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THE KORAN Everyman Translated from the Arabic by J. M. Rodwell 1909 INTRODUCTION Page xxiii "In addition Sura 18 includes two stories from the Christian periphery to the north of Arabia; the so-called legend of the Seven Sleepers" NOTES Page 460 2 The valley, or mountain, in which the Cave
of the Seven Sleepers was situated. See Gibbon's Decline and Fall,
ch. xxxiii., especially the concluding sentences.
Page 189 (omitted) SURA 18 - THE CAVE
SAY: God best knoweth how long they
tarried: With Him are Page 192
And I do not think that "the Hour"
will come: and even if I be taken back to my Lord, I shall surely find
a better than it in exchange.' Page194 And those cities did we destroy when they
became impious; and of their coming destruction we gave them warning. Page 195 Moses said, 'If after this I ask thee aught, then let me
be thy comrade no longer; but now hast thou my excuse.' We stablished his power upon the earth, and made for him
a way to everything. And a route he followed, Page196 Thus it was. And we had full knowledge
of the forces that were with him. Page 197 They shall remain therein for ever: they shall wish
for no change from it.
SURA 19 - MARY "Kaf. Ha. Ya. Ain. Sad! A recital of
thy Lord's mercy to his servant Zachariah; Page198
Page 199 It said,15
'Verily, I am the servant of God; He hath given me the Book, and He hath
made me a prophet; Page 200
He said, 'Peace be on thee! I will pray my
Lord for thy forgiveness, for he is gracious to me: Page 201 We21 come
not down from Heaven but by thy Lord's command. His, whatever is
before us and whatever is behind us, and whatever is between the two!
And thy Lord is not forgetful, - Page 202 No! we will certainly write down what he
saith, and will lengthen the length of his chastisement:
SURA 29 Page 472 Notes 3 "The word SAY - the usual address of God or Gabriel to Muhammad - must either be considered as spoken by God to Abraham, in which case we have a curious instance of the manner in which Muhammad identifies himself with Abraham, and makes Abraham speak in words which he constantly elsewhere uses himself; or with Wahl
Page 431 SURA 1 "The word Sura occurs nine times in the Koran" THE WORD SURA OCCUR NINE TIMES IN THE KORAN
Page 424 SURA 98 - CLEAR EVIDENCE "The unbelievers among the people of
the Book, and the Polytheists, did not waver, until the CLEAR EVIDENCE
had come to them; Page 423/4 SURA 99 - THE EARTHQUAKE
On that day shall men come forward in
throngs to behold their works, SURA 100 - THE CHARGERS
Ah! knoweth he not, that when that which
is in the graves shall be laid bare, Verily their Lord shall on that day be informed concerning them?"
9 NUMBER 9 THE SEARCH FOR THE SIGMA CODE Cecil Balmond 1998 Page 214 / 15 NAMING The 99 Names of Allah Allah The Mighty The Independent The Compassionate The Forgivng The Powerful The Merciful The Grateful The Dominant The King/Sovereign The High The Giver The Holy The Great The Retarder The Source of Peace The Preserver The First The Giver of Faith The Protector The Last The Overall Protector The Reckoner The Manifest The Strong The Sublime The Hidden The Almighty The Bountiful The Governor The Majestic The Watcher The High Exalted The Creator The Responsive The Righteous The Maker The Infinite - The Relenting The Fashioner The Wise The Forgiver The Great Forgiver The Loving The Avenger The Dominant The Glorious The Compassionate The Bestower The Resurrector The Ruler of the Kingdom The Provider The Witness The Lord of Majesty and Bounty The Opener The True The Equitable The All-Knowing The Advocate The Gatherer The Restrainer The Most Strong The Self-Sufficient The Extender The Firm The Enricher The Humbler The Patron The Bestower The Exalter The Praiseworthy The Withholder The Empowerer The Numberer The Propitious The Humiliator The Commencer The Distresser The All-Hearing The Restorer The Light The All-Seeing The Giver of Life The Guide The Judge The One Who Gives Death The Eternal The Just The Living One The Everlasting The Kindly One The Self-Subsisting The Heir The Gracious The Perceiver The Guide to the Right Path The Clement The One The Patient
9 NUMBER 9 THE SEARCH FOR THE SIGMA CODE Cecil Balmond 1998 Page 221 Enjil's Mark
