The Time Sphere

by A. E. Albert

  All these horses are really getting annoying, thought Billy.

  Billy, Georgii and Dickens immediately ran to her side. “Gianna, how do you fare?” exclaimed Georgii with concern in his voice.

  At the same time, Billy yelled, “You could have been killed, Jeanie!” She looked up at both young men and smiled, revealing a soft, plump and snow white rabbit in her arms.

  Billy looked at Jeanie with a deadpan expression. “Jeanie, the people around here shoot those things for dinner and you risked your life for it?” But no one was listening to Billy’s protest, as everyone’s attention was focused on the twitching creature in her arms.

  “Is he not a handsome fellow,” cooed Dickens, appearing not too concerned over Jeanie’s foolishness.

  Billy stood impatiently behind the group, with his hands on his hips, as they fussed over the rabbit. Suddenly, he heard, “Halbuldus, Halbuldus!” Billy watched as a middle aged Italian man came running toward the group. “Oh, Halbuldus,” he said out of breath, “that is the last time I let you off your leash for sweet grass.” He began shaking his finger at the rabbit, whose only response to this reprimand was to wiggle his nose.

  “Signor Leonardo, I should have known he was one of yours!” Georgii laughed, gently taking the rabbit from Jeanie’s arms and giving it to the distressed little man.

  His hair was brown, liberally laced with grey. His eyes were a warm caramel color, with numerous laugh lines spreading out from the corners. He had an easy smile, the kind that made people like a person right away.

  “My dear girl, how can I ever thank you for saving my Halbuldus!” The little man then leaned over and kissed her hand, causing a blush to form on her cheeks.

  “Oh, I love animals! I couldn’t have let anything happen to him,” she assured him, as she petted Halbuldus’ fur.

  The man looked at each of the visitors and introduced himself. “My name is Leonardo Pisano,” he said, bowing to the small group. Billy saw a flash of recognition in Dickens’s eyes. “You are strangers to the great city of Pisa. What business do you have here?” the man asked, purely out of innocent curiosity. “Have you come to join in the festivities?”

  “My name is Dickens. These are my wards, Jeanie and Billy,” Dickens replied as he gestured to the two children. “Actually, we have come to see you.” Billy quickly glanced at Dickens and then at their new acquaintance, wondering who this seemingly meek and mild man was.

  “Me?” Leonardo exclaimed, sounding surprised but very pleased.

  “Your work is legendary, Signor Pisano. But of course, only if it is convenient for you,” he amended with a slight nod of his head.

  “I am always flattered when others who appreciate my work come to pay their respects. I would be delighted, Signor Dickens,” answered Leonardo, returning the nod.

  “Yes, I have read your book and wanted very much to discuss your theories and findings with you.”

  “I see. Are you a business man? Much of my work is used as an economic tool by the merchant class.”

  Dickens shook his head and laughed. “No, just a simple man I’m afraid, one who seeks knowledge only as a pastime.”

  “Well, I must say, it is a very worthy one indeed,” said the little man with a laugh.

  “We are weary from our travels. Could you recommend an inn for the duration of our stay?”

  “Oh, Pisa boasts of many very comfortable inns, indeed.” A frown creased Leonardo’s brow as he said, “However, the inns are full due to the celebrations.” The little man rubbed his chin, then looked up and smiled. “Why do not all of you stay at my home?” he offered.

  “We couldn’t possibly...” Dickens sputtered. But Billy knew Dickens well enough by now to see that circumstances were progressing exactly how he wanted them to.

  Leonardo waved his hand in the air. “No, no, no we Italians pride ourselves on our hospitality. Besides, I owe a debt of gratitude to the little signora here,” he said as he motioned to Jeanie.

  “Well then, I guess it’s decided,” announced Dickens, with that secret smile.

  “Come, the day is ending and I am too old to stay out this late at night. I shall leave the merry making to the young people. Besides, it will be dinner time soon.”

  As the small band followed Leonardo home, Billy witnessed what seemed to be a triumphant smile on Dickens’ face directed at Leonardo’s back. He had a feeling that Leonardo was about to play an important role during their stay in Pisa.

