by Harold Lamb
At rare intervals Master Ali would clothe himself in his gray brocade dress of honor and would depart for Nisapur on the riding mule, with his parasol and a black slave to beat the mule. His house was at the edge of the sown land, to the south of the Nisapur plain, within sight of the white salt beds of the desert. Here Master Ali had perfect seclusion for his labors.
He was finishing a treatise on al-jebr w'al muqabala—the knitting together of opposites—which had been ordered by the Sultan's Minister several years before. The assistants called it algebra for convenience. Their duty was to copy out commentaries dictated by the master, to work out experimental calculations when he wished, and to search other books for such information as he required. In return Master Ali lectured them for three hours of the afternoon on mathematical science, and fed them.
He knew the names and the mental shortcomings of all eight of them, and being a conscientious man he endeavored to implant within their minds as much as possible of his wisdom, so that after his death mathematical science would not perish in that portion of Allah's world. Of the eight he felt most doubt as to the future of Omar of the Tentmakers who had joined his household only ten months before.
Omar, he believed, had a gift for solving knotty problems, and a dangerous quality of imagination.
"Mathematics," Master Ali had assured his disciples often enough, "is the bridge by which you may pass from the unknown to the known. There is no other bridge."
The pure speculation of the infidel Greeks he disliked as much as he admired the mathematics of the ancient Egyptians, who had first made numerals their servants. Their calculations had served to erect huge buildings.
"Yah Khwaja Imam" one of his disciples asked, "O Master, of what use is it to trace the movements of the stars? The Moon gives us the measure of our months, as decreed by our Lord Muhammad, upon whom be peace! The Sun gives light. But what good would come of studying the stars?"
Master Ali nodded reflectively. He wore the green turban of one who has made the pilgrimage to Mecca; he clipped his white mustache neatly and his spare figure was as erect as a tent pole. He had no faith in astrological prediction, but since the Sultan and all the great nobles believed in it, he would not express an opinion against it.
"Yet, Master," persisted the disciple, "is it not true beyond doubt that the planet Mercury,* which is so named by the Greeks, influences the movements of quicksilver, while the Sun hath influence upon gold, as the Moon hath upon silver? I—I have heard it said."
*[In this book the customary English names for the planets and constellations are used.]
Now it was always possible that the great Minister who was Master Ali's patron had placed a spy in his household, to make certain that he had no dealings with infidels or black magic And he fancied that Omar might be the spy of the Minister. In the first place Omar had come to him alone, on foot, wandering out of Nisapur, saying that he desired to study under the great master of mathematics. Strangely, Omar had insisted that he had no patron. In the second place this youth with the body of a warrior and the restless energy of a lion on the prowl, was obviously not studying to be a teacher. Why then had he buried himself here in seclusion at the edge of the salt desert?
Having thought out his reply, Master Ali delivered it in his dry voice.
"The learned Abu Rayhan Biruni says in the first chapter of his treatise upon astrology that the knowledge of the stars is a science, and that prognostication of the cycle of events, politics, changes in fortune of cities, princes and men, is a special use of that science. So, you may become perfect in the knowledge of the stars without prognosticating, but you cannot prognosticate without a perfect knowledge of the stars."
The disciple received this wisdom with an inclination of the head. He was searching, so far without success, among the master's books for some hidden formula that would enable him to make gold.
"In the al magest," he observed timidly, "it is written that the influence of the Sun upon gold is self-evident, because fire is the essence of the Sun, and—and fire is the only means of approaching the nature of gold. If the essence of fire could be concentrated——"
"In a furnace," assented another.
"Of sufficient force," put in an elder sagely.
"That," said Master Ali, "is Cosmography, which deals with the natures of celestial and terrestrial bodies. It can never be an exact science like Mathematics. What believer could doubt that when Allah in his wisdom created the outer fire and the inner air which surrounds the water which in turn envelops this motionless sphere of our world, He also created the gold that is found within the earth? What true believer would be so devoid of wisdom as to endeavor to create what Allah had caused to be?"