Page 222 The Last Movement Page 227 Nine is the centre and binding rim of the prayer wheel of numbers. And the last movement of nine never seems to come, each revelation or discovery simply deepens the mystery. The fascination grows. Like a spiral the shape of nine continues to evade a simple end, winding itself further into enigma and exploration. Enjil said that the Mandala and his quest for nine was but a reflection on life: Who is the man or woman, he asked, who would not like to know the hidden path that holds on to all movement? Was he not right? In the labyrinth of appearances with all its shouting, twists and turns, most of us become lost and bewildered. To find our way we need a code. On the surfaces of bent experience the straightness of our logic is not enough - there are no clues to a deeper understanding, no whispers that we must hear to make our inner world hold strong and have meaning. At the heart of the story of Enjil and the Mandalas is the simple truth, that a secret in itself is beautiful and once that is known, then somehow the fact gains power and multiplies. The world that grows around it is never barren or wasted, for in every part we see the trace of the original idea. The many that is one has always been the greatest treasure to find. In the eternal abstraction of points, number 9, will always find connections. To those who know how to look, the insights will grow. There is no end, as long as there are the numbers." 9 NUMBER 9 THE SEARCH FOR THE SIGMA CODE Cecil Balmond 1998 Page 209
"No doubt for the pure mathematician the algebraic explanations are succinct, simple and elegant; but what is fun is to find a graphical way of explaining these abstractions. To most people mathematics is a taboo area, an area they do not feel comfortable with. That is a pity, because mathematics is beautiful; the delight being in chasing purely mental constructs. The strange power of number nine may be written out in only a few lines of algebra yet there is something more, something much more interesting when a picture emerges from out of the abstraction. Page 210 The sigma circle is such an invention. In one orbit it explains the unique property of nine. And in some ways it is more powerful than the mathematics, because the picture penetrates deeper into the area behind our rational mind. The saying goes that a picture says much more than words; in that sense the sigma circle and the greater inspiration of its Mandalas speaks volumes, sharpening our intuition beyond a number itself into patterns and characters. Whereas mathematics describes, a picture inspires. Equations demand our intellect, but the Mandalas demand curiosity and our poetry. From pure mathematics we can see that nine owes its character to the unique position it has in our decimal system. But number nine has also travelled far beyond these computational confines. From another route, through the mists of time and long before the invention of our decimal system, number nine grew and developed its own archetypes and mystery. Vishnu took three strides to create the universe. Three times three is potency magnified beyond measure. That beginning of the great rebirth of the seasons, the winter solstice, is in the ninth house of the Zodiac; and the infant takes nine months to be born. Unaided by any mathematical proofs number nine grew its own equations in the human imagination. And Allah was honoured and blessed and was called by ninety nine names.
Page 183 The Golden Section The Golden Section is special in classical
art and architecture. It is the particular ratio given by sub-dividing
a line so that the greater part is to the lesser part as the whole is
to the greater part. This was said to be the proportion found most pleasing in the rectangle and was used in the planning of the Parthenon and numerous other architectural works. Page 184 The golden ratio is also found in a triangle when it is isosceles (in which the two opposite sides are equal), but with a particular base angle. The ratio of the long side of the triangle to the shorter base is in the golden ratio when the base angle is 72�. This means the angle at the top vertex is 36�. Each angle of the Golden Triangle sums to nine! The Greeks believed that at the heart of perfect proportion was the golden ratio and is it not pleasing to find number nine buried in the works, to those of us who chase its tail? The unique property of the golden rectangle is that if a square is taken away from it, the remaining part is a rectangle, which has the same proportions to the original rectangle. That means it is golden as well. The process continues, with each removal of a square, leaving another golden rectangle. Smaller and smaller we go and if the points of the construction are joined together in a smooth curve, we enter a spiral, winding down into its vanishing point, the hidden eye. The eye of the spiral is of course the shape of a vanishing 9."