  As Billy trotted down the lane with the others, he noticed the sturdy homes built side by side, lining the narrow streets. These dwellings seemed to be made of stone or brick with clay tiled roofs. They were squeezed tightly together and generally built to accommodate two or more stories. The windows were small with wooden shutters at the sides. It was not what Billy expected from a medieval town, for the prosperity was evident everywhere he looked.

  Leonardo approached a three story house similar to the others lining the street. He opened the door, stretched out his arm and announced, “Welcome to my home.”

  As Billy entered the small doorway, the first thing to hit him was an overwhelming musty and foul stench. The next thing to hit him was the sight of at least two hundred rabbits scattered about the rooms.

  There were rabbits everywhere. There were on the tables and chairs; even crawling in and out of pots and pans lying about the counters. He turned toward Jeanie and Dickens. Their faces held the same horrified expression as his own.

  Leonardo must have seen their looks of disgust, for he said with some embarrassment, “I must apologize for the condition of my home at the moment. A local boy, Aczo, helps with the cleanup. But his mama recently broke her leg and he must stay at home to help her.”

  “Not to worry, Leonardo! I have a strapping young lad who would be more than glad to help you around here,” offered Dickens, slapping Billy’s back

  “Thanks a lot,” Billy muttered under his breath, suddenly not looking forward to the next few days here.

  “Signor Leonardo,” called out a high voice behind him, belonging to Georgii. “I would be most willing to help Billy with this chore. Of course, after I help my father at the bakery,” he added hastily with his hand on his heart, giving Billy a small nod.

  Billy knew that this was Georgii’s way of thanking him for his help with Niccolo. He couldn’t help but groan inwardly. He didn’t want to spend any more time with the weird kid then he had to. Billy did grudgingly admit that the little scenario with the mayor’s son put him back in the good with Jeanie. So he would just have to tolerate him.

  After Georgii left, everyone sat around the table eating a late dinner of cheese and bread smeared with olive oil and a side of seasoned pork. Leonardo introduced a number of his beloved pets to his guests, who Billy was rapidly starting to despise. They would hop onto the table as everyone was eating. He would take one off, only for it to be replaced with another furry intruder.

  Billy and Jeanie excitedly recounted for the older gentlemen the interesting sights and experiences they had during their day at the fair. However, they left out their misadventure with Niccolo de Fabiano.

  As Billy and Jeanie cleaned up after their meal, Leonardo and Dickens discussed the mathematician’s work. They were quickly caught up in a debate about its applications in the Pisan business world.

  The night grew late, so Leonardo showed Billy and Jeanie to the rooms that would be theirs for the duration of their stay. As Leonardo prepared Billy’s room for bed, Billy asked him who the strange young baker’s son was.

  The older man instantly smiled. “Ah, Georgii de Villana. He is an interesting boy, is he not?” he said, giving a little chuckle.

  “Ya, interesting. Um, why does he carry a wooden sword around?”

  Leonardo sat on the bed, folded his hands and rested them on his lap. “Georgii is a special boy, you understand. He is very small and not very strong for a boy of fourteen years. Unlike other boys, he has a peculiar way of thinking. You see, Georgii wishes to
be a knight of the realm. He is a baker’s son and as you know, can never be more so. However, he is very persistent in this fantasy. Unfortunately, because of this, he has very little friends to speak of.”

  Leonardo stood and walked to the door. He turned around and in a soft voice said, “Young man, Georgii may have an odd mind, but he is a good boy. Please be kind to him.” Leonardo then quietly left the room, shutting the door behind him.

  Later, Billy settled into his bedroll on the cold stone floor, with Dickens snoring softly in the bed above him. As he stared out into the black of night, his mind recalled Leonardo’s words. Billy had treated Georgii like the annoying kid he thought he was. He couldn’t believe that the small boy was actually older than him! As he fell asleep, something unidentifiable bothered Billy, causing a fitful and troubled slumber.

