Gurn levered himself up from his bed of furs, hoping he hadn’t cried out. A few embers glowed in the fire pit, casting warm light on the roof of skins. Around him, he heard only gentle breathing and the snoring of his mother. No one else was awake. No one’s pulse raced but his.
He could never sleep after a visit from the white figure, and so he rose, naked, and quietly skirted the fire pit to reach the entrance of the lodge. When he pulled back the flap, cool air brushed his body, and he took a deep breath to cleanse his head of the vision. But he could not help a darting glance among the other huts. She was not there, of course.
One of the dogs raised his head, black eyes glittering in the starlight. Gurn walked a pace and knelt to scratch the dog’s head. Looking up, he could see the shaman’s mountain, dark above the ovals of the other lodges. He knew where the white figure came from, and who had sent her.
When he abandoned Shomar, prematurely ending his apprenticeship, he had feared the old man’s wrath. But he, Gurn, would become a hunter. He would provide for his village. An old man’s curse could not change that. And he did not want to live alone in a cave. He drew comfort from the closeness of his clan. He had heard stories of villages that had vanished over the winter. They had starved or died from coughing sickness. But his tribe was strong. The hunters would provide for all, and the shaman would….
The shaman. Shomar.
Gurn’s leave-taking had hurt the old man. And it had hurt him as well. He should go back; he should reconcile with his former master, convince him of the wisdom of the choice he had made.
With a final stroke of the dog’s shaggy head, he stood. Glowing dimly above the mountain he saw the tail of the bear that ever circled in the night sky. The last thing that Shomar had said to him was that his future, both their futures, lay among the stars, but then Shomar often spoke in riddles.
Gurn climbed the barren mountainside, worry of the encounter to come adding weight to every step. The last time he had sought the cave of his former master, the path had been covered with ice. But now, the stones were only cool against his feet, the sun having yet to clear the mountains behind him.
In one hand, he carried his spear thrower, though uncertain why he brought it. Perhaps to prove his new status to Shomar?
In the other hand, he hefted a reed basket with his savory offering wrapped in leaves. It was good for the tribe to honor their elders, and by now, the old shaman might have reconciled to Gurn’s decision.
Reaching a broad outcrop of rock, he turned to look back at the lodges clustered at the river’s edge. Wisps of pale smoke rose from holes at the top of their mounded roofs.
Almost, he started back to the village, but turning again to the path, he came at last to the dark opening of the cave. The cracked skull of an aurochs rested on a narrow ledge above the entrance, its horns spread wide. He remembered, as a child, being frightened by the skeletal head.
Taking a deep breath, he leaned forward and called out. “Honored one. May I enter?”
His words reverberated from within the cave.
Motionless, he waited. Shomar had become thin and frail since the last snows, and it occurred to him that he might be too late to present his offering to the aged shaman.
Gurn pressed his lips into a thin line and crept to the narrow entry between the cold fire pits. Bending, he stepped from sunlight into shadows. Before his eyes could adjust, the smell of Shomar enveloped him, bringing to mind the mornings of his boyhood when he crept reverently into the damp cave, eager to learn the mysteries of spells, and of herbs, and of the reading of bones.
A rustling came from one side of the cavern, and he saw Shomar, his back turned, his skeletal shoulders topped by a tangle of white hair. Gurn quietly backed out into the sunlight.
“You may enter,” came a frail voice from the darkness.
Inside once more, Gurn was troubled to see that Shomar sat on his rock of judgment, his hyena skin hanging from his shoulders, his necklace of lion’s teeth resting on his sunken chest. In his hand, he held the horsehair switch that Gurn had made for him. Grunting, the old man gestured with the switch, indicating the stone where Gurn should sit.
Seeing that Shomar was already seated, Gurn walked stooped at the waist to show respect. In his childhood, he had crawled into Shomar’s presence.
“Yesterday’s hunt was successful,” he said kneeling before Shomar and placing the basket before him. “I killed a spotted horse and have brought you a shank.” He had brought one of the rear shanks, smoked overnight, and usually reserved for the chief. He watched to see if the old man would accept.
Shomar pulled the basket to him and lifted one of the broad leaves in which the shank was wrapped. He bent closer to sniff and then raised his eyebrows. “The spotted horse is fast and wary.”