Page 185 Geometry is cornered around 9. The triangle is a line that bends twice to close on itself. enclosing en route a total of 180� in its internal angles. A square is a line that is more formal in its bending around corners, enclosing each time a right angle so that the sum of the internal angles is 4 x 90� = 360�. A circle is a line that bends round continuously, about a centre point, enclosing the angle of 360�. In general, any regular polygon encloses For a pentagon n = 5 Sum of internal angles = 540� For a hexagon n = 6 Sum of internal angles = 720� For an octagon n = 8 Sum of internal angles = 1080� For a decagon n = 10 Sum of internal angles = 1440� etc. In all cases the digits in the sum of internal
angles add up to nine or multiples of nine. In other words for regular
polygons Page 124 For example, the radiating arm of [2] has
the values - reading from the centre outwards - Then it hits the outer boundary of nine and travels along the circle coming back on its complement of nine, number 7. The order is now reversed from the inside to the outside along the radiating arm [7] 7 - 5 3 1 8 6 4 2 And so on, the symmetries and the reflections grow. I lose myself in wonder at the beauty and the intricacy in which the numbers depend on each other, in secret. On the surface one would never imagine this closed circuit of intrigue. In the Mandala of nine, the digits have life-long partnerships, number ONE with EIGHT, TWO with SEVEN, THREE with SIX, FOUR with FIVE. Each pairing has an identical shape - when its multiplication sequence is plotted on the sigma circle, one is the reverse of the other. Like partners in an eternal dance they turn, their bond being the number nine which holds them together and at the same time keeps them apart. Behind the whole revolution is this special mark, the character that keeps secrets and takes on several disguises - now a boundary, now a mirror, now unseen, and then taking complete hold of another's identity. Whichever way we turn in the circles, we find that all paths out of the labyrinth lead to 9. Page 125 It is one grand act of conservation. Each orbit adds up to nine, as does each radiating arm. And in one magnificent homage, all the values of all the circles add up to nine. Everything in this hidden cosmos of numbers comes to the same thing, the uniqueness of 9. Its component parts, the digits one to eight,
hold in tight confidence this secret of the first revolution of the MANDALA. Hidden by all permutations of arithmetic the numbers of the code spin quietly. In the music of the spheres the sigma code comes together; layer upon layer; orbiting in a secret universe. It is a revolution of numbers beyond that which any of the Elders could imagine. Like the planets in the sky, the code revolves in full nine orbits. Enjil said numbers are not fixed, but ultimately rotations. Page 126 The Elders had never seen it coming. The young Master was elated as the crowd cheered, each one of them understanding how simple it was. They saw for the first time the basic nature of the numbers themselves, their shapes, the stars and the triangles, the crossing polygons and the spinning discs. Underneath the clutter of the arithmetic was the simple nine number code, which seemed to rotate all around their heads as the young master drew fantastic circles on the blackboard with radiating arms. But when the boy master had worked out his thesis and drafted those lovely circles of nine, he was not content. He saw the completeness of it but something was not quite right. There was too much balance. It was not satisfying how the nines bordered the figure yet the reflection and the reversals did not catch the spirit of what was in his head. Enjil wanted a deeper clarity - to match the swirling movements he had first seen - so that the diagram would show better what actually was going on, if that was at all possible. Like the Elders and wise Masters who had
come before him, everyone believed in the perfection of the circle. The
world was created round, the sun was / Page 127 / round,
the stars wrapped around the vast bowl of the sky in a great orbit. Mathematicians
knew that numbers had a perfection not corrupted by daily affairs and
that the concept of a number was But to Enjil nine was the number through which everything else flowed. It was also the number that must give reversal and the more he thought of the pattern, of circle upon circle, the more dissatisfied he became. It was too static, too stationary. It did not move. Number nine was full of vigour; it did things to other numbers - it was a catalyst. And yet it had to be stationary to allow other things through it - this was still the problem to solve. But how? In the afternoon before the day of the examination he saw the breeze gust up and whip up trails of dust in the compound. Minor sand storms that eddied and whirled and zigzagged. He saw spirals and the vortices, as the force in the wind moved his mind into action. He felt then that number nine was an even greater concept than he had first imagined; it must be like the secret, unseen force of the wind itself, and this would be the force that moved the other numbers. The pattern he sought then must have only one point of reference- number nine itself! Not a circle of numbers, but a condensation of the nature of that first innermost circle. It summed to nine, it had nine parts, it had three hundred and sixty degrees which in turn compressed to nine as three plus six plus zero." Page 73
Four Precious Mirrors
"The sigma code lays down a trace of how numbers work in secret, we can peer into their basic patterns. But it is only when these patterns are seen as a whole that the beauty of the code is revealed and the astonishing truth of number nine at the heart of our number system."
