He had learned something powerful when he’d laid siege to the city-state of Syracuse seven years earlier. Archimedes’ defense of the city had proven to him that mathematics had applications he had never dreamed of. When I became part of the Roman plunder, and Marcellus learned that I had been Archimedes’ slave, he immediately wanted to speak with me. He wanted to know what I had learned from the mathematician. He was impressed enough by what I said to make me a freedman—with the condition that I would tutor his son. I was sixteen. He saved my life with that gesture. I held the man in the highest esteem. He was not overly warm. In fact, he was often cold. But he was clear-headed and fair, perfect for soldiering and commanding the respect of many thousand men.
“As accurately as you can, Timon, sketch the layout of Hannibal’s camp,” he said, pointing to the northeast end of the valley. “I plan to make him defend it.”
I looked into his face as he said this. What he had been hoping for since the beginning of the war lay before him and blazed in his eyes, shimmering with opportunity. He was certain that defeating Hannibal was his destiny. After many dark months of waiting, the sun was out in his soul; he believed Hannibal would be his by nightfall. Unfortunately he was mistaken.
Hannibal had scouted the hill two days earlier. Immediately upon setting camp, he had dispatched one thousand Numidians to hide on the wooded hill. Even now, they were watching us from the forest, creeping up close, absolutely beside themselves with what they had ensnared—two Roman consuls. Armed with pilums, broad-bladed spears, and atlatls to launch metal darts, they shouted a rabid battle cry, then let go with a shower of weaponry. There was no time for reaction. The blade of a spear exploded out of Marcellus’ breastplate from behind. It would have struck me if he hadn’t been in the way. His eyes went wide. I swear I knew his final thought: Hannibal has tricked me! He fell from his horse, mortally wounded.
Many men in our contingent went down. Crispinus received a dart in the arm, but remained mounted. The allied soldiers immediately rode off in any direction they could, while the brave Fregellae closed in around the officers. But the situation was hopeless. Crispinus took charge, ordering us to make our way down as a group. With only a stylus to defend myself, I stared down transfixed by the fate of Marcellus. Marcus grabbed the reins of my horse and yanked me to my senses. Amid a continuous rain of spears and darts, we careened recklessly down the creek bed on our horses, out of the forest, and back to the camp.
The soldiers in the camp had seen it all happen. But it was over so quickly there was nothing they could have done. They took our horses as we rode up to the gate. Many of our party were severely wounded. Forty were left behind dead, including Marcellus. Crispinus took a second dart on the way down. He was in a bad way. One of the Fregellae had guided his horse at the end. Marcus also received a serious injury in his thigh. But worst of all was the death of Marcellus. It deflated the morale of both Roman armies. We retreated from our position. There would be no battle that day or the next.
We marched north for two days. Crispinus rode in a litter, passing in and out of consciousness. Marcus’ leg was heavily wrapped. He rode in a cart, despondent over his father’s death. I walked beside the cart, glumly thinking of the promise I had made five years earlier to Archimedes. In a small pouch, hanging from my neck by a leather thong, was a clear crystal disk and a small glass bead the size and shape of a lentil. They were my most prized possessions. I could not face Marcus because of what they represented. The secret I had kept for five years might have changed his father’s fate that morning in Apulia. But in that secret is also the story of my time with Archimedes and how I first saw a Roman warship at such a great distance it should have been invisible.
PART I
HIERO II
“You are aware the universe is the name given by most astronomers to the sphere the center of which is the center of the Earth, while its radius is equal to the straight line between the center of the Sun and the center of the Earth. This is the common account as you have heard from astronomers. But Aristarchus has brought out a book consisting of certain hypotheses, wherein it appears, as a consequence of the assumptions made, that the universe is many times greater than the universe just mentioned. His hypotheses are that the fixed stars and the Sun remain unmoved, that the Earth revolves about the Sun on the circumference of a circle, the Sun lying in the middle of the floor, and that the sphere of the fixed stars, situated about the same center as the Sun, is so great that the circle in which he supposes the Earth to revolve bears such a proportion to the distance of the fixed stars as the radius of the Earth bears to our planet’s distance from the Sun.”
-Archimedes, The Sand Reckoner.
CHAPTER 1
I was ten years old when Hannibal brought his army out of Iberia through the Alps and into Italy intent on sacking Rome. I lived with my parents on the southern coast of Italy at the time, in the Greek colony of Croton. News of each Roman setback came to us like word of the plague.
Hannibal would remain in Italy for fifteen years. The war became the constant background and far too often the foreground of my early life. Although forty years have passed since Hannibal’s eventual defeat, nothing, save my study of mathematics and geometry, did more to influence who I am today than that terrible war.
In the end, the Fabian defensive strategy did prove out. Some argue it saved Rome, but at the time it was controversial, and to some extent left Hannibal with a strategy that was more likely to succeed than a siege of Rome. Hannibal and his army were allowed to roam freely across the Italian farmland and confront each Latin city or Greek colony they encountered with a simple choice—support the Carthaginian cause or suffer the consequences. When all of Italy but Rome was his, then Rome, too, would fall.
