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OSIRIS ISIS 7 ISIS OSIRIS
THE MAGICALALPHABET
I AM THE OPPOSITE OF THE OPPOSITE I AM THE OPPOSITE OF OPPOSITE IS THAT AM I AM AZAZAZAZAZAZAZAZAZZAZAZAZAZAZAZAZAZA
NUMBER 9 THE SEARCH FOR THE SIGMA CODE Cecil Balmond 1998 Page 5 " To begin the search... "It is like a detective story, gradually unfolding, because that is how it happened; not just for me but for Enjil, the boy mathematician who discovered the secret behind the mysterious world of numbers. In his case though he would have come to it quickly - but I laboured long many a night to find the answer. The thing to do is to follow the path until all the clues are in place and let your mind run free. It is only then that you find what the young master saw: the fixed points in the wind. I had little to go on, just the stories without any detail, more legend than fact about how the numbers worked in secret and, in particular. the magic of one number. My grandfather first told me about those stories and the special drawings and number shapes. Only the remotest people of the mountain village knew about these, he said, but it was all too distant and far away for me to give it any further thought. I was at university and more interested in working out how to put a rocket on the moon; playing with arithmetic was not for me - my mind was occupied with higher things. Then one day I came across a children's book on numbers. One. . . two. . . three. . . . My eye went over the figures. Suddenly I saw something. There were hidden patterns; the old man's story about secret numbers came back to me and I became curious. I started to look into these simple ideas and the more I searched the more fascinated I became. Something was indeed going on underneath the surface of arithmetic and what appeared as a unique calculation to the outsideworld was something quite different when viewed from below. Looked at another way, six and six was not necessarily twelve but something much more exciting - the number 3, of a secret code. I was won over. I began to look at numbers differ ently. I used the special code I had stumbled on to find out more and track what Enjil had done; I spoke to people and read books; I looked for the answer to the riddle that made the Elders blanch and stir uncomfortably on that fateful day of the Examination. And I finally visi- ted the mountain villages where the pupils in the schools stared at the pictures before they did any cal- culations, in order that they may inspire themselves for the rigours of the task ahead. The pictures of course had been added to and decorated heavily but at their centre stood the original spirit of Enjil's drawings, powerful and beautiful. Through Enjil's investigation and my own research I have learnt many things I was never taught at school. When I think of the effort and the monotony I went through learning by rote, suffering numbers as necessary evils, I shudder. No teacher talked of the spirit of numbers, no teacher showed me the shape of a number. No one introduced me to a secret code that made lightning work of numbers and opened up worlds of wonderful possibilities hidden from the day-to-day grind; I found that other peoples too, in ancient times and in other lands, understood numbers as secret and special and alive, and not as mere counters, not just fodder for tiring calculations. / Page 7 / So I set out on the path Enjil took. My own labours overlap his and our two stories have now become one. But that is how a personal search should be - with the spirit of that first discovery reaching out and embracing one until no difference can be found between one's own research and the inspiration that was first taken in. What was the author's becomes yours - which must be the meaning of original, something that embraces and absorbs all those inquisitive enough to enquire of others' inventions. And it is in this spirit I dedicate the journey to you. Follow the clues, build up the jigsaw piece by piece and make your own investigations; become part of the search. Go back in time and let the free spirit in you enter. Talk to it, play, ask the strangest questions. Start to count again in the simplest of ways, one, two, three, four... up to nine. You need to do this, but you will also need nine clues. And to begin with there is the story of Enjil himself, the talisman I conjure up whenever I think of numbers and of the fixed patterns that turn in the wind. JUPITER WHEN STOOD IN LINE WEIGHS IN AT NUMBER 99 �
"I had little to go on, just the stories without any detail, more legend than fact about how the numbers worked in secret and, in particular. the magic of one number."
THE MAGIC OF ONE NUMBER
Arthur C. Clarke 1972 Page 15 "Beyond Mars, there were greater worlds, and mightier problems. Enigmatic Jupiter, with a thousand times the bulk of Earth, teased the minds of men with its mysteries. Perhaps there was life far beneath those turbulent clouds of ammonia and methane, thriving in the hot darkness at pressures unmatched in the deepest terrestrial seas. If so, / Page 16 / it would be as unreachable as another universe; for no ship yet imagined could fight its way down through that immense gravitational field, or withstand the forces that were raging in the Jovian atmosphere. Some robot probes had been launched on that fearful journey; none had survived. One day, perhaps in the early years of the new century, there would be manned expeditions to the moons of Jupiter-to Io, Europa, Ganymede and Callisto, the beloved of the father of the gods, large enough to be called planets in their own right. But there was so much to do nearer home, with the buildup of the lunar colony and the establishment of a bridgehead on Mars, that the outer worlds must wait. Though there would be robot fly-by missions to all the giant planets, and even out into the comet-haunted darkness beyond Pluto, no men would travel on these lonely flights. As for voyaging outside the Solar System, to the still- undiscovered planets of other stars, few scientists believed that it would ever be possible. At the best, interstellar travel was certainly a dream of the very distant future, of no practical concern during the first few centuries of space flight. That was a very sensible, very reasonable prediction, repeated over and over again in the writings of the '70's and '80's. For who could possibly have guessed- Page 24 bothering to use my feet. At the rim I paused and waved to my companion; then I scrambled over the edge and stood upright, staring ahead of me. You must understand that until this very moment I had been almost completely convinced that there could be nothing strange or unusual for me to find here. Almost, but not quite; it was that haunting doubt that had driven me forward. Well it was a doubt no longer, but the haunting had scarcely begun. I was standing on a plateau perhaps a hundred feet across. It had once been smooth-too smooth to be natural-but falling meteors had pitted and scored its surface through immeasurable eons. It had been leveled to support a glittering, roughly pyramidal structure, twice as high as a man, that was set in the rock like a gigantic, many- faceted jewel. Probably no emotion at all filled my mind in those first few seconds. Then I felt a great lifting of my heart, and a strange, inexpressible joy. For I loved the Moon, and now I knew that the creeping moss of Aristarchus and Eratosthenes was not the only life she had brought forth in her youth. The old, discredited dream of the first explorers was true. There had, after all, been a lunar civilization- and I was the first to find it. That I had come perhaps a hundred million years too late did not distress me; it was enough to have come at all. My mind was beginning to function normally, to analyze and to ask questions. Was this a building, a shrine- or something for which my language had no name? If a building, then why was it erected in so uniquely inaccessible a spot? I wondered if it might be a temple, and I could picture the adepts of some strange priesthood calling on their gods to preserve them as the life of the Moon ebbed with the dying oceans-and calling on their gods in vain. I took a dozen steps forward to examine the thing more closely, but some sense of caution kept me from going too near. I knew a little archaeology, and tried to guess the cultural level of the civilization that must have smoothed this mountain and raised the glittering mirror surfaces that still dazzled my eyes. The Egyptians could have done it, I thought, if their workmen had possessed whatever strange materials these far more ancient architects had used. Because of the thing's smallness, it did not occur to me that I might be looking at the handiwork of a race more advanced than / Page 25 / my own. The idea that the moon had possessed intelligence at all was still almost too tremendous to grasp, and my pride would not let me take the final, humiliating plunge. And then I noticed something that set the scalp crawling at the back of my neck-something so trivial and so innocent that many would never have noticed it at all. I have said that the plateau was scarred by metours; it was also coated inches deep with the cosmic dust that is always filtering down upon the surface of any world where there are no winds to disturb it. Yet the dust and the meteor scratches ended quite abruptly in a wide circle enclosing the little pyramid, as though an invisible wall was protecting it from the ravages of time and the slow but ceaseless bombardment from space. There was someone shouting in my earphones, and I realized that Garnett had been calling me for some time. I walked unsteadily to the edge of the cliff and signaled him to join me, not trusting myself to speak. Then I went back toward that circle in the dust. I picked up a fragment of splintered rock and tossed it gently toward the shining enigma. If the pebble had vanished at that invisible barrier I should not have been surprised, but it seemed to hit a smooth, hemispherical surface and slide gently to the ground. I knew then that I was looking at nothing that could be matched in the antiquity of my own race. This was not a building, but a machine, protecting itself with forces that had challenged Eternity. Those forces, whatever they might be, were still operating, and perhaps I had already come too close. I thought of all the radiations man had trapped and tamed in the past century. For all I knew, I might be as irrevocably doomed as if I had stepped into the deadly, silent aura of an unshielded atomic pile. I remember turning then toward Garnett, who had joined me and was now standing motionless at my side. He seemed quite oblivious to me, so I did not disturb him but walked to the edge of the cliff in an effort to marshal my thoughts. There "below me lay the Mare Crisium-Sea.of Crises, indeed-strange and weird to most men, but reassuringly familiar to me. I lifted my eyes toward the crescent Earth, lying in her cradle of. stars, and I wondered what her clouds had covered when these unknown builders had finished their work. Was it the steaming jungle of the Carboniferous, the bleak shoreline over which the first amphibians must crawl to conquer the / Page 26 / land-or, earlier still, the long loneliness before the coming of life? Do not ask me why I did not guess the truth sooner- the truth that seems so obvious now. In the first excitement of my discovery, I had assumed without question that this crystalline apparition had been built by some race belonging to the Moon's remote past, but suddenly, and with overwhelming force, the belief came to me that it was as alien to the Moon as I myself. In twenty years we had found no trace of life but a few degenerate plants. No lunar civilization, whatever its doom, could have left but a single token of its existence. I looked at the shining pyramid again, and the more remote it seemed from anything that had to do with the Moon. And suddenly I felt myself shaking with a foolish, hysterical laughter, brought on by excitement and over exertion: for I had imagined that the little pyramid was speaking to me and was saying: "Sorry, I'm a stranger here myself." It has taken us twenty years to crack that invisible shield and to reach the machine inside those crystal walls. What we could not understand, we broke at last with the savage might of atomic power, and now I have seen the fragments of the lovely, glittering thing I found up there on the mountain. They are meaningless. The mechanisms-if indeed they are mechanisms-of the pyramid belong to a technology that lies far beyond our horizon, perhaps to the technology of paraphysical forces. The mystery haunts us all the more now that the other planets have been reached and we know that only Earth has ever been the home of intelligent life in our Solar System. Nor could any lost civilization of our own world have built that machine, for the thickness of the meteoric dust on the plateau has enabled us to measure its age. It was set there upon its mountain before life had emerged from the seas of Earth. When our world was half its present age, something from the stars swept through the Solar System, left this token of its passage, and went again upon its way. Until we destroyed it, that machine was still fulfilling the purpose of its builders; and as to that purpose, here is my guess. Nearly a hundred thousand million stars are turning in the circle of the Milky Way, and long ago other races on the worlds of other suns must have scaled and passed the / Page 27 / heights that we have reached. Think of such civilizations, far back in time against the fading afterglow of Creation, masters of a universe so young that life as yet had come to only a handful of worlds. Theirs would have been a loneliness we cannot imagine, the loneliness of gods looking out across infinity and finding none to share their thoughts. They must have searched the star clusters as we have searched the planets. Everywhere there would be worlds, but they would be empty or peopled with crawling, mindless things. Such was our own Earth, the smoke of the great volcanoes still staining the skies, when that first ship of the peoples of the dawn came sliding in from the abyss beyond Pluto. It passed the frozen outer worlds, knowing that life could play no part in their destinies. It came to rest among the inner planets, warming themselves around the fire of the sun and waiting for their stories to begin. Those wanderers must have looked on Earth, circling safely in the narrow zone between fire and ice, and must have guessed that it was the favorite of the sun's children. Here, in the distant future would be intelligence; but there were countless stars before them still, and they might never come this way again. So they left a sentinel, one of millions they have scattered throughout the Universe, watching over all worlds with the promise of life. It was a beacon that down the ages has been patiently signaling the fact that no one had discovered it. Perhaps you understand now why that crystal pyramid was set upon the Moon instead of on the Earth. Its builders were not concerned with races still struggling up from savagery. They would be interested in our civilization only if we proved our fitness to survive-by crossing space and so escaping from the Earth, our cradle. That is the challenge that all intelligent races must meet, sooner or later. It is a double challenge, for it depends in turn upon the conquest of atomic energy and the last choice between life and death. Once we had passed. that crisis, it was only a matter of time before we found the pyramid and forced it open. Now its signals have ceased, and those whose duty it is will be turning their minds upon Earth. Perhaps they wish to help our infant civilization. But they must be very, very old; and the old are often insanely jealous of the young. I can never look now at the Milky Way without wondering from which of those banked clouds of stars the / Page 28 / emissaries are coming. If you will pardon so commonplace a simile, we have set off the fire alarm and have nothing to do but to wait. I do not think we will have to wait for long.