"(And here we must thank zero for even allowing the sigma code to exist. For without zero the process of reduction would not work. Adding digits to pare down to a single digit is dependent on our unique placement value system of units, tens, hundreds, etc. Zero allows the code to be bound within the range 1-9). Page 40 Then there are the tales of great spirits and strange forms that govern the beginning and endings of things. They are the stories across cultures which invoke nine as a magic ingredient in rites of passage. The Seeds of Nine Yang formed the Heavens and Yin formed the Earth. And Pan Ku, who was in the middle, changed his form nine times a day, sometimes into a God in heaven or into a saint here on earth. A dead person must cross the Chinvat or 'grading' bridge, which is as wide as nine spears laid end to end for the just, and as narrow as the finest edged razor blade for the wicked. (From Persia) The dwelling place of the dead is not
easy to get to; there are steep mountains to climb, terrible deserts to
cross and poison- ous snakes to confront. The wind pierces the body and
the weary soul looks for a final resting place but first must cross Hell's
frightening rivers, all nine of them. Page 41 Homer wrote in the Odyssey: At the age of nine, they were nine orbits wide and nine fathoms tall and they threatened the Immortals by bringing the tumult of war to Olympus. They wanted to pile Mount Ossa onto Olympus and Mount Pelion with the restless leaves onto Mount Ossa in order to mount their assault on Heaven. Haephaestus was a magician, unique in
the world of the Gods, but he was lame and his mother thought him ugly
and dropped him from Olympus. He was brought up for nine years
in an underwater cave by Tethys and Eurynome and he there learned handicrafts
and the art of jewellery and the making of neck laces. It took Vulcan nine days to reach the island of Lemnos when he was banished from Olympus. The voyages of Odysseus lasted for nine years before he arrived home. The duration of the siege of the City of Troy was nine years. The Ark of Delucion was tossed about for nine days when it became stranded on top of Mount Parnassus. When the fallen angels were cast out of heaven for "nine days they fell. " (Milton, Paradise Lost)
THE CONCISE OXFORD DICTIONARY First Edition 1911 Page 48 ar'changel (-kanj - n Angel of highest rank; one of the eighth ORDER of ninefold celestial hierarchy; hence archangelic (Ranj -) a [OE,f. AF archangele f.eccl. Lf. eccl. GK arkhaggelos [as ARCH,-ANGEL]
Page 42 Niobe, the wife of Amphion,
King of Thebes, boasted of the number of children she had.
Latona raging with mad In the old ways of the Norse, Odin was a great traveller; and he wanted to understand everything. But wisdom could not be bought by gold or silver; so he gave his eye to the woman who guarded the fountain of Mimir; so that he could truly see. And Odin discovered the runes, the sacred writing which allowed thought itself to be set down and passed on. To do this he hung from the tree which was battered by the winds for nine long terrible nights, pierced by a spear. Without having eaten or drunk he picked up the runes shouting out he knew how to increase and prosper. He engraved the runes into wood carvings. Heimdallr, the God of the Norse people, could see everything and never closed his eyes. He could hear everythinq, the grass climbing out of the earth and the wool growing on the back of sheep. He guarded the foot of the rainbow which led to the Gods. Heimdallr; the special one, was born of nine mothers.
Page 43 There were nine Muses; they were the children of Zeus and Mnemosyne. They were not only divine singers but they were patrons of all intellectual activities of the times, including the highest, which was everything that freed man and gave access to the eternal truths. These included Eloquence, Persuasion, Wisdom, Knowledge, Mathematics, Astronomy as well as Poetry, Music and Dancing. There were also nine virgin priestesses of the ancient oracle. Dryden wrote in The Flower and The Leaf: The Jews were Joshua, David, and Judas Maccabaeus; The Gentiles were Hector, Alexander, and Julius Caesar; The Christians were Arthur, Charlemagne, and Godfrey of Bouillon. Sometimes the nine worthies were referred to as being three from the Bible, three from the Classics and three from romance. Page 44 But nine covers Hell and the dark side in thrice three-fold ways as well. At last appear To make a charm the witches chant: Page 45 Buddha was the ninth incarnation of Vishnu. Vishnu created the world in three strides. He pushed apart the universe and placed the sky, the heavens and the earth in their rightful place. Three times three, the trinity of trinities, gains select status then as the doubling and resourcing of special power. 3 x 3 = 9 From ancient times number nine was seen
as a full complement; it was the cup of a special promise that brimmed
over. Seraphims Cherubims Thrones Dominions Powers Virtues Principalities Archangels Angels To the Greeks a person was a full chord of eight notes; the ninth was the all embracing sound of the deity."
