Spatial Quotes

I could not help feeling that they were evil things-- mountains of madness whose farther slopes looked out over some accursed ultimate abyss. That seething , half-luminous cloud-background held ineffable suggestions of a vague, ethereal beyondness far more than terrestrially spatial; and gave appalling reminders of the utter remoteness, separateness, desolation, and aeon-long death of this untrodden and unfathomed austral world.

Our sense of justice depends on our sense of time. Justice is a phenomenon only of consciousness, because time spread out in a spatial succession is its very essence. And this is possible only in a spatial metaphor of time.

Sense of place is the sixth sense, an internal compass and map made by memory and spatial perception together.

Nothing disappears completely ... In space, what came earlier continues to underpin what follows ... Pre-existing space underpins not only durable spatial arrangements, but also representational spaces and their attendant imagery and mythic narratives.

As bad as we are at remembering names and phone numbers and word-for-word instructions from our colleagues, we have really exceptional visual and spatial memories.

Two aesthetics exist: the passive aesthetic of mirrors and the active aesthetic of prisms. Guided by the former, art turns into a copy of the environment's objectivity or the individual's psychic history. Guided by the latter, art is redeemed, makes the world into its instrument, and forges, beyond spatial and temporal prisons, a personal vision.

What we call 'time' isn't chronological but spatial; what we call 'death' is merely a transition between different kinds of matter.

But “nowhere” does not mean nothing; rather, region in general lies therein, and disclosedness of the world in general for essentially spatial being-in. Therefore, what is threatening cannot come closer from a definite direction within nearness, it is already “there” - and yet nowhere. It is so near that it is oppressive and takes one’s breath - and yet it is nowhere.

We’ve found that magic happens when we use big whiteboards to solve problems. As humans, our short-term memory is not all that good, but our spatial memory is awesome. A sprint room, plastered with notes, diagrams, printouts, and more, takes advantage of that spatial memory. The room itself becomes a sort of shared brain for the team.

The experience of high-dimensional spatial sense was a spiritual baptism. In one moment, concepts like freedom, openness, profundity, and infinity all gained brand-new meanings.

[Patricia Greenfield] concluded that “every medium develops some cognitive skills at the expense of others.” Our growing use of the Net and other screen-based technologies has led to the “widespread and sophisticated development of visual-spatial skills.” We can, for example, rotate objects in our minds better than we used to be able to. But our “new strengths in visual-spatial intelligence” go hand in hand with a weakening of our capacities for the kind of “deep processing” that underpins “mindful knowledge acquisition, inductive analysis, critical thinking, imagination, and reflection.

It was called evolutionary biology. Under its sway, the sexes were separated again, men into hunters and women into gatherers. Nurture no longer formed us; nature did. Impulses of hominids dating from 20,000 B.C. were still controlling us. And so today on television and in magazines you get the current simplifications. Why can't men communicate? (Because they had to be quiet on the hunt.) Why do women communicate so well? (Because they had to call out to one another where the fruits and berries were.) Why can men never find things around the house? (Because they have a narrow field of vision, useful in tracking prey.) Why can women find things so easily? (Because in protecting the nest they were used to scanning a wide field.) Why can't women parallel-park? (Because low testosterone inhibits spatial ability.) Why won't men ask for directions? (Because asking for directions is a sign of weakness, and hunters never show weakness.) This is where we are today. Men and women, tired of being the same, want to be different again.

The novel integrates several forms of human intelligence - verbal intelligence (for the style), psychological intelligence (for the characters), logical intelligence (for the plot), spatial intelligence (for the symbolic and metaphorical content as well as the setting), and even musical intelligence (for pacing and rhythm.

The really important facts were that spatial relationships had ceased to matter very much and that my mind was perceiving the world in terms of other than spatial categories. At ordinary times the eye concerns itself with such problems as where? — how far? — how situated in relation to what? In the mescaline experience the implied questions to which the eye responds are of another order. Place and distance cease to be of much interest. The mind does its perceiving in terms of intensity of existence, profundity of significance, relationships within a pattern.

Architecture and urban design, both in their formal and spatial aspects, are seen as fundamentally configurational in that the way the parts are put together to form the whole is more important than any of the parts taken in isolation.

Here I want to stress that perception of losing one’s mind is based on culturally derived and socially ingrained stereotypes as to the significance of symptoms such as hearing voices, losing temporal and spatial orientation, and sensing that one is being followed, and that many of the most spectacular and convincing of these symptoms in some instances psychiatrically signify merely a temporary emotional upset in a stressful situation, however terrifying to the person at the time. Similarly, the anxiety consequent upon this perception of oneself, and the strategies devised to reduce this anxiety, are not a product of abnormal psychology, but would be exhibited by any person socialized into our culture who came to conceive of himself as someone losing his mind.

It is generally recognized that women are better than men at languages, personal relations and multitasking, but less good at map-reading and spatial awareness. It is therefore not unreasonable to suppose that women might be less good at mathematics and physics. It is not politically correct to say such things....But it cannot be denied that there are differences between men and women. Of course, these are differences between the averages only. There are wide variations about the mean.

Just as the universal family of gifted writers transcends national barriers, so is the gifted reader a universal figure, not subject to spatial or temporal laws. It is he—the good, the excellent reader—who has saved the artists again and again from being destroyed by emperors, dictators, priests, puritans, philistines, political moralists, policemen, postmasters, and prigs. Let me define this admirable reader. He does not belong to any specific nation or class. No director of conscience and no book club can manage his soul. His approach to a work of fiction is not governed by those juvenile emotions that make the mediocre reader identify himself with this or that character and “skip descriptions.” The good, the admirable reader identifies himself not with the boy or the girl in the book, but with the mind that conceived and composed that book. The admirable reader does not seek information about Russia in a Russian novel, for he knows that the Russia of Tolstoy or Chekhov is not the average Russia of history but a specific world imagined and created by individual genius. The admirable reader is not concerned with general ideas; he is interested in the particular vision. He likes the novel not because it helps him to get along with the group (to use a diabolical progressive-school cliche); he likes the novel because he imbibes and understands every detail of the text, enjoys what the author meant to be injoyed, beams inwardly and all over, is thrilled by the magic imageries of the master-forger, the fancy-forger, the conjuror, the artist. Indeed of all the characters that a great artist creates, his readers are the best. (“Russian Writers, Censors, and Readers”)

of the actual objects of physical reality. Physical objects are not in space, but these objects are spatially extended.

Every story is a travel story – a spatial practice.

In the beginning was the Topos. Before – long before – the advent of the Logos, in the chiaroscuro realm of primitive life, lived experience already possessed its internal rationality; this experience was producing long before thought space, and spatial thought, began reproducing the projection, explosion, image and orientation of the body.

First, if it is true that a spatial order organizes an ensemble of possibilities (e.g., by a place in which one can move) and interdictions (e.g., by a wall that prevents one from going further), than the walked actualizes some of these possibilities. In that way, he makes them exist as well as emerge. But he also moves them about and he invents others, since the crossing, drifting away, or improvisation of walking privilege, transform, or abandon spatial elements.