THE LOST WORLDS OF 2001 Arthur C. Clarke 1972 Page 50 ( Chapter 6) THE DAWN OF MAN "During November 1950 I wrote a short story about a meeting in the remote past between visitors from space and a primitive ape-man. An editor at Ballantine Books gave it the ingenious title "Expedition to Earth" when it was published in the book of that name, but I prefer "Encounter in the Dawn." However, when Harcourt, Brace and World brought out my own selection of favorites, The Nine Billion Names of God, it was mysteriously changed to "Encounter at Dawn." There the matter rests at present. Though "Encounter" was not one of the half-dozen stories originally purchased by Stanley,' it greatly influenced my thinking during the early stages of our enterprise. At that time-and indeed until-very much later-we assumed that we wovld actually show-some type of extraterrestrial entity, probably not too far from the human pattern. Even this presented frightful problems of make- up and credibility. The make-up problems could be solved-as Stuart Freeborn later showed with his brilliant work on the ape-men. (To my fury, at the 1969 Academy Awards a special Oscar was presented for make-up-to Planet of the Apes! I wondered, as loudly as possible, whether the Judges had passed over 2001 because they thought we used real apes.) The problem of credibility might be much greater, for there was danger that the result might look like yet another monster movie. After a great deal of experimenting the whole issue was sidestepped, both in the movie and the novel, and there is no doubt that this was the correct solution. But before we arrived at it, it seemed reasonable to / Page 51 / show an actual meeting between ape-men and aliens, and to give far more details of that encounter in the Pleisto- cene, three million years ago. The chapters that follow were our first straightforward attempt to show how ape- men might be trained, with patience, to improve their way of life. It was part of Stanley's genius that he spotted what was missing in this approach. It was too simple minded; worse than that, it lacked the magic he was seeking, as he explained in item 24 of his memorandum, quoted earlier. In the novel, we were finally able to get the effect we wanted by cutting out the details and introducing the super-teaching machine, the monolith-which, even more important, provided the essential linking theme between the different sections of the story. In the film, Stanley was able to produce a far more intense emotional effect by the brilliant use of slow-motion photography, extreme close- ups, and Richard Strauss's Zarathustra. That frozen moment at the beginning of history, when Moon-Watcher, foreshadowing Cain, first picks up the bone and studies it thoughtfully, before waving it to and fro with mounting excitement, never fails to bring tears to my eyes. And it hit me hardest of all when I was sitting behind U Thant and Dr. Ralph Bunche in the Dag Hammarskjold Theater, watching a screening which we had arranged at the Secretary General's request. This, I suddenly realized, is where all the trouble started-and this very building is where we are trying to stop it. Simultaneously, I was struck by the astonishing parallel between the shape of the monolith and the UN Headquarters itself; there seemed something quite uncanny about the coincidence. If it is one. . . . The skull-smashing sequence was the only scene not filmed in the studio; it was shot in a field, a couple of - hundred yards away-the only time Stanley went on location. A small platform had been set up, and Moon-Watcher (Dan Richter) was sitting on this, surrounded by bones. Cars and buses were going by at the end of the field, but as this was a low-angle shot against the sky they didn't get in the way-though Stanley did have to pause for an occasional airplane. The shot was repeated so many times, and Dan smashed so many bones, that I was afraid we were going to run out of wart-hog (or tapir) skulls. But eventually Stanley was satisfied, and as we walked back to the studio he began to throw bones up in the air. At first I thought / Page 52 / this was sheer joi de vivre, but then he started to film them with a hand-held camera-no easy task. Once or twice, one of the large, swiftly descending bones nearly impacted on Stanley as he peered through the viewfinder; if luck had been against us the whole project might have ended then. To misquote Ardrey (page 34), "That intel-ligence would have perished on some forgotten Elstree field." When he had finished filming the bones whirling against, the sky, Stanley resumed the walk back to the studio; but: now he had got hold of a broom, and started tossing that up into the air. Once again, I assumed this exercise was pure fun; and perhaps it was. But that was the genesis of the longest flash-forward in the history of movies-three million years, from bone club to artificial satellite, in a twenty-fourth of a second.
Page 66 9 GIFT FROM THE STARS Jupiter was a brilliant star, almost vertically above him, as Clindar walked through the sleeping bush an hour before dawn. Up there, half a billion miles away, was the entrance of the Star Gate, and the road across the light- years that led to his infinitely more distant home. It was a road with many branches, most of them still unexplored and leading to destinations which were perhaps unimaginable. Down a few of those byways were the lonely civilizations scattered so sparsely throughout this arm of the galactic spiral. One day this world might be among them; but that time could not come for at least a million years. The hominids never left their cave during the hours of darkness, but Clindar could hear them barking and quarreling sleepily as they prepared to meet the new day. He placed his bribe-a young boar-at the foot of the cliff, where they were bound to pass. This time, however, he did not withdraw. He sat down only a few feet away from the sacrifice, and waited. The stars faded from the sky, Jupiter last of all. Presently the rays of the rising sun began to gild the face of the cliff, moving slowly downward until they shone straight into the cave. Then, from the interior, came a sudden excited chattering, and the high-pitched "Eek- Eek" which Clindar had grown to recognize as an alarm signal. The hominids had spotted him. He could see their hairy figures milling around in the entrance, undecided what to do next. If they did not pluck up enough courage to come down in a reasonable time, Clindar would leave. But he would take the boar with him, and hope that they would draw the conclusion that food and friendship were inseparably linked Page 68 To his pleased suprise he did not have long.to wait. Moving slowly but steadily , Moon-watcher was descending the face of the cliff. He got to within twenty feet of ground level and then paused to survey the situation..." "Clindar pulled a knife from his equipment belt, and with rather more energy than skill, started to disjoint the boar. It must, he thought, look like magic to Moon-watcher to see how swiftly the tough meat came apart; he was performing in a few seconds acts which took the homids many minutes of tearing and biting. when he had detached a foreleg, he held it out to his fascinated spectator..." "He was patient, and Moon-Watcher was hungry, but the result was not inevitable..." At last it made its decision, and gathered all its courage together. Still prepared for instant flight, Moon Watcher dropped from the face of the cliff and started to sidle towards Clindar,..." "It took him several minutes, with numerous retreats to and hesitations to cross the last few feet. While he was doing this, Clindar pretended to chew avidly at the leg of boar, holding it out invitingly from time to time. Abruptly it was snatched from his hand, and in seconds Moon-Watcher was half way up the cliff carrying his prize between his teeth. Patiently, Clindar started to slice away at the carcass once more, waiting for the next move. It came when Moon-Watcher returned for a second helping..." "So the experiment in primitive diplomacy continued, day after day - sometimes in the morning before the homids had left ther cave, sometime in the evening as they returned from a days foraging. By the end of the week Clindar had become accepted as an honorary member of the tribe..." To Clindar it was a weird, almost unreal existence this daily switching between two worlds a million years apart..." "Because speech still lay a million years in the future, the only way to instruct these creatures was by example..." �"Clindar was sooon the most efficient hunter on the planet..." His favourite weapon was the thighbone of one of the larger antelopes; with its knobbly end , it formed a perfect natural club..." "With a single well-placed blow it could kill animals up to the size of the homids themselves, and it could drive off creatures that were far larger. Clindar was anxious to prove this, and had thought of staging a demonstration. As it turned out, his wish was granted him without any deliberate planning..."
Page 70 "Clindar held out the second, unbroken club in his right hand, and waited. This was the moment; no better one would ever come. If Moon-Watcher had not learned the lesson now, he would never do so. The hominid came slowly toward him, then squatted down only five feet away; he had never approached so closely before. Holding his head slightly on one side in an attitude of intense concentration, he stared at the bone held rigidly in Clindar's hand. Then he reached out a paw and touched the crude club. His fingers grasped the end, and tugged gently at it. Clindar held firm for a moment, then released his grip. Moon-Watcher drew the bone away from him, looked at it intently, then began to sniff and nibble at it. A spasm of disappointment shot through Clindar's mind; the lesson was already forgotten. This was just another morsel of food-not a key to the future, a tool that could lead to the mastery of this world, and of many others. Then Moon-Watcher suddenly remembered. He jumped to his feet, and began to darice around waving the club in his right paw. As long as he kept moving, he could rear almost upright; only when he stood still did he have to use his free forelimb as a support. He had already begun to make the awesome and irrevocable transition from quadruped to biped. The little dance lasted about five seconds; then Moon-Watcher shot off on a tangent. He raced toward the dead hyena in such a frenzy of excitement that his companions, who had already started to quarrel over the feast, scattered in fright. Awkwardly, but with an energy that made up for his lack of skill, Moon-Watcher began to pound the carcass with his club, while the others looked on with awed astonishment. Clindar alone understood what was happening, and knew that this world had come to a turning point in time. To the most promising of its creatures, he had given the first tool; and the history of yet another race had begun."
