Spherical Quotes

You have to live spherically - in many directions. Never lose your childish enthusiasm - and things will come your way.

All at once, I couldn’t figure out why I was methodically tossing a spherical object through a toroidal object. It seemed like the stupidest thing I could possibly be doing.

This is the excellent foppery of the world, that when we are sick in fortune (often the surfeits of our own behavior) we make guilty of our disasters the sun, the moon, and stars, as if we were villains on necessity; fools by heavenly compulsion; knaves, thieves, and treachers by spherical predominance; drunkards, liars, and adulterers by an enforced obedience of planetary influence; and all that we are evil in, by a divine thrusting on. An admirable evasion of whoremaster man, to lay his goatish disposition on the charge of a star! My father compounded with my mother under the Dragon's tail, and my nativity was under Ursa Major, so that it follows I am rough and lecherous. I should have been that I am, had the maidenliest star in the firmament twinkled on my bastardizing.

We now know the basic rules governing the universe, together with the gravitational interrelationships of its gross components, as shown in the theory of relativity worked out between 1905 and 1916. We also know the basic rules governing the subatomic particles and their interrelationships, since these are very neatly described by the quantum theory worked out between 1900 and 1930. What's more, we have found that the galaxies and clusters of galaxies are the basic units of the physical universe, as discovered between 1920 and 1930. ...The young specialist in English Lit, having quoted me, went on to lecture me severely on the fact that in every century people have thought they understood the universe at last, and in every century they were proved to be wrong. It follows that the one thing we can say about our modern 'knowledge' is that it is wrong... My answer to him was, when people thought the Earth was flat, they were wrong. When people thought the Earth was spherical they were wrong. But if you think that thinking the Earth is spherical is just as wrong as thinking the Earth is flat, then your view is wronger than both of them put together. The basic trouble, you see, is that people think that 'right' and 'wrong' are absolute; that everything that isn't perfectly and completely right is totally and equally wrong. However, I don't think that's so. It seems to me that right and wrong are fuzzy concepts, and I will devote this essay to an explanation of why I think so. When my friend the English literature expert tells me that in every century scientists think they have worked out the universe and are always wrong, what I want to know is how wrong are they? Are they always wrong to the same degree?

This,” James said, when he had disappeared. “This is the excellent foppery of the world, that, when we are sick in fortune—often the surfeit of our own behavior—we make guilty of our disasters the sun, the moon, and the stars … as if we were villains on necessity; fools by heavenly compulsion; knaves, thieves, and treachers by spherical predominance; drunkards, liars, and adulterers by an enforc’d obedience of planetary influence; and all that we are evil in, by a divine thrusting-on!

To suppose that the eye with all its inimitable contrivances for adjusting the focus to different distances, for admitting different amounts of light, and for the correction of spherical and chromatic aberration, could have been formed by natural selection, seems, I confess, absurd in the highest degree...The difficulty of believing that a perfect and complex eye could be formed by natural selection , though insuperable by our imagination, should not be considered subversive of the theory.

When people thought the Earth was flat, they were wrong. When people thought the Earth was spherical they were wrong. But if you think that thinking the Earth is spherical is just as wrong as thinking the Earth is flat, then your view is wronger than both of them put together

Why do you keep saying that " he asked in response "Apples and oranges aren't that different really. I mean they're both fruit. Their weight is extremely similar. They both contain acidic elements. They're both roughly spherical. They serve the same social purpose. With the possible exception of a tangerine I can't think of anything more similar to an orange than an apple. If I was having lunch with a man who was eating an apple and-while I was looking away-he replaced that apple with an orange I doubt I'd even notice. So how is this a metaphor for difference I could understand if you said 'That's like comparing apples and uranium ' or 'That's like comparing apples with baby wolverines ' or 'That's like comparing apples with the early work of Raymond Carver ' or 'That's like comparing apples with hermaphroditic ground sloths.' Those would all be valid examples of profound disparity.

If there is a lot of matter, gravity will cause space to curve back on itself, yielding the spherical shape. If there is little matter, space is free to flare outward in the Pringles shape. And if there is just the right amount of matter, space will have zero curvature.*

As Aristotle put it, the beginning of philosophy is wonder. I am simply amazed to find myself living on a ball of rock that swings around an immense spherical fire. I am more amazed that I am a maze—a complex wiggliness, an arabesque of tubes, filaments, cells, fibers, and films that are various kinds of palpitation in this stream of liquid energy.

THE PRESOCRATIC PROBLEM [all snap flags] Parmenides named his gun The Hot Power of the Stars. His gun was one, uncreated, imperishable, timeless, changeless, perfect, spherical. Spherical was the problem.

Our television signals leave this planet and go out into space...the signals spread out from the earth in spherical waves, a little like ripples in a pond. They travel at the speed of light, 186,000 miles a second, and essentially go on forever. The better some other civilizations receivers are, the farther away they could be and still pick up our tv signals. Even we could detect a strong tv transmission from a planet going around the nearest star.' President: 'You mean everything? You mean to say all that crap on television - the car crashes, wrestling, the porno channels, the evening news?

I'm also part of the great conspiracy of global scientists to promote the myths of climate change, evolution, vaccination, and a spherical earth. After all, there's nobody on earth wealthier and more powerful than scientists, and they can't risk losing this exalted position by people finding out how the world really works.

I have journeyed back in thought --with thought hopelessly tapering off as I went-- to remote regions where I groped for some secret outlet only to discover that the prison of time is spherical and without exits. Short of suicide I have tried everything.

I visit the orchards of God and look at the spheric product And look at quintillions ripened, and look at quintillions green.

Without an observer at a twenty three degree angle to the light being reflected off a cloud of spherical droplets, there is no rainbow. The whole universe is like that. Our spirits stand at a twenty three degree angle to the universe. There is some new thing created at the contact of photon and retina, some space created between rock and mind.

Jin made a sound as high pitched as a tea kettle as his spherical body vibrated with excitement. "Pirate hunters. We're going to be pirate hunters." Damn it. She'd lost him. Jin bobbed up and down, looking like a jack in the box. "I never say this, but be yourself, Kira, and we can realize our lifelong dream." Jin screamed to himself as he careened in a circle. "We'll get a big fancy hat and an artificial leg. This is going to be great.

Organic life beneath the shoreless waves Was born and rais’d in Ocean’s pearly caves First forms minute, unseen by spheric glass, Move on the mud, or pierce the watery mass; These, as successive generations bloom, New powers acquire, and larger limbs assume; Whence countless groups of vegetation spring, And breathing realms of fin, and feet and wing.

The young specialist in English Lit, having quoted me, went on to lecture me severely on the fact that in every century people have thought they understood the Universe at last, and in every century they were proved to be wrong. It follows that the one thing we can say about our modern 'knowledge' is that it is wrong. The young man then quoted with approval what Socrates had said on learning that the Delphic oracle had proclaimed him the wisest man in Greece. 'If I am the wisest man,' said Socrates, 'it is because I alone know that I know nothing.' The implication was that I was very foolish because I was under the impression I knew a great deal. Alas, none of this was new to me. (There is very little that is new to me; I wish my correspondents would realize this.) This particular theme was addressed to me a quarter of a century ago by John Campbell, who specialized in irritating me. He also told me that all theories are proven wrong in time. My answer to him was, 'John, when people thought the Earth was flat, they were wrong. When people thought the Earth was spherical, they were wrong. But if you think that thinking the Earth is spherical is just as wrong as thinking the Earth is flat, then your view is wronger than both of them put together.

When people thought the earth was flat, they were wrong. When people thought the earth was spherical, they were wrong. But if you think that thinking the earth is spherical is just as wrong as thinking the earth is flat, then your view is wronger than both of them put together. —ISAAC ASIMOV, THE RELATIVITY OF WRONG, 1989

Suppose that which is taking place here and now is not reality, but only a tale, a tale of some higher order that contains within it the tale of the machine: a reader might well wonder why you and your companions are shaped like spheres, inasmuch as that sphericality serves no purpose in the narration and would appear to be a wholly superfluous embellishment...