The long poem of walking manipulates spatial organizations, no matter how panoptic they may be: it is neither foreign to them (it can take place only within them) nor in conformity with them (it does not receive its identity from them). It creates shadows and ambiguities within them. It inserts its multitudinous references and citations into them (social models, cultural mores, personal factors). Within them it is itself the effect of successive encounters and occasions that constantly alter it and make it the other's blazon: in other words, it is like a peddler carrying something surprising, transverse or attractive compared with the usual choice. These diverse aspects provide the basis of a rhetoric. They can even be said to define it.

If we start to look into the nature of the relationship between time and the dynamics of social exchange, we quickly discover that temporal considerations are equally important as spatial ones when examining the causes of disjunction that can separate familiarization and alienation. Synchronization, it seems, is often in thrall to serendipity — temporal disjunction, like entropy, is one of the irresistible forces of nature.

The empire of cotton has continued to facilitate a giant race to the bottom, limited only by the spatial constraints of the planet.

The scale of man—spatially—is about midway between the atom and the star.

The Greek word for "return" is nostos. Algos means "suffering." So nostalgia is the suffering caused by an unappeased yearning to return. To express that fundamental notion most Europeans can utilize a word derived from the Greek (nostalgia, nostalgie) as well as other words with roots in their national languages: añoranza, say the Spaniards; saudade, say the Portuguese. In each language these words have a different semantic nuance. Often they mean only the sadness caused by the impossibility of returning to one's country: a longing for country, for home. What in English is called "homesickness." Or in German: Heimweh. In Dutch: heimwee. But this reduces that great notion to just its spatial element. One of the oldest European languages, Icelandic (like English) makes a distinction between two terms: söknuour: nostalgia in its general sense; and heimprá: longing for the homeland. Czechs have the Greek-derived nostalgie as well as their own noun, stesk, and their own verb; the most moving, Czech expression of love: styska se mi po tobe ("I yearn for you," "I'm nostalgic for you"; "I cannot bear the pain of your absence"). In Spanish añoranza comes from the verb añorar (to feel nostalgia), which comes from the Catalan enyorar, itself derived from the Latin word ignorare (to be unaware of, not know, not experience; to lack or miss), In that etymological light nostalgia seems something like the pain of ignorance, of not knowing. You are far away, and I don't know what has become of you. My country is far away, and I don't know what is happening there. Certain languages have problems with nostalgia: the French can only express it by the noun from the Greek root, and have no verb for it; they can say Je m'ennuie de toi (I miss you), but the word s'ennuyer is weak, cold -- anyhow too light for so grave a feeling. The Germans rarely use the Greek-derived term Nostalgie, and tend to say Sehnsucht in speaking of the desire for an absent thing. But Sehnsucht can refer both to something that has existed and to something that has never existed (a new adventure), and therefore it does not necessarily imply the nostos idea; to include in Sehnsucht the obsession with returning would require adding a complementary phrase: Sehnsucht nach der Vergangenheit, nach der verlorenen Kindheit, nach der ersten Liebe (longing for the past, for lost childhood, for a first love).

Study after study has shown almost all behavioral and psychological differences between the sexes to be small or nonexistent. Cambridge University psychologist Melissa Hines and others have repeatedly demonstrated that boys and girls have little, if any, noticeable gaps between them when it comes to fine motor skills, spatial visualization, mathematics ability, and verbal fluency.

The person of the therapist is the converting catalyst, not his order or credo, not his spatial location in the room, not his exquisitely chosen words or denominational silences. So long as the rules of a therapeutic system do not hinder limbic transmission - a critical caveat - they remain inconsequential, neocortical distractions. The dispensable trappings of dogma may determine what a therapist thinks he is doing, what he talks about when he talks about therapy, but the agent of change is who he is. (187)

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...

Translation involves a spatial dimension - a literal transportation of texts across conquered territory, words delivered likes spices from an alien land. Words mean something quite different when they journey from the palaces of Rome to the tea-rooms of today’s Britain.

To say that we actually believed in vampires or werewolves would be a carelessly inclusive statement. Rather must it be said that we were not prepared to deny the possibility of certain unfamiliar and unclassified modifications of vital force and attenuated matter; existing very infrequently in three-dimensional space because of its more intimate connexion with other spatial units, yet close enough to the boundary of our own to furnish us occasional manifestations which we, for lack of a proper vantage-point, may never hope to understand.

She'd learned since rescuing it a couple of days ago that this particular cat was not like most others; it lacked all grace and spatial awareness, as evident by its current path of evacuation. Streaking off in the direction of the bedroom, it managed to hit the sofa, the base of a standing lamp, and the door frame before making good its escape. Chloe had decided that this nervous clumsiness marked the two of them as a fated pair.

I looked at Judith. "This sounds strange, but I don't suppose you saw three mad women with a cauldron of boiling tea pass by this way?" "No," she replied. The polite voice of reasonable people scared of exciting the madman. "Flash of light? Puff of smoke? Erm..." I tried to find a polite way of describing the symptoms of spontaneous teleportation without using the dreaded "teleportation" word. I failed. I slumped back into the sand. What kind of mystic kept a spatial vortex at the bottom of their cauldrons of tea anyway?

Something, most certainly, happens to a diver’s emotions underwater. It is not merely a side effect of the pleasing, vaguely erotic sensation of water pressure on the body. Nor is it alone the peculiar sense of weightlessness, which permits a diver to hang motionless in open water, observing sea life large as whales around him; not the ability of a diver, descending in that condition, to slowly tumble and rotate in all three spatial planes. It is not the exhilaration from disorientation that comes when one’s point of view starts to lose its “lefts” and “down” and gains instead something else, a unique perception that grows out of the ease of movement in three dimensions. It is not from the diminishment of gravity to a force little more emphatic than a suggestion. It is not solely exposure to an unfamiliar intensity of life. It is not a state of rapture with the bottomless blue world beneath one’s feet…it is some complicated mix of these emotions, together with the constant proximity of real terror.

It is the intense pain that destroys a person's self and world, a destruction experienced spatially as either the contraction of the universe down to the immediate vicinity of the body or as the body swelling to fill the entire universe.

Empirical studies show that New Zealanders are the most widely traveled people on the planet. The computer and the Internet have made a major difference. Insularity, distance, and isolation may have been important in an earlier period of New Zealand’s history, but not today. The rapid progress of communications has wrought a revolution in the spatial condition of New Zealand, and yet its culture remains very distinctive. This fact suggests that distance itself is not the key.

Diasporas are transnational, spatially and temporally sprawling sociocultural formations of people, creating imagined communities whose blurred and fluctuating boundaries are sustained by real and/or symbolic ties to some original 'homeland.

That thing we call a place is the intersection of many changing forces passing through, whirling around, mixing, dissolving, and exploding in a fixed location. To write about a place is to acknowledge that phenomena often treated separately—ecology, democracy, culture, storytelling, urban design, individual life histories and collective endeavors—coexist. They coexist geographically, spatially, in place, and to understand a place is to engage with braided narratives and sue generous explorations.