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http://www.crystalinks.com/2001z.html '2001: A Space Odyssey' - 'Thus Spake Zarathrustra' ...... Planet Earth 1968 ..... Stanley Kubrick creates a film called '2001 A Space Odyssey'. '2001: A Space Odyssey' is a landmark, science fiction, classic, epic film containing more spectacular imagery than verbal dialogue. It impacts on the viewer and taps into subconscious memories of creation. Though it shows human evolving from ape - the missing link of that evolution is left open. The plot follows a spaceship that crosses the universe, searching for the source of life itself. A link is made to a creational intelligence perhaps linked to human evolution. Again this is linked to a computer that comes into conscious awareness and confusion as to its prime objective. As with all of the themes I have been writing about in Crystalinks - '2001: A Space Odyssey' - is based strongly on mythological metaphors and tales. It is closely linked with the Prometheus myth. The concept of the the pillar sent down from Jupiter is exactly the same as that of Prometheus bring fire to humans. Even the source being Jupiter fits, as Jupiter was the Roman name for Zeus - the leader of the Greek pantheon. Like the Prometheus myth, the gift given to humans proves to be beyond their control. This time it is in the form of a computer, Hal. Hal goes out of control and begins to kill humans, and disobeys all orders given to him. He begins to think for himself. This actually sets the stage for an Odyssey parallel in the form of the visit to the cave of Polyphemus, though this time the roles are reversed. In 2001: 'A Space Odyssey,' the human, Dave, is attempting to get into the ship rather than out of a cave. To do this, he has to use his brute strength versus Hal's genius, a complete reversal of the mythological roles. Nonetheless it it is far too similar to be coincidence. "The breathtaking, - richly eloquent film - deliberately filmed at a slow pace, is based on the short story The Sentinel, by science fiction author Arthur C. Clarke. "Its screenplay was co-authored by director Stanley Kubrick and Clarke from an expanded novelization..."
"In the opening scene - the camera pans upward from the pock-marked surface of the Moon in the foreground. The perspective is from behind the moon. In the distance is a view of the Sun rising over the Earth-crescent in the vastness of space. The image shows the heavenly bodies of the Earth, Moon, and Sun in a vertically-symmetrical alignment or conjunction. Later in the film, it is revealed that a monolith was buried on the Moon, possibly at the moment of this 'magical' conjunction. The opening trinitarian chords [C, G, and again C] of Richard Strauss' 'Thus Spake Zarathustra' accompany and welcome this striking shot of orbital and visual alignment. This music was inspired by the book . . . Thus Spake Zarathrustra. Its five opening notes embody the ascension of man into spheres reserved for the gods. It projects the power of creation and Zarathrustra. The music is associated in the film with the first entry of man's consciousness into the universe - and with the eventual passage of that consciousness onto a new level, symbolized by the Star Child at the end of the film.
The Dawn of Man 'The Dawn of Man' opens in the prehistoric past in the Pleistocene era four million years ago, the location where the human race was supposedly born - evolving from primitive apes. The sun rises on the dawn of civilization in a primordial landscape of arid, wasteland desert. As dawn passes and mid-day approaches on the barren African savannah, animal skeletons lie dormant on the rocky ground - the first sign of life. A peaceful band or tribe of prehistoric ape-men (Australopithecines) appear, squat and hairy, eating grass. Although herds of tapirs graze closeby, the ape-men are vegetarians who forage for grass and roots. They have not developed the means or tools necessary to attack and kill or eat the tapirs like other predators. Symbolically, there are endless eons of time that pass during which the apes live in eternal boredom - and cope with the struggle for survival. A group of apes scratches and chatters in groups around a slowly diminishing watering hole. A rival, warring band of ape competitors approaches the watering hole, led by an almost-upright, tall and bright man-ape named Moonwatcher in Arthur Clarke's novel. By shrieking, they scare away the other apes from the water and aggressively establish dominance and territoriality. During the first night, a leopard with glowing eyes guards the carcass of a fallen zebra in the moonlight. The band of vegetarian man-pes huddles protectively together in their cramped den for comfort and support - living and sleeping in fear. In the first light of the prehistoric dawn on the second day, a tall, black, rectangular monolithic slab, with an eerie humming sound - symbolic of the religious/spiritual unknown - materializes in the midst of their den. The massive artificial monolith, in contrast to its natural surroundings, stands in a shallow depression in the rocks where the man-apes gather around a water hole. In Arthur Clarke's novel, the monolith is a technological machine belonging to aliens in space, one of hundreds of such monoliths sent to Earth to test, teach and transform the apes into higher-order beings. The unusual, out-of-place object with straight-edges causes them to be alarmed and they react nervously. They approach it cautiously, drawn to its color, form, and smooth surface. The leader of the clan of man-apes is the first to reach out fearfully and hypnotically for the black object. His boldness encourages the rest of the group to gather around. In a mute, primitive, but poetic moment, they herd around it and huddle by it, just as another celestial alignment or configuration occurs. With the mysterious monolith in the foreground, the glowing Sun rises over the black slab, directly beneath the crescent of the Moon A quick, almost-subliminal shot of the celestial alignment with the monolith is flashed on the screen - indicating that it will inspire a new idea or cause what is to happen the discovery that the bone can function as a weapon. In a slow-motion sequence - accompanied by the slowly-building tone of Strauss's Thus Spoke Zarathustra - he picks up an animal bone and uses it to smash at and shatter the skeleton, first tentatively and then more vigorously. In a slow-motion closeup, his hairy fist grasps the skeleton bone over his head as he brings it down forcefully like a cudgel. As he smashes and pulverizes parts of the skeleton on the ground, the soundtrack bursts forth in an ecstatic, jubilant climax. In one brilliant inter-cut image, a tapir falls to the ground - the vegetarian man-ape will be able to hunt for food and kill a tapir with his new utilitarian tool. No longer vegetarian after the breakthrough, the man-ape becomes carnivorous, squatting while eating a raw piece of tapir flesh in his hands. The rest of the clan share in the meat of the fresh kill later that afternoon and evening. Somehow, the monolith has been presented as a gift to mysteriously assist the man-ape in his transition to a higher order (or lower order depending upon one's interpretation) with an ability to reason and the power to use tools (such as bones) - for murder. The man-ape is on the verge of intelligence - the beginning of steps toward humanity as he learns to use skeleton bones as tools - extending his reach. The sun sets. On the third day, when other man-apes come over to the water hole, the intelligent, carnivorous man-apes dominate and drive the weaponless (and tool-less) neighboring creatures away with their newfound strike power - this is humanity's first bloody war. They swing with their bone-tools - using them as weapons to threaten the nearest other tribe of rival proto-humans. The leader man-ape uses the bone to attack, crush an opponent's skull, and kill him - making them capable of survival in the hostile environment. The 'enlightened' apes gain domination in the animal world, establish their territorial domain, and take an evolutionary step or leap toward (or away from) humanity. In slow-motion, the man-ape leader flings his weapon, a fragmented piece of the bone, exultantly and jubilantly into the air. It flies and spins upwards, twisting and turning end-over-end. Four millions years later . . . The tossed bone (tool/weapon) instantly rotates and dissolves into an orbiting space satellite from Earth - a technological instrument, tool, or machine from another era that was ultimately derived from the first tool-weapon. The toss of the ape-man's bone is metaphoric for a lift-off from Earth toward the Moon, and for the tremendous technological advances that have occurred in the interim. The year 2000 - the Earth drifts by, the camera's perspective is from somewhere between Earth and the Moon. Two different kinds of satellites (one slightly rectangular, the other cylindrical) float by, circling around the globe of Earth." "Dave, the last surviving astronaut, escapes HAL's coolly-plotted machinations and manages to dismantle him. Dave then continues the odyssey alone. In the end, Dave is captured in an inter-galactic net, apparently by the makers of the slab. We find him facing himself as an old man, sitting in a room on the other side of the universe. No explanations are given. The huge embryo comes on the screen, and the film ends." "The 'star gate' sequence is a sound and light journey"
THE LOST WORLDS OF 2001 Arthur C. Clarke 1972 Page179 "I'm afraid," he said, "that there's something seriously wrong with space." "A long time ago," said Kaminski, "I came across a remark that I've never forgotten-though I can't remember who made it. 'Any sufficiently advanced technology is indistinguishable from magic.' That's what we're up against here. Our lasers and mesotrons and nuclear reactors and neutrino telescopes would have seemed pure magic to the best scientists of the nineteenth century. But they could have understood how they worked-more or less- if we were around to explain the theory to them." "I'd be glad to settle without the theory," remarked Kimball, "if I could even understand what this thing is-or what it's supposed to do." "It seems to me," said Bowman, "that there are two possibilities-both just about equally impossible. The first is that Jupiter V is hollow-and there's some kind of micro-universe down there. A whole galaxy a hundred miles across." "But the probes went thousands of miles, according to the radar readings," "There could be some kind of distortion. Suppose the probes got smaller and smaller as they went in. Then they might seem to be thousands of miles away, when they were still really quite close." "And that," said Kaminski, "reminds me of another quotation-one of Niels Bohr's. 'Your theory is crazy- but not crazy enough to be true.' " "You have a crazier one?" asked Hunter. "Yes, I do. I think the stars-and that sun down there- are part of our own universe, but we're seeing them through some new direction of space." "I suppose you mean the fourth dimension." "I doubt if it's anything as simple as that. But it probably does involve higher dimensions of some kind. Perhaps non-Euclidean ones." "I get the idea. If you went down that hole, you'd come out hundreds or thousands of light-years away. But how long would the journey really be?" "How long is the journey from New York to Washington? Two hundred miles if you fly south. But twenty-four / Page 180 / thousand if you go in the other direction, over the North Pole. Both directions are equally real." "I seem to remember," said Bowman, "that back on Earth you once told me that shortcuts through space-time were scientific nonsense-pure fantasy." "Did I?' replied Kaminski, unabashed. "Well, I've changed my mind. Though I reserve the right to change it back again, if a better theory comes along." "I'm a simpleminded engineer," said Hunter rather aggressively. "I see a hole going into Jupiter V, and not coming out anywhere. But you tell me that it does come out. How?" " Everyone waited hopefully for Kaminski to answer. For a moment he hemmed and hawed; then he suddenly brightened. "I can only explain by means of analogy. Suppose you were a Flatlander, an inhabitant of a two-dimensional world like a sheet of paper-unable to move above or below it. If I drew a circle in your flat world, but left a small gap in it, you would say that the gap was the only way into the circle. Right?" ".Right." "If anyone went into the circle, they could only come out the same way?" . "So that's what you're driving at. The circle could be a cross-section of a tube passing through Flatland. If I was clever enough to crawl up the tube, by moving into the third dimension, I would leave my flat universe altogether." "Exactly. But the tube might bend back into Flatland again, and you could come out somewhere else. To your friends, it would seem that you'd traveled from A to B without crossing the space between. You'd have disappeared down one hole and emerged from a totally different one, maybe thousands of miles awav." "But what advantage would that be? Surely the straight line in Flatland itself would still be the shortest distance between A and B." "Not necessarily. It depends what you mean by a straight line. Flatland might really be wrinkled, though the Flatlanders wouldn't be able to detect it. I'm not a topologist, but I can see how there might be lines that were straighter than straight, if some of them went through other dimensions."