Hannibal further advanced this strategy by infiltrating the cities under Roman influence with scores of highly paid undercover agents and provocateurs. During the first few years of the war, the peninsula grew into a beehive of Carthaginian networks, buying or conniving their way into the political discussion of nearly every Italian city. Such was the situation when Carthaginian influence came to a head in Croton and my story begins.
I was thirteen, naïve, and unsettled by the mere mention of the Carthaginian chieftain’s name, and yet there were larger issues brewing in our city. The Senate, composed of the wealthiest of our citizens, was unshakable in its loyalty to Rome, but the general populace was drawn to the idea of breaking free from Roman arrogance, especially after the disaster at Cannae, when it seemed certain that Carthage would win the war.
My father, Nicoledes Leonidas, was Greek. An advanced geometer, he spent most of his life trying to rebuild the Pythagorean School in Croton. My mother, Arathia Arathemus Leonidas, was an Etruscan immigrant and twenty years younger than my father. They were not wealthy and were definitely not part of the aristocracy, but they did side with Rome. My father, a man of high intellect and volatile emotions, felt very strongly about this.
Early in the spring of the 294th year of the Roman Republic, a member of Croton’s senate by the name of Aristomachus was approached by one of Hannibal’s agents and bought with purses of gold. Aristomachus immediately began arguing the Carthaginian cause in the Senate and building cells of dissidents in the city. I was too young to fully understand the politics, but Aristomachus’ people eventually instigated several large demonstrations, some turning violent. On two occasions my father attended these Carthaginian-financed spectacles to speak out against Aristomachus and the notion of siding with Hannibal. On both occasions, my father nearly came to blows with the demonstrators.
A few days after the second of these incidents, following our evening meal, my mother got out her lyre and lit some frankincense, believing its sweet, warm aroma helped soothe the soul. She entertained my father and me that evening by singing a few of my favorite pieces of poetry. The lyre was a recent gift to my mother from my father. Its body was made from a beautifully polished tortoise shell, and it had a rich, full sound that
went well with my mother’s voice. I loved to hear my mother sing and always sat quietly listening, watching the movement of her fingers on the strings. Some of the songs she played that night were celebratory and uplifting; others were sad and filled with melancholy.
After my mother had put away her lyre and retired to the back of the house, I asked my father about the emotional quality of the music. “How is it that there can be so much feeling in the simple strumming and plucking of strings? The music reaches right into me. Sometimes it nearly brings me to tears just by the way it sounds.”
My father smiled at my observation. He was a Platonist and a Pythagorean, and to him everything was philosophy and numbers. “Timon,” he said, “music is a gift from the heavens. It can touch your heart and your soul.”
He got up from his desk, where he was working out some numeric riddle, and retrieved his monochord from the cabinet behind him. This old wooden instrument had just one string and could in no way match the music of my mother’s lyre. But my father considered the monochord more than a device for entertainment. It had mathematical significance to him, and my question gave him an opportunity to wax philosophical. This was always my favorite time with my father, when he inspired me to think.
He placed the monochord—it was about as long as his arm—on the desk and moved its adjustable bridge so that it divided the string into two unequal lengths. He plucked the string on each side of the bridge. “Did you hear that, Timon? How different the sounds were and how unpleasant they were together?”
It was obvious and I nodded.
My father then moved the bridge so that the string on one side was twice the length of that on the other. “Now listen very closely,” he said. He plucked the string on each side of the bridge. “Notice the shorter length of string vibrates faster.” He plucked the strings again. “They make different sounds—related to the rate at which they vibrate—but together they are pleasing to the ear.”
The shorter string did visibly vibrate at a higher rate, and its sound blended pleasantly with that of the longer string as they faded to silence.
“Pythagoras called the difference in these sounds an eighth,” continued my father. “And it is the same for any length of string divided into two parts—where one is twice the length of the other.”
He moved the bridge so that one side of the string was half again as long as the other. He lifted his finger, signaling for me to listen closely, then plucked the string on each side of the bridge very deliberately and with great care to get a clear ringing in the strings.
The sounds were different—one higher than the other, but again they seemed to be complementary and came to resonance as they died out.
“Pythagoras called the difference in these sounds a fifth.” My father moved the bridge a third time, making one side of the string a third again as long as the other. He raised a finger to get my attention. “A fourth,” he said, and plucked the string on one side then the other.
Again I heard the higher vibration rate of the shorter string but also the subtle tonal relationship as the two sounds conjoined into silence. “So what is this?” I asked.
“Harmonics, Timon. Harmonics are at the core of the Pythagorean numeric mysteries. Pythagoras spoke of the music of the spheres, meaning the natural harmony contained in the motion of the planets. This was of the highest order of knowledge to Pythagoras and is directly connected to the relationship of the numbers to themselves. One to two. Two to three. Three to four.”
“I don’t follow.”
“Those are the ratios of the string lengths I just used in adjusting the monochord’s bridge. They answer your question. Music becomes quite powerful when it matches the harmonics created by those intrinsic ratios—which also match the harmonics of the planets. That’s why you can feel your emotions rising when your mother sings. She’s harmonizing with the music of the spheres—and using that to tap the deepest sentiments of her soul—and ours.”