That (labyrinth)...became a world whose rules I lived by, and I understood the moral of mazes: sometimes you have to turn your back on your goal to get there, sometimes you're farthest away when you're closest, sometimes the only way is the long one. After that careful walking and looking down, the stillness was deeply moving...It was breathtaking to realize that in the labyrinth, metaphors and meanings could be conveyed spatially. That when you seem farthest from your destination is when you suddenly arrive is a very pat truth in words, but a profound one to find with your feet.

I had a dream about you. You had just died, and I was debating putting your body into either a coffin or a shoebox. My decision was based solely on spatial concerns, so I chose the ashtray, because I thought it best to smoke your essence like a cigarette. 


Time if the inner form of animal sense that animates events-the still frames-of the spatial world. The mind animates the world like the motor and gears of a projector. Each weaves a series of still pictures-a series of spatial states-into an order, into the 'current' of life. Motion is created in our minds by running "film cells" together. Remember that everything you perceive-even this page-is actively, repeatedly, being constructed inside your head. It's happening to you right now. Your eyes cannot see through the wall of the cranium; all experience including visual experience is an organized whirl of information in your brain. If your mind could stop its "motor" for a moment, you'd get a freeze frame, just as the movie projector isolated the arrow in one position with no momentum. In fact, time can be defined as the inner summation of spatial states.

Hey, flow charts are one thing, spatial skills another.

Last is D, the number of spatial dimensions. Due to interest in M-theory, physicists have returned to the question of whether life is possible in higher or lower dimensions.

Riemann found that in four spatial dimensions, one needs a collection of ten numbers at each point to describe its properties.

Somewhere among the commotion I grew rather depressed. The depression stayed with me for over a year; it was like an animal, a well-defined, spatially localizable thing. I would wake up, open my eyes, listen-is it here or isn’t it? No sign of it. Perhaps it’s asleep. Perhaps it will leave me alone today. Carefully, very carefully, I get out of bed. All is quiet. I go to the kitchen, start breakfast. Not a sound. TV-Good Morning America, David what’s-his-name, a guy I can’t stand. I eat and watch the guests. Slowly the food fills my stomach and gives me strength. Now a quick excursion to the bathroom, and out for my morning walk-and here she is, my faithful depression: “Did you think you could leave without me?" I had often warned my students not to identify with their work. I told them, “if you want to achieve something, if you want to write a book, paint a picture, be sure that the center of your existence if somewhere else and that it’s solidly grounded; only then will you be able to keep your cool and laugh at the attacks that are bound to come." I myself had followed this advice in the past, but now I was alone, sick with some unknown affliction; my private life was in a mess, and I was without a defense. I often wished I had never written that fucking book.

Freud gave these conceptions spatial form because he still thought, as in his ‘Project’, that it would eventually be possible to locate them within the brain as described by neurology.

Space-time is not necessarily something to which one can ascribe a separate existence, independently of the actual objects of physical reality. Physical objects are not in space, but these objects are spatially extended. In this way the concept "empty space" loses its meaning.

Places are fragmentary and inward-turning histories, pasts that others are not allowed to read, accumulated times that can be unfolded but like stories held in reserve, remaining in an enigmatic state, symbolizations encysted in the pain or pleasure of he body. 'I feel good here': the well-being under-expressed in the language it appears in like a fleeting glimmer is a spatial practice.

I guess the basic difference is that animation is sequential in time but in spatially juxtaposed as comics are. Each successive frame of a movie is projected on exactly the same space--the screen--while each frame of comics must occupy a different space. Space does for comics what time does for film!

My past has its space, its paths, its nameplaces, and its monuments. Beneath the crossed but distinct orders of succession and simultaneity, beneath the train of synchronizations added onto line by line, we find a nameless network--constellations of spatial hours, of point-events. Should we even say 'thing,' should we say 'imaginary' or 'idea,' when each thing exists beyond itself, when each fact can be a dimension, when ideas have their regions? The whole description of our landscape and the lines of our universe, and of our inner monologue, needs to be redone. Colors, sounds, and things--like Van Gogh's stars--are the focal points and radiance of being.

Nothing among all human emotions is more beautiful and more hopeless than the wish to be loved for oneself alone. Who are you anyway, next to countless others, to deserve such preference ? We do not want to be interchangeable; let no one be able to pinch-it for us. A figurative unmistakability claiming to be spatial and siritual. As though the earth had only one heaven, and heaven only one earth, we lay claim to the validity of both and, if we have one, we want to be the other. In reality, however, we are filled with planets, and countless heavens open their doors to us.

Pe potecile lunecoase ale amanuntelor si ale interpretarilor va gasi reazem si o mai adanca dezlegare? Va afla ceva mai multa impacare decat acea sete, care nu se poate potoli in vis? De altfel, cand e un acord aproape unanim asupra relativitatii spatiale, de ce n-am crede ca sistemul de repercutare al cauzelor nu poate afla nicaieri un punct absolut.

Historically, the 'deadline' was the line around a prison beyond which prisoners were eligible for shooting. In keeping with shifts in the exercise of control, what one was delineated spatially over life is now enforced temporarily over labor.

Coonskin caps and silly putty were just not going to cut it anymore. The good mother got her kids toys that were educational, that advanced gross and fine motor skills, that gave them the spatial sensibilities and design aptitude of Frank Lloyd Wright, and that taught Johnny how to read James Joyce at age three. God forbid that one second should pass where your child was idle and that you were not doing everything you could to promote his or her emotional, cognitive, imaginative, quantitative, or muscular development.

Destiny never consists in step-by-step deterministic relations between presents which succeed one another according to the order of a represented time. Rather, it implies between successive presents non-localisable connections, actions at a distance, systems of replay, resonance and echoes, objective chances, signs, signals, and roles which transcend spatial locations and temporal successions.

A human being is a spatially and temporally limited piece of the whole of what we call the "universe". He experiences himself and his feelings as separated from the rest, an optical illusion of his consciousness. The quest for liberation from this bondage [or delusion] is the sole object of real religion. Not nurturing the delusion but only overcoming it gives us the attainable measure of inner peace.

Their story begins on ground level, with footsteps. They are myriad, but do not compose a series. They cannot be counted because each unit has a qualitative character: a style of tactile apprehension and kinesthetic appropriation. Their swarming mass is an innumerable collection of singularities. Their intertwined paths give their shape to spaces. They weave places together. In that respect, pedestrian movements form one of these 'real systems whose existence in fact makes up the city.' They are not localized; it is rather they that spatialize. They are no more inserted within a container than those Chinese character speakers sketch out on their hands with their fingertips.

I think you need to spatially separate your work and your rest. If you were stressed at work, you ought to be relaxing when you’re home, but you’re sitting at home listening to recordings of yourself. This mixes up the two spaces, which makes you feel near-constant shame and anxiety

The universe is but one immense unit; it cannot be separated into spatial domains that are totally empty and others that are completely filled with matter. Matter and space can be distinguished from each other, but where we draw the blurred line between them is largely a matter of taste.