MATHEMATICS AND THE IMAGINATION Edward Kasner and James Newman 1940 Page 127 "Now, if a third dimension is essential for the solution of certain two -dimensional problems, a fourth dimension would make possible the solution of otherwise unsolvable problems of three dimensions. To be sure, we are in the realm of fancy, and it need hardly be pointed out that a fourth dimension is not at hand to make Houdinisof us all. Yet, in theoretical inquiries, a fourth dimension 33 and 34 (omitted) Page 128 is of signal importance, and part of the warp and woof of modern theoretical physics and mathematics. Ex-amples chosen from these subjects are quite difficult and would be out of place, but some simpler ones in the lower dimensions may prove amusing. If we lived in a two-dimensional world, so graphically described by Abbott in his famous romance, Flatland, our house would be a plane figure, as in Fig. 34. Entering through the door at A, we would be safe from our friends and enemies once the door was closed, even though there were no roof over our head, and the walls and windows were merely lines. To climb over these lines would mean getting out of the plane into a third dimension, and of course, no one in the two-dimensional world would have any better idea of how to do that than we know how to escape from a locked safe..deposit vault by means of a fourth dimension. A three-dimensional cat might peek at a two-dimensional king, but he would never be the wiser. When winter comes to Flatland, its inhabitants wear gloves. Three-dimensional hands look like this: Page 129 (figure omitted)
Page 130 Mathematics and the Imagination
Modern science has as yet devised no relief for the man who finds himself with two right gloves instead of a right and a left. In Flatland, the same prqblem would exist. But there, Gulliver, looking down at its inhabitants from the eminence of a third dimension would see at once that, just as in the case of the two triangles on page 127, all that is necessary to turn a right glove into a left one is to lift it up and turn it over. Of course, no one in Flatland would or could lift a fInger to do that, since it involves an extra dimension. If then, we could be transported into a fourth dimen-sion, there is no end to the miracles we could perform- starting with the rehabilitation of all ill-assorted pairs of gloves. Lift the right glove from three-dimensional space into a fourth dimension, turn it around, bring it back and it becomes a left glove. No prison cell could hold the four-dimensional Gulliver-far more of a men-ace than a mere invisible man. Gulliver could take a knot and untie it without touching the ends or breaking it, merely by transporting it into a fourth dimension and slipping the solid cord through the extra loophole. Or he might take two links of a chain apart without breaking them. All. this and much more would seem absurdly simple to him, and he would regard our help-lessness with the same amusement and pity as we look upon the miserable creatures of Flatland. Our romance must end. If it has aided some readers in making a fourth dimension more real and has satisfied a common anthropomorphic thirst, it-has served its pur-pose. For our own part, we confess that the fables have never made the facts any clearer. An idea originally associated with ghosts and spirits / Page 131 / needs, if it is to serve science, to be as far removed as possible from fuzzy thinking. It must be clearly and courageously faced if its true essence is to be discovered. But it is even more stupid to reject and deride than to glorify and enshrine it. No concept that has come out of our heads or pens marked a greater forward step in our thinking, no idea of religion, philosophy, or science broke more sharply with tradition and commonly accepted knowledge, than the idea of a fourth dimension. Eddington has put it very well: 6 However successful the theory of a four-dimensional world may be, it is difficult to ignore a voice inside us which whispers: "At the back of your mind, you know that a fourth dimension is all nonsense." I fancy that voice must often have had a busy time in the past history of physics. What nonsense to say that this solid table on which I am writing is a collection of electrons moving with prodigious speed in empty spaces, which relatively to electronic dimensions are as wide as the spaces between the planets in the solar system! What nonsense to say that the thin air is trying to crush my body with a load of 14 lbs. to the square inch! What nonsense that the star cluster which I see through the telescope, obviously there now, is a glimpse into a past age 50,000 years ago! Let us not be beguiled by this voice. It is discredited. . . . We have found a strange footprint on the shores of the un-known. We have devised profound theories, one after another to account for its origin. At last, we have succeeded in !econ- structing the creature that made the footprint. And lo! It is our own. We have emphasized the fact that pure geometry is divorced from the physical space which we perceive about us, and we are now prepared to tackle an idea which is slightly tougher. There is no harm, however / Page 132 / in first distinguishing somewhat differently than before between space as it is ordinarily conceived and the space manifolds of mathematics. Perhaps this distinction will help to make our new concept-the non-Euclidean geometries-seem less strange. We are quite used to thinking of space as infinite, not in the technical mathematical sense of infinite classes, but simply meaning that space is boundless--without end. To be sure, experience teaches us nothing of the kind. The boundaries of a private citizen rarely go much further than the end of his right arm. The boundaries of a nation, as bootleggers once learned, do not go beyond the twelve-mile limit. Most of what we believe about the infinitude of space comes to us by hearsay, and another part comes from what we think we see. Thus, the stars look as if they were millions of miles away, although on a dark night a candle half a mile off would give the same impression. Moreover, if we imagined ourselves the size of atoms, a pea at a distance of one inch would appear mightier and far more distant than the sun. '];'he distinction between the space of the individual and "public space" soon becomes apparent. Our personal knowledge of space does not show it to be either infinite, homogeneous, or isotropic. We do not know it to be infinite because we crawl, hop, and fly around in only tiny portions. We do not know it to be homogeneous because a skyscraper in the distance seems much smaller than the end of our nose; and the feather on the hat of the lady in front of us shuts off our vision of the cinema screen. And we know it is not isotropic, that is, it "does not possess the same properties in every direction," 7 because there are blind spots in our vision and our sense : / Page 133 / of sight is never equally good in all directions. The notion of physical or "public" space which we abstract from our individual experience is intended to free us from our personal limitations. We say physicaJ space is infinite, homogeneous, isotropic, and Euclidean. These compliments are readily paid to an ideal entity about which very litde is actually known. If we were to ask the physicist or astronomer, "What do you think about space?" he might reply: "In order to carry out experimental measurements and describe them with the greatest convenience, the physical scientist decides upon certain conventions with respect to his measuring appa- ratus and operations performed with it. These are, strictly speaking, conventions with regard to Physical objects and Physical operations. However, for practical purposes, it is convenient to assume for them a generality beyond any particular set of objects or operations. They then become, as we say, properties of space. That is what is meant by physical space, which we may define, in brief, as the abstract construct possessing those properties of rigid bodies that are independent of their material content. Physical space is that on which almost the whole of physics is based, and it is, of course, the space of everyday affairs." 8 On the other hand, the spaces, or more generally the manifolds, which the mathematician considers are con- structed without any reference to physical operations, such as measurement. They possess only those properties expressed in the postulates and axioms of the particular geometry in question, as well as those properties deducible from them. I t may well be that the postulates are themselves suggested, in part or in whole, by the physical space of / Page 134 / our experience, but they are to be regarded as full-grown and independent. If experiments were to show that some, or all, of our ideas about physical space are wrong (as the theory of relativity has, in fact, done) we would have to rewrite our texts on physics, but not our geometries. But this approach to the concept of space, as well as to geometry, is comparatively recent. There has been no more sweeping movement in the entire history of science than the development of non-Euclidean geometry, a movement which shook to the foundations the age-old belief that Euclid had dispensed eternal truths. Compe-tent and accurate as a measuring tool since Egyptian times, intuitively appealing and full of common sense, sanctified and cherished as one of the richest of intel- lectual legacies from Greece, the geometry of Euclid stood for more than twenty centuries in lone, resplendent, and irreproachable majesty. It was truly hedged by divinity, and if God, as Plato said, ever geometrized, he surely looked to Euclid for the rules. The mathematicians who occasionally had doubts soon expiated their heresy by votive offerings in the form of further proofs in corroboration of Euclid. Even Gauss, the "Prince of Mathematicians," dared not offer his criticisms for fear of the vulgar abuse of the "Boethians." Whence came the doubts? Whence the inspiration of those who dared profane the temple? Were not the postu- lates of Euclid self-evident, plain as the light of day? And the theorems as unassailable as that two plus two equals four? The center of the ever-increasing storm, which finally broke in the nineteenth century was the famous fifth pos-tulate about parallel lines. Assorted Geometries-Plane and Fancy
This postulate may be restated as follows: "Through / Page 135 / any point in the plane, there is one, and only one, line parallel to a given line." There is some evidence to show that Euclid, himself, did not regard this postulate as "quite so self-evident" as his others.9 Philosophers and mathematicians, intent on vindicating him, attempted to show that it was really a theorem and thus deducible from his premises. All of " iliese attempts failed for the very good reason which Eu- clid, much wiser than those who followed him, had al- ready recognized, namely, that the fifth postulate was merely an assumption and hence could not be mathe- matically proved.
More than two thousand years after Euclid, a German, a Russian, and a Hungarian came to shatter two in- disputable "facts." The first, that space obeyed Euclid; the second, that Euclid obeyed space. Gauss we credit on faith. Not knowing the extent of his investigations, in deference to his greatness as well as to his integrity, we are hospitable to his statement that he had independently arrived at conclusions resembling those of the Hungarian, I Bolyai, some years before Bolyai's father informed Gauss I of his son's work. Lobachevsky, the Russian, and Bolyai, both in the 1830's, presented to the very apathetic scientific world their remarkable theories. They argued that the trouble-; making postulate could not be proved, could not be I deduced from the other axioms, because it was only a postulate. Any other hypothesis about parallels could be substituted in its place, and a different geometry-just as consistent and just as "true"- would follow. All the other postulates of Euclid were to be retained, only, in place of the fifth, a substitution was to be made:
Arthur C. Clarke 1972
"I can only explain by means of analogy. Suppose you were a Flatlander, an inhabitant of a two-dimensional world like a sheet of paper-unable to move above or below it. If I drew a circle in your flat world, but left a small gap in it, you would say that the gap was the only way into the circle. Right?" ".Right." "If anyone went into the circle, they could only come out the same way?" . "So that's what you're driving at. The circle could be a cross-section of a tube passing through Flatland. If I was clever enough to crawl up the tube, by moving into the third dimension, I would leave my flat universe altogether." "Exactly. But the tube might bend back into Flatland again, and you could come out somewhere else. To your friends, it would seem that you'd traveled from A to B without crossing the space between. You'd have disappeared down one hole and emerged from a totally different one, maybe thousands of miles awav." "But what advantage would that be? Surely the straight line in Flatland itself would still be the shortest distance between A and B." "Not necessarily. It depends what you mean by a straight line. Flatland might really be wrinkled, though the Flatlanders wouldn't be able to detect it. I'm not a topologist, but I can see how there might be lines that were straighter than straight, if some of them went through other dimensions." "We can argue this-until kingdom come," said Hunter. "But supposing it's true-what shall we do about it?'
/ Page 181 / "There's not much we can do. Even if we had an unlimited fuel and oxygen supply, it might be suicide to go into that thing. Though it may be a shortcut, it could be a damn long one. Suppose it comes out somewhere a thousand light-years away-that won't help us, if the trip takes a century. We wouldn't appreciate saving nine hundred years." That was perfectly true; and there might be other dangers, as inconceivable to the mind of man as this anomaly in space itself. Discovery had come to the end of her travels; she must remain here in an eternal orbit, just a few miles from a mystery that she could never approach. Like Moses looking into the promised land, they must stare at marvels beyond their reach.