I was all about resurrecting the lost art of the midrange jumper, but then one day I was shooting free throws—just standing at the foul line at the North Central gym shooting from a rack of balls. All at once, I couldn’t figure out why I was methodically tossing a spherical object through a toroidal object. It seemed like the stupidest thing I could possibly be doing. “I started thinking about little kids putting a cylindrical peg through a circular hole, and how they do it over and over again for months when they figure it out, and how basketball was basically just a slightly more aerobic version of that same exercise.

I HAVE SOME QUESTIONS ABOUT KING TRITON. Specifically, King, why are you elderly but with the body of a teenage Beastmaster? How do you maintain those monster pecs? Do they have endocrinologists under the sea? Because I am scheduling you some bloodwork... ...Question: How come, when they turn back into humans at the end of Beauty and the Beast, Chip is a four-year-old boy, but his mother, Mrs. Potts, is like 107? Perhaps you're thinking, "Lindy, you are remembering it wrong. That kindly, white-haired, snowman-shaped Mrs. Doubtfire situation must be Chip's grandmother." Not so, champ! She's his mom. Look it up. She gave birth to him four years ago... As soon as you become a mother, apparently, you are instantly interchangeable with the oldest woman in the world, and / or sixteen ounces of boiling brown water with a hat on it. Take a sec and contrast Mrs. Pott's literally spherical body with the cut-diamond abs of King Triton, father of seven.

THE BOTTOM LINE •  Parallel universes are not a theory, but a prediction of certain theories. •  Eternal inflation predicts that our Universe (the spherical region of space from which light has had time to reach us during the 14 billion years since our Big Bang) is just one of infinitely many universes in a Level I multiverse where everything that can happen does happen somewhere. •  For a theory to be scientific, we need not be able to observe and test all its predictions, merely at least one of them. Inflation is the leading theory for our cosmic origins because it’s passed observational tests, and parallel universes seem to be a non-optional part of the package. •  Inflation converts potentiality into reality: if the mathematical equations governing

I thought about soccer in history, the inspiration for wars, truces, rampaging mobs. The game was a global passion, spherical ball, grass or turf, entire nations in spasms of elation or lament. But what kind of sport is it that disallows the use of players' hands, except for the goalkeeper? Hands are essential human tools, the things that grasp and hold, that make, take, carry, create. If soccer were an American invention, wouldn't some European intellectual maintain that our historically puritanical nature has compelled us to invent a game structured on anti-masturbatory principles?

The room contains a few dozen living human bodies, each one a big sack of guts and fluids so highly compressed that it will squirt for a few yards when pierced. Each one is built around an armature of 206 bones connected to each other by notoriously fault-prone joints that are given to obnoxious creaking, grinding, and popping noises when they are in other than pristine condition. This structure is draped with throbbing steak, inflated with clenching air sacks, and pierced by a Gordian sewer filled with burbling acid and compressed gas and asquirt with vile enzymes and solvents produced by the many dark, gamy nuggets of genetically programmed meat strung along its length. Slugs of dissolving food are forced down this sloppy labyrinth by serialized convulsions, decaying into gas, liquid, and solid matter which must all be regularly vented to the outside world lest the owner go toxic and drop dead. Spherical, gel-packed cameras swivel in mucus-greased ball joints. Infinite phalanxes of cilia beat back invading particles, encapsulate them in goo for later disposal. In each body a centrally located muscle flails away at an eternal, circulating torrent of pressurized gravy. And yet, despite all of this, not one of these bodies makes a single sound at any time during the sultan’s speech.

Spheres are indeed fertile theoretical tools that help us gain insight into all manner of astrophysical problems. But one should not be a sphere-zealot. I am reminded of the half-serious joke about how to increase milk production on a farm: An expert in animal husbandry might say, "Consider the role of the cow's diet..." An engineer might say, "Consider the design of the milking machines..." But it's the astrophysicist who says, "Consider a spherical cow...

Asimov’s “The Relativity of Wrong”:3 When people thought the earth was flat, they were wrong. When people thought the earth was spherical, they were wrong. But if you think that thinking the earth is spherical is just as wrong as thinking the earth is flat, then your view is wronger than both of them put together.

Back in the 1930s, when men with handlebar moustaches played football in long johns and tails, and the ball was a spherical clod of bitumen, did fans weep in the stands when their team lost? No. They limited their responses to a muttered 'blast' or a muted 'hurrah' before going home to smoke a pipe and lean on the mantelpiece.

For instance, supposing that the planet earth were not a sphere but a gigantic coffee table, how much difference in everyday life would that make? Granted, this is a pretty farfetched example; you can't rearrange facts of life so freely. Still, picturing the planet earth, for convenience sake, as a gigantic coffee table does in fact help clear away the clutter—those practically pointless contingencies such as gravity and the international dateline and the equator, those nagging details that arise from the spherical view. I mean, for a guy leading a perfectly ordinary existence, how many times in the course of a lifetime would the equator be a significant factor?

And in this city a man will go mad with paresis, another with terror, a third will drown himself and the newspapers will report death from cancer and cerebral hemorrhage among our leading citizens, and there will casual mention of various epidemics, of lust murders, of famine and starvation, and the decline of Utilities on the New York Exchange. But all that’s forgotten tonight, God’s asleep. And if you have any questions to ask about the chaotic conditions on this little spherical toy of his, you’ll have to refer them to his secretary, who will send you form letter No. X99 explaining that accidents will happen and that of course God’s ways are necessarily rather obscure to man.

I'm so well-rounded I'm almost spherical.

He probably wouldn’t give her an opening (Robin was a perfectly spherical branch manager of uniform density: he had no handles or rough edges for blackmail),

if one neglected pressure, a uniform spherically systematic symmetric star would contract to a single point of infinite density. Such a point is called a singularity.

To suppose that the eye with all its inimitable contrivances for adjusting the focus to different distances, for admitting different amounts of light, and for the correction of spherical and chromatic aberration, could have been formed by natural selection, seems, I freely confess, absurd in the highest degree,” he writes. But if we look at the whole tree of life, Darwin says, we can find innumerable gradations from extremely simple eyes consisting of hardly more than a nerveless cluster of pigment cells, which are rudimentary light sensors, to the marvels of the human eye, which are more impressive pieces of work than the human telescope.

Gaia is a thin spherical shell of matter that surrounds the incandescent interior; it begins where the crustal rocks meet the magma of the Earth’s hot interior, about 100 miles below the surface, and proceeds another 100 miles outwards through the ocean and air to the even hotter thermosphere at the edge of space. It includes the biosphere and is a dynamic physiological system that has kept our planet fit for life for over three billion years. I call Gaia a physiological system because it appears to have the unconscious goal of regulating the climate and the chemistry at a comfortable state for life. Its goals are not set points but adjustable for whatever is the current environment and adaptable to whatever forms of life it carries.

What may be called linear thinking goes straight out from one pole or from one idea of the cosmos of ideas, which every true philosophy is. This idea, cut off from its interrelations and interdependencies with the cosmos,[linear thinking] then fanatically thinks to a finish. Then it becomes radical individualism or socialism or totalitarianism or anarchism. This linear thinking, so characteristic of the modern mind and irs countless -isms, is a stranger to Catholic political philosophy. For Catholic political philosophy is spheric thinking.

Using freshman level calculus you can show that the one and only shape that has the smallest surface area for an enclosed volume is a perfect sphere. In fact, billions of dollars could be saved annually on packaging materials if all shipping boxes and all packages of food in the supermarket were spheres. For example, the contents of a super-jumbo box of Cheerios would fit easily into a spherical carton with a four-and-half inch radius. But practical matters prevail - nobody wants to chase packaged food down the aisle after it rolls off the shelves.

Faerie was divided into seasons that mirrored the mortal realm, except all four seasons coexisted here. This world wasn’t spherical like Earth. Faerie was more of a geographic map, and it was possible to fall off the edges. Though it was more likely you would be eaten before that happened.