Only shallow people insist on disbelief. You and I know better. We understand how reality is invented. A person sits in a room and thinks a thought and it bleeds out into the world. Every thought is permitted. And there's no longer a moral or spatial distinction between thinking and acting.

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

Quantum mechanics challenges this view by revealing, at least in certain circumstances, a capacity to transcend space; long-range quantum connections can bypass spatial separation. Two objects can be far apart in space, but as far as quantum mechanics is concerned, it’s as if they’re a single entity.

It was the merit of Gestalt psychology to make us aware of the remarkable performance involved in perceiving shapes. Take, for example, a ball or an egg: we can see their shapes at a glance. Yet suppose that instead of the impression made on our eye by an aggregate of white points forming the surface of an egg, we were presented with another, logically equivalent, presentation of these points as given by a list of their spatial co-ordinate values. It would take years of labour to discover the shape inherent in this aggregate of figures - provided it could be guessed at all. The perception of the egg from the list of co-ordinate values would, in fact, be a feat rather similar in nature and measure of intellectual achievement to the discovery of the Copernican system.

There’s a lot of scientific evidence demonstrating that focused attention leads to the reshaping of the brain. In animals rewarded for noticing sound (to hunt or to avoid being hunted, for example), we find much larger auditory centers in the brain. In animals rewarded for sharp eyesight, the visual areas are larger. Brain scans of violinists provide more evidence, showing dramatic growth and expansion in regions of the cortex that represent the left hand, which has to finger the strings precisely, often at very high speed. Other studies have shown that the hippocampus, which is vital for spatial memory, is enlarged in taxi drivers. The point is that the physical architecture of the brain changes according to where we direct our attention and what we practice doing.

psychical life is neither unity nor multiplicity, that it transcends both the mechanical and the intellectual, mechanism and finalism having meaning only where there is "distinct multiplicity," "spatiality," and consequently assemblage of pre-existing parts: "real duration" signifies both undivided continuity and creation.

t is generally recognized that women are better than men at languages, personal relations and multitasking, but less good at map-reading and spatial awareness. It is therefore not unreasonable to suppose that women might be less good at mathematics and physics. It is not politically correct to say such things....But it cannot be denied that there are differences between men and women. Of course, these are differences between the averages only. There are wide variations about the mean.

Long before the Aryan Judeo-Christian plagiarization of the Semite's Scripture took place, the ancient Egyptian concept of the Trinity was a calendrical system of theology. The Aryan Osirian Jew annexed the ancient Egyptian calendar through Osiris' Scepter, while the Aryan Atenian Christian did so through Horus' Scepter. Both Scepters, however, symbolize that very same calendrical anchor when the cow-god YHWH annually rested in ancient Egypt; an event which the Jew and the Christian projected weekly and commemorated on Scepterday and Sonday, consecutively. The Jew has temporally reduced the symbol of the Scepter to the Sabbath, whereas the Christian has spatially reduced it to the Sun; a temporospatial ancient Egyptian unholiness of plagiarizing Semitic Scripture and its seven-days week calendar. That Judeo-Christian Trinity -which the former is trying so hard to conceal while the latter shies not from proclaiming- consists of the three ancient Egyptian calendrical elements: Sky, Moon and Sun. These elements were Hathor, Osiris and Horus who later on became to be identified as YHWH, the departed King coming as the Holy Spirit and the Son.

It goes something like this: I am one person among 6.5 billion people on Earth at the moment. That's one person among 6,500,000,000 people. That'a lot of Wembley Stadiums full of people, and even more double-decker buses (apparently the standard British measurements for size). And we live on an Earth that is spinning at 67,000 miles an hour through space around a sun that is the centre of our solar system (and our solar system is spinning around the centre of the Milky Way at 530,000 mph). Just our solar system (which is a tiny speck within the entire universe) is very big indeed. If Earth was a peppercorn and Jupiter was a chestnut (the standard American measurements), you'd have to place them 100 metres apart to get a sense of the real distance between us. And this universe is only one of many. In fact, the chances are that there are many, many more populated Earths - just like ours - in other universes. And that's just space. Have a look at time, too. If you're in for a good run, you may spend 85 years on this Earth. Man has been around for 100,000 years, so you're going to spend just 0.00085 percent of man's history living on this Earth. And Man's stay on Earth has been very short in the context of the life of the Earth (which is 4.5 billion years old): if the Earth had been around for the equivalent of a day (with the Big Bang kicking it all off at midnight), humans didn't turn up until 11.59.58 p.m. That means we've only been around for the last two seconds. A lifetime is gone in a flash. There are relatively few people on this Earth that were here 100 years ago. Just as you'll be gone (relatively) soon. So, with just the briefest look at the spatial and temporal context of our lives, we are utterly insignificant. As the Perspective Machine lifts up so far above the woods that we forget what the word means, we see just one moving light. It is beautiful. A small, gently glowing light. It is a firefly lost somewhere in the cosmos. And a firefly - on Earth - lives for just one night. It glows beautifully, then goes out. And up there so high in our Perspective Machine we realize that our lives are really just like that of the firefly. Except the air is full of 6.5 billion fireflies. They're glowing beautifully for one night. Then they are gone. So, Fuck It, you might as well REALLY glow.

all forms of vitality are forms of velocity, and no wonder a growing child desires to out-Nature Nature by filling a minimum stretch of time with a maximum of spatial enjoyment. Innermost in man is the spiritual pleasure derivable from the possibilities of outtugging and outrunning gravity, of overcoming or re-enacting the earth's pull.

Feminism has both undone the hierarchy in which the elements aligned with the masculine were given greater value than those of the feminine and undermined the metaphors that aligned these broad aspects of experience with gender. So, there goes women and nature. What does it leave us with? One thing is a political mandate to decentralize privilege and power and equalize access, and that can be a literal spatial goal too, the goal of our designed landscapes and even the managed ones -- the national parks, forests, refuges, recreation areas, and so on.

This qualification aside, I shall use the term gathering to refer to any set of two or more individuals whose members include all and only those who are at the moment in one another’s immediate presence. By the term situation I shall refer to the full spatial environment anywhere within which an entering person becomes a member of the gathering that is (or does then become) present. Situations begin when mutual monitoring occurs, and lapse when the second-last person has left. In order to stress the full extent of any such unit, I will sometimes employ the term situation at large.

And, without question, all those different planes, upon which Time, since I had regained it at this reception, had exhibited my life, by reminding me that in a book which gave the history of one, it would be necessary to make use of a sort of spatial psychology as opposed to the usual flat psychology, added a new beauty to the resurrections my memory was operating during my solitary reflections in the library, since memory, by introducing the past into the present without modification, as though it were the present, eliminates precisely that great Time-dimension in accordance with which life is realised.