Page188 34 THE WORLDS OF THE STAR GATE "A writer who sets out to describe a civilization superior to his own is obviously attempting the impossible. A glance at the science fiction of fifty--or even twenty-years ago shows how futile it is to peer even a little way into the mists of time, and when dealing merely with the world of men. Longer-range anticipations are clearly even less likely to be successful; imagine what sort of forecast one of the Pilgrim Fathers could have made of the United States in the year 1970! Practically nothing in his picture would have had any resemblance to the reality-which, in fact, would have been virtually incomprehensible to him. But Stanley Kubrick and I were attempting, at the climax of our Odyssey, something even more outrageous. We had to describe--and to show on the screen-the activities and environments, and perhaps the physical nature, of creatures millions of years ahead of man. This was, by definition, impossible. One might as well expect Moon-Watcher to give a lucid description of David Bowman and his society. Obviously, the problem had to be approached indirectly. Even if we showed any extraterrestrial creatures and their habitats, they would have to be fairly near us on the evolutionary scale--say, not more than a couple of centuries ahead. They could hardly be the three-million-year- old entities who were the powers behind the Black Monolith and the Star Gate. But we certainly had to show something, though there were moments of despair when I feared we had painted ourselves into a corner from which there was no possible escape-except perhaps a "Lady or the Tiger" ending / Page189 / where we said goodbye to our hero just as he entered the Star Gate. That would have been the lazy way out, and would have started people queuing at the box office to get their money back. (As Jerry Agel has recorded,' at least one person did just this-a Mrs. Patricia Attard of Denver, Colorado. If the manager of the handsome Cooper Cinerama did oblige, I shall be happy to reimburse him.) Our ultimate solution now seems to me the only possible one, but before arriving at it we spent months imagining strange worlds and cities and creatures, in the hope of finding something that would produce the right shock of recognition. All this material was abandoned, but I would not say that any of it was unnecessary. It contained the alternatives that had to be eliminated, and therefore first had to be created. Some of these Lost Worlds of the Star Gate are in the pages that follow. In working on them, I was greatly helped by two simple precepts. The first is due to Miss MaryPoppins: "I never explain anything." The other is Clarke's Third* Law: "Any sufficiently advanced technology is indistinguishable from magic." . Stanley once claimed if anything could be written, he could film it. I am prepared to believe him-if he was given unlimited time and budget. However, as we were eventually a year and four million dollars over estimate, it was just as well that the problem of creating explicit super-civilizations was by-passed. There are things that are better left to the imagination-which is why so many 'horror' movies collapse when some pathetic papier-mache monster is finally revealed. Stanley avoided this danger by creating the famousm "psychedelic" sequence-or, as MGM eventually called it, "the ultimate trip." I am assured, by experts, that this is best appreciated under the influence of various chemicals, but do not intend to check this personally. It was certainly not conceived that way, at least as far as Stanley and I were concerned, though I would not presume to speak for all the members of the art and special-effects departments. I raise this subject because some interested parties have *Oh, very well. The First: "When a distinguished but elderly scientist says that something is possible, he is almost certainly right. When he says it is impossible, he is very probably wrong." (Profiles of the Future) The Second: "The only way of finding the limits of the possible is by going beyond them into the impossible." I decided that if three laws were good enough for Newton, they were good enough for me. Page 192 REUNION Of the Clindar who had walked on Earth, in another dawn, three million years ago, not a single atom now remained; yet though the body had been worn away and rebuilt times beyond number, it was no more than a temporary garment for the questing intelligence that it housed. It had been remodeled into many strange forms, for unusual missions, but always it had reverted to the basic humanoid design. As for the memories and emotions of those three million years, spent on more than a thousand worlds, not even the most efficient storage system could hold them all in one brain. But they were available at a moment's notice, filed away in the immense memory vault that ringed the planet. Whenever he wished, Clindar could relive any portion of his past, in total recall. He could look again upon a flower or an insect that had fleetingly caught his eye ten thousand years before, hear the voice of creatures that had been extinct for ages, smell the winds of worlds that had long since perished in the funeral pyres of their own suns. Nothing was lost to him-if he wished to recall it. So when the signal had come in, and while the golden ship was being prepared for its journey, he had gone to the Palace of the Past and let his ancient memories flow back into his brain. Now it seemed that only yesterday- not three million years ago-he had hunted with the ape-men and shown Moon-Watcher how to find the stones that could be used as knives and clubs. "They are awake," said a quiet voice in the depths of his brain. "They are moving around inside their Ship." That was good; at .least they were alive. The robot's / Page 193 / first report had indicated a ship of the dead, and it had been some time before the truth was realized. They were going to have a surprise, thought Clindar, when they woke so far from home, and he hoped they would appreciate it. There were few things that an immortal welcomed and valued more greatly than surprise; when there was none left in the universe, it would be time to die. He walked slowly across the varying landscape of his little world, savoring this moment-for each of these encounters was unique, and each contributed something new to the pattern and the purpose of his life. Though he was alone upon this floating rock, unknown myriads of others were looking through his eyes and sharing his sensations, and myriads more would do so in the ages yet to come. Most of them would approximately share his shape, for this was a meeting that chiefly concerned those intelligences that could be called humanoid. But there would be not a few much stranger creatures watching, and many of them were his friends. To all these multiformed spectators he flashed a wry greeting-an infinitely complex and subtle variation on the universal jest that could be crudely expressed in the words, "I know all humanoids look the same-but I shall be the one on the right." This sky-rock was not Clindar's only home, but it was the one he loved the best, for it was full of memories that needed no revival in the Palace of the Past. He had shared it thirty thousand years ago with a mating group long since dispersed through the Galaxy, and the radiance of those days still lingered, like the soft caress of the eternal dawn. And because it was far from the shattering impact of the great centers of civilization, it was a perfect place to greet and reassure startled or nervous visitors. They were awed, but not overwhelmed; puzzled, but not alarmed. Seeing only Clindar, they were unaware of the forces and potentialities focused within him; they would know of these things when the time was ripe, or not at all. The upper surface of the great rock was divided into three levels, with the villa at the highest end, and the flat apron of the landing stage at the lowest. Between them, and occupying more than half the total area, were the lawns and pools and courtyards and groves of trees among which Clindar had scattered the souvenirs of a thousand worlds and a hundred civilizations. ��TWO EYES YOU ARE TWO EYES YOU BE I SEE YOU ARE 2 WISE FOR ME
HOLY BIBLE Scofield References ZECHARIAH Page 968 Chapter 4. B.C.519 Verse 10 " For who hath despisd the day of small things? for they shall rejoice, and shall see the plummet in the hand of Zerubbabel with those seven; they are the eyes of the LORD, which run to and fro through the whole earth. "
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THE CONCISE OXFORD DICTIONARY OF QUOTATIONS 1964 Page 74
"16. On the Rampage. Pip. and off the Rampage. Pip; such is Life! [Joe Gargery.] Great Expectations, ch. 15"
27 " 'Yes, I have a pair of eyes,' replied Sam, 'and that's just it, If they wos a pair o' patent double million magni-fyin' gas microscopes of hextra power, p'raps I might be able to see through a flight o' stairs and a deal door; but bein' only eyes, you see my wision's limited,' " Charles Dickens 1812-1870
NUMBER 9 THE SEARCH FOR THE SIGMA CODE Cecil Balmond 1998 Cycles and Patterns Page165 The essence of mathematics is to look for patterns. "Our minds seem to be organised to search for relationships and sequences. We look for hidden orders. These intuitions seem to be more important than the facts themselves, for there is always the thrill at finding something, a pattern, it is a discovery - what was unknown is now revealed. Imagine looking up at the stars and finding the zodiac! Suddenly the counters fall into place and a connection is found, not necessarily a geometric one, but a relationship between numbers, pictures of the mind, that were not obvious before. There is that excitement of finding order in something that was otherwise hidden. And there is the knowledge that a huge unseen world lurks behind the facades we see of the numbers themselves."
IN SEARCH OF SCHRODINGER'S CAT John Gribbin 1984 NOTHING IS REAL Page 1 "The cat of our tide is a mythical beast, but Schrodinger was a real person. Erwin Schrodinger was an Austrian scientist instrumental in the development, in the mid-1920s, of the equations of a branch of science now known as quantum mechanics. Branch of science is hardly the correc{ expression, however, because quantum mechanics provides the fundamental underpinning of all of modern science. The equations describe the behavior of very small objects-generally speaking, the size of atoms or smaller-and they provide the only understanding of the world of the very small. Without these equations, physicists would be unable to design working nuclear power stations (or bombs), build lasers, or explain how the sun stays hot. Without quantum mechanics, chemistry would still be in the Dark Ages, and there would be no science of molecular biology-no under-standing of DNA, no genetic engineering-at all. Quantum theory represents the greatest achievement of science, far more significant and of far more direct, prac-tical use than relativity theory. And yet, it makes some very strange predictions. The world of quantum mechanics is so strange, indeed, that even Albert Einstein found it in-comprehensible, and refused to accept all of the implica- tions of the theory developed by Schrodinger and his colleagues. Einstein, and many other scientists, found it more comfortable to believe that the equations of quantum mechanics simply represent some sort of mathematical trick, which just happens to give a reasonable working guide to the behavior of atomic and subatomic particles but that conceals some deeper truth that corresponds more closely to our everyday sense of reality. For what quantum mechanics says is that nothing is real and that we cannot say anything about what things are doing when we are not looking at them. Schrodinger's mythical cat was invoked to make the differences between the quantum world and the everyday world clear. In the world of quantum mechanics, the laws of phys- ics that are familiar from the everyday world no longer work. Instead, events are governed by probabilities. A radio-active atom, for example, might decay, emitting an electron, say; or it might not. It is possible to set up an experiment in such a way that there is a precise fifty-fifty chance that one of the atoms in a lump of radioactive material will decay in a certain time and that a detector will register the decay if it does happen. Schrodinger, as upset as Einstein about the implications of quantum theory, tried to show the absurdity of those implications by imagining such an experiment set up in a closed room, or box, which also contains a live cat and a phial of poison, so arranged that if the radioactive decay does occur then the poison container is broken and the cat dies. In the everyday world, there is a fifty-fifty chance that the cat will be killed, and without looking in- side the box we can say, quite happily, that the cat inside is either dead or alive. But now we encounter the strangeness of the quantum world. According to the theory, neither of the two possibilities open to the radioactive material, and therefore to the cat, has any reality unless it is observed. The atomic decay has neither happened nor not happened, the cat has neither been killed nor not killed, until we look / Page 3 / inside the box to see what has happened. Theorists who accept the pure version of quantum mechanics say that the cat exists in some indeterminate state, neither dead nor alive, until an observer looks into the box to see how things are getting on. Nothing is real unless it is observed. The idea was anathema to Einstein, among others. "God does not play dice," he said, referring to the theory that the world is governed by the accumulation of outcomes of essentially random "choices" of possibilities at the quan- tum level. As for the unreality of the state of Schrodinger's cat, he dismissed it, assuming that there must be some un- derlying "clockwork" that makes for a genuine fundamen- tal reality of things. He spent many years attempting to devise tests that might reveal this underlying reality at work but died before it became possible actually to' carry out such a test. Perhaps it is as well that he did not live to see the outcome of one line of reasoning that he initiated. In the summer of 1982, at the University of Paris- South, in France, a team headed by Alain Aspect completed a series of experiments designed to detect the underlying reality below the unreal world of the quantum. The under- lying reality-the fundamental clockwork-had been given the name "hidden variables," and the experiment con- cerned the behavior of two photons or particles of light fly- ing off in opposite directions from a source. It is described fully in Chapter Ten, but in essence it can be thought of as a test of reality. The two photons from the same source can be observed by two detectors, which measure a property called polarization. According to quantum theory, this prop- erty does not exist until it is measured. According to the hidden-variable idea, each photon has a "real" polarization from the moment it is created. Because the two photons are emitted together, their polarizations are correlated with one another. But the nature of the correlation that is actually measured is different according to the two views of reality. The results of this crucial experiment are unam- biguous. The kind of correlation predicted by hidden- variable theory is not found; the kind of correlation pre- dicted by quantum mechanics is found, and what is more, again as predicted by quantum theory, the measurement / Page 4 / that is made on one photon has an instantaneous effect on the nature of the other photon. Some interaction links the two inextricably, even though they are flying apart at the speed of light, and relativity theory tells us that no signal can travel faster than light. The experiments prove that there is no underlying reality to the world. "Reality," in the everyday sense, is not a good way to think about the be-havior of the fundamental particles that make up the uni- verse; yet at the same time those particles seem to be inseparably connected into some indivisible whole, each aware of what happens to the others.