The earth’s shadow on the moon was always round, which would be true only if the earth was spherical. If the earth had been a flat disk, the shadow would have been elongated and elliptical, unless the eclipse always occurred at a time when the sun was directly under the center of the disk.

The soul which fathoms every league of the celestial arc--knows, as a mariner the sea, the distant latitudes where comets flame, and worlds career, and constellations shake their awful clusters--wanders amid the spectral nebula, and makes suns and systems to be but glittering beads upon the aspiring thread of its induction, cannot perish. There is a future life. In a universe so spherical and whole as this, reason argues that its own incompleteness and capacity for more are suggestive--are prophetical. Under-shadows and cross-lights of mystery, these filmy depths of present being, shudder in sympathy with something beyond.

On a night like tonight, without goggles, it’s hard to know where the ocean ends and the sky begins. With no horizon reference, flight decks resemble little more than lighted postage stamps, floating in the middle of space. Everything seems to float—the stars, radio antennas, buoys, ships—in one vast, black, spherical void.

In fact, it is not a question of going back to the past, but of connecting with it-and also, by that very fact, in a spherical conception of history, to connect to the eternal and cause it to surge back, to have consonance in life, and to disentangle itself from the tyranny of the logos, the terrible tyranny of the Law, so as to reestablish the school of the mythos and life.

Comparing the bioavailability of all other oral vitamin C delivery with your oral liposomal delivery is like comparing a squirt gun to a fire hose. Not only am I convinced that the efficacy of Lypo-Spheric(tm) Vitamin C far surpasses any traditional oral vitamin C supplement, but my recent personal experience with it suggests that it may sometimes be better than IV injection.

Three weapons firing. Long guns. All the same. Distinctive. Flat solid barks, and the crack of fast bullets in the air. NATO rounds out of M16s, if Reacher was a gambling man. All of them so far missing. Understandable. It was a deceptive shot. Two hundred yards, absolutely flat, eye to eye. Except it was absolutely curved, because it was part of a spherical planet. Hence the miscalculation.

Dark gray, flexible, and infinitely tough. Seven-foot membranous wings of same color, found folded, spread out of furrows between ridges. Wing framework tubular or glandular, of lighter gray, with orifices at wing tips. Spread wings have serrated edge. Around equator, one at central apex of each of the five vertical, stave-like ridges are five systems of light gray flexible arms or tentacles found tightly folded to torso but expansible to maximum length of over three feet. Like arms of primitive crinoid. Single stalks three inches diameter branch after six inches into five substalks, each of which branches after eight inches into small, tapering tentacles or tendrils, giving each stalk a total of twenty-five tentacles. At top of torso blunt, bulbous neck of lighter gray, with gill-like suggestions, holds yellowish five-pointed starfish-shaped apparent head covered with three-inch wiry cilia of various prismatic colors. Head thick and puffy, about two feet point to point, with three-inch flexible yellowish tubes projecting from each point. Slit in exact center of top probably breathing aperture. At end of each tube is spherical expansion where yellowish membrane rolls back on handling to reveal glassy, red-irised globe, evidently an eye. Five slightly longer reddish tubes start from inner angles of starfish-shaped head and end in saclike swellings of same color which, upon pressure, open to bell-shaped orifices two inches maximum diameter and lined with sharp, white tooth like projections - probably mouths. All these tubes, cilia, and points of starfish head, found folded tightly down; tubes and points clinging to bulbous neck and torso. Flexibility surprising despite vast toughness. At bottom of torso, rough but dissimilarly functioning counterparts of head arrangements exist. Bulbous light-gray pseudo-neck, without gill suggestions, holds greenish five-pointed starfish arrangement. Tough, muscular arms four feet long and tapering from seven inches diameter at base to about two and five-tenths at point. To each point is attached small end of a greenish five-veined membranous triangle eight inches long and six wide at farther end. This is the paddle, fin, or pseudofoot which has made prints in rocks from a thousand million to fifty or sixty million years old. From inner angles of starfish-arrangement project two-foot reddish tubes tapering from three inches diameter at base to one at tip. Orifices at tips. All these parts infinitely tough and leathery, but extremely flexible. Four-foot arms with paddles undoubtedly used for locomotion of some sort, marine or otherwise. When moved, display suggestions of exaggerated muscularity. As found, all these projections tightly folded over pseudoneck and end of torso, corresponding to projections at other end.

I am a thin layer of all those beings on [samadhi level] 3, mingling, connected with one another in a spherical surface around the whole known universe. Our "backs" are to the void. We are creating energy, matter and life at the interface between the void and all known creation. We are facing into the known universe, creating it, filling it. I am one with them; spread in a thin layer around the sphere with a small, slightly greater concentration of me in one small zone. I feel the power of the galaxy pouring through me. I am following the programme, the conversion programme of void to space, to energy, to matter, to life, to consciousness, to us, the creators. From nothing on one side to the created everything on the other. I am the creation process itself, incredibly strong, incredibly powerful. This time there is no flunking out, no withdrawal, no running away, no unconsciousness, no denial, no negation, no fighting against anything. I am "one of the boys in the engine room pumping creation from the void into the known universe; from the unknown to the known I am pumping". I am coming down from level +3. There are a billion choices of where to descend back down. I am conscious down each one of the choices simultaneously. Finally I am in my own galaxy with millions of choices left, hundreds of thousands on my own solar system, tens of thousands on my own planet, hundreds in my own country and then suddenly I am down to two, one of which is this body. In this body I look back up, see the choice-tree above me that I came down. Did I, this Essence, come all the way down to this solar system, this planet, this place, this body, or does it make any difference? May not this body be a vehicle for any Essence that came into it? Are not all Essences universal, equal, anonymous, and equally able? Instructions for this vehicle are in it for each Essence to read and absorb on entry. The new pilot-navigator reads his instructions in storage and takes over, competently operating this vehicle.

And now I am fit for rivalship with your clocks, papa having given me an Aeolian harp for the purpose. Do you know the music of an Aeolian harp, and that nothing below the spherical harmonies is so sweet and soft and mournfully wild? The amusing part of it is (after the poetical) that Flushie is jealous and thinks it is alive, and takes it as very hard that I should say ‘beautiful’ to anything except his ears!

But how explain all of myself, all of my sickness, recorded in these pages? And I subsided and walked obediently. ... A leaf torn off a tree by a sudden blast of wind obediently falls downward, but on the way it whirls, catches at every familiar branch, fork, knot And I, too, was catching at every silent spherical head, at the transparent ice of the walls, at the blue spire of the Accumulator Tower piercing a cloud.

ORGANIC LIFE beneath the shoreless waves Was born and nurs'd in Ocean's pearly caves; First, forms minute, unseen by spheric glass, Move on the mud, or pierce the watery mass; These, as successive generations bloom, New powers acquire, and larger limbs assume; Whence countless groups of vegetation spring, And breathing realms of fin, and feet, and wing. Thus the tall Oak, the giant of the wood, Which bears Britannia's thunders on the flood; The Whale, unmeasured monster of the main, The lordly Lion, monarch of the plain, The Eagle soaring in the realms of air, Whose eye undazzled drinks the solar glare, Imperious man, who rules the bestial crowd, Of language, reason, and reflection proud, With brow erect, who scorns this earthy sod, And styles himself the image of his God; Arose from rudiments of form and sense, An embryon point, or microscopic ens!

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.

Finally when he climbed below deck after dark, wondering where his dinner was, perhaps with a storm come up and rough seas and blinding rains, I'd sulk and lure him into the warm and steamy darkness and from the hairs of his warm body I'd breed a myriad smiling, sparkle-eyed one-year-olds, my broods, my flocks. In the churning seas, below the waves, together inside our hammock woven in coarse sailcloth by Unguentine's deft hands, a spherical webbed sack which hung and swivelled between the two walls of our bedroom, we would spin round and round with lapping tongues and the soft suction of lips, whirling, our amorous centrifuge, all night long, zipped inside against the elements. Now, years and years later, those nights, the thought and touch of them is enough to make me throw myself down on the ground and roll in the dust like a hen nibbled by mites, generating clouds, stars and all the rest.