When the brain runs out of sugar, the undernourished ego grows weak, can’t be bothered to undertake the necessary chores, and loses all interest in those spatial and temporal relationships which mean so much to an organism bent on getting on in the world. As Mind at Large seeps past the no longer watertight valve, all kinds of biologically useless things start to happen. In some cases there may be extra-sensory perceptions. Other persons discover a world of visionary beauty. To others again is revealed the glory, the infinite value and meaningfulness of naked existence, of the given, unconceptualized event. In the final stage of egolessness there is an “obscure knowledge” that All is in all—that All is actually each. This is as near, I take it, as a finite mind can ever come to “perceiving everything that is happening everywhere in the universe.

Even here in these sentences, I place my hands on your back and see how dark they are as they lie against the unchangeable white backdrop of your skin. Even now, I see … your waist and hips as I knead out the tensions, the small bones along your spine, a row of ellipses no silence translates. Even after all these years, the contrast between our skin surprises me–the way a blank page does when my hand, gripping a pen, begins to move through its spatial field, trying to act upon its life without marring it. But by writing, I mar it. I change, embellish, and preserve you all at once. — Ocean Vuong, On Earth We’re Briefly Gorgeous (Penguin, 2019)

As a cop trying to anticipate how burglars might use the city, you have to think three-dimensionally. Volumetrically. You have to think in a fundamentally different spatial way about the city laid out below, including how neighborhoods are actually connected and what the most efficient routes might be between them. After all, this is how criminals think, Burdette explained, and this is how they pioneer new geographic ways to escape from you.

It is random discharges of this type, set off by the creation of anti-galaxies in space, which have led to the depletion of the time store available to the materials of our own solar system. Just as a super-saturated solution will discharge itself into a crystalline mass, so the super-saturation of our solar system leads to its appearance in a parallel spatial matrix. As more and more time leaks away, the process of super-saturation continues, the original atoms and molecules producing spatial replicas of themselves, substance without mass, in an attempt to increase their foothold upon existence. The process is theoretically without end, and it may be possible for a single atom to produce an infinite number of duplicates of itself, and so fill the entire universe, from which simultaneously all time is expired, an ultimate macrocosmic zero beyond the wildest dreams of Plato and Democritus.

We perceive our environment in three dimensions, but we don’t actually live in a 3-D world. 3-D is static. A snapshot. We have to add a fourth dimension to begin to describe the nature of our existence. The 4-D tesseract doesn’t add a spatial dimension. It adds a temporal one. It adds time, a stream of 3-D cubes, representing space as it moves along time’s arrow. This is best illustrated by looking up into the night sky at stars whose brilliance took fifty light-years to reach our eyes. Or five hundred. Or five billion. We’re not just looking into space, we’re looking back through time. Our path through this 4-D spacetime is our worldline (reality), beginning with our birth and ending with our death. Four coordinates (x, y, z, and t [time]) locate a point within the tesseract. And we think it stops there, but that’s only true if every outcome is inevitable, if free will is an illusion, and our worldline is solitary. What if our worldline is just one of an infinite number of worldlines, some only slightly altered from the life we know, others drastically different? The Many-Worlds interpretation of quantum mechanics posits that all possible realities exist. That everything which has a probability of happening is happening. Everything that might have occurred in our past did occur, only in another universe. What if that’s true? What if we live in a fifth-dimensional probability space? What if we actually inhabit the multiverse, but our brains have evolved in such a way as to equip us with a firewall that limits what we perceive to a single universe? One worldline. The one we choose, moment to moment. It makes sense if you think about it. We couldn’t possibly contend with simultaneously observing all possible realities at once. So how do we access this 5-D probability space? And if we could, where would it take us? —

If only I could cry. I am beyond that. The light, the light, lending itself to empty downtown Saturday, but still the stupid insensate cars flush by oblivious to their stupidity, my silent plea. It isn't Mexico. It's not Paris. It's a painting by Hopper come to life. I am trapped inside a dead thing. Language is impossible here, even in English. Who has the arrogance to say: I'm mad, this is my crazy view of things, help me. I'm trapped in a silent world, a tableau of forty years ago. The walls are different, the tables, the heights of the veiling and the chairs. I loom above this letter. The view past the rows of cakes in the plate glass window is unfamiliar. I am a ghost. There is nothing now between me and death. Death is the unfamiliarity of everything, the strangeness of the once familiar. The same spatial configurations only the light is hollow, sick. I think I lack the energy to hit expensive discos which I don't know where they are to be rejected tonight. I look passable. My energy's low. I love to dance but despair is not a good muse. This Mexico, babe. Men who don't love you but act wildly as if they do initially. Self-involved, narcissistic men... The men drink and philosophize about pain. The women live it solo and culturelessly. No one cries, except easily, sentimentally. The devil, therefore God, exists. Oaxaca was a pushover compared to this. Pain had boundaries there. Spare us big cities, oh lord!

God is not, like creatures, made up of parts. God is spirit, without bodily dimensions. Firstly, no body can cause change without itself being changed. Secondly, things with dimensions are potential of division. But the starting-point for all existence must be wholly real and not potential in any way: though things that get realized begin as potential, preceding them is the source of their realization which must already be real. Thirdly, living bodies are superior to other bodies; and what makes a body living is not the dimensions which make it a body (for then everything with dimensions would be living), but something more excellent like a soul. The most excellent existent of all then cannot be a body. So when the scriptures ascribe dimensions to God they are using spatial extension to symbolize the extent of God's power; just as they ascribe bodily organs to God as metaphors for their functions, and postures like sitting or standing to symbolize authority or strength.

The theological perspective of participation actually saves the appearances by exceeding them. It recognizes that materialism and spiritualism are false alternatives, since if there is only finite matter there is not even that, and that for phenomena really to be there they must be more than there. Hence, by appealing to an eternal source for bodies, their art, language, sexual and political union, one is not ethereally taking leave of their density. On the contrary, one is insisting that behind this density resides an even greater density – beyond all contrasts of density and lightness (as beyond all contrasts of definition and limitlessness). This is to say that all there is only is because it is more than it is. (...) This perspective should in many ways be seen as undercutting some of the contrasts between theological liberals and conservatives. The former tend to validate what they see as the modern embrace of our finitude – as language, and as erotic and aesthetically delighting bodies, and so forth. Conservatives, however, seem still to embrace a sort of nominal ethereal distancing from these realities and a disdain for them. Radical orthodoxy, by contrast, sees the historic root of the celebration of these things in participatory philosophy and incarnational theology, even if it can acknowledge that premodern tradition never took this celebration far enough. The modern apparent embrace of the finite it regards as, on inspection, illusory, since in order to stop the finite vanishing modernity must construe it as a spatial edifice bound by clear laws, rules and lattices. If, on the other hand, following the postmodern options, it embraces the flux of things, this is an empty flux both concealing and revealing an ultimate void. Hence, modernity has oscillated between puritanism (sexual or otherwise) and an entirely perverse eroticism, which is in love with death and therefore wills the death also of the erotic, and does not preserve the erotic as far as an eternal consummation. In a bizarre way, it seems that modernity does not really want what it thinks it wants; but on the other hand, in order to have what it thinks it wants, it would have to recover the theological. Thereby, of course, it would discover also that that which it desires is quite other than it has supposed

Hinton spent most of his adult years trying to visualize higher spatial dimensions. He had no interest in finding a physical interpretation for the fourth dimension. Einstein saw, however, that the fourth dimension can be taken as a temporal one. He was guided by a conviction and physical intuition that higher dimensions have a purpose: to unify the principles of nature. By adding higher dimensions, he could unite physical concepts that, in a three-dimensional world, have no connection, such as matter and energy.