Gurn nodded, gratified the old man appreciated both the skill that it took to bring down such an animal and the generosity of his gift. He had decided that morning, after the sleepless remainder of his night, to bring the shank as tribute and to persuade Shomar that he had, indeed, become a hunter, and a hunter he would remain.
It had been three long moons ago that he walked from Shomar’s cave, leaving his younger brother to train as the tribe’s next shaman. Since that day he had thrilled to the hunt. He had learned hand signals for stalking and excelled at the flaking of stone.
“I practice long and hard with my atlatl.” He raised his spear thrower. “The cup is made according to a new image in my mind.”
Shomar glanced at him before reaching out and taking the smooth wooden rod. He nodded as he rolled his thumb in the bowl at the end of the shaft. “This is a fine thrower.”
Gurn took back the rod and nodded again, pleased at the old man’s praise.
“You do not visit me as often as you used to.”
The smile left Gurn’s face and he shifted on the stone. “It is the hunt, honored one, and the making of my weapons. They take all my time.”
“Do the other children still call you Shomar’s boy?”
Gurn’s shoulders tensed. “No, honored one. My brother Cullen is now Shomar’s boy.”
“Ah, do they call him that?”
“Not yet, but he has only apprenticed with you three faces of the moon.” When Shomar did not respond he added. “I hope he learns his lessons.”
“He is not attentive.”
“Then I shall strike his ears. He will learn to be an honored shaman one day, like you.”
Shomar waved his hair switch as if to dismiss Gurn’s response. “Nevermind. We shall celebrate your hunt. The baskets in back,” he said, inclining his head to a shelf at the rear of the cave, “fetch me—the sixth one.”
Gurn raised himself, and again bending at the waist, crept farther into the shadows where the air was laden with dampness and the odor of mold. On a shelf, which he, himself, had gouged into the wall, he could barely see a line of small baskets.
He counted to the sixth and reached for it, but stopped. Shomar could be devious. Gurn would not be manipulated by the old man, although he could not be certain what Shomar intended, if anything. He picked up the fifth.
Returning, he knelt and placed the small basket before Shomar. It contained dried berries.
The old man rocked forward and back. “Ah, you remember ‘six’ like I taught you.”
Gurn frowned and lowered himself onto the sitting stone again. “I am afraid most of the numbers no longer remain in my head.”
“Yes, memory is fleeting like the forest bison. There,” he pointed with the switch. “Take some. They are the berries of contentment.”
Gurn raised his eyebrows and looked at the old man for reassurance. Berries of contentment were rare, greatly sought after and hardly ever used outside the ancestor rites. Shomar nodded, and so Gurn took a handful and put some of them in his mouth. A bitter flavor rolled on his tongue as he began to chew. He had never actually tasted them before, but he knew that a pleasant feeling would come. Shomar had responded with a gift worthy of his own. The meeting was going better than he had hoped.
Meanwhile, the old man had taken out a shell that contained white powder, spat onto it and stirred with his finger. He made a vertical mark on his forehead ending at the bridge of his nose, and then began to draw horizontal marks on his wrinkled cheeks.
“You will hear the wisdom of my words.”
Gurn bowed his head to signal his acceptance and to hide his dismay. He had hoped to be gone from the cave by now, escaping while Shomar was still in a good mood, yet reverence forbad his departure until he was dismissed. While the old man was occupied, Gurn reached for more berries. At the least he would feel contentment the rest of the day.
Shomar wiped the remaining pigment from his finger onto his loin cloth, and then reached behind him to bring out a handful of bones.
“Do you know how many there are?” he said, throwing them on the ground between them.
Now, there was no doubt that Shomar was testing him. He counted nine, but suspecting what Shomar intended, he said “seven.”
“Ah,” Shomar’s voice fell. “You do not know your numbers as well as I thought.”
“As I said, honored one, I am a hunter now. The numbers you taught me have vanished with my childhood. I am not fit to be a great shaman like you.”
“But you counted the baskets correctly. All but the sixth contained berries of death.”
Gurn’s eyes widened, and he looked at the remaining berries in the basket and then at those in his hands. His gaze returned to Shomar in time to see the faintest curl of his lips.
“Ah,” he drew out the sound again. “It seems that I’m all out of death berries today. Perhaps you would like to count the bones again?”