As, when the sun shines above the earth, the shadow is spread over its lower part, because its spherical shape makes it impossible for it to be clasped all round at one and the same time by the rays, and necessarily, on whatever side the sun’s rays may fall on some particular point of the globe, if we follow a straight diameter, we shall find shadow upon the opposite point, and so, continuously, at the opposite end of the direct line of the rays shadow moves round that globe,

But how was I going to explain my whole being, this whole disease that I've been jotting down in these pages? So I shut up and went along peacefully. A leaf torn off a tree by a sudden gust of wind falls peacefully downward, but on the way it twists, catches at every twig, offshoot, branch that it knows. That is just how I caught at each silent spherical head, at the transparent ice of the walls, at the light blue needle of the Accumulator Tower as it thrust up into the clouds.

Time: 0529:45. The firing circuit closed; the X-unit discharged; the detonators at thirty-two detonation points simultaneously fired; they ignited the outer lens shells of Composition B; the detonation waves separately bulged, encountered inclusions of Baratol, slowed, curved, turned inside out, merged to a common inward-driving sphere; the spherical detonation wave crossed into the second shell of solid fast Composition B and accelerated; hit the wall of dense uranium tamper and became a shock wave and squeezed, liquefying, moving through; hit the nickel plating of the plutonium core and squeezed, the small sphere shrinking, collapsing into itself, becoming an eyeball; the shock wave reaching the tiny initiator at the center and swirling through its designed irregularities to mix its beryllium and polonium; polonium alphas kicking neutrons free from scant atoms of beryllium: one, two, seven, nine, hardly more neutrons drilling into the surrounding plutonium to start the chain reaction.

She looked past the building to the sky. It was a deep, blue velvet night, and the moon hung heavy and supernaturally spherical in the sky. “I wonder who built this engine,” Sadie said. “It’s good work,” Sam said. “The God rays are nicely done, but the moon is almost too beautiful. The scale seems off.” “How is it so large and low? And it needs more texture. A bit of Perlin noise. It should look a little rougher, otherwise it doesn’t seem real.” “But maybe that’s the look they were going for?” “Maybe so.

Ivy passed by the same location a few moments later, slowed for a moment, and glanced down the length of the tube. It was possible to see straight down its length, across the spherical Pod, and through its windows to the Earth. Normally this meant the blue light of the oceans and the white light of clouds and ice caps. Sometimes, a lot of green when they were passing over well-watered parts of the world, or some yellow when over the Sahara. Right now the light was orange because the Earth was on fire. People

I am Ding Yi.” He opened up two folding chairs and motioned for us to sit down, then returned to his chair. He said, “Before you tell me why you’ve come, let me discuss with you a dream I’ve just had.… No, you’ve got to listen. It was a wonderful dream, which you interrupted. In the dream I was sitting here, a knife in my hand, around so long, like for cutting watermelon. Next to me was this tea table. But there wasn’t an ashtray or anything on it. Just two round objects, yea big. Circular, spherical. What do you think they were?” “Watermelon?” “No, no. One was a proton, the other a neutron. A watermelon-sized proton and neutron. I cut the proton open first. Its charge flowed out onto the table, all sticky, with a fresh fragrance. After I cut the proton in half, the quarks inside tumbled out, tinkling. They were about the size of walnuts, in all sorts of colors. They rolled about on the table, and some of them fell onto the floor. I picked up a white one. It was very hard, but with effort, I was able to bite into it. It tasted like a manaizi grape.… And right then, you woke me up.

Strophalos comes from the root to twist and as such, is an appropriate term for all the variations of twisting ritual tools employed and discussed in this section. The Byzantine historian and philosopher Michael Psellus provide a description of the strophalos dating to the eleventh century CE, many centuries after the Chaldean Oracles. Psellus provides information on different designs of the iynges, describing spherical and triangular objects, covered in symbols which were spun. “The strophalos of Hekate is a golden sphere with lapis lazuli enclosed in its centre, which is spun by means of a leather thong, and which is covered with symbols: as it was spun they [the Theurgists] made their invocations. These spheres were generally called iynges and could be either spherical or triangular or of some other form. And while they were making their invocations they emitted inarticulate or animal cries, laughing and whipping the air. So the Oracle teaches that it is the motion of the strophalos which works the ritual, on account of its ineffable power. It is called ‘of Hekate’ and consecrated to Hekate.

Whenever I try to forget you, Erick, something brings you back into my memory. And whenever I want to drive emotions away from me, they quickly return as thoughts or dreams . . . or the words of an old woman. Perhaps loneliness has forced me to hang on to the faint spectrum of your memory—kept my heart longing in painstaking eagerness. But no . . . no more, and not again. How long can my heart withstand the seesaw of emotions? If I had one wish, I would want you and me to be two parallel lines, either on flat or spherical earth . . . never to meet.

Broadening or burrowing to the moon's phases, turbid with pulverized wastemantle, on through flatter, duller, hotter, cotton-gin country it scours, approaching the tidal mark where it puts off majesty, disintegrates, and through swamps of a delta, punting-pole, fowling-piece, oyster-tongs country, wearies to its final act of surrender, effacement, atonement in a huge amorphous aggregate no cuddled attractive child ever dreams of, non-country, image of death as a spherical dew-drop of life. Unlovely monsters, our tales believe, can be translated too, even as water, the selfless mother of all especials.

I believe there’s a strong possibility that God exists. But I also believe there’s an equally strong possibility that God is a concept humans created because we didn’t understand things like gravity and lightning and DNA, and that we perpetuate because the thought of being one tiny speck out of billions of tiny specks on a large spherical mass orbiting a huge ball of fire, which is just one of immeasurable balls of fire out there in a pitch-black sky, is scary as fuck. And quite frankly, I don’t understand how anyone who has given the topic considerable, rational thought can be 100 percent certain either way. But that’s not important right now. What

4.5 billion years ago, an object the size of Mars crashed into Earth, blowing out enough material to form a companion sphere, the Moon. Within weeks, it is thought, the flung material had reassembled itself into a single clump, and within a year it had formed into the spherical rock that companions us yet. Most of the lunar material, it is thought, came from the Earth’s crust, not its core, which is why the Moon has so little iron while we have a lot. The theory, incidentally, is almost always presented as a recent one, but in fact it was first proposed in the 1940s by Reginald Daly of Harvard. The only recent thing about it is people paying any attention to

The “solar wheel is activated” means that everything that is peripheral is submitted to being directed by the center. This is why in this case movement is just another word for master. It is to tour oneself, to delimit oneself so that, under the direction of the center, entry is gained into all aspects of the personality. This amounts to designating self-knowledge as self-incubation. And in the end the sequence of images takes us to this archetype of the complete man that Plato drew as a perfectly spherical being—that is, total and complete, reuniting in himself both masculine and feminine (the essential elemental body awaiting resurrection in the land of Hurqalya).

In addition to the ax, knife, quiver, and arrows, Ötzi had shoes, clothing, two birchbark canisters, a sheath, a bowstave, miscellaneous small tools, some berries, a piece of ibex meat, and two spherical lumps of birch fungus, each about the size of a large walnut and carefully threaded with sinew. One of the canisters had contained glowing embers wrapped in maple leaves, for starting fires. Such an assemblage of personal effects was unique. Some of the items were, as it were, really unique in that they had never been imagined, much less seen. The birch fungus was a particular mystery because it was obviously treasured, and yet birch fungus is not known to be good for anything.

