Chapter Three

Page 63 6+3 = 9

"There is a simple trick involving numbers that can be guaran-teed to produce astonishment at any party. You ask someone to write down his telephone number, then to write it a second time with the figures jumbled up. Next, tell him to subtract the smaller from the larger number, and keep on adding up the figures in the answer until he has reduced it to one figure. (5019 becomes 10, which in turn becomes 1 plus 0 - that is, 1.) When he has finished, you may tell him authoritatively: 'The answer is nine.'

You can afford to be dogmatic; for the answer is always nine. It works with any set of figures, no matter how small or how large. Jumble up the figures, subtract one from the other, and the answer always reduces to 9.

I have no idea why this is so, and have never come across a mathematician who could explain it. It is just one of those peculiar properties of numbers."

Page 15

'Th9s 9s a sl9ghtly unusual request,'said Dr Wagner, w9th what he hoped was commendable restra9nt.' As far as 9 know, 9t's the f9rst t9me anyone's been asked to supply a T9betan monastery with an Automat9c Sequence Computer.9 don't w9sh to be 9nqu9s9t9ve, but 9 should hardly have thought that your - ah - establ9shment had much use for such a ma-ch9ne.Could you expla9n just what you 9ntend to do w9th 9t?'

'Gladly,' repl9ed the lama, readjust9ng h9s s9lk robes and carefully putting away the sl9de rule he had been us9ng for currency convers9ons. 'Your Mark V Computer can carry out any rout9ne mathemat9cal operat9on 9nvolv9ng up to ten d9g9ts. However, for our work we are 9nterested 9n letters, not numbers. As we w9sh you to mod9fy the output c9rcu9ts,the mach9ne w9ll be pr9nt9ng words not columns of f9gures.'

'9 dont qu9te understand…'

'Th9s 9s a project on wh9ch we have been work9ng for the last three centur9es - s9nce the lamasery was founded, 9n fact. 9t 9s somewhat al9en to your way of thought, so 9 hope you w9ll l9sten with an open m9nd wh9le 9 expla9n 9t

'Naturally.'

'9t is really qu9te s9mple.We have been comp9l9ng a l9st wh9ch shall conta9n all the poss9ble names of God'

'9 beg your pardon?' / Page16 / 'We have reason to bel9eve' continued the lama 9mper-turbably, ' that all such names can be wr9tten with not more than n9ne letters 9n an alphabet we have dev9sed,'

'And you have been do9ng th9s for three centur9es?

'Yes: we expected 9t would take us about f9fteen thousand years to complete the task.'

'Oh, Dr Wagner looked a l9ttle dazed. 'Now 9 see why you wanted to h9re one of our mach9nes. But what exactly 9s the purpose of th9s project ?

'The lama hes9tated for a fract9on of a second, and Wagner wondered 9f he had offended h9m. 9f so there was no trace of annoyance 9n the reply.

'Call 9t r9tual, 9f you l9ke, but 9t's a fundamental part of our bel9ef. All the many names of the Supreme Being - God , Jehova , Allah , and so on - they are only man made labels. There 9s a ph9losoph9cal problem of some difficulty here, which 9 do not propose to d9scuss, but somewhere among all the poss9ble comb9nat9ons of letters that can occur are what one may call the real names of God. By systemat9c per-mutat9on of letters, we have been trying to l9st them all'

'9 see. You've been start9ng at 1111111 . . . and work- ing up to 88888888 . . .'Exactly - though we use a spec9al alphabet of our own. Mod9fy9ng the electromat9c typewr9ters to deal w9th th9s 9s of course tr9v9al. A rather more 9nterest9ng problem 9s that of dev9s9ng su9table c9rcu9ts to el9m9nate r9d9culous com-b9nat9ons. For example, no letter must occur more than three t9mes 9n sucess9on.'

'Three? Surely you mean two.'

'Three 9s correct; 9 am afra9d 9t would take too long to expla9n why , even 9f you understood our language.'/ Page 17 / '9'm sure 9t would,' sa9d Wagner hast9ly. 'Go on.'