  Chapter 19

  Billy walked down the stone steps leading into the kitchen, yawning and feeling like he didn’t get any sleep what so ever. Jeanie and Dickens were already eating breakfast. As he sat down at the table, he put his head in his hands.

  “What’s wrong? Didn’t have a good sleep?” Dickens laughed, biting into a piece of bread.

  Billy just groaned. “Not when you have to sleep on a cold stone floor and have rabbits trying to sleep on your head.”

  Jeanie laughed. “They did the same to me, but I liked it,” she said while passing Billy a decanter of milk.

  As Billy was pouring himself a cup, he asked, “So, Dickens, I got the impression yesterday that Leonardo may be helpful to us.” He stopped to look about the room. “Where is he, by the way?”

  “He’s gone to the market to buy us dinner, and of course, an excuse to walk Barzo and Ballius.” At seeing Billy’s confused face, he added, “Two more of his beloved pets.”

  Billy couldn’t contain the look of disgust on his face. “What’s with the rabbits? I wish we could stay at an inn; it stinks in here!” His expression turned into a smirk as he said, “So what is Leonardo, anyway, the medieval version of a cat lady?” He then added darkly, “He seems nice and all, but I think he might be crazy.”

  Dickens gave the cranky young man an exasperated smile. “Billy, what you call crazy, others would define as passion. Besides, the rabbits have everything to do with why Leonardo is significant to us.”

  Billy reached for some grapes sitting in a bowl in the middle of the table. “And how is he significant? Hopefully, this time we can get somewhere,” he complained as he popped the grapes into his mouth.

  Dickens rose from the table and swiftly went to a nearby window. He poked his head out and looked down the street in both directions. “All right, Leonardo does not seem to be coming, so we have a few minutes. This is a perfect time to fill you both in.”

  Dickens sat back down, rubbed his hands together and began. “Leonardo Pisano, more commonly known as Fibonacci, was born to an Italian merchant. His father owned a trading post in Bugia, North Africa. It’s in Algeria, I believe. Anyway, from a young age, he was fascinated with the great knowledge found in the Arabic world. While there with his family, he spent his time learning everything he could of the Hindu-Arabic numbering system and various forms of mathematics.”

  “Wait, I thought this was the middle ages. You know, knowledge is lost and all that,” inquired Jeanie.

  “That is very true in Europe, but not so in other parts of the world. There were many great men and actually some women of knowledge who either carried on the works of the ancient world or figured out formulas or equations on their own. There was Bhaskara II in India, Yang Hiu of China and Al-Karaji from the Arabic world, to just name a few. Anyway, Leonardo is considered to be one of the most gifted European mathematicians of the middle ages. Although he was a superb mathematician himself, what he is most known for is introducing the Hindu-Arabic number system to Europe. He published what he learned in North Africa in a book called the Book of Calculation.”

  Billy shook his head. “I know that most people weren’t very educated in this time, but I do know they could at least count.”

  “Well, no, the general masses were so ignorant, many of them couldn’t count. However, Europe did have a number system, but it was based on Roman numerals. The Hindu-Arabic system is based on the numbers one through nine. It is much more efficient and was, as we know, embraced very quickly. It was and is obviously still used for bookkeeping, calculation of interest, conversion of weights and measurements and so on. You must understand that not only Italy is experiencing an economic boom, but so is all of Europe. The system came in very handy where money changing was involved.”

  “Our numbers come from Asia?” asked Jeanie in astonishment.

  “Jeanie, our alphabet comes from Ancient Phoenicia, which is Lebanon in your time and apart of the Arabic world.”

  “Oh,” was all she could think of to say.

  “That’s all very interesting, Dickens, but how it going to help us and what do the rabbits have to do with anything?” Billy asked in an irritated voice, as he picked a rabbit off of the table and set it back on the floor.

  “Leonardo learned of a sequence of numbers from India, which originated in the ancient world. He used rabbits and their mating habits to illustrate the formula. For example, start with a female and a male and see how many offspring you have in a month or a year. This became known as the Fibonacci Sequence, where the number is the sum of the previous two numbers, 0, 1, 1, 2, 3, 5, 8 and so on.”