She was still getting organized, trying to get the books she'd taken out to fit into the shelf under the stroller. She would shove a book in, and then something, a juice cup, a Binky, or one disturbing Barbie-doll head, would fall out the other side. She would shove that back in, and then something else would leak out the other side. Her stroller was like a poorly designed clown car. I went over and helped. It was a good thing spatial relations were a strength of mine, because it required the geometry skills of Newton to get everything slotted into place.

Cheng Xin gazed up at the giant black columns reaching into space. They lifted up the domed sky and seemed to turn the universe into a Palace of Death. Is this the ultimate end for everything? In the sky, Cheng Xin could see the end of the columns. She pointed in that direction. “So the ships entered lightspeed at the end?” “That’s right. These are only about a hundred kilometers high. We’ve seen columns even shorter than these, presumably left by ships that entered lightspeed almost instantaneously.” “Are these the most advanced lightspeed ships?” “Maybe. But this is a rarely seen technique. Death lines are usually the products of Zero-Homers.” “Zero-Homers?” “They’re also called Resetters. Maybe they’re a group of intelligent individuals, or a civilization, or a group of civilizations. We don’t know exactly who they are, but we’ve confirmed their existence. The Zero-Homers want to reset the universe and return it to the Garden of Eden.” “How?” “By moving the hour hand of the clock past twelve. Take spatial dimensions as an example. It’s practically impossible to drag a universe in lower dimensions back into higher dimensions, so maybe it’s better to work forward in the other direction. If the universe can be lowered into zero dimensions and then beyond, the clock might be reset and everything returned to the beginning. The universe might possess ten macroscopic dimensions again.

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.

That campaign was about a demarcation of time. So it’s interesting, and certainly troubling, to understand the decline in labor unions in the last several decades alongside a similar decline in the demarcation of public space. True public spaces, the most obvious examples being parks and libraries, are places for—and thus the spatial underpinnings of—“what we will.” A public, noncommercial space demands nothing from you in order for you to enter, nor for you to stay; the most obvious difference between public space and other spaces is that you don’t have to buy anything, or pretend to want to buy something, to be there.

The sphere to end all spheres—the largest and most perfect of them all—is the entire observable universe. In every direction we look, galaxies recede from us at speeds proportional to their distance. As we saw in the first few chapters, this is the famous signature of an expanding universe, discovered by Edwin Hubble in 1929. When you combine Einstein’s relativity and the velocity of light and the expanding universe and the spatial dilution of mass and energy as a consequence of that expansion, there is a distance in every direction from us where the recession velocity for a galaxy equals the speed of light. At this distance and beyond, light from all luminous objects loses all its energy before reaching us. The universe beyond this spherical “edge” is thus rendered invisible and, as far as we know, unknowable. There’s a variation of the ever-popular multiverse idea in which the multiple universes that comprise it are not separate universes entirely, but isolated, non-interacting pockets of space within one continuous fabric of space-time—like multiple ships at sea, far enough away from one another so that their circular horizons do not intersect. As far as any one ship is concerned (without further data), it’s the only ship on the ocean, yet they all share the same body of water.

Novels begin and end with, consist of, and indeed in one sense are nothing but voices. So reading is learning to listen sensitively, and to tune in accurately, to varying frequencies and a developing programme. From the opening words a narrative voice begins to create its own characteristic personality and sensibility, whether it belongs to an 'author' or a 'character'. At the same time a reader is being created, persuaded to become the particular kind of reader the book requires. A relationship develops, which becomes the essential basis of the experience. In the modulation of the fictive voice, finally, through the creation of 'author' and 'reader* and their relationship, there is a definition of the nature and status of the experience, which will always imply a particular idea of ordering the world. So much is perhaps familiar enough, and a useful rhetoric of Voice' has developed. Yet I notice in my students and myself, when its vocabulary is in play, a tendency to become rather too abstract or technical, and above all too spatial and static. Perhaps we need to remind ourselves what it can be like to listen to close friends, talking animatedly and seriously in everyday experience, in order to make sure that a vocabulary which often points only to broad strategies does not tempt us to underplay the extraordinary resourcefulness, variety and fluctuation of the novelist's voice.

The fifth principle emphasizes another human strength: whenever possible, we should take measures to re-spatialize the information we think about. We inherited “a mind on the hoof,” as Andy Clark puts it: a brain that was built to pick a path through a landscape and to find the way back home. Neuroscientific research indicates that our brains process and store information—even, or especially, abstract information—in the form of mental maps. We can work in concert with the brain’s natural spatial orientation by placing the information we encounter into expressly spatial formats: creating memory palaces, for example, or designing concept maps. In the realm of education research, experts now speak of “spatializing the curriculum”—that is, simultaneously drawing on and strengthening students’ spatial capacities by having them employ spatial language and gestures, engage in sketching and mapmaking, and learn to interpret and create charts, tables, and diagrams. The spatialized

The feeling of inner detachment and isolation is not in itself an abnormal phenomenon but is normal in the sense that consciousness has withdrawn from the phenomenal world and got outside time and space. You will find the clearest parallels in Indian philosophy, especially in Yoga. In your case the feeling is reinforced by your psychological studies. The assimilated unconscious apparently disappears in consciousness without trace, but it has the effect of detaching consciousness from its ties to the object. I have described this development in my commentary on the Golden Flower. It is a sort of integration process and an anticipation of consciousness. The cross is an indication of this, since it represents an integration of the 4 (functions). It is perfectly understandable that, when consciousness detaches itself from the object, the feeling arises that one does not know where one stands. Actually one is standing nowhere, because standing has a below and an above. But there one has no below and above at all, because spatiality pertains to the world of the senses, and consciousness possesses spatiality only when it is in participation with that world. It is a not-knowing, which has the same positive character as nirvana in the Buddhist definition, or the wu-wei, not-doing, of the Chinese, which does not mean doing nothing. The profound doubt you seem to be suffering from is quite in order as it simply expresses the detachment of consciousness and the resultant explanation of the objective world as an illusion.

Seeing the God statement Suppose the statement Blessed Are the pure in heart, for they shall see God were placed like a wreath of violets, Lilies, laurel, and olive, blossoms strung together Like words in a sentence, a garland Launched, set out on a flowing creek Imagine that wreath carried Down the frothy rapids, tossed, floating Slipping over water-smooth, moss-colored Boulders, in and out of slow, dark pools, Through poplar and willow shadows. It dips, Sinks momentarily, emerges, travels, maitains Its ring, its declaration and syntax. At times it widens in a broad, deep Current, makes sense as a gift. The pure becomes inclusive, spatial, Generous. God and heart are two Spread wings of one open reading. And at times it narrows, restricts. Violets and heart entangle With God. The blessed braces, Overlaps lilies and laurel. Still, at any point you might reach down yourself, catch that ring of blossoms, lift it up, wear its beauty and blooming distinction across your forehead. Look into a mirror. See what you can see.