About 4.6 billion years ago, a great swirl of gas and dust some 15 billion miles across accumulated in space where we are now and began to aggregate. Virtually all of it—99.9 percent of the mass of the solar system—went to make the Sun. Out of the floating material that was left over, two microscopic grains floated close enough together to be joined by electrostatic forces. This was the moment of conception for our planet. All over the inchoate solar system, the same was happening. Colliding dust grains formed larger and larger clumps. Eventually the clumps grew large enough to be called planetesimals. As these endlessly bumped and collided, they fractured or split or recombined in endless random permutations, but in every encounter there was a winner, and some of the winners grew big enough to dominate the orbit around which they traveled. It all happened remarkably quickly. To grow from a tiny cluster of grains to a baby planet some hundreds of miles across is thought to have taken only a few tens of thousands of years. In just 200 million years, possibly less, the Earth was essentially formed, though still molten and subject to constant bombardment from all the debris that remained floating about. At this point, about 4.5 billion years ago, an object the size of Mars crashed into Earth, blowing out enough material to form a companion sphere, the Moon. Within weeks, it is thought, the flung material had reassembled itself into a single clump, and within a year it had formed into the spherical rock that companions us yet. Most of the lunar material, it is thought, came from the Earth’s crust, not its core, which is why the Moon has so little iron while we have a lot. The theory, incidentally, is almost always presented as a recent one, but in fact it was first proposed in the 1940s by Reginald Daly of Harvard. The only recent thing about it is people paying any attention to it. When Earth was only about a third of its eventual size, it was probably already beginning to form an atmosphere, mostly of carbon dioxide, nitrogen, methane, and sulfur. Hardly the sort of stuff that we would associate with life, and yet from this noxious stew life formed. Carbon dioxide is a powerful greenhouse gas. This was a good thing because the Sun was significantly dimmer back then. Had we not had the benefit of a greenhouse effect, the Earth might well have frozen over permanently, and life might never have gotten a toehold. But somehow life did. For the next 500 million years the young Earth continued to be pelted relentlessly by comets, meteorites, and other galactic debris, which brought water to fill the oceans and the components necessary for the successful formation of life. It was a singularly hostile environment and yet somehow life got going. Some tiny bag of chemicals twitched and became animate. We were on our way. Four billion years later people began to wonder how it had all happened. And it is there that our story next takes us.

Most people-all, in fact, who regard the whole heaven as finite-say it lies at the centre. But the Italian philosophers known as Pythagoreans take the contrary view. At the centre, they say, is fire, and the earth is one of the stars, creating night and day by its circular motion about the centre. They further construct another earth in opposition to ours to which they give the name counterearth. In all this they are not seeking for theories and causes to account for observed facts, but rather forcing their observations and trying to accommodate them to certain theories and opinions of their own. But there are many others who would agree that it is wrong to give the earth the central position, looking for confirmation rather to theory than to the facts of observation. Their view is that the most precious place befits the most precious thing: but fire, they say, is more precious than earth, and the limit than the intermediate, and the circumference and the centre are limits. Reasoning on this basis they take the view that it is not earth that lies at the centre of the sphere, but rather fire. The Pythagoreans have a further reason. They hold that the most important part of the world, which is the centre, should be most strictly guarded, and name it, or rather the fire which occupies that place, the 'Guardhouse of Zeus', as if the word 'centre' were quite unequivocal, and the centre of the mathematical figure were always the same with that of the thing or the natural centre. But it is better to conceive of the case of the whole heaven as analogous to that of animals, in which the centre of the animal and that of the body are different. For this reason they have no need to be so disturbed about the world, or to call in a guard for its centre: rather let them look for the centre in the other sense and tell us what it is like and where nature has set it. That centre will be something primary and precious; but to the mere position we should give the last place rather than the first. For the middle is what is defined, and what defines it is the limit, and that which contains or limits is more precious than that which is limited, see ing that the latter is the matter and the former the essence of the system. (2-13-1) There are similar disputes about the shape of the earth. Some think it is spherical, others that it is flat and drum-shaped. For evidence they bring the fact that, as the sun rises and sets, the part concealed by the earth shows a straight and not a curved edge, whereas if the earth were spherical the line of section would have to be circular. In this they leave out of account the great distance of the sun from the earth and the great size of the circumference, which, seen from a distance on these apparently small circles appears straight. Such an appearance ought not to make them doubt the circular shape of the earth. But they have another argument. They say that because it is at rest, the earth must necessarily have this shape. For there are many different ways in which the movement or rest of the earth has been conceived. (2-13-3)

About 4.6 billion years ago, a great swirl of gas and dust some 24 billion kilometres across accumulated in space where we are now and began to aggregate. Virtually all of it – 99.9 per cent of the mass of the solar system21 – went to make the Sun. Out of the floating material that was left over, two microscopic grains floated close enough together to be joined by electrostatic forces. This was the moment of conception for our planet. All over the inchoate solar system, the same was happening. Colliding dust grains formed larger and larger clumps. Eventually the clumps grew large enough to be called planetesimals. As these endlessly bumped and collided, they fractured or split or recombined in endless random permutations, but in every encounter there was a winner, and some of the winners grew big enough to dominate the orbit around which they travelled. It all happened remarkably quickly. To grow from a tiny cluster of grains to a baby planet some hundreds of kilometres across is thought to have taken only a few tens of thousands of years. In just 200 million years, possibly less22, the Earth was essentially formed, though still molten and subject to constant bombardment from all the debris that remained floating about. At this point, about 4.4 billion years ago, an object the size of Mars crashed into the Earth, blowing out enough material to form a companion sphere, the Moon. Within weeks, it is thought, the flung material had reassembled itself into a single clump, and within a year it had formed into the spherical rock that companions us yet.

When I was a young person reading whatever I could get my hands on, I came across some old books of my fathers, in a series called Everyman's Library. The endpapers of that date were a sort of William Morris design, with leaves and flowers and a lady in graceful medieval draperies carrying a scroll and a branch with three apples or other spherical fruit on it. Interwoven among the shrubbery there was a motto: 'Everyman I will go with thee and be thy guide, In thy most need to go by thy side.' This was very reassuring to me. The books were declaring that they were my pals; they promised to accompany me on my travels; and they would not only offer me some helpful hints, they'd be right there by my side whenever I really needed them. It's always nice to have someone you can depend on.

The stars of the Milky Way galaxy trace a big, flat circle. With a diameter-to-thickness ratio of one thousand to one, our galaxy is flatter than the flattest flapjacks ever made. In fact, its proportions are better represented by a crépe or a tortilla. No, the Milky Way’s disk is not a sphere, but it probably began as one. We can understand the flatness by assuming the galaxy was once a big, spherical, slowly rotating ball of collapsing gas. During the collapse, the ball spun faster and faster, just as spinning figure skaters do when they draw their arms inward to increase their rotation rate. The galaxy naturally flattened pole-to-pole while the increasing centrifugal forces in the middle prevented collapse at midplane. Yes, if the Pillsbury Doughboy were a figure skater, then fast spins would be a high-risk activity. Any stars that happened to be formed within the Milky Way cloud before the collapse maintained large, plunging orbits. The remaining gas, which easily sticks to itself, like a mid-air collision of two hot marshmallows, got pinned at the mid-plane and is responsible for all subsequent generations of stars, including the Sun. The current Milky Way, which is neither collapsing nor expanding, is a gravitationally mature system where one can think of the orbiting stars above and below the disk as the skeletal remains of the original spherical gas cloud. This general flattening of objects that rotate is why Earth’s pole-to-pole diameter is smaller than its diameter at the equator. Not by much: three-tenths of one percent—about twenty-six miles. But Earth is small, mostly solid, and doesn’t rotate all that fast. At twenty-four hours per day, Earth carries anything on its equator at a mere 1,000 miles per hour. Consider the jumbo, fast-rotating, gaseous planet Saturn. Completing a day in just ten and a half hours, its equator revolves at 22,000 miles per hour and its pole-to-pole dimension is a full ten percent flatter than its middle, a difference noticeable even through a small amateur telescope. Flattened spheres are more generally called oblate spheroids, while spheres that are elongated pole-to-pole are called prolate. In everyday life, hamburgers and hot dogs make excellent (although somewhat extreme) examples of each shape. I don’t know about you, but the planet Saturn pops into my mind with every bite of a hamburger I take.