Page 47 On the Sermon on the Mount there are nine categories called Blessed: Blessed are the poor in
spirit; the patient; Blessed are those who hunger
and thirst for-holiness; Blessed are the peace-makers;
those who suffer persecution in the cause of right; and those who are
reviled and have all manner of evil spoken against them in His name. Jesus was crucified at the Third hour. (Mark 15, 25:39) Page 48 Beyond the stories there are the numbers themselves: the Great Year of Babylon; The Babylonian Great Year is 432 000 years long. Written thousands of years ago, that most sacred Hymn and first recorded poem of existence, the Rg-Veda of the first Hindus, has stanzas 10800 in number. In the Book of Revelation a choir of 144000 angels redeemed the Earth. For the devout Buddhist, Hell can last 576 million years! Valhalla is said to have up to 5 400 gates to Hell. Allah has 99 names. Page 49 432000 - 4+3 +2+0+0+0 = 9 10800 - 1+0+8+0+0 = 9 144000 - 1+4+4+0+0+0 = 9 576 - 5 + 7 + 6 = 18; 1 + 8 = 9 5400 - 5+4+0+0 = 9 99
- 9 + 9 = 18; 1 + 8
= 9 Deep down in the fabric of the numbers that describe and classify these great events is number nine, planted like a hidden seed. Throughout sacred literature this number keeps cropping up as the mark of auspicious events, acting as a trigger point of initiation or departure. Even in the archetypes of our hands,
nine is a catalyst to counting. Each finger can be divided vertically
into 9 points, a series of 3 on each side and one up the
middle. The points on one finger can then be allocated numbers 1-9.
The next finger can be marked from 10-90 another 100-900
and so on, until with one hand, as the early Chinese did, one can count
up to ninety-nine thousand, nine hundred and ninety-nine. Page 6 world 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 differently. 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 visited the mountain villages where the pupils in the schools stared at the pictures before they did any calculations, 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." Page 8 number omitted "NINE FIXED POINTS IN THE WIND" Page 9 number omitted "MOVEMENTS OF NINE" Page 12 Talisman Enjil slept uncomfortably, his mind full of torment in fear of the Examination to come. He was standing in front of the Elders, those of the supreme rank, and he had nothing to say! He had not found a proof or a clever hypothesis to place before them on this auspicious day. And the day could not be put back - it marched right up to him, dragging him out brutally into the open, while the Elders, in their crimson robes, sat at the high table waiting for him. They motioned him to come up. He climbed up the steps and went to the blackboard and picked up the dry chalk in his wet, nervous hands. Villagers crammed the square to see him perform. Word had gone out that the boy with the limp had magic powers; for when he lay dying from smallpox a strange bird had suddenly flown in and settled on his fevered brow, pecking at it. Superstition said it was the devil who seized a person's brain at such times, to give out great powers only to suck it back again at the moment of death, to prevent that tender soul from being re-born. And amazingly, as the bird flew away Enjil recovered and began talking in strange languages and writing down sheets of numbers, confusing everyone with ideas that they had never heard of. Page 14 His thesis was done - he had a proof written out in the higher algebra which his mentor had said would easily give him the title of Master; it was the sort of thing the Elders would like, for it was similar to the studies each of them had done. "It is not about being original, Enjil", his mentor said, "for you must not sit uncomfortably in your superiors' minds. If you present something they do not understand, or agree with as high learning, they will fail you. Conform, and then privately get on with your real discoveries. That is what we all do. " His teacher shrugged at the way life was at the Academy and worry grew on the old man's face at the thought of what his stubborn student might do. But Enjil had listened, he had conformed - his thesis was as fine a piece of complicated mathematics as one could wish for, deliberately put together in an obscure way so that difficulties abounded in every line of the argument. In truth, Enjil had a much simpler proof but it would appear too easy. So he had put it to one side and applied himself to obscurities in the demonstration of his thesis, knowing this approach would be more favoured by the Elders. And the peace of the night said he had nothing to worry about but go back to sleep and wait happily for that day of the Examination. As he lay there looking up at the moon, his mind began to wander over the ideas he really loved to think about, like the expansion of (symbol ommited). Was there a pattern to it? Or how many unlike squares could fit into a rectangle or another square? This was a problem no one at the Academy could solve, though / Page 15 / Enjil had come near. Was every even integer the sum of two prime numbers as ten was the sum of three plus seven? And there was more - the multiplication patterns along diagonals used by the Chinese or the elegant ratios used by the ancient geometers that gave beauty and shape to the spiral and to the growth of the leaves around a stalk or the petals in a flower. As he roamed through the numbers in his
mind a strange thing then happened. A moon beam suddenly reached out to
him and dropped to Earth and turned into a shining woman. "So here
you are!", she said smiling. "I have kept looking out for you.