Cold crept into Gurn’s gut. The meeting was not going as well as he thought. He moistened his lips. “There are nine.”
“And do you know what they are?”
“As any hunter would know, they are leg bones of the baboon.”
Shomar spat. “Look again. Look beyond the eyes of a hunter.”
Gurn remembered his lessons as a child, when Shomar struck his ears if he gave the wrong answer. Scowling, he saw that each bone had been crossed with a series of horizontal scores.
“There are marks upon the bones,” he said.
“And how many on the one that is pointing toward you?”
Gurn picked it up. Clearly, the old man had sawed each mark with a cutter. Furrowing his brow, Gurn began to count. After several moments he said, “More than twice two hands.”
“Two hands twice and seven.”
Gurn thought for a moment. “Yes, I can see that.”
“It is the number of our tribe.”
Gurn looked up.
“You must learn to count, boy.”
“I am a hunter, Shomar. I do not play with bones.”
Quick as a snake the old man’s hand shot forward, striking Gurn across the mouth. Gurn cried out. The blow was not heavy, but his heart thumped in his chest as if he had been struck by a much greater force.
“Do not prattle about what you will not do!” The old man’s voice trembled with rage. “If the goddess speaks, you will listen.” And then he snatched something from his lap, raised it and struck the ground. When he removed his hand the pale image of the goddess faced Gurn. Pure white, carved from the tooth of the great mammoth, the small figure stood erect, its pointed feet stuck into the earth between them. “Tell her that you will not be a shaman.”
Chills traveled up Gurn’s spine, tingling into his scalp. It was the image from his dreams. The carving itself he had seen but twice before, and again he was overwhelmed by the ample breasts and bountiful hips. No woman in the tribe was her equal. Shomar’s hand closed over the tiny statue, and it was removed from his sight.
Trying to hold at bay the fear that had swept over him, Gurn spoke quietly. “My deepest regrets, honored one. All tremble before the goddess, but you know that the hunt calls to me, and I despair at so much to learn. It is Cullen, my brother, who dreams of being shaman.”
“Cullen dreams of wearing this,” Shomar clutched the lion tooth necklace, causing it to rattle. “He does not understand that,” and he pointed to the bones.
Gurn ground his teeth, determined to resist the old man, even the goddess if he must. “This is only the leg of a baboon,” he said, shaking his head and lifting the bone before the face of Shomar. “You offer the tribe bones, while I offer meat. Our children will not cry for food in the dead of winter, because our hunters will provide. I will not be an old man sitting alone in a cave, dependent on others to bring me food.”
“And that is exactly what your brother would be, but you are not like your brother. I have seen behind your eyes the working of your thoughts. It is within your grasp to understand.”
“What is there to understand?”
Shomar grinned, ignoring the disrespect and leaned forward. “If you can count a thing, you can rule it.”
Gurn looked down at the bone again. They were only marks, yet marks could be numbers and numbers could be things. Shomar had taught him that, like six for the basket of berries he had just fetched—or was it five? His thoughts had become clouded. Perhaps he had eaten too many of the berries.
The old man bent closer. “You are the next shaman. I shall teach you to enter the eye of the falcon, to possess the dreaded cave lion, and to understand—the magic within numbers.” The old man traced a spiral sign in the air above his head and then reached out, extending a gnarled finger, and touched Gurn on the chest.
The touch caused Gurn’s breath to leave him, and he began to tremble. More potent even than the slap, it drove thoughts from his head. He could not speak.
Shomar’s white eyes floated in the shadows. “I have discovered that there are numbers big enough to count all things, and thus all things can be ruled.”
Gurn gasped, trying to resist the spell. “How is that possible?”
“The goddess gave me a vision. She did not give it to my teacher, Bargwa, or to Sundar, his teacher, she gave it to me alone, and yet…” he spread his hands and closed his eyes, “it is not for me to fulfill that vision.”
“But your knowledge is vast, honored one. Surely, more numbers are known to you than any other shaman.”
“You do not realize how great the task.” Shomar raised his hand, his first finger extended. “Hear now the vision that the goddess gave to me: One night in the far future a great shaman will step forth from his cave and look into the night sky. He will raise his hands and see far, very far. And then he will count the stars, and he will rule over them.