Not all social animals are social with the same degree of commitment. In some species, the members are so tied to each other and interdependent as to seem the loosely conjoined cells of a tissue. The social insects are like this; they move, and live all their lives, in a mass; a beehive is a spherical animal. In other species, less compulsively social, the members make their homes together, pool resources, travel in packs or schools, and share the food, but any single one can survive solitary, detached from the rest. Others are social only in the sense of being more or less congenial, meeting from time to time in committees, using social gatherings as ad hoc occasions for feeding and breeding. Some animals simply nod at each other in passing, never reaching even a first-name relationship.

Finally, there was the formidable difficulty of navigation. Making extraordinarily complex spherical trigonometry calculations based on figures taken from a crowd of instruments, navigators groped over thousands of miles of featureless ocean toward targets or destination islands that were blacked out at night, often only yards wide, and flat to the horizon. Even with all the instruments, the procedures could be comically primitive. “Each time I made a sextant calibration,” wrote navigator John Weller, “I would open the escape hatch on the flight deck and stand on my navigation desk and the radio operator’s desk while [the radioman] held on to my legs so I would not be sucked out of the plane.” At night, navigators sometimes resorted to following the stars, guiding their crews over the Pacific by means not so different from those used by ancient Polynesian mariners. In a storm or clouds, even that was impossible.

For Aristotle, physics works as follows: first, it is necessary to distinguish between the heavens and Earth. In the heavens, everything is made up of a crystalline substance that moves in a circular motion and turns eternally around Earth in great concentric circles, with the spherical Earth at the center of everything. On Earth, on the other hand, it is necessary to distinguish between forced motion and natural motion. Forced motion is caused by a thrust and ends when the thrust ends. Natural motion is vertical—upward or downward—and depends both on the substance and the location. Each substance has a “natural place,” that is to say, a proper altitude to which it always returns; earth at the bottom, water a little way above it, air a little higher still, and fire even higher. When you pick up a stone and let it fall, the stone moves downward because it wants to return to its natural level. Air bubbles in water, fire in the air, or children’s flying balloons move upward instead, again seeking their natural place.

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.

Darwin singled out the eye as posing a particularly challenging problem: 'To suppose that the eye with all its inimitable contrivances for adjusting the focus to different distances, for admitting different amounts of light, and for the correction of spherical and chromatic aberration, could have been formed by natural selection, seems, I freely confess, absurd in the highest degree.' Creationists gleefully quote this sentence again and again. Needless to say, they never quote what follows. Darwin's fulsomely free confession turned out to be a rhetorical device. He was drawing his opponents towards him so that his punch, when it came, struck the harder. The punch, of course, was Darwin's effortless explanation of exactly how the eye evolved by gradual degrees. Darwin may not have used the phrase 'irreducible complexity', or 'the smooth gradient up Mount Improbable', but he clearly understood the principle of both. 'What is the use of half an eye?' and 'What is the use of half a wing?' are both instances of the argument from 'irreducible complexity'. A functioning unit is said to be irreducibly complex if the removal of one of its parts causes the whole to cease functioning. This has been assumed to be self-evident for both eyes and wings. But as soon as we give these assumptions a moment's thought, we immediately see the fallacy. A cataract patient with the lens of her eye surgically removed can't see clear images without glasses, but can see enough not to bump into a tree or fall over a cliff. Half a wing is indeed not as good as a whole wing, but it is certainly better than no wing at all. Half a wing could save your life by easing your fall from a tree of a certain height. And 51 per cent of a wing could save you if you fall from a slightly taller tree. Whatever fraction of a wing you have, there is a fall from which it will save your life where a slightly smaller winglet would not. The thought experiment of trees of different height, from which one might fall, is just one way to see, in theory, that there must be a smooth gradient of advantage all the way from 1 per cent of a wing to 100 per cent. The forests are replete with gliding or parachuting animals illustrating, in practice, every step of the way up that particular slope of Mount Improbable. By analogy with the trees of different height, it is easy to imagine situations in which half an eye would save the life of an animal where 49 per cent of an eye would not. Smooth gradients are provided by variations in lighting conditions, variations in the distance at which you catch sight of your prey—or your predators. And, as with wings and flight surfaces, plausible intermediates are not only easy to imagine: they are abundant all around the animal kingdom. A flatworm has an eye that, by any sensible measure, is less than half a human eye. Nautilus (and perhaps its extinct ammonite cousins who dominated Paleozoic and Mesozoic seas) has an eye that is intermediate in quality between flatworm and human. Unlike the flatworm eye, which can detect light and shade but see no image, the Nautilus 'pinhole camera' eye makes a real image; but it is a blurred and dim image compared to ours. It would be spurious precision to put numbers on the improvement, but nobody could sanely deny that these invertebrate eyes, and many others, are all better than no eye at all, and all lie on a continuous and shallow slope up Mount Improbable, with our eyes near a peak—not the highest peak but a high one.

And what of all these spices? They're worth a pretty fortune." She waves a juddering arm across the table, at the tins and glass jars and earthenware pots. All at once a shaft of thin northern light swoops over them, jolting them into luminous life: bubbled glass jars of briny green peppercorns, salted capers, gleaming vanilla pods, rusted cinnamon sticks, all leaping and glinting. The sudden startling beauty of it, the palette of hues--ocher, terra-cotta, shades of earth and sand and grass---the pale trembling light. All thoughts of running a boardinghouse vanish. I reach for a jar, lift its cork lid. The scent of bark, earth, roots, sky. And for a second I am somewhere else. "The mysterious scent of a secret kingdom," I murmur. The jar contains little pellets, brown, spherical, unexotic. How marvelous that something so plain can have such an enthralling perfume, I think. "Oh, Miss Eliza. Always the poetess! It's only allspice." Cook gives a wan smile and gestures at the ceiling, where long bunches of herbs hang from a rack. Rosemary, tansy, sage, nettles, woodruff. "And what of these? All summer I was collecting these and they still ain't properly dry." "May I lower it?" Not waiting for an answer I wind down the rack until the drying herbs are directly in front of me---a farmyard sweetness, a woody sappy scent, the smell of bruised apples and ripe earth and crushed ferns.

Despite Imbry's demurrals, Ghyll never missed an opportunity to expound on his creed, and was now again launched upon a lecture. "Life, after all," he said, "is but a succession of greater and lesser probabilities—a melange of maybes, as the Grand Prognosticator so aptly put it. Look at you, here in the supposed security of Bolly's Snug, supping and swilling with nary a care. Yet can you deny that a fragment of some asteroid, shattered in a collision far out in thither space back when humankind was still adrip with the primordial slime, having spent millions of years looming toward us, might now, its moment come, lance down through the atmosphere at immense speed and obliterate you where you stand?" "I do not deny the possibility," said Imbry. "I say that the likelihood is remote." "Yet still it exists! And if we couple that existence to a divine appetite for upsetting mortal plans—" "I can think of other, less far-fetched scenarios that might lead to the obliteration of someone in this room," said the thief. He accompanied the remark with an unwinking stare that ought to have caused Ghyll to stop to consider that, though Imbry was so corpulent as to be almost spherical, he was capable of sudden and conclusive acts of violence. And that consideration would have led, in turn, to a change of subject. But the Computant was too deeply set in his philosophy to take note of how others responded to it, and continued to discourse on abstruse concerns.