I find you here of all places, in a musty old Academy or is it a temple?"
She wrinkled up her nose at the small room he slept in. The woman stroked
his leg - "Does your leg hurt? I saw you as a child, limping,
dragging your leg through the She patted him on the head and stroked his hair. Enjil could see the beautiful colours in her eyes. Her energy flowed into him. She took his thoughts away and she spoke to him: Page 16 "There are the cumbersome proofs you follow that only the few will ever understand. Your proofs are carrion for those vultures, the Elders. So why don't you do something else, something amazingly different for your Examination? You are capable of it! Why give the elders what they want, such a narrow outcome from your learning; why not something that everyone can enjoy? Imagine even the villagers following your every sign on the blackboard, understanding it and seeing a simple but great truth unravelling right before their eyes. Something that lies under their noses, wouldn't that be fun? How about drawing the many different shapes of squares it takes to fit in just one square. Ah - I know you were thinking of this already. You see I know your thoughts - so I count them out. And I'll spoil it for you anyway, I'm going to give you the answer; twenty-four! Yes, don't look so amazed, it takes that many different squares to fit into one square. You want to know the size of the square that allows this to happen? Ah, that is harder. That you must work out for yourself" She smiled teasingly and added, "Do you know the answer to the simpler problem; how many different squares does it take to fit in one rectangle? I'll tell you. It's nine! Nine unequal squares go to make up a rectangle." "But why bother about geometry; why
not something simpler than that? What is it that everyone
knows and feels expert about? I'll tell you. It's numbers of course! Imagine
the village folk clapping hands and cheering as they see you, their
/ Page 17 / new master; working with the humble materials
of numbers, the tools they use every day of their lives to count coins
and goats and sacks of grain from the harvest. Let your mind dwell on
this: numbers! Take the most simple ones. Think of their make up. Don't
be afraid of the Elders; they are not bad men, but men with too much oldness
stuffed into their What is the fixed point in the wind?" The woman withdrew along the moonbeam and vanished as if she had never been. Page 18 Enjil sat up. He looked hard at the moon, staring into the white disc of cold light - and the moment of magic vanished. Was it a trick? Was Vivek his arch rival for the title of Master trying to hypnotise him from a distance? If he listened to the woman it would be like suicide. Standing in that great open courtyard and speaking about simple things that did not need proofs would have the Elders laughing at him, baying like jackals at his feeble efforts. Certainly he would be thrown out. This must indeed be a hex put on him by his enemies! But what was the fixed point in the wind? The question intrigued and teased him. How can something be unmoving in the swirling wind; what. was its fix, if indeed there was such a point? For hours he lay awake struggling with these thoughts until his tired brain came to a stop and wanted rest. Finally Enjilfell asleep. The woman in the moon entered his dreams. And he woke up with a new conviction - the doubts and torments of the night well behind him. He whistled and even smiled at Vivek, winking at his arch rival as if to say he had prepared a brilliant proof Enjil laughed to himself when he thought of the title he would introduce to his Elders on the day of the Examination. He would wear the yellow robe of scholarship, go up to the blackboard and announce in his most stern voice the customary words, "My respectful Elders and Seniors. I submit for your Examination and proper adjudication this thesis I have now prepared for the award of the Most Expert Master of Mathematics, the honour I now seek, / Page 19 / and pronounce as the title of my learned subject: 'The Fixed Points in the Wind'." He could see them writhing in agony, splitting their sides with laughter and thirsting for his blood. The images made him break out in a cold sweat. But a small voice spoke inside saying, "Don't be afraid - of course you can do it - after all it is an easy question - so solve it like a child, think like one, just like I said. " To solve the riddle Enjil went to a secluded spot and sat in the shade of a banyon tree and blanked everything he knew out of his mind. The great blackness descended. Nothing moved. Shadows went into deeper shadows, layer into layer. A black disc grew. First as a dot, then a circle, then a rushing blind movement. Then the numbers came out, tumbling one over the other; rolling the patterns over in his head. There were the star patterns, zigzags, squares, cubes, seesaws and the weaving patterns going in and out, all twisting over each other. Mindful of the woman spirit, he looked at the simplest numbers; he followed their trails, the white and black patterns, some, dotted with colour, moving like the wind, changing shape and turning all the time. And there in the simplest patterns were points that did not move or change, no