The search for Schrodinger's cat was the search for quantum reality. From this brief outline, it may seem that the search has proved fruitless, since there is no reality in the everyday sense of the word. But this is not quite the end of the story, and the search for Schrodinger's cat may lead us to a new understanding of reality that transcends, and yet includes, the conventional interpretation of quantum mechanics. The trail is a long one, however, and it begins with a scientist who would probably have been even more horrified than Einstein if he could have seen the answers we now have to the questions he puzzled over. Isaac New- ton, studying the nature of light three centuries ago, could have had no conception that he was already on the trail - leading to Schrodinger's cat."
SUPERNATURE Lyall Watson 1974 Edition Page 97 "Sound, of course, is a vibration that can be conducted only through an elastic medium; it cannot travel through a vac-uum. Electromagnetic waves do travel through free space, and we know far less about factors governing their resonance. There is however, one quite extraordinary piece of evidence which suggests that shape could be important in receiving even cosmic stimuli. It comes from those favourites of mystics throughout the ages-the pyramids of Egypt. 'The most celebrated are those at Giza built during the fourth. dynasty of which the largest is the one that housed the pharaoh Khufu, better known as Cheops. This is now called the Great Pyramid Some years ago it was visited by a French-man named Bovis, who took refuge from the midday sun in the pharaoh's chamber, which is situated at the center of the pyramid, exactly one third of the way up from the base He found it unusually humid there,but what really surprised / Page 98 9 x 8 = 72 7 + 2 = 9 / him were the garbage cans that contained, among the usual tourist litter,the bodies of a dead cat and some small desert animals that had wandered into the pyramid. Page 98 9 x 8 = 72 "Bovis made an accurate scale model of the Cheops pyramid and placed it like the original with the base lines,facing precisely north-south east-west. Inside the model one third of the way up, he put a dead cat. It became mummified and he concluded that the pyramid promoted rapid dehy-dration."
ALICE'S ADVENTURES IN WONDERLAND Lewis Carroll "A boat, beneath a sunny sky, Lingering onward dreamily In an evening of july- Children three that nestle near, Eager eye and willing ear, Pleased a simple tale to hear- Long has paled that sunny sky: Echoes fade and memories fade: Autumn frosts have slain july. Still she haunts me, phantomwise, Alice moving under skies Never seen by waking eyes. Children yet, the tale to hear, Eager eye and willing ear, Lovingly shall nestle near. In a Wonderland they lie, Dreaming as the days go by, Dreaming as the summers die: Ever drifting down the stream- Lingering in the golden gleam- Life, what is it but a dream?
THE EXPANDING UNIVERSE Arthur Eddington 1932 THE UNIVERSE AND THE ATOM Page 99 "For whatever embodies this comparison unit is ipso facto the space of physics. Physical space therefore cannot be featureless. As a matter of geo-metrical terminology features of space are described as curvatures (including hypercurvatures); as already ex- plained, no metaphysical implication of actual bending in new dimensions is intended. We have therefore no option but to look for the natural standard of length among the radii of curvature or hypercurvature of space-time.To the pure geometer the radius of curvature is an incidental characteristic-like the grin of the Cheshire cat. To the physicist it is an indispensable 'charac- teristic. It would be going too far to say that to the physicist the cat is merely incidental to the grin. Physics is concerned with interrelatedness such as the interrelatedness of cats and grins. In this case the "cat without a grin" and the "grin without a cat are equally set aside as purely mathematical phantasies.
ALICES ADVENTURES IN WONDERLAND Lewis Carroll "I think.' And she began thinking over other children she knew, who might do very well as pigs, and was just saying to herself, 'if one only knew the right way to change them-' when she was a litde startled by seeing the Cheshire Cat sitting on a bough of a tree a few yards off. The Cat only grinned when it saw Alice. It looked good- natured, she thought: still it had very long claws and a great many teeth, so she felt that it ought to be treated with respect. 'Cheshire Puss,' she began, rather timidly, as she did not at all know whether it would like the name: however, it only grinned a little wider. Come, it's pleased so far,' thought Alice,and she went on. 'Would you tell me, please, which way I ought to go from here?' 'That depends a good deal on where you want to get to,' said the Cat. 'I don't much care where-' said Alice. 'Then it doesn't matter which way you go,' said the Cat. '-so long as I get somewhere,' Alice added as an explanation. 'Oh, you're sure to do that;' said the Cat, 'if you only walk long enough.' Alice felt that this could not be denied, so she tried another question. 'What sort of people live about here?' 'In that direction,' the Cat said, waving its right paw round, 'lives a Hatter: and in that direction,' waving the other paw, 'lives a March Hare. Visit either you like: they're both mad.' 'But I don't want to go among mad people,' Alice remarked. 'Oh, you ca'n't help that,' said the Cat: 'we're all mad here. I'm mad. You're mad.' 'How do you know I'm mad?' said Alice. 'You must be,' said the Cat; 'or you wouldn't have come here.' .Alice didn't think that proved it at all: however, she went on, , And how do you know that you're mad?' 'To begin with,' said the Cat, 'a dog's not mad. You grant that?' 'I suppose so,' said Alice. Well, then,' the Cat went on, 'you see a dog growls when it's angry, and :wags its tail when it's pleased. Now I growl when I'm pleased, and wag my tail when I'm angry therefore I'm mad.'I call it purring, not growling, said Alice. Call it what you like,' said the Cat. 'Do you play croquet with the Queen to-day?' Ishould like it very much,' said Alice, 'but I haven't been invited yet.' You'll see me there,' said the Cat, and vanished. .. Alice was not much surprised at this, she was getting so used i to queer things happening. While she was looking at the place~ where it had been, it suddenly appeared again. . 'By-the-bye, what became of the baby?' said the Cat. ' I'd nearly forgotten to ask.' 'I t turned into a pig,' Alice quietly said, just as if it had come back in a natural way. 'I thought it would,' said the Cat, and vanished again. Alice waited a little, half expecting to see it again, but it did not appear, and after a minute or two she walked on in the direction in which the March Hare was said to live. 'I've seen hatters before,' she said to herself; 'the March Hare will be much the most interesting, and perhaps, as this is May, it won't be raving mad-at least not so mad as it was in March.' As she said this, she looked up, and there was the Cat again, sitting on a branch of a tree. 'Did you say pig, or fig?' said the Cat. 'I said pig,' replied Alice; 'and I wish you wouldn't keep appearing and vanishing so suddenly: you make one quite giddy.' 'All right,' said the Cat; and this time it vanished quite slowly, beginning with the end of the tail, and ending with the grin, which remained some time after the rest of it had gone. Page 64 'Well! I've often seen a cat without a grin,' thought Alice; 'but a grin without a cat! It's the most curious thing I ever saw in all my life!' she had not gone much farther before she came in sight of the house of the March Hare: she thought it must be the right house, because the chimneys were shaped like ears and the roof was thatched with fur. It was so large a house, that she did not like to go nearer till she had nibbled some more of the left-hand bit of mushroom, and raised herself to about two feet high: even then she walked up towards it rather timidly, saying to herself' Suppose it should be raving mad after all! I almost wish I'd gone to see the Hatter instead!'..." THE COSMIC CODE QUANTUM PHYSICS AS THE LANGUAGE OF NATURE Heinz Pagels 1982 THE ROAD TO QUANTUM REALITY Page160 "You ruled out real nonlocal influences because each " record was truly 'random.' " Ask the mathematicians," came the reply. "They don't know what randomness is," says the heckler. "Neither do I," says the local reality salesman. "But true randomness is unbeatable, which in this case means it will always defeat you if you try to detect real nonlocal influences. 'There's no randomness like quantum randomness." The crowd begins to drift out of the Objective Reality Shop toward the Local Reality Shop, led by the salesman, who is feeling rather good after his speech. Someone is asking why he is so critical of the occultists and pseudoscientists, and he begins a little story. "When I was ten I became fascinated with magic. I learned simple card tricks, built apparatus, and bought magic tricks from mail-order catalogues. The opportunity to perform magic came at friends' birthday parties or holiday occasions, and it was a polished magic show. As a magician and enter- tainer I responded to the interests of the audience. What struck me was the difference in the response to magic tricks by children and adults. The adults accepted the tricks as entertainment; they wanted to be fooled. Not the children. Their capacity for the suspension of belief was not developed- they wanted to know how the tricks were done. For them it wasn't entertainment; it was a violation of their trust in physi-cal reality. "A real magician makes no claim to violate physical laws; he only appears to do so. However, when pseudoscientists make claims to discover dramatic new phenomena, going beyond current physical theory, like telepathy or mental metal bending, then, like children, we must insist on seeing how the trick is done or as adults sit back and enjoy the entertainment. " As we enter the Local Reality Shop we see it is already quite crowded with lots of physicists and others who swear by the Copenhagen interpretation of quantum theory only be- cause their heroes, Bohr and Heisenberg, invented it. The salesman who broke up the discussion in the other shop and led us here clearly is the merchant of this one. As the crowd thickens he begins his sales pitch. "The basis of physics," he begins, "indeed the whole of science, is predicated on the principle of local causality-that / Page 161 / material events occurring in a region of space are due to adjacent material events. How can we have a science if an event on the other side of the universe is instantaneously influencing events here now? Quantum theory obeys the prin-ciple of local causality, If we accept this principle, then we have to take a hard look at what is meant by objectivity-the assumption that the microworld has a definite state of exis- tence like the macroworld. Scientists are accustomed to think- ing in terms of what we actually know to be true about the world, not what we fantasize, and the microworld is a fantasy if 'we are not actually observing it. Until measurements are actually performed you cannot even talk about the objective properties of things. Physicists all accept that, and I urge you to accept it also." "But doesn't this imply reality is observer-determined?" someone in the audience questions. "What kind of reality is that?" "True enough," says the merchant, "but we only have to worry about the observer-determined reality for quantum- sized objects. Of course, quantum-level events influence the macroscopic world-that was the point of Schrodinger's cat- and therefore it seems that the quantum weirdness leaks out into the world of ordinary objects. But that is pushing the Copenhagen interpretation too far, because there is a qualita- tive difference between the microworld and macroworld-the macroworld can store information while the microworld can- not. We concluded our discussion of Schrodinger's cat with the realization that the observer-determined reality is only for atomic-sized objects. The reality of these is a distribution of events. By the act of observing we change one random distribution to another random distribution. You can hardly call that an observer-determined reality. It was like those nonlocal influence advocates who turned out to be saying no more than that one random sequence shifted to another." One distinguished scientist in our group politely asks the salesman how he can be absolutely certain an observation has been made if observation depends on temporally irrevers- ible processes which are themselves only statistical-highly irreversible but not absolutely so. Before the salesman can answer, someone shouts a question at him. "But suppose there is only one event and not a se-quence?" asks the heckler, who has followed the crowd here. Page 163 Suppose there is only one event, not a distribution of events, and that event determines whether the human species lives or dies, not just a cat." "Single quantum events have no significance in quantum theory. They occur at random," says the salesman. "What is randomness ?" asks the heckler. We have heard this before. Our heads are spinning anyway, and the air in the room is very hot. We go out of the shop just as another argument bursts into a shouting match. It is something about consciousness being implied by the Copenhagen interpreta- tion. We never do hear the end of it but are grateful to be outside where the air is fresh. Time for a walk to think things over and clear our heads. Not far from the reality marketplace we find a cool park, and there, on the bench smoking a pipe, sits an old man whose presence projects both warmth and confidence. "Have you bought a reality yet?" we ask. "No, not yet, and I'm doubtful I will," he replies in a thick Danish accent. "I have thought about the problem for a long time and have come to some conclusions in discussions with Einstein." "Where is Einstein now? What reality did he purchase?" we ask our informant. "Einstein left the reality marketplace a long time ago, leaving his cash to me. He would have none of it and took to wandering farther down the road, like the wanderer he was in his youth. I have no idea what he found there, if anything. As for myself, I have come to terms with quantum reality.