About 4.6 billion years ago, a great swirl of gas and dust some 24 billion kilometres across accumulated in space where we are now and began to aggregate. Virtually all of it – 99.9 per cent of the mass of the solar system21 – went to make the Sun. Out of the floating material that was left over, two microscopic grains floated close enough together to be joined by electrostatic forces. This was the moment of conception for our planet. All over the inchoate solar system, the same was happening. Colliding dust grains formed larger and larger clumps. Eventually the clumps grew large enough to be called planetesimals. As these endlessly bumped and collided, they fractured or split or recombined in endless random permutations, but in every encounter there was a winner, and some of the winners grew big enough to dominate the orbit around which they travelled. It all happened remarkably quickly. To grow from a tiny cluster of grains to a baby planet some hundreds of kilometres across is thought to have taken only a few tens of thousands of years. In just 200 million years, possibly less22, the Earth was essentially formed, though still molten and subject to constant bombardment from all the debris that remained floating about. At this point, about 4.4 billion years ago, an object the size of Mars crashed into the Earth, blowing out enough material to form a companion sphere, the Moon. Within weeks, it is thought, the flung material had reassembled itself into a single clump, and within a year it had formed into the spherical rock that companions us yet. Most of the lunar material, it is thought, came from the Earth’s crust, not its core23, which is why the Moon has so little iron while we have a lot. The theory, incidentally, is almost always presented as a recent one, but in fact it was first proposed in the 1940s by Reginald Daly of Harvard24. The only recent thing about it is people paying any attention to it. When the Earth was only about a third of its eventual size, it was probably already beginning to form an atmosphere, mostly of carbon dioxide, nitrogen, methane and sulphur. Hardly the sort of stuff that we would associate with life, and yet from this noxious stew life formed. Carbon dioxide is a powerful greenhouse gas. This was a good thing, because the Sun was significantly dimmer back then. Had we not had the benefit of a greenhouse effect, the Earth might well have frozen over permanently25, and life might never have got a toehold. But somehow life did. For the next 500 million years the young Earth continued to be pelted relentlessly by comets, meteorites and other galactic debris, which brought water to fill the oceans and the components necessary for the successful formation of life. It was a singularly hostile environment, and yet somehow life got going. Some tiny bag of chemicals twitched and became animate. We were on our way. Four billion years later, people began to wonder how it had all happened. And it is there that our story next takes us.

A strange structure untangled itself out of the background like a hallucination, not part of the natural landscape. It was a funny-shaped, almost spherical, green podlike thing woven from living branches of trees and vines. A trellis of vines hung down over the opening that served as a door. Wendy was so delighted tears sprang to her eyes. It was her Imaginary House! They all had them. Michael wanted his to be like a ship with views of the sea. John had wanted to live like a nomad on the steppes. And Wendy... Wendy had wanted something that was part of the natural world itself. She tentatively stepped forward, almost swooning at the heavy scent of the door flowers. Languorously lighting on them were a few scissorflies, silver and almost perfectly translucent in the glittery sunlight. Their sharp wings made little snickety noises as they fluttered off. Her shadow made a few half-hearted attempts to drag back, pointing to the jungle. But Wendy ignored her, stepping into the hut. She was immediately knocked over by a mad, barking thing that leapt at her from the darkness of the shelter. "Luna!" Wendy cried in joy. The wolf pup, which she had rescued in one of her earliest stories, stood triumphantly on her chest, drooling very visceral, very stinky dog spit onto her face. "Oh, Luna! You're real!" Wendy hugged the gray-and-white pup as tightly as she could, and it didn't let out a single protest yelp. Although... "You're a bit bigger than I imagined," Wendy said thoughtfully, sitting up. "I thought you were a puppy." Indeed, the wolf was approaching formidable size, although she was obviously not yet quite full-grown and still had large puppy paws. She was at least four stone and her coat was thick and fluffy. Yet she pranced back and forth like a child, not circling with the sly lope Wendy imagined adult wolves used. You're not a stupid little lapdog, are you?" Wendy whispered, nuzzling her face into the wolf's fur. Luna chuffed happily and gave her a big wet sloppy lick across the cheek. "Let's see what's inside the house!" As the cool interior embraced her, she felt a strange shudder of relief and... welcome was the only way she could describe it. She was home. The interior was small and cozy; plaited sweet-smelling rush mats softened the floor. The rounded walls made shelves difficult, so macramé ropes hung from the ceiling, cradling halved logs or flat stones that displayed pretty pebbles, several beautiful eggs, and what looked like a teacup made from a coconut. A lantern assembled from translucent pearly shells sat atop a real cherry writing desk, intricately carved and entirely out of place with the rest of the interior. Wendy picked up one of the pretty pebbles in wonder, turning it this way and that before putting it into her pocket. "This is... me..." she breathed. She had never been there before, but it felt so secure and so right that it couldn't have been anything but her home. Her real home. Here there was no slight tension on her back as she waited for footsteps to intrude, for reality to wake her from her dreams; there was nothing here to remind her of previous days, sad or happy ones. There were no windows looking out at the gray world of London. There was just peace, and the scent of the mats, and the quiet droning of insects and waves outside. "Never Land is a... mishmash of us. Of me," she said slowly. "It's what we imagine and dream of- including the dreams we can't quite remember.

They pop in the mouth, just like salmon roe! But inside... ... is the savory saltiness of seaweed!" "Those pearls are seaweed?!" But how?!" "Delicious! Not only is the pop of the pearl a fun texture, the salty, savory flavor of the seaweed melts seamlessly with the rice! I can barely stop myself! It's an addicting combination!" "Wait... how do you know that technique? Those pearls are seaweed extract gelled into a spherical shape. The only way to do that is by using a calcium-chloride bath and an alginic-acid gelling agent!" "What the heck?!" "That's food science!" "Yukihira pulled a page from Alice Nakiri's own book!" "I've experimented with this stuff before, y'know. When I was a little kid, anyway." "Wha-?! But that's-" "Convenience store Dagashi Candy?!" "Dagashi?! What's that?" Both chemicals are on the ingredients list! "It's what's called an educational candy. Kids play with that to learn how to make their own jelly pearls. I had a blast with it when I was little. I made lots of different stuff." "Dad, look! I made miso pearls!" "Aha ha ha! That's great! Now don't let any of the customers see that." "You can get both alginic acid and calcium chloride at any pharmacy. I used those, along with some seasoned seaweed extract and a little bit of ingenuity... ... to make these savory seaweed bombs- my own spin on the traditional seaweed bento!" "That's right! There were some educational candies in that pile of sweets he got from the kids yesterday!" "The transfer student used a food-science trick?" "And it was one he got off of a package of children's dagashi candy?!" "Hmm? What's this? I see something that looks like okaka minced tuna hiding inside the rice..." Mmmm! It's dried tunatsukudani! This, too, earns full marks for flavor! And its smooth, juicy texture is a wonderful contrast to the pop of the seaweed pearls!

against the velvet rope force fields that kept everyone without an invitation at bay. As I walked toward the entrance, the crowd bombarded me with a mix of insults, autograph requests, death threats, and tearful declarations of undying love. I had my body shield activated, but surprisingly, no one took a shot at me. I flashed the cyborg doorman my invitation, then mounted the long crystal staircase leading up into the club. Entering the Distracted Globe was more than a little disorienting. The inside of the giant sphere was completely hollow, and its curved interior surface served as the club’s bar and lounge area. The moment you passed through the entrance, the laws of gravity changed. No matter where you walked, your avatar’s feet always adhered to the interior of the sphere, so you could walk in a straight line, up to the “top” of the club, then back down the other side, ending up right back where you started. The huge open space in the center of the sphere served as the club’s zero-gravity “dance floor.” You reached it simply by jumping off the ground, like Superman taking flight, and then swimming through the air, into the spherical zero-g “groove zone.” As I stepped through the entrance, I glanced up—or in the direction that was currently “up” to me at the moment—and took a long look around. The place was packed. Hundreds of avatars milled around like ants crawling around the inside of a giant balloon. Others were already out on the dance floor—spinning, flying, twisting, and tumbling in time with the music, which thumped out of floating spherical speakers that drifted throughout the club. In the middle of all the dancers, a large clear bubble was suspended in space, at the absolute center of the club. This was the “booth” where the DJ stood, surrounded by turntables, mixers, decks, and dials. At the center of all that gear was the opening DJ, R2-D2, hard at work, using his various robotic arms to work the turntables. I recognized the tune he was playing: the ’88 remix of New Order’s “Blue Monday,” with a lot of Star Wars droid sound samples mixed in. As I made my way to the nearest bar, the avatars I passed all stopped to stare and point in

For as whipp'd tops and bandied balls, The learned hold, are animals; So horses they affirm to be Mere engines made by geometry

Takoyaki are octopus balls- not, thankfully, in the anatomical sense. They're a spherical cake with a chunk of boiled octopus in the center, cooked on a special griddle with hemispherical indentations. If you're familiar with the Danish pancakes called aebleskivers, you know what a takoyaki looks like; the pan is also similar. Takoyaki are not unknown in the U.S., but I've only ever seen them made fresh at cultural festivals. Iris is a big fan, but I've always been more into the takoyaki aesthetic than the actual food. Takoyaki are always served in a paper or wooden boat and usually topped with mayonnaise, bonito flakes, shredded nori, and takoyaki sauce.