matter what the numbers were. And they were fixed points. When the woman in the moon had talked of the wind Enjil knew she must have spoken of numbers, jumping over each other in gusts of multiplications or blowing steadily in ordered breezes of additions and subtractions. But within these patterns, there was one number and point through which all the others Page 20 / seemed to gather - it indeed must be the fixed point. Could that be the answer to the riddle? Then Enjil opened his eyes and composed his thesis. It was so simple that he laughed out loud. Never mind the Elders - they would have to love it, for he would draw the movements of all numbers in one simple diagram. What was clever about it was the method he had in his mind. He would take the secret code the Elders knew about but had never thought of using to look beyond their rituals of prophecy, for they would take the letters of someone 's name and use such secret numbers to divine the character of that person. But Enjil vowed to go beyond this. That night he wrote out his thesis. When he had finished he went out into the deserted courtyard and held up each page to the moon. "Look", he said to the woman in the moon, "I have finished - the task is done. I pray these are the answers." A shape seemed to move across the face of the yellow disc though he could not be sure. But the woman did not appear. The wind picked up, the night chill made him shiver. Tomorrow was the day, and Vivek would be hoping for his downfall; and his teacher would fret to the last moment as the Elders assembled, sharpening their wits in readiness to humble the nervous candidate. The crowd would gather and settle. Everyone would be waiting, watching. Still Enjil was at peace. His ideas were simple ,innocent; he believed they would shine through no matter what. While Vivek performed great feats / Page 21 / of algebra Enjil would offer to the Elders and the gathered crowd the four precious mirrors of arithmetic. They could all laugh or puzzle at the reflections he would show them, but in time their doubts would vanish or be blown away, just as the gusting wind cleans out the dirt lying on the ground. Suddenly a bright light flared, lighting up the compound for an instant, and then faded. Had the woman come to him and acknowledged his answer? Enjil rolled up the pages of his thesis and held up his hand, just in case, to the night sky in salute and farewell and then went to bed. He slept the peace of the innocent, a fixed point himself in that night of swirling anxieties and jealousies. Tomorrow would be a new beginning. I wear Enjil's Talisman now, whenever I calculate and look into numbers, and remember the mathematician who was a boy. He inspires me to look afresh at things. Enjil went on to be famous. He surprised the Elders with his arguments of the fixed point in numbers; he astonished the crowd. And if not for them cheering as they did at what was being drawn on the board, the Elders would surely have failed him - the old men being insulted that there was no high algebra or long- winded, obscure complications to be resolved. Enjil's workings were just basic arithmetic, they grumbled, which even a nine year old could follow, they whispered to each other. It was laughable; it was ridiculous and all too simple. But the crowd cheered and cried out, "Master, Master," so many times, that the Elders / Page 22 / gave in. On the boy's shoulders they placed the purple sash of Master embroidered with winding circular motifs in gold thread, and then they held up Enjil's hand to the crowd who in turn roared, "Mas-Ter, Mas-Ter". The four syllable chant rocked the compound. When the dust cleared and the noise subsided and the courtyard was empty, the temple still hummed long into the night with stories of the new Master's cheek and sheer luck. So Enjil went on to be the real Master of the Academy, outshining everyone and everything. He proved many things, much of it beyond the best minds in that Academy of high learning. But he kept faithful, from what we know of his teachings, to the simple and straightfoward, and always the beautiful and intriguing. The Master saw patterns where others only saw calculations. Then disaster struck. In the wars that ravaged
the country the Academy was set on fire and the intellectuals speared
to death. Enjil and his papers and all the great library of learning in
the Academy were lost forever. No one found the young mathematician's
body. Soon the story went out confirming Enjil as a spirit child, one
that visited Earth now and then to remind us of the greater glories that
hid elsewhere. Others said it was the work of the devil, who flew in to
collect the soul that he had claimed for himself long ago, when the little
boy had lain dying from a fierce attack of smallpox.
Whatever the truth of it the crooked smile
and limping walk of the Master was no more, severely missed by those who
loved him. Those who were there / Page 23 / on that day of the Examination
told others. And the words and diagrams spread. The ideas travelled from
community to community; changes and additions were made along the way.
But the basic structure Enjil proposed is still there in the teaching.
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