“Alas, it will not be me to fulfill this vision, or even you, but you will learn the symbols for many numbers, so many numbers that they could fill this cave with bones.”
“You condemn me to sit in a cave marking bones while others hunt the forest bison and the tusked pig. It is they who provide for the future of the tribe.”
“There are many hunters, and they provide but for the following day. The shaman, there is but one, and he provides for generations to come. There is a long future, Gurn, longer than you can imagine. I cannot master so many symbols before I die, but if I teach you… “
“No!” Gurn rose to his knees, his breath coming in gasps, his heart pounding. “You know I do not want to be shaman. Why do you do this to me?”
“Because I do not want to die.”
Gurn stared at the old man, withered, bent and frail, yet defiant. A soft light gleamed from his white eyes. Gurn said quietly, “I do not want to die either, but… ”
“It may be a very long time before the vision of the goddess is fulfilled. My own eyes no longer reach the stars, but in my youth, when I began counting, I learned that there are far more stars than I thought. And stranger still, there may be even more numbers, for although the stars will end, I do not think the numbers will. But with the symbols I teach you, you will count farther than I, and you will hand down the numbers to your apprentice, and he to his, so that when the time comes, and the great shaman steps forth, he will count the stars, and they will be his. And on the night that happens… ” His eyes grew watery, and he struggled to speak. “At that moment I, Shomar, will live, as will you, and all the shamans that come after us.”
Gurn raised his head but closed his eyes.
“I am asking,” the old shaman said, “to live forever. You have the power to give me that gift. And one day, you in turn will ask another that you, too, will live, and the line not be broken.”
Desperate, Gurn staggered to his feet and backed away. “I cannot,” he stammered. He willed his legs to move, to carry him to the mouth of the cave. But at the entrance a white figure blazed before him, radiant with sunlight. He gasped and raised his hands against her brilliance. Turning his head away, he saw the light stream past him and strike a flat stone embedded in the back wall of the cave.
Chipped into the stone were symbols, scattered on the smooth surface. They had not been there his last visit to Shomar’s cave, but he knew at once what they were.
The glare from the White Figure behind him faded. It was simply sunlight. He had withstood the spell, had resisted Shomar. But the symbols drew him. Mesmerized, he crept forward, reaching out to touch the stone as if to assure himself that it was real.
“Ah, you have discovered my symbols.” The old man hobbled to his side. Both their shadows overlay the stone.
“What does this one mean?” Gurn pointed to one of the figures.
“That one is ‘five.’ You can recognize it by the cross stroke.”
“Then that one must be ten?” He pointed to another.
“How quickly you grasp their meanings. It is a rare gift. It is from the goddess.”
Gurn turned and looked at the old man, but said nothing.
Somar looked down and shrugged.
“What about this one?” Gurn pointed to one near the edge of the rock a lone symbol, different from the others. It was a bone scored with cross cuts.
A wrinkled smile spread across Shomar’s face, “I will let you ponder upon that one.”
Gurn nodded. It was Shomar’s sign, of course. Gurn knew already what he would chose for himself. It would be a spear thrower.
When Gurn left the cave, he looked up into the night sky and wondered about counting the stars. There were so many.
His brother, Cullen, would not take the news well, that Gurn would be the next shaman. He sighed. He’d give Cullen his spear thrower; his brother was easily distracted. And Shomar was right, Cullen would never understand the numbers.
And he wondered about dying and about what it was like not to die. No one else in the tribe would understand that, either, but if, one day, the great shaman were to count the stars, he would need the patterns that Shomar had shown him. Gurn would learn them all and pass them on to the shaman who would come after him, and he to the next, and to the next. That pleased him. He pictured the line of his successors stretching to the edge of the valley and on to the horizon, and he wondered how long it would be before the great shaman came to count the stars.
Author’s note: In Ishango, near the headwaters of the Nile, a baboon bone was discovered in 1960 with sequenced notches dating from the upper Paleolithic. According to The Math Book (Sterling Publishers), by Clifford Picking, the notches were arranged to show a knowledge of doubles, odd and prime numbers. Older sticks have since been found, in Swaziland a 37,000-year-old stick and in Czechoslovakia a 32,000-year-old tibia that displays notches in groups of five. The makers of these artifacts were surely the pioneers of mathematics.