Kitchen units will be devised that will prepare ‘automeals,’ heating water and converting it to coffee; toasting bread; frying, poaching or scrambling eggs, grilling bacon, and so on. Breakfasts will be ‘ordered’ the night before to be ready by a specified hour the next morning. Communications will become sight-sound and you will see as well as hear the person you telephone. The screen can be used not only to see the people you call but also for studying documents and photographs and reading passages from books. Synchronous satellites, hovering in space will make it possible for you to direct-dial any spot on earth, including the weather stations in Antarctica. [M]en will continue to withdraw from nature in order to create an environment that will suit them better. By 2014, electroluminescent panels will be in common use. Ceilings and walls will glow softly, and in a variety of colors that will change at the touch of a push button. Robots will neither be common nor very good in 2014, but they will be in existence. The appliances of 2014 will have no electric cords, of course, for they will be powered by long- lived batteries running on radioisotopes. “[H]ighways … in the more advanced sections of the world will have passed their peak in 2014; there will be increasing emphasis on transportation that makes the least possible contact with the surface. There will be aircraft, of course, but even ground travel will increasingly take to the air a foot or two off the ground. [V]ehicles with ‘Robot-brains’ … can be set for particular destinations … that will then proceed there without interference by the slow reflexes of a human driver. [W]all screens will have replaced the ordinary set; but transparent cubes will be making their appearance in which three-dimensional viewing will be possible. [T]he world population will be 6,500,000,000 and the population of the United States will be 350,000,000. All earth will be a single choked Manhattan by A.D. 2450 and society will collapse long before that! There will, therefore, be a worldwide propaganda drive in favor of birth control by rational and humane methods and, by 2014, it will undoubtedly have taken serious effect. Ordinary agriculture will keep up with great difficulty and there will be ‘farms’ turning to the more efficient micro-organisms. Processed yeast and algae products will be available in a variety of flavors. The world of A.D. 2014 will have few routine jobs that cannot be done better by some machine than by any human being. Mankind will therefore have become largely a race of machine tenders. Schools will have to be oriented in this direction…. All the high-school students will be taught the fundamentals of computer technology will become proficient in binary arithmetic and will be trained to perfection in the use of the computer languages that will have developed out of those like the contemporary “Fortran". [M]ankind will suffer badly from the disease of boredom, a disease spreading more widely each year and growing in intensity. This will have serious mental, emotional and sociological consequences, and I dare say that psychiatry will be far and away the most important medical specialty in 2014. [T]he most glorious single word in the vocabulary will have become work! in our a society of enforced leisure.

Two observations take us across the finish line. The Second Law ensures that entropy increases throughout the entire process, and so the information hidden within the hard drives, Kindles, old-fashioned paper books, and everything else you packed into the region is less than that hidden in the black hole. From the results of Bekenstein and Hawking, we know that the black hole's hidden information content is given by the area of its event horizon. Moreover, because you were careful not to overspill the original region of space, the black hole's event horizon coincides with the region's boundary, so the black hole's entropy equals the area of this surrounding surface. We thus learn an important lesson. The amount of information contained within a region of space, stored in any objects of any design, is always less than the area of the surface that surrounds the region (measured in square Planck units). This is the conclusion we've been chasing. Notice that although black holes are central to the reasoning, the analysis applies to any region of space, whether or not a black hole is actually present. If you max out a region's storage capacity, you'll create a black hole, but as long as you stay under the limit, no black hole will form. I hasten to add that in any practical sense, the information storage limit is of no concern. Compared with today's rudimentary storage devices, the potential storage capacity on the surface of a spatial region is humongous. A stack of five off-the-shelf terabyte hard drives fits comfortable within a sphere of radius 50 centimeters, whose surface is covered by about 10^70 Planck cells. The surface's storage capacity is thus about 10^70 bits, which is about a billion, trillion, trillion, trillion, trillion terabytes, and so enormously exceeds anything you can buy. No one in Silicon Valley cares much about these theoretical constraints. Yet as a guide to how the universe works, the storage limitations are telling. Think of any region of space, such as the room in which I'm writing or the one in which you're reading. Take a Wheelerian perspective and imagine that whatever happens in the region amounts to information processing-information regarding how things are right now is transformed by the laws of physics into information regarding how they will be in a second or a minute or an hour. Since the physical processes we witness, as well as those by which we're governed, seemingly take place within the region, it's natural to expect that the information those processes carry is also found within the region. But the results just derived suggest an alternative view. For black holes, we found that the link between information and surface area goes beyond mere numerical accounting; there's a concrete sense in which information is stored on their surfaces. Susskind and 'tHooft stressed that the lesson should be general: since the information required to describe physical phenomena within any given region of space can be fully encoded by data on a surface that surrounds the region, then there's reason to think that the surface is where the fundamental physical processes actually happen. Our familiar three-dimensional reality, these bold thinkers suggested, would then be likened to a holographic projection of those distant two-dimensional physical processes. If this line of reasoning is correct, then there are physical processes taking place on some distant surface that, much like a puppeteer pulls strings, are fully linked to the processes taking place in my fingers, arms, and brain as I type these words at my desk. Our experiences here, and that distant reality there, would form the most interlocked of parallel worlds. Phenomena in the two-I'll call them Holographic Parallel Universes-would be so fully joined that their respective evolutions would be as connected as me and my shadow.