At some very low level, we all share certain fictions about time, and they testify to the continuity of what is called human nature, however conscious some, as against others, may become of the fictive quality of these fictions. It seems to follow that we shall learn more concerning the sense-making paradigms, relative to time, from experimental psychologists than from scientists or philosophers, and more from St. Augustine than from Kant or Einstein because St. Augustine studies time as the soul's necessary self-extension before and after the critical moment upon which he reflects. We shall learn more from Piaget, from studies of such disorders as déjà vu, eidetic imagery, the Korsakoff syndrome, than from the learned investigators of time's arrow, or, on the other hand, from the mythic archetypes. Let us take a very simple example, the ticking of a clock. We ask what it says: and we agree that it says tick-tock. By this fiction we humanize it, make it talk our language. Of course, it is we who provide the fictional difference between the two sounds; tick is our word for a physical beginning, tock our word for an end. We say they differ. What enables them to be different is a special kind of middle. We can perceive a duration only when it is organized. It can be shown by experiment that subjects who listen to rhythmic structures such as tick-tock, repeated identically, 'can reproduce the intervals within the structure accurately, but they cannot grasp spontaneously the interval between the rhythmic groups,' that is, between tock and tick, even when this remains constant. The first interval is organized and limited, the second not. According to Paul Fraisse the tock-tick gap is analogous to the role of the 'ground' in spatial perception; each is characterized by a lack of form, against which the illusory organizations of shape and rhythm are perceived in the spatial or temporal object. The fact that we call the second of the two related sounds tock is evidence that we use fictions to enable the end to confer organization and form on the temporal structure. The interval between the two sounds, between tick and tock is now charged with significant duration. The clock's tick-tock I take to be a model of what we call a plot, an organization that humanizes time by giving it form; and the interval between tock and tick represents purely successive, disorganized time of the sort that we need to humanize. Later I shall be asking whether, when tick-tock seems altogether too easily fictional, we do not produce plots containing a good deal of tock-tick; such a plot is that of Ulysses.

The formerly absolute distinction between time and eternity in Christian thought--between nunc movens with its beginning and end, and nunc stans, the perfect possession of endless life--acquired a third intermediate order based on this peculiar betwixt-and-between position of angels. But like the Principle of Complementarity, this concord-fiction soon proved that it had uses outside its immediate context, angelology. Because it served as a means of talking about certain aspects of human experience, it was humanized. It helped one to think about the sense, men sometimes have of participating in some order of duration other than that of the nunc movens--of being able, as it were, to do all that angels can. Such are those moments which Augustine calls the moments of the soul's attentiveness; less grandly, they are moments of what psychologists call 'temporal integration.' When Augustine recited his psalm he found in it a figure for the integration of past, present, and future which defies successive time. He discovered what is now erroneously referred to as 'spatial form.' He was anticipating what we know of the relation between books and St. Thomas's third order of duration--for in the kind of time known by books a moment has endless perspectives of reality. We feel, in Thomas Mann's words, that 'in their beginning exists their middle and their end, their past invades the present, and even the most extreme attention to the present is invaded by concern for the future.' The concept of aevum provides a way of talking about this unusual variety of duration-neither temporal nor eternal, but, as Aquinas said, participating in both the temporal and the eternal. It does not abolish time or spatialize it; it co-exists with time, and is a mode in which things can be perpetual without being eternal. We've seen that the concept of aevum grew out of a need to answer certain specific Averroistic doctrines concerning origins. But it appeared quite soon that this medium inter aeternitatem et tempus had human uses. It contains beings (angels) with freedom of choice and immutable substance, in a creation which is in other respects determined. Although these beings are out of time, their acts have a before and an after. Aevum, you might say, is the time-order of novels. Characters in novels are independent of time and succession, but may and usually do seem to operate in time and succession; the aevum co-exists with temporal events at the moment of occurrence, being, it was said, like a stick in a river. Brabant believed that Bergson inherited the notion through Spinoza's duratio, and if this is so there is an historical link between the aevum and Proust; furthermore this durée réelle is, I think, the real sense of modern 'spatial form,' which is a figure for the aevum.

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.

So much of the most important personal news I'd received in the last several years had come to me by smartphone while I was abroad in the city that I could plot on a map, could represent spatially the events, such as they were, of my early thirties. Place a thumbtack on the wall or drop a flag on Google Maps at Lincoln Center, where, beside the fountain, I took a call from Jon informing me that, for whatever complex of reasons, a friend had shot himself; mark the Noguchi Museum in Long Island City, where I read the message ("Apologies for the mass e-mail...") a close cousin sent out describing the dire condition of her newborn; waiting in line at the post office on Atlantic, the adhan issuing from the adjacent mosque, I received your wedding announcement and was shocked to be shocked, crushed, and started a frightening multi week descent, worse for being so embarrassingly cliched; while in the bathroom at the SoHo Crate and Barrel--the finest semipublic restroom in lower Manhattan--I learned I'd been awarded a grant that would take me overseas for a summer, and so came to associate the corner of Broadway and Houston with all that transpired in Morocco; at Zucotti Park I heard my then-girlfriend was not--as she'd been convinced--pregnant; while buying discounted dress socks at the Century 21 department store across from Ground Zero, I was informed by text that a friend in Oakland had been hospitalized after the police had broken his ribs. And so on: each of these experiences of reception remained, as it were, in situ, so that whenever I returned to a zone where significant news had been received, I discovered that the news and an echo of its attendant affect still awaited me like a curtain of beads.

universe.” Tan’elKoth’s tone remained dry and precise, but his face grew ever more grim. “Chambaraya is, one might say, a smaller knot of mind within the Worldmind: what the elves call T’nnalldion. Through Faith, the Bog can get its corporate fingers into that knot, unbind it, and tie it again in their own image.” Avery shook her head blankly, uncomprehending. Tan’elKoth’s expression was bleak as an open grave. “They’ll make of it a world like this one.” “Is that all?” Avery asked, frowning. “You make it sound like a catastrophe.” “It will be an Armageddon unimaginable; it will be genocide on a scale of which Stalin could not have dreamed.” “Wiping out magick doesn’t seem like such a bad thing.” “Businessman,” Tan’elKoth said patiently, “you don’t understand. Magick has not been wiped out on Earth; it is a function of Flow, which is the energy of existence itself. But its state can be altered. And it has been. Once, Earth was home to fully as many magickal creatures as was Overworld: dragons and sea serpents and mermaids, rocs and djann and primals and stonebenders and all. But creatures such as these require higher levels of certain frequencies of Flow than does humanity; as the pattern of Earth degraded, these creatures not only died, but their very bones gave up their integrity. They vanished into the background Flow of your universe.” “You’re saying magick works on Earth?” Avery said skeptically. “Magick works, as you say, everywhere. But the manner in which magick works on Earth is a local aberration; the physics of this planet and its spatial surrounds have been altered to conditions that favor the ascendance of humanity.” “And what’s wrong with that?” “I did not say it was wrong. I do not debate morality. In my zeal to protect my Children, I once favored such a fate for my own world. But it is unnatural. It is both the cause and the result of the ugly twisting of human nature that we see around