'True—true," murmured the disciples.
Master Ali was quite confident in saying this. The Minister and even the Sultan himself had discovered that in spite of many charlatans who professed to have the secret, no one had yet been able to make gold out of baser bodies. Still, he glanced covertly at Omar who was listening with half an ear while he drew with a pen upon a sheet of paper on his lap-board. Alone among the disciples Omar sometimes worked at his papers during the Master's discussions.
At first Master Ali had assumed that Omar was making notes, to refresh his memory. Now he wondered if these notes might not be meant for the Minister's eye. Omar, it seemed, kept papers locked up in a sandalwood chest by his sleeping quilt.
Rising suddenly, the aged mathematician advanced to his pupil and peered at the paper. He saw a drawing of two cubes bisected by many lines, with numerals scattered about.
"What is this?" he asked in surprise.
'The problem in cube roots," Omar answered promptly.
Master Ali recalled that he had assigned to the scion of the Tentmakers that week a difficult equation in cube roots.
"How far hast thou progressed?" he asked.
"It is done."
To Master Ali this seemed doubtful. He knew that the Greeks had arrived at a solution, but he had been unable to work it out.
So he took the paper, requesting Omar to come with him to his room, and dismissing the others. When he was comfortably seated by his window Master Ali examined the paper, holding it close to his eyes.
"Well," he said at last, "my understanding fails to perceive the meaning of this. I see only that thou hast bisected the cubes to a minute degree, and here thou hast reached the solution of the Greeks."
"How did they reach it?" Omar asked eagerly.
"That," responded the master slowly, "is not revealed to me as yet."
He remembered that he had not given Omar the answer to the equation. Among his papers, however, he had a notation of the problem with its solution. These papers lay with the Koran upon the settee beside him. He had not taken them out of his room, and his pupils were not allowed to enter the room in his absence. So it appeared evident that Omar had either worked it out by this fantastic drawing, or had searched secretly among the master's papers.
"I see only," he added, "that thou hast traced cube roots through the dimensions of these solid squares. In what way didst thou arrive at a solution?"
"The answer is there." Omar bent over the drawing. "Subtract this segment, and this, and this. Add this——"
"I am not blind. But, by the Kiblah, this is geometry, after the fashion of the infidel Euclid. This is not algebra."
"Nay—yet it is the solution. I could not deal with the roots in an algebraic equation."
Master Ali smiled. "Was it not an algebraic equation?"
"Certainly. From this it can be cast in the symbols of algebra. In this manner." Kneeling beside the master, and studying the cubes, Omar wrote down line after line of familiar figures. Looking only at the figures Master Ali saw that his problem had been solved. Now it could be added to his treatise.
He felt a thrill of satisfaction. Kharesmi himself had not ventured to touch this problem in his book. How Master Ustad would grind his teeth in the Baghdad academy!
"Hast
thou made attempt at other problems in this manner?" he asked quickly.
Omar hesitated. "Yes, often," he admitted.
"And reached solutions?"
"Usually—not always."
"May I see the demonstrations?" Strangely, Master Ali asked the question almost humbly.
For a moment Omar was silent. "I have eaten thy salt, O Master," he said, "I have sat at thy feet, learning much. What thou gavest to me to do, I have done. But these other problems are my own, and—I would keep them."
Master Ali's beard seemed to come to a sharper point, and his eyes to harden. "Keep them! For what purpose, O son of Ibrahim?"
Looking out of the window at the dried-up garden, Omar did not appear either ashamed or troubled. "I do not know yet," he answered.
Of all things, Master Ali had not anticipated this. Suspicion grew upon him, as he pondered. Omar had spoken much too casually.
"These demonstrations," the old mathematician persisted, "are kept in that chest of thine which is locked?"
"Yes."
"But I have not locked my door. There is naught in all my papers that may not be seen." He glanced up into the young man's face. "Even the answer of the Greeks in this equation lies—on the floor beside thee."