'Luck9ly, 9t w9ll be a s9mple matter to adapt your Automat9c Sequence Computer for th9s work, s9nce once 9t has been programmed properly 9t w9ll permute each letter 9n turn and pr9nt the result. What would have taken us f9fteen thousand years 9t w9ll be able to do 9n a hundred days.'

'Dr Wagner was scarcely conscious of the faint sounds from the Manhatten streets far below. He was in a different world, a world of natural, not man-made mountains. High up in their remote aeries these monks had been patiently at work generation after generation, compiling their lists of meaningless words. Was there any limits to the follies of mankind ? Still, he must give no hint of his inner thoughts. The customer was always right…"

OR

ARITHMETIC REVISITED

Herbert McKay

1940

"Multiplication does not always increase a number. If the multiplier is less than 1 we have a decrease. When we. multiply by ^.5 we get a half of the original number; when we multiply by 1 we reduce the number to a tenth of itself; and so on. The square of a small number (less than 1) is a very small number; the cube is an extremely small number.Thus: ^.001²= ^.00001, ^.001³ = ^.000000001.

Even when a number is a very little less than one, con-tinual multiplication of it by itself (raising it to higher and higher powers) finally reduces it to an exceedingly small quantity.

^.99999 is a mere one-hundred-thousandth less than 1; if we multiply any number by it we deduct a one-hundred-thousandth of the number. Thus ^.99999² is a very little more than ^.99998. ^.99999¹⁰ is a little more than ^.99990.

^.99999 to the power 1000 is about ^.99015.

^.99999 to the power 1,000,000 is ^.00005.

^.99999 to the power 10,000,000 is the tenth power of ^.00005.

We should have a string of 42 noughts before the significant figures begin. For the l00,000,000th power we / Page 148 / should have over 400 noughts before the significant figures begin."

Page 147

Page 16

Page 108

"An American mathematician noticed that the earlier pages in books of logariths kept in his university library were dirtier than later ones, indicating that science students, for some rea-son, had more occasion to calculate with numbers beginning with 1 than with any other number. (261) He made a collection of tables and calculated the relative frequency of each digit from 1 to 9. Theoretically they should occur equally of-ten, but he found 30per cent of the numbers were 1, whereas 9 only occupied 5 per cent of the space. These are almost exactly the proportions given to these numbers on the scale of a slide rule, so the designers of that instrument clearly recognized that such a bias existed. This preponderance of the number 1 may have been caused by the fact that the tables were not really random, but bigger tables provide a similar bias."

Page 273

"The precessional numbers highlighted by Sellers in the Osiris myth are 360, 72, 30 and 12."

"These he joined to the 360 days of which the year then consisted (emphasis added)."

"Elsewhere the myth informs us that the 360 - day year consists of "12 months of 30 days each".

Note 6

And in general,as Sellers observes , "phrases are used which prompt simple mental calculations and an attention to numbers ". note 7 "Elsewhere the myth informs us that the 360-day year consists of '12 months of 30 days each'.

Thus far we have been provided with three of Seller's precessional: 360, 12 and 30. The fourth number,which occurs later in the text, is by far the most important. As we saw in Chapter Nine, the evil deity known as Set led a group of conspirators in a plot to kill Osiris. The number of these conspirators was 72."

Page 231/233

"Three o'clock and a still starlight night in mid-September in Upper Egypt. At this hour the village is usually asleep, but to-night it is a stir for this is Nauruz Allah, the New Year of God, and the narrow streets are full of the soft sound of bare feet moving towards the Nile. The village lies on a strip of ground; one one side is the river, now swollen to its height, on the other are the floods of the inundation spread in a vast sheet of water to the edge of the desert. On a windy night the lapping of wavelets is audible on every hand; but to-night the air is calm and still, there is no sound but the muffled tread of unshod feet in the dust and the murmur of voices subdued in the silence of the night.

In ancient times throughout the whole of Egypt the night of High Nile was a night of prayer and thanks giving to the great god , the Ruler of the river, Osiris himself. Now it is only in this Coptic village that the ancient rite is preserved, and here the festival is still one of prayer and thanksgiving. In the great cities the New Year is a time of feasting and processions, as blatant and uninteresting as a Lord Mayor's Show, with that additional note of piercing vulgarity peculiar to the East.