Page 162 (Continues) "There is no quantum world like the ordinary world of familiar objects like tables and chairs, and we should stop looking for it. The entities of the microworld like electrons, protons, and photons certainly exist, but some of their ...properties--basic properties such as their location in space - exist only on a contingency basis. Previous to the invention of the quantum theory, physicists could think of the world in terms of its objects independent of how they knew that world existed. Quantum reality also has things - the quanta -like electrons and photons - but given along with that world is a structure of information which is ultimately reflected in how we speak about quantum reality. Quantum measurement theory is an information theory. The quantum world has disap-peared into what we can know about it, and what we can / Page163 / know about it must come from actual experimental arrange-ments-there is no other way. "What I am certain of is that quantum reality is not classical reality-there is no way you can fit it into classical reality. Quantum theory does not predict individual events and classical theory would; the two theories are logically distinct. But even in our attempt to characterize what quan- tum reality is not, we appeal to classical concepts such as objectivity and local causality. We have no choice in doing this, because we are macroscopic beings and live in a classi-cal, visualizable world to which those concepts apply. "We can imagine that .quantum reality is like a sealed box out of which we receive messages. We can ask questions about the contents of the box but never actually see what is inside of it. We have found a theory-the quantum theory- of the messages, and it is consistent. But there is no way to visualize the contents of the box. The best attitude one can take is to become a 'fair witness'-just describe what is actu-ally observed without projecting fantasies on it. This is a minimalist approach to reality and the one I advocate. "Those people in the reality marketplace have forgotten something I told .them long ago, or perhaps they never heard it properly-the principle of complementarity. This principle asserts that in describing reality we must invoke complementary concepts that exclude each other-they can- not both be true. But not only do they exclude each other conceptually, they depend on each other for their very defini- tion. For example, male and female can be understood as complementary concepts. If you imagine that there is a choice of sex as you are born, then you may pick either female or male. But if the world had only one sex, then there is no concept of sex-the very concepts of male and female define each other as well as exclude each other. Such complemen- tary concepts are different representations of the same single reality-in this example that is the reality of humanity. "My favorite illustration of complementarity is the pic- ture of a vase made of two profiles used by the gestalt psychologists. Is it a vase or two profiles? You can see it as either, depending on which image is figure and which is background. But you cannot see it as both simultaneously. It is a perfect example of observer-created reality-you decide the reality you are going to see. And yet the definitions of / Page 164 / what is the vase and what is the profile depend on each other-you cannot have one without the other. They are - different representations of the same underlying reality-here simply a piece of black and white paper. Now you know why I stopped going to the reality marketplace. Those two shops for objective and local reality are 'actually run by two brothers, and other members of the family run the other shops. If you think carefully about the objectivity and locality of the microworld, they turn out to be complementary concepts in the quantum theory-just like the vase and profiles. That is the beautiful feature brought out by Bell's experiment. If you fantasize that the photons exist in a definite state as the flying nails exist in a definite state, then you see that reality must be nonlocal. But the moment you actually try to verify the actual state of a flying photon-which is the same as trying to verify real acausal nonlocal influences-you must upset the first condition of the experiment, which is that the two photon polarizations are correlated precisely. Conversely, if you accept strict local causality then there is no option but to give up the idea of objectivity for individual photons. That is how the principle of complementarity applies to Bell's experiment. "From the macroscopic view all we have are the records at A and B, and these are certainly objective in the usual sense. Like the live or dead cat they cannot be erased. But the information on these records can never be used to infer real nonlocal or acausal influences. I know there are people who claim the quantum theory requires we give up objectiv-ity or locality for the macroworld of tables and chairs. But they haven't understood that the macroworld and microworld are qualitatively distinct. There is no macroscopic quantum weirdness. "Arguing whether the microworld is local or objective is like arguing over whether the picture represents a vase or profiles. They are two mutually exclusive ways of speaking about the same reality. You must pick one if you are going to describe quantum reality. But within the framework of material possibilities your reality is a matter of choice. Once your mind accepts this, the world will never be the same again. The material world actually imposed this way of thinking on us. I cannot stop wondering about that. The real mystery of the physical world is why there is no mystery-nothing seems / Page 165 / to be ultimately hidden. That we may not always know reality is not because it is so far from us but because we are so close to it." We feel excited by his remarks, though the old uneasiness has not left us. Yet listening to him is certainly better than that marketplace. After a long silence our old friend gives us his final words. "What quantum reality is, is the reality marketplace. The house of a God that plays dice has many rooms. We can live in only one room at a time, but it is the whole house that is reality." He gets up and leaves us. Only the smoke from his pipe remains, and then, like the smile of the Cheshire cat, that too disappears. ? WAS IT A NUMBER 9 BUS WAS IT A NUMBER 9 TRAM WAS IT EITHER OR NEITHER NEITHER OR EITHER OR WAS IT THE 9 IN THE 9 OF THE 9 THAT I AM
CATCHING THE LIGHT THE ENTWINED HISTORY OF LIGHT AND MIND Arthur Zajonc 1993 Opposite page viii I'll tell you how the sun rose a ribbon at a time. Emily Dickinson I am the one who openeth his eyes, and there is light; When his eyes close, darkness falleth. the Egyptian god Ra, 1300 B.C.
If the light rises in the Sky of the heart. . . and, in the utterly pure inner man attains the brightness of the sun or of many suns. . . then his heart is nothing but light, his subtle body is light, his material covering is light, his hearing, his sight, his hand, his exterior, his interior, are nothing but light. Najm Razi, 1256
All the fifty years of conscious brooding have brought me no closer to the answer to the question, "What are light quanta?" Of course today every rascal thinks he knows the answer, but he is deluding himself. Albert Einstein, 1951"
Martin Amis Page 9 "thirty three" ninth line up Page 33 "(at least three times)" "...Andromeda always thought: life! Here is life..." Page 54 "...pure momentum and mass, forever subject to their laws...."
CATCHING THE LIGHT THE ENTWINED HISTORY OF LIGHT AND MIND Arthur Zajonc 1993 THE GIFT OF LIGHT
Page 21 "... Earth that makes night by coming in the way of the [sun's] rays,"16 an astute observation for the time. He seems, however, to have considered sunlight as only part of the whole process, and recognized that something more was required for vision, some- thing essential provided by man: the light of the body. Plato, like Empedocles, was permitted to study the secret doc- trines of Pythagoras, at least until he (again like Empedocles) betrayed Pythagoras' teachings to the uninitiated through his writings. Plato's account of vision is, not surprisingly, similar to, if fuller than, that of Empedocles. When blended together with the later geometrical tradition of sight begun by Euclid and the medical tradition codified by Galen, Plato's treatment would persist for almost 1,500 years! In this tradition, the light of the eye played fully as important a role as the light of the sun. According to Plato, the fire of the eye causes a gentle light to issue from it. This interior light coalesces with the daylight, like to like, forming thereby a single homogeneous body of light. That body, a marriage of inner light and outer, forges a link between the objects of the world and the soul. It becomes the bridge along which the subtle motions of an exterior object may pass, causing the sensation of sight.17 In this view, two lights-an inner and outer-come together and act as the mediator between man and a dark, cavernous external world. Once the link of light is formed, the message may pass, like Iris, Homer's messenger goddess, from one world to the other. The eye and the sun display to Plato a deep har- mony, one still appreciated by the German poet Goethe when, in the introduction to his own Theory of Color (1810), he penned the poem: Page 22 How could we behold the light? if God's might and ours were not as one, How could His work enchant our sight?18 Once again, the mind's eye is not passive, but plays its own significant part in the activity of seeing. The image of an interior ocular fire captured vividly the ancient sense of that action, so convincingly that it dominated philosophy for 1,500 years. We come to know the world, in large part, through sight. Quite naturally, Plato used sight as a metaphor for all knowing, calling the psyche's own organ of perception the "eye of the soul or minds eye.19 our word theory has Its origin in the Greek word theoria, meaning "to behold." To know is to have seen, not passively but actively, through the action of the eye's fire, which reaches out to grasp, and so to apprehend the world. Our activity, present in seeing and knowing, is an element integral to the Platonic understandin,g of vision. Sight entails the seer in an essential, formative action of image making or imagination. To such as Moreau's child or to S.B., the effort of that constructive act was a constant and exhausting reminder of their past blindness. To us who see, the world is instantly and effortlessly intelligible; at least most of the time. Consider the figure on page 23.(Figure omitted) It is but one of many similarly "ambiguous figures." Allow yourself time to play with it. At first only one figure shows itself, an old woman or a young girl. Without an iota's change on the "objective" printed page, the delicate chin of the young girl becomes the lumped nose of an old hag. Feel the shift from one picture to the other. It takes place entirely within you. With a little practice you can even control what you see. The physical difference between one image and the other is nil, while the "soul distance" between them is huge. What has changed? Your own activity; the character of your participation / Page 23 / can shape and reshape itself, and you can feel it. With every act of perception, we participate unawares in making a mean- ingful world. In response to outer light, an interior light flashes, bringing intelligence with it. It is the light that did not brighten the newly opened eye of Moreau's child when turned to see its first light. Times of Transition In the Bhagavad-Gita, in Homer, Empedocles, and Plato, vision entails an essential human activity of movement out from the eye into the world. In the centuries following Plato, a shift gradually took place that only reached its conclusion with Rene Descartes in the seventeenth century. The concerns of science changed during this long period. The influence of Plato and then of Aristotle lingered long into the medieval period. As long as this was the case, sight was as much or more a soul-spiritual / Page 24 / process as a physical one. By the sixteenth century, however, a profound shift seems nearly mature. Natural philosophers such as Kepler and, to a much greater extent, Galileo are less con-cerned with the soul's translation of external stimulation into meaningful perception, and more preoccupied with the physics of the eye viewed as an inanimate, physical instrument. The change is not universal, swift, or uniform, but a watershed is crossed nonetheless, first by those few scientists in the oft-dangerous vanguard of research. In their hands, sight becomes a question of mechanics rather than a species of soul-spiritual activity so characteristic of many earlier thinkers. The shift is characteristic and of central importance. We meet it first in the evolution of man's experience of seeing. We will discover it again when we study light itself. What begins as a lively, soul-spiritual experience, be it of light or sight, attenuates, clarifies, and divides into optics and psychology. More than an interesting historical observation, our changing view of light is symbolic of a major change in consciousness, an im-portant threshold crossed in the history of the mind. Like the ambiguous figure, nature presents herself in indef-inite guises. How we see her depends as much on us as on her. Only together do meaningful worldly images arise. The wa- tershed crossed, therefore, is not the divide between ignorance and wisdom, but more like the ambiguous shift from young girl to old woman. Therefore as we read the history of science, we must be ever conscious of the individuals who enacted it. Their eyes saw, their hearts yearned for knowledge, and out of their being ways of seeing the world were born, flourished, and died. One way of seeing became for a time the way of many, until a fresher, more congenial view appeared."