Omar did not turn his head toward the table with the Koran and the papers where the notation really was, nor did he show a trace of surprise. If he had ransacked Master Ali's room, he had the self-command of a diplomat, or a spy.
After Master Ali had dismissed his young assistant, he pored over the solution of the cubes for hours. To the amazement of his class, he forgot completely the afternoon lecture. He was trying to approach another problem, as Omar had done, without success. His well-schooled mind could not make geometry do the work of algebra—he could not think in terms of solid masses.
"Avicenna could not do it!" he thought, in exasperation. "And yet——"
It was a vague idea. His own lifework, algebra, had served to solve problems that mere arithmetic could not master. What if this preposterous geometry of the Greeks could solve, in similar fashion, problems beyond the scope of algebra? What if some yet-unguessed art could progress beyond the three dimensions of geometry, to deal with numbers to the point of infinity? Master Ali threw pen and paper from him in disgust.
He had wasted an afternoon. All this was ignoble imagination; it had nothing to do with the exact science of mathematics. Omar, he decided, had merely stolen into his room, discovered the solution to the problem, and by aid of the solution had concocted these deceptive cubes. Probably he had no others locked up in his chest. Probably he was a spy, and he kept his reports in the chest until he should be able to go to Nisapur with them or send them, somehow.
Master Ali, having reached this conclusion, put away Omar's solution of the problem, glanced out the window at the water clock, uttered an exclamation of dismay when he saw that he had only a moment before the time of evening prayer, and hastened to the pool to wash his feet and wrists.
A week later the old mathematician had reason to cogitate again about Omar of the Tentmakers.
That afternoon a horse drew up at his gate. The horse was escorted by a half-dozen staff bearers on foot. A carpet slave hastened to unroll a narrow strip of rug from the horse to the inner side of Master Ali's gate, while another slave ran in to announce that Tutush desired to visit Master Ali.
Tutush followed the announcement of his name. He had a round and rolling body clad in silk, a voluminous turban of sheer turquoise blue, and a voice of marvelous modulations. The instant he ceased ordering his own followers about, he was beseeching the slaves of Master Ali for assurance as to the health of their distinguished lord. When Master Ali appeared at last, in his best somber black, Tutush uttered an exclamation of joy and clasped him in his short arms.
"Praise and glory to the Lord of the Two Worlds that the health of the world-renowned Mirror of Wisdom is unfailing! May the Mirror be untarnished for uncounted years! May it continue to reflect the wisdom of the age—of the century—upon us poor slaves of ignorance!"
To this polite greeting, Master Ali objected with becoming humility. But Tutush waved aside all objection. "Nay, is it not well known in Nisapur that your Honor is the superior of Kharesmi, and the master of that stupid Ustad of Baghdad? Had Avicenna greater knowledge of the sciences? Nay, he had not!"
Master Ali fared badly in this exchange of compliments when they were seated on the guest carpet, with fruit and sherbet piled before them. For one thing, he could not check the flow of Tutush's voice; for another, he knew little about his visitor except that Tutush was the agent of the Minister, who in turn was Master Ali's patron. In Nisapur they said that he collected turquoises and delicate porcelain and old manuscripts. But he admitted to no title and no one seemed to remember where he lived.
When they had discussed the progress of Master Ali's book for an hour, Tutush asked to see a graduate student named Omar Khayyam. Master Ali pricked up his ears, and watched the two men covertly after Omar had appeared from the garden and had seated himself on a corner of the rug with his arms folded politely in his sleeves.
"In the last moon," observed Tutush casually, "we had tidings from the east. Romanus Diogenes, the Emperor of the Christians, was seized by his own people and blinded so savagely that he died of his hurt."
Omar looked up with a frown. It reminded him of the battle and his milk-brother.
"It is strange," added Tutush, glancing at him, "that this king was spared by our lord the Sultan—may he live forever—and then slain by his own people. Who could have foreseen that?" And he looked at Omar.