Various cultures can point to games that involved kicking a ball, but, for all the claims of Rome, Greece, Egypt, the Caribbean, Mexico, China or Japan to be the home of football, the modern sport has its roots in the mob game of medieval Britain. Rules – in as much as they existed at all – varied from place to place, but the game essentially involved two teams each trying to force a roughly spherical object to a target at opposite ends of a notional pitch. It was violent, unruly and anarchic, and it was repeatedly outlawed.

The sphere is a symbol of the cosmos and the totality of manifest creation. Very large and very small things in nature tend to be spherical. Einstein discovered that a point in four dimensions (i.e. you here and now) is a sphere expanding at the speed of light, and all we can see of the entire universe is inside an event-horizon sphere. The cube represents the earth.

The natural sciences have the clearest patterns. Physics admits of a lovely unification, not just at the level of fundamental forces, but when considering its extent and implications. Classifications like ‘optics’ or ‘thermodynamics’ are just straitjackets, preventing physicists from seeing countless intersections. Even putting aside aesthetics, the practical applications that have been overlooked are legion; years ago engineers could have been artificially generating spherically symmetric gravity fields. Having

The creature prodded The Horse’s belly with an antenna. When he didn’t respond, it emitted a clicking sound, perhaps of approval. From The Horse, it sidled to the webbing, and moved up the line from the doe to the raccoon, then to Karigan. Eye stalks wavered as it inspected its prey. It poked her ribs with an antenna, and softly whistled to itself. Karigan jerked away and slapped her free hand at the antenna. “Get away!” But already the creature’s attention was on the spherical objects. It nudged one or two with its claw to a more satisfactory position, then trundled away. Karigan

Believing that random probability is the answer to ‘Life, the Universe and Everything’ is like believing that a spherical die, thrown from the top of an infinite incline, will come up ‘boxcars’. If you think that means, you will wait forever, for something to happen and it never will; you would be correct. If you think that it doesn’t make any sense; you would also be correct.

Crime stories were paralleled in popularity by the occasional hoaxes the paper concocted. In August 1835 Day began publishing a series of articles recounting life on the moon—spherical amphibians rolling about—as supposedly revealed by a powerful new telescope.

Something deep inside the caverns of your psyche is beginning to transform. Can you feel the magic beckon? Are you ready to reclaim, repair, and knit together all the pieces of the authentic you that were lost within when you were wounded in your past? They can serve you now, but you have to illuminate them and see them in a new light. The old stories of your life can take on new meaning. When you free yourself from their stamp on your identity, miracles can and do happen. All it takes is willingness to let go and let something new reveal itself to you. A map is appearing for you now, and it’s like a spherical, sparkling hologram, calling you to journey home to who you truly are. Unlike maps in the modern physical world, this map of the soul has plenty of uncharted places. And the map itself is only revealed when you take blind steps inward, led by your first sense. Those steps you take will lead you into the dark, mysterious world of your inner psyche, where you can come to know yourself and Spirit and experience unconditional love and acceptance. There’s no reason to be afraid, because Spirit is always with you. You will know that and feel it when you say the words that bring in the magic: not “abracadabra” but “thank you.” Thank you! This abracadabra is simple and profound. Immersing yourself in a meditation on deep, immense gratitude invokes Spirit to fill your consciousness and remind you that you are blessed to be given the gift of life—the gift of being able to co-create reality. While we always live between the pillars of what is and what might be, we reclaim our power to be the storytellers of our own lives when we connect with Spirit through gratitude.

I try to push past it, to feel around its edges, but it’s a spherical pit that won’t be breached.

The Jacob was hidden in the grey Wall for I respond you.

Life is spherical now.

To suppose that the eye, with all its inimitable contrivances for adjusting the focus to different distances, for admitting different amounts of light, and for the correction of spherical and chromatic aberration, could have been formed by natural selection, seems, I freely confess, absurd in the highest degree. - Charles Darwin, The Origin of Species

average electric field in a spherical control volume | 119 R θ x′ x Figure 5.9 Geometry used to evaluate the surface integral in (5.41). and hence ¿ SR dS |x − x | = żπ 0 (2πRsinθ)(cos θ x/ x )(R dθ) (Rcos θ − |x |)2 + (Rsinθ)2 = 2πR2 x |x | ż 1 −1 χ dχ R2 + |x | 2 − 2R|x |χ , (5.42) where χ = cos θ. The integral on the second line of (5.42) may now be evaluated using the indefinite integral ż χ dχ √a − bχ = 2 b2 a − bχ 3 − a a − bχ, and after a little work we obtain ¿ SR dS |x − x | = ⎧ ⎨ ⎩ 4π 3 x, x < R, (5.43a) 4π 3 R3 |x| 3 x, x > R. (5.43b) Thus our integral of E over VR becomes ż VR E(x)dx = VR 4πε0 ż |x|>R ρe(x) (−x) |x | 3 dx − 1 3ε0 ż VR x ρe(x )dx, (5.44) or equivalently ż VR E(x)dx = VREqout(0) − pqin 3ε0. (5.45) We have arrived back at (5.39), albeit after a great deal of integration. Although this particular derivation of (5.39) is rather long-winded, some ofthe results we have deduced on route, such as (5.43a, b), will prove useful when it comesto our discussion of magnetostatics.

Perhaps there is a very very commonplace person inside me. But perhaps I have aristocratic blood in my veins. I don’t know. But one thing I do know for certain: in later life I shall be a charming, utterly spherical zero.

in a word, their geometry will be the spherical geometry.

The Aryabhatiya covers arithmetic, squares, cubes, square roots, cube roots, triangles, the properties of a circle, algebra, fractions, quadratic equations and sines, and it utilises the decimal system with place value. It contains a very close approximation of the value of pi – 3.1416 – and perfected the ‘rule of three’ still used to compute ratios. It also deals with spherical trigonometry. The ease of making calculations using this system had direct implications for astronomy and allowed Aryabhata to calculate the movements of the planet, eclipses, the size of the earth and, astonishingly, the exact length of the solar year to an accuracy of seven decimal points.

by the time of Emperor Ashoka, in the middle of the third century bce, India had adopted the twelve signs of the originally Babylonian Zodiac, as well as Hellenistic spherical geometry, celestial coordinate systems and the basic trigonometry of chords, all of which had their genesis in ancient Greece.

The room contains a few dozen living human bodies, each one a big sack of guts and fluids so highly compressed that it will squirt for a few yards when pierced. Each one is built around an armature of 206 bones connected to each other by notoriously fault-prone joints that are given to obnoxious creaking, grinding, and popping noises when they are in other than pristine condition. This structure is draped with throbbing steak, inflated with clenching air sacks, and pierced by a Gordian sewer filled with burbling acid and compressed gas and asquirt with vile enzymes and solvents produced by the many dark, gamy nuggets of genetically programmed meat strung along its length. Slugs of dissolving food are forced down this sloppy labyrinth by serialized convulsions, decaying into gas, liquid, and solid matter which must all be regularly vented to the outside world lest the owner go toxic and drop dead. Spherical, gel-packed cameras swivel in mucus-greased ball joints. Infinite phalanxes of cilia beat back invading particles, encapsulate them in goo for later disposal. In each body a centrally located muscle flails away at an eternal, circulating torrent of pressurized gravy.