Page 24 (Continues) "The delicate beginnings of the transition to a mechanical conception of seeing were evident by 300 B.C.. in the optical studies attributed to the great Alexandrian mathematician Euclid. In his book Optics he provided a brilliant geometrical / Page 25 / treatment of sight. Euclid continued to believe that a visual ray was primary to the whole process of vision, and advanced several very sensible arguments in favor of the position. For example, we often do not see things even when looking at them. Drop a needle on the ground, Euclid suggests, and then wonder as you search for it why you don't see it immediately. Your field of view certainly encompasses the needle. In modem terms, the needle is certainly imaged on the retina, but remains unseen. Then suddenly, in a flash, you see it. If sight depends only on light from outside falling on objects, and then traveling into the eye, one would see it immediately. Obviously light was being reflected from the needle and into the eye throughout the search, so, reasoned Euclid, sight cannot in the first place depend on external light. The puzzle is solved, however, if we adopt the doctrine of the visual ray. In searching for the needle, the eye's own visual ray reaches out and passes back and forth across the ground. Only when it strikes the needle do we see it! The visual ray of Euclid is different in important ways, however, from the luminous and ethereal emanation of Plato and Empedocles. In Euclid's hands, the eye's fiery emanation has become a straight line, a visual ray, susceptible to deductive logic and geometric proof. His extensive mathematical studies yielded many fruits and became the basis for later Arab inves-tigations and for laying the foundation for the discovery of linear perspective by Brunelleschi, Alberti, and Durer centuries later. But mathematization came at a price. It distanced man from the earlier and more immediate experience reflected in the Platonic understanding of vision. The significance of mathematization should not be underes- timated. Without abstraction, science as we know it cannot exist. Yet in order to analyze one must stop experiencing and go on to represent the object of study with thoughts of crystalline clarity, for example, with mathematical concepts. Euclid did / Page 26 / just this. Plato's somewhat elusive, immaterial bridge of light between object and eye, became through Euclid a geometry of visual rays, cones, and angular measurement. Everything needed for the study of geometrical optics was developed, but in the process one can detect an important distancing from the subjective human experience of seeing. Euclid's meticulous mathematical style of argumentation has replaced the more po- etic treatment of Empedocles or Plato. As every physicist knows, the elegant forms of mathematics can easily outshine the dull stirrings of experience, and eventually come to replace the phe- nomena they originally were invented to describe. Euclid's handling of light foreshadows the growing separation of sight as lived experience from sight as a formal object of investigation. The history of light has turned a corner, and with it the mystery of sight entered a new phase, one that blossomed first in Arab lands, to culminate finally in the work of another great geometer and mathematician, Rene Descartes." �
THE MAGIC MOUNTAIN Thomas Mann 1924 The Thunderbolt Page 706 SEVEN years Hans Castorp remained amongst those up here. Partisans of the decimal system might prefer a round number, though seven is a good handy figure in its way, picturesque, with a savour of the mythical; one might even say that it is more filling to the spirit than a dull academic half-dozen. Our hero had sat at all seven of the tables in the dining-room, at each about a year, the last being the bad " Russian table, and his company there two Armenians, two Finns, a Bokharian, and a Kurd. He sat at the "bad" Russian table, wearing a recent little blond beard, vaguish in cut, which we are disposed to regard as a sign of philosophic indiffer-ence to his own outer man. Yes, we will even go further, and relate his carelessness of his person to the carelessness of the rest of the world regarding him. The authorities had ceased to devise him distractions. There was the morning inquiry, as to whether he had slept well, itself purely rhetorical and summary; and that aside, the Hofrat did not address him with any particularity; while Adriatica von Mylendonk - she had, at the time of which we write, a stye in a perfect state of maturity - did so seldom, in fact scarcely ever. They let him be. He was like the scholar in the " peculiarly happy state of never being "asked" any more; of never having a task, of being left to sit, since the fact of his being left behind is established, and no one troubles about him further - an orgiastic kind of freedom, but we ask ourselves whether, in-deed, freedom ever is or can be of any other kind. At all events, here was one on whom the authorities 'no longer needed to keep ".an eye, being assured that no wild or defiant resolves were ripen-ing in his breast. He was " settled," established. Long ago he had ceased to know where else he should go, long ago he had ceased to be capable of a resolve to return to the flat-land. Did not the very fact that he was sitting at the "bad " Russian table wimess a certain abandon? No slightest adverse comment upon the said table being intended by the remark! Among all the seven, no single one could be said to possess definite tangible advantages or / Page 707 / disadvantages. We make bold to say that here was a democracy of tables, all honourable alike. The same tremendous meals were served here as at the others; Rhadamanthus himself occasionally folded his huge hands before the doctor's place at the head; and the nations who ate there were respectable members of the human race, even though they boasted no Latin, and were not exag-geratedly dainty at their feeding. Time - yet not the time told by the station clock, moving with a jerk five minutes at once, but rather the time of a tiny timepiece, the hand of which one cannot see move, or the time the grass keeps when it grows, so unobservably one would say it does not grow at all, until some morning the fact is undeni-able - time, a line composed of a succession of dimensionless points (and now we are sure the unhappy deceased Naphta would interrupt us to ask how dimensionless points, no matter how many of them, can constitute a line), time, we say, had gone on, in its furtive, unobservable, competent way, bringing about changes. For example, the boy Teddy was discovered, one day- not one single day, of course, but only rather indefinitely from which day - to be a boy no longer. No more might ladies take him on their laps, when, on occasion, he left his bed, changed his pyjamas for his knickerbockers, and came downstairs. Im-perceptibly that leaf had turned. Now, on such occasions, he took them- on his instead, and both sides were as well, or even better pleased. He was become a youth; scarcely could we say he had bloomed into a youth; but he had shot up. Hans Castorp had not noticed it happening, and then, suddenly, he did. The shooting-up, however, did not suit the lad Teddy; the temporal became him not. In his twenty-first year he departed this life; dying of the disease for which he had proved receptive; and they cleansed and fumigated after him. The fact makes little claim upon our emotions, the change being so slight between his one state and his next. But there were other deaths, and more important; deaths down in the flat-land, which touched, or would once have touched, our hero more nearly. We are thinking of the recent decease of old Consul Tienappel, Hans's great-uncle and foster-father, of faded memory. He had carefully avoided unfavourable conditions of atmospheric pressure, and left it to Uncle James to stultify him- self; yet an apoplexy carried him off after all; and a telegram, couched in brief but feeling terms - feeling more for the departed than for the recipient of the wire - was one day brought to Hans Castorp where he lay in his excellent chair. He acquired / Page 708 / some black-bordered note-paper, and wrote to his uncle-cousins: he, the doubly, now, so to say, triply orphaned, expressed him-self as being the more distressed over the sad news, for that cir- cumstances forbade him interrupting his present sojourn even to pay his great-uncle the last respects. To speak of sorrow would be disingenuous. Yet in these days Hans Castorp's eyes did wear an expression more musing than common. This death, which could at no time have moved him greatly, and after the lapse of years could scarcely move him at all, meant the sundering of yet another bond with the life below; gave to what he rightly called his freedom the final seal. In the time of which we speak, all contact between him and the flatland had ceased. He sent no letters thither, and received none thence. He no longer ordered Maria Mancini, having found a brand up here to his liking, to which he was now as faithful as once to his old-time charmer: a brand that must have carried even a polar explorer through the sorest and severest trials; armed with which, and no other solace, Hans Castorp could lie and bear it out indefinitely, as one does at the sea-shore. It was an especially well cured brand, with the best leaf wrapper, named "Light of Asia "; rather more compact than Maria, mouse-grey in colour with a blue band, very tractable and mild, and evenly consuming to a snow-white ash, that held its shape and still showed traces of the veining on the wrapper; so evenly and regularly that it might have served the smoker for an hour-glass, and did so, at need, for he no longer carried a timepiece. His watch had fallen from his night-table; it did not go, and he had neglected to have it regulated, perhaps on the same grounds as had made him long since give up using a calendar, whether to keep track of the day, or to look out an approaching feast: the grounds, namely, of his "freedom." Thus be did honour to his abiding-everlasting, his walk by the ocean of time, the hermetic enchantment to which he had proved so extraordinarily susceptible that it had become the fundamental adventure of his life, in which all the alchemisti-cal processes of his simple substance had found full play. Thus he lay; and thus, in high summer, the year was once more rounding out, the seventh year, though he knew it not, of his sojourn up here."
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THE FINDING OF THE THIRD EYE Vera Stanley Alder 1968 THB SCIENCE OF NUMBERS Page115 The number Nine represents the perfect and completed man, who having fully developed himself, must now forget himself in Sacrifice and Service. Here we have the great lover, humani- tarian and artist. Through this number beats the most high powered of human vibrations, which has great force to be used for either good or evil. To write all that is known about numbers would fill volumes. We have not space to do more than take this glance at the primary numbers. They, of course, each belong to their Colour, Planet and Sound. When, after some study, it is seen how com-pletely all these facets of life dove-tail and fit into their places like an intricate vast Chinese puzzle it will be realized that these marvellous 'theories' are too perfect and too near to the truth to have been invented by the brains of human beings. This indeed is the reward of a study of these matters-a gradual realization of the amazing fact that there really is a whole universe of marvels and of sublime promise for those who seek. The science of numbers is exhaustive, instructive, and useful if applied with an honest desire for progress and understanding. Modem scientists are busily expressing the ancient beliefs in their own manner. They are measuring the vibrations of diseases, of thoughts, of will-power and of many other activities and getting them all numbered. They are numerologists in their own way, although they still turn their backs rigidily upon the ancient sciences. Nevertheless, they are bringing to light one funda-mental fact, and that is that everything exists through the forma- tion of a different number, and therefore that numbers must constitute a language, a key, and a clue to many secrets in life, if we can learn to decipher them. There are various systems of numerology. The sifting of the true from the false will do much to develop the student's own powers of deciphering numbers.
THE MAGICALALPHABET
BLESSED ART THOU THOU ART BLESSED
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