I nodded, but still didn’t understand. “What’s the music of the spheres again? I don’t hear any music now. The room is quiet except for our voices.”
“The music of the spheres has no audible sound. It’s a mathematical ideal,” he said. “Plato considered it a sacred concept and felt music should only be used as a way to appreciate the resonances inherent in the universe. He would have called the songs your mother sings frivolous and improper.”
“That can’t be right,” I said. “Listening to her sing and play is one of my favorites pastimes.”
My father smiled. “Mine also. Now go to bed. I have work to finish.”
I retired to my bedroom off the courtyard at the back of our small house. My mother was already in her room preparing for bed. I climbed straight into mine and was nearly asleep when I heard three loud knocks on our front door.
I rolled onto my back to listen. I heard men’s voices. They became elevated and forceful very quickly. Even in my bedroom, I could hear their words, punctuated by the calm, firm replies of my father.
“We think it would be wise for you to keep your thoughts to yourself, Nicoledes,” said one of the men to my father. “It’s not the place for a teacher to take part in politics.”
“And if you continue to speak out,” said a second man, “the future of your school will be as doubtful as the fate of Rome.”
It sounded like my father laughed. “What do you mean? The Pythagorean School has nothing to do with this.”
The first man answered at increased volume. “That’s right, so we want you to mind your own business.”
“And to keep your mouth shut,” added the second man.
I got out of my bed to listen more closely. It quickly became apparent that the argument was related to the demonstrations paid for by Aristomachus.
My father was not a big man, but he could get quite indignant. “I’ve had enough of this, gentlemen. You have no influence over me at all. Please leave.”
“We aren’t going anywhere, Nicoledes,” said a third man louder still, “without securing your silence one way or another.”
“What kind of threat is that?” My father’s disdain was evident even in my bedroom.
“One you should heed,” was the chilling reply.
At this point, my mother, a force unto herself, stormed out of her bedroom. “I will not have this bullying in my house,” she announced entering the front room. “Now please, do as my husband has asked—leave our home.”
“Quiet, witch,” was shouted back at her.
I crept out of my room into the courtyard. I saw our two slaves, Lucretia and Adeon, coming from the back of the house, also drawn from their rooms by the loud voices.
I heard my mother command, “Out of my house. Now!” Then a loud slap and my mother’s shriek.
I motioned to Lucretia and Adeon to stay back, then made a dash for the front room. From the doorway I saw my father leap at one of the men and grab him by the throat. The man to his left drew a dagger and stabbed my father through the ribs. My mother screamed as my father fell to the floor. I charged into the room and dove at the man with the dagger. He swatted me away like an annoying bug, then went after my mother. I tried to protect her but received a swift kick to the face and another to the temple that knocked me unconscious.
CHAPTER 2
I woke up lying on the floor in a dark room. My hands and feet were chained. My nose throbbed and my head ached. I could feel dried blood on my face and taste clots of it at the back of my throat. I became aware of heavy breathing very close by. Then I heard a cough and a series of snorts a little farther off. Could that be my parents? I was too frightened to move or call out.
Gradually daylight filtered into the room through cracks in the poorly constructed mud and brick outbuilding. Three men I’d never seen before were stretched out on the dirt floor and also shackled. There were no windows and one closed wooden door. As quietly as I could, I tried to stand, but halfway up my left knee buckled with a stabbing pain. I cried out and nearly fell onto the m
an lying beside me.
Someone came up to the building from the outside. The door opened. A short, stout man stood in silhouette against the dawn. He entered the room. I recognized him immediately as a local, a Bruttian. He was an ugly man with a jaw that was cocked to one side. He gripped a thick staff in his right hand, and a bullwhip hung on his left hip.
He saw that I was looking at him. “Get up,” he said, rough and loud, in the local dialect that I knew somewhat. The others were waking up. One was a man with skin the color of mahogany. He was very thin, with peculiar markings on his face and chest. His hair was long and black, twisted up on his head with a short, straight piece of bone pinning it in place. The other two, as I would learn later, were thieves from Thrace. They appeared to be brothers, with scraggily black beards and matching scowls.
The Bruttian shouted at us again, “Get up.”
The chains made it difficult. My aching knee didn’t help. I fell twice, while the others got right up. Frightened and confused, I felt like crying, but willed myself to my feet.
The man with the whip used his staff to move us out of the little building and force us into a chicken cart. I slowly pieced together that we were going south to Locri. From there we would take a ship to the city-state of Syracuse on the island of Sicily to be auctioned off. My situation could hardly have been worse. I had no idea what had happened to my parents, and I, the son of a free man, was about to be sold into slavery.
The cart we traveled in was small, let out a sharp screech with each turn of its wheels, and stank of chickens. The four of us were pinched in pretty tight. As the smallest and youngest, I got the worst of it—the least space to occupy, the dregs of what little water we were given, and the last bits of bread that were tossed into the cart.
The Siege of Syracuse Page 2