  “Ya, so?” Billy couldn’t help but laugh. “What’s so great and important about that?”

  “Well, Mr. know it all, if you would let me finish,” Dickens replied in a testy manner. “Now, as you go up higher in the sequence the two numbers divided by each other will approach the Golden Ratio.”

  Dickens smiled at the children as if that explained everything. However, going by the lost expressions on the two children’s faces, he continued. “Uhhh, alright then, let me illustrate. Imagine a line, and then draw through it, creating two segments of a different length. Now, the ratio of the short line to the long line will equal the ratio of the longer line to the overall line, which is approximately 1.618.”

  Billy still had no idea what the old man was talking about. Dickens put his head in his hand and let out a deep breath. “Let me try again. The Golden Ratio is perfect proportion. All through history, man has attempted to understand these numbers and their significance. These proportions are found in the Great Pyramids, the Parthenon and the Mona Lisa. This mystery has not only marveled mathematicians, but artists, musicians, architects, historians and many more for thousands of years. This ratio is found in the human body and in nature. It can not only be manifested by man, but it exists in the very fabric of our physical world. Do you understand?”

  Billy drew his brows together in thought. “I think so, but I still don’t see how Leonardo and this ratio are going to help us,” he said, as he shook his head.

  “The Golden Ratio is an irrational number and it has an infinite number of decimal points, never repeating itself.”

  Dickens stared at his wards, looking as though he was fighting for the right words. He leaned forward and in a soft voice said, “Children, we’re in Medieval Europe and happen to be in the same city of one of the very few men of this time who understands the concept of infinitesimal numbers. If anyone is going to be able to help us figure out the workings of the Device, it’s Leonardo Pisano.”

  Staring at the wooden table, Jeanie appeared thoughtful. Finally, she looked up and turned to Billy. “Remember what Dickens said Billy, there are no coincidences. If we’re in this time and Leonardo happens to be here in this city, it has to be for a reason,” she said with conviction.

  “Thank you, Jeanie,” added Dickens with a smile. He turned to Billy. “Please, trust me. I think Leonardo is our only hope here.”

  Billy knew deep down that Dickens was right; that he needed to trust him if they were going to get back home. He observed Dickens with curiosity, wondering how the old man always knew so
much.

  As if right on cue, Leonardo walked through the front door. Jeanie ran to him, taking a large basket full of food out of his hands.

  “Thank you, my dear. Holding that basket and trying to manage these two ruffians at once has been trying.” From what Billy noticed about rabbits, the issue is getting them to move and not the other way around. “And how did everyone sleep last night? I hope my little babies did not keep anyone awake,” he asked jovially, as he unleashed his rabbits.

  Billy opened his mouth to say something, when Dickens replied, “It was very fine, Leonardo, thank you again for your hospitality,” as he gave Billy a look that said to be quiet.

  Leonardo began cutting up carrots, aided by Jeanie, as he informed the group, “I saw Georgii at the bakery; he should be here any moment.”

  At hearing this, Billy made an internal groan. He grudgingly appreciated Georgii’s offer of help, but he didn’t want to spend hours in his annoying company. If he said ‘Gianna’ one more time, he was going to barf!

  Just then the front door slammed and Georgii entered the room. He gave Leonardo and Dickens a low bow. “Good morning, my Signors.” He turned to Jeanie with a look of awe. “My Gianna, you look more beautiful this morning than the sun at-”

  “Ok, ok, let’s get to work!” said Billy, rolling his eyes.

  “Oh, Billy, good morning!” He wore a sincere smile, as he nodded his head.

  The worst part about Georgii, Billy thought, was that he seemed real. He was so disgustingly nice and helpful, that it was getting harder and harder to not like him. Of course, that didn’t mean Billy couldn’t find him totally annoying.

  Then, out of the corner of his eye, Billy noticed that Dickens was standing at the front door wearing his surcoat and helping Jeanie put on her own.

  “Where are you guys going?” he demanded in a panic stricken voice.