"No one," observed Omar, since an answer seemed to be expected of him.
After Omar had been dismissed from the presence of the elder men, Tutush sat in silence for the first time, playing with an ivory rosary at his throat as if musing upon something.
"Believest thou," he asked idly, "in the science of prognostication? Is it possible, O Master, to foretell what is to be?"
But Master Ali was not to be drawn into such an admission, least of all by the secret agent of his powerful patron.
"By my faith, all is possible with Allah. As for me, my poor knowledge is devoted to the perfection of my book."
Tutush murmured assent. "Suppose that a certain man should predict three things. Would it be possible—I seek the answer from thy wisdom—for all three to come to pass by accident?"
This touched the old teacher's instinct. "Two such happenings might transpire by chance, but never three. Yet where would a soothsayer be found foolish enough to make a threefold prediction?"
"Where? Hast thou not among thy disciples at least one who is skilled in casting horoscopes? This young student to whom I spoke just now?"
"Omar?" Master Ali's beard quivered curiously, as if he had almost smiled. "That is the last thing I would expect him to do."
"My soul! Then what does he do?"
"He solves cubic equations as easily as thou, O my guest, dost slip those ivory beads upon the silk string."
"Eh? Then he hath skill of a kind? What does he in his leisure?"
"He reads all my books; he wanders along the desert's edge alone; he eats pomegranates and plays at backgammon, and says little enough. And," Master Ali added, not without malice, "he makes calculations that he hides in a chest."
"Why should a young man walk about the desert? W'allah—our blood, O Mirror of Wisdom, is thin and cool after these many years, but the blood of a youngling is hot. Perhaps this student hath found him a comely maid in your wilderness."
'There is no woman about, other than the laundry hags who are full of fleas and warts."
Tutush grimaced. He seemed to be irresolute as a man who seeks a garden and finds himself in an empty courtyard, and still looks for the garden. The beads of the rosary clicked under his fingers and his brown eyes snapped. "Eh, eh. This is a strange student, with his skill and his silence. Perhaps his gift is of the Invisible—or, it may be, of a devil. Now it behooves One whom thou
knowest to ascertain if any here makes secret practice of the arts of a devil. Wilt thou test this skill of the man of the Tentmakers to the utmost, and discover what he seeks to do with it? Write down his skill upon paper, seal it and put it in his hand to bring to me in one month, upon Friday-eve at the Takin gate of Nisapur. Now——" Tutush rose with a sigh and a smile, "—I who gather knowledge must go from thy house where knowledge is. Alas, I have caused thee much trouble."
When his guest had departed, Master Ali spent some time in cogitation. It seemed strange that he had been asked to observe Omar, whom he had suspected of observing him. And stranger still that he should be asked to write down the result. He wondered if the two had not exchanged some hidden message under his very nose, and he wondered why Omar should have been summoned to Nisapur. Master Ali saw everything with the eyes of suspicion.
Yet at the end of the month Master Ali had not succeeded in ferreting out Omar's secret. He could not understand why his pupil was indifferent to routine algebra and still eager to solve new problems. Certainly he seemed to depend upon no occult aid. Omar worked things out by mathematical formulas of his own. That was all—but not enough to satisfy the master's jealous curiosity.
In the last evening he tried to surprise Omar into confession, as he had tried before in the matter of the cubes.
"When wilt thou return to the Arranger of the World?" he asked casually.
Nizam al Mulk, the Arranger of the World, was the great Minister of the Sultan Alp Arslan, a power in the land, and the patron of Master Ali as well as Tutush.
"Return? I have never seen him."
'Then in the name of Allah, why art thou here?"
Omar explained that he had come to study. After the death of his father, Omar had made his home at the house of his milk-brother Rahim. But when he had returned from the war, Rahim's family had treated the foster son as a person of ill-omen—as if by Rahim's death Omar had forfeited his right to be in their house. They had taken Zoë from him to sell as a slave in the bazaar.