If the law of gravitation be regarded as universal, the point may be stated as follows. The laws of motion require to be stated by reference to what have been called kinetic axes: these are in reality axes having no absolute acceleration and no absolute rotation. It is asserted, for example, when the third law is combined with the notion of mass, that, if m, m' be the masses of two particles between which there is a force, the component accelerations of the two particles due to this force are in the ratio m2 : m1. But this will only be true if the accelerations are measured relative to axes which themselves have no acceleration. We cannot here introduce the centre of mass, for, according to the principle that dynamical facts must be, or be derived from, observable data, the masses, and therefore the centre of mass, must be obtained from the acceleration, and not vice versâ. Hence any dynamical motion, if it is to obey the laws of motion, must be referred to axes which are not subject to any forces. But, if the law of gravitation be accepted, no material axes will satisfy this condition. Hence we shall have to take spatial axes, and motions relative to these are of course absolute motions. 465. In order to avoid this conclusion, C. Neumann* assumes as an essential part of the laws of motion the existence, somewhere, of an absolutely rigid “Body Alpha”, by reference to which all motions are to be estimated. This suggestion misses the essence of the discussion, which is (or should be) as to the logical meaning of dynamical propositions, not as to the way in which they are discovered. It seems sufficiently evident that, if it is necessary to invent a fixed body, purely hypothetical and serving no purpose except to be fixed, the reason is that what is really relevant is a fixed place, and that the body occupying it is irrelevant. It is true that Neumann does not incur the vicious circle which would be involved in saying that the Body Alpha is fixed, while all motions are relative to it; he asserts that it is rigid, but rightly avoids any statement as to its rest or motion, which, in his theory, would be wholly unmeaning. Nevertheless, it seems evident that the question whether one body is at rest or in motion must have as good a meaning as the same question concerning any other body; and this seems sufficient to condemn Neumann’s suggested escape from absolute motion.

Now to picture the mechanism of this process of construction and not merely its progressive extension, we must note that each level is characterized by a new co-ordination of the elements provided—already existing in the form of wholes, though of a lower order—by the processes of the previous level. The sensori-motor schema, the characteristic unit of the system of pre-symbolic intelligence, thus assimilates perceptual schemata and the schemata relating to learned action (these schemata of perception and habit being of the same lower order, since the first concerns the present state of the object and the second only elementary changes of state). The symbolic schema assimilates sensori-motor schemata with differentiation of function; imitative accommodation is extended into imaginal significants and assimilation determines the significates. The intuitive schema is both a co-ordination and a differentiation of imaginal schemata. The concrete operational schema is a grouping of intuitive schemata, which are promoted, by the very fact of their being grouped, to the rank of reversible operations. Finally, the formal schema is simply a system of second-degree operations, and therefore a grouping operating on concrete groupings. Each of the transitions from one of these levels to the next is therefore characterized both by a new co-ordination and by a differentiation of the systems constituting the unit of the preceding level. Now these successive differentiations, in their turn, throw light on the undifferentiated nature of the initial mechanisms, and thus we can conceive both of a genealogy of operational groupings as progressive differentiations, and of an explanation of the pre-operational levels as a failure to differentiate the processes involved. Thus, as we have seen (Chap. 4), sensori-motor intelligence arrives at a kind of empirical grouping of bodily movements, characterized psychologically by actions capable of reversals and detours, and geometrically by what Poincaré called the (experimental) group of displacement. But it goes without saying that, at this elementary level, which precedes all thought, we cannot regard this grouping as an operational system, since it is a system of responses actually effected; the fact is therefore that it is undifferentiated, the displacements in question being at the same time and in every case responses directed towards a goal serving some practical purpose. We might therefore say that at this level spatio-temporal, logico-arithmetical and practical (means and ends) groupings form a global whole and that, in the absence of differentiation, this complex system is incapable of constituting an operational mechanism. At the end of this period and at the beginning of representative thought, on the other hand, the appearance of the symbol makes possible the first form of differentiation: practical groupings (means and ends) on the one hand, and representation on the other. But this latter is still undifferentiated, logico-arithmetical operations not being distinguished from spatio-temporal operations. In fact, at the intuitive level there are no genuine classes or relations because both are still spatial collections as well as spatio-temporal relationships: hence their intuitive and pre-operational character. At 7–8 years, however, the appearance of operational groupings is characterized precisely by a clear differentiation between logico-arithmetical operations that have become independent (classes, relations and despatialized numbers) and spatio-temporal or infra-logical operations. Lastly, the level of formal operations marks a final differentiation between operations tied to real action and hypothetico-deductive operations concerning pure implications from propositions stated as postulates.

You don’t need to pity them. Really, let me tell you: don’t. The reality of the universe is not something to envy.” “Why?” Yifan lifted a hand and pointed at the stars of the galaxy. Then he let the 3G force pull his arm back to this chest. “Darkness. Only darkness.” “You mean the dark forest state?” Guan Yifan shook his head, a gesture that appeared to be a struggle in hypergravity. “For us, the dark forest state is all-important, but it’s just a detail of the cosmos. If you think of the cosmos as a great battlefield, dark forest strikes are nothing more than snipers shooting at the careless—messengers, mess men, etc. In the grand scheme of the battle, they are nothing. You have not seen what a true interstellar war is like.” “Have you?” “We’ve caught a few glimpses. But most things we know are just guesses.… Do you really want to know? The more you possess of this kind of knowledge, the less light remains in your heart.” “My heart is already completely dark. I want to know.” And so, more than six centuries after Luo Ji had fallen through ice into that lake, another dark veil hiding the truth about the universe was lifted before the gaze of one of the only survivors of Earth civilization. Yifan asked, “Why don’t you tell me what the most powerful weapon for a civilization possessing almost infinite technological prowess is? Don’t think of this as a technical question. Think philosophy.” Cheng Xin pondered for a while and then struggled to shake her head. “I don’t know.” “Your experiences should give you a hint.” What had she experienced? She had seen how a cruel attacker could lower the dimensions of space by one and destroy a solar system. What are dimensions? “The universal laws of physics,” Cheng Xin said. “That’s right. The universal laws of physics are the most terrifying weapons, and also the most effective defenses. Whether it’s by the Milky Way or the Andromeda Galaxy, at the scale of the local galactic group or the Virgo Supercluster, those warring civilizations possessing godlike technology will not hesitate to use the universal laws of physics as weapons. There are many laws that can be manipulated into weapons, but most commonly, the focus is on spatial dimensions and the speed of light. Typically, lowering spatial dimensions is a technique for attack, and lowering the speed of light is a technique for defense. Thus, the dimensional strike on the Solar System was an advanced attack method. A dimensional strike is a sign of respect. In this universe, respect is not easy to earn. I guess you could consider it an honor for Earth civilization.

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.