In this village, far from all great cities, and-as a Coptic community-isolated from and therefore uninfluenced either by its Moslem neighbours or by foreigners, the festival is one of simplicity and piety. The people pray as of old to the Ruler of the river, no longer Osiris, but Christ; and as of old they pray for a blessing upon their children and their homes.

There are four appointed places on the river bank to which the village women go daily to fill their water-jars and to water their animals. To these four places the villagers are now making their way, there to keep the New Year of God.

The river gleams coldly pale and grey; Sirius blazing in the eastern sky casts a narrow path of light across the mile-wide waters. A faint glow low on the horizon shows where the moon will rise, a dying moon on the last day of the last quarter.

The glow gradually spreads and brightens till the thin crescent, like a fine silver wire, rises above the distant palms. Even in that attenuated form the moonlight eclipses the stars and the glory of Sirius is dimmed. The water turns to the colour of tarnished silver, smooth and glassy; the palm-trees close at hand stand black against the sky, and the distant shore is faintly visible. The river runs silently and without a ripple in the windless calm; the palm fronds, so sensitive to the least movement of the air, hang motionless and still; all Nature seems to rest upon this holy night.

The women enter the river and stand knee-deep in the running stream praying; they drink nine times, wash the face and hands, and dip themselves in the water. Here is a mother carrying a tiny wailing baby; she enters the river and gently pours the water nine times over the little head. The wailing ceases as the water cools the little hot face. Two anxious women hasten down the steep bank, a young boy between them; they hurriedly enter the water and the boy squats down in the river up to his neck, while the mother pours the water nine times with her hands over his face and shaven head. There is the sound of a little gasp at the first shock of coolness, and the mother laughs, a little tender laugh, and the grandmother says something under her breath, at which they all laugh softly together. After the ninth washing the boy stands up, then squats down again and is again washed nine times, and yet a third nine times; then the grandmother takes her turn and she also washes him nine times. Evidently he is very precious to the hearts of those two women, perhaps the mother's last surviving child. Another sturdy urchin refuses to sit down in the water, frightened perhaps, for a woman's voice speaks encouragingly, and presently a faint splashing and a little gurgle of childish laughter shows that he too is receiving the blessing of the Nauruz of God.

A woman stands alone, her slim young figure in its wet clinging garments silhouetted against the steel-grey water. Solitary she stands, apart from the happy groups of parents and children; then, stooping , she drinks from her once, pauses and drinks again; and so drinks nine times with a short pause between every drink and a longer pause between every three. Except for the movement of her hand as she lifts the water to her lips, she stands absolutely still, her body tense with the earnestness of her prayer, the very atmosphere round her charged with the agony of her supplication. Throughout the whole world there is only one thing which causes a woman to pray with such intensity, and that one thing is children. " This may be a childless woman praying for a child, or it may be that, in this land where Nature is as careless and wasteful of infant life as of all else, this a mother praying for the last of her little brood, feeling assured that on this festival of mothers and children her prayers must perforce be heard. At last she straightens herself, beats the water nine times with the corner of her garment, goes softly up the bank, and disappears in the darkness.

Little family parties come down to the river, a small child usually riding proudly on her father's shoulder. The men often affect to despise the festival as a woman's affair, but with memories in their hearts of their own mothers and their own childhood they sit quietly by the river and drink nine times. A few of the rougher young men fling themselves into the water and swim boisterously past, but public feeling is against them, for the atmosphere is one of peace and prayer enhanced by the calm and silence of the night.

Page 232 and 233 Continued.

For thousands of years on the night of High Nile the mothers of Egypt have stood in the great river to implore from the God of the Nile a blessing upon their children; formerly from a God who Himself has memories of childhood and a Mother. Now, as then, the stream bears on its broad surface the echo of countless prayers, the hopes and fears of human hearts; and in my memory remains a vision of the darkly flowing river, the soft murmur of prayer, the peace and calm of the New Year of God.

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Page number missing assumed to be 415

THE MAGIC MOUNTAIN