Chapter 22
THE LAST PIECE OF THE PUZZLE
The journalist from The Times had been waiting for half an hour when Elmer Galway rushed into the Senior Common Room clutching a pile of papers and file folders to his chest with one arm. He stopped for a moment to catch his breath, looked around, and then headed toward his visitor.
“I’m terribly sorry for being so late, Mr. Morrison,” he said, extending his free hand. “I was held up at a very important meeting; the fate of our scholarly journals was at stake.”
Thomas Morrison flashed an understanding smile, got to his feet, and shook Galway’s hand. He was a gentle, mild-mannered fellow in his thirties who had joined the London newspaper only recently after struggling many years as a freelance writer. On reading the press release—“English-Italian team discovers 500 BC Greek mathematical papyrus”—he had immediately contacted Galway asking for an interview, one of the numerous such requests the Oxford professor had received over the past two weeks.
“It’s quite alright, Professor Galway,” he said in response to Galway’s apology. “I assumed you would be very busy since the announcement of the discovery and didn’t expect to get to interview you this soon anyway.”
“It’s been pretty hectic indeed,” Galway admitted, “but I don’t mind. I’m happy to see archaeology and history instead of physics and cosmology make news for a change. All those stories about teleportation, dark matter, and multiple universes may well catch the public’s imagination, but where’s the evidence? They’re little more than pure speculation, if you want my opinion.”
Morrison hesitated and finally chose not to comment for fear of being dragged into an unwanted confrontation with the professor on the issue. Galway, who hadn’t expected a reaction from the journalist, was already leading the way to a quiet corner of the room, where he invited Morrison to sit down before slumping into an armchair.
“Do you mind if I record our conversation?” asked Morrison, producing a small tape recorder from his briefcase.
Galway replied that he didn’t and the interview got under way.
“Could you first tell me the circumstances leading to the discovery of the papyrus?”
The professor shifted in his chair and began his story.
“We, that is, my Italian colleague Doctor Antonio Marcheggiano and I, first learned of the existence of the papyrus from a medieval book that surfaced in London last autumn and was later auctioned. I was called in to give an expert opinion on the authenticity and historical value of the book, a thirteenth-century Arabic text on parchment. To the best of my knowledge, the book was a translation of a Greek letter written around 500 BC by one of the disciples of the famous philosopher and mathematician Pythagoras to another of his followers. Among other things of enormous value to historians, the letter mentioned the existence of a manuscript in Pythagoras’ own hand, which at the time, 500 BC, could only have been a papyrus scroll. Although the letter gave no indication of its content or possible location, it did mention that the manuscript should be ‘protected at all costs.’ We therefore concluded that some extraordinary precautions might have been taken to preserve the papyrus from the ravages of time, increasing the probability that it still existed after 2,500 years.”
Galway paused and again shifted in his chair.
“And you had no idea of where the papyrus might be hidden?” asked Morrison.
“Not the slightest idea; and the story might well have ended there, had it not been for the discovery of another book, or rather, another part of the same book.”
“It turned out that the medieval book originally contained eight more pages of elaborate artistic drawings. These pages had been cut out, presumably to be sold separately, but we managed to obtain photocopies of them. We strongly suspected that those skillfully crafted drawings, arabesques, and mathematical symbols contained cleverly concealed clues to the location of Pythagoras’ papyrus. Problem was, despite all our efforts we were unable to decipher the hidden information and began to doubt there was any information at all.”
Galway then went on to tell Morrison about his discovery of the sketch of the serpent bas-relief among his late father’s papers, which, combined with the drawing they had earlier unsuccessfully tried to decipher, all but revealed the place where the papyrus was hidden. After obtaining the necessary permits from the Italian authorities, he and his colleague had searched the Neo-Pythagorean basilica at the appropriate spot and made the sensational discovery: a 2,500-year-old papyrus, believed to have been written by Pythagoras and miraculously well-preserved.
“And what is the papyrus about?” asked the journalist.
“We’re still studying it, but can say for sure that it contains many results of Greek mathematics until now only known indirectly, through writings and translations dating from centuries after Pythagoras’ time. It is the oldest extant record of some Greek mathematical discoveries, and as such, a document of incalculable value for the history of mathematics.”
“I suppose the vast majority of papyri from Pythagoras’ days, if not all of them, were lost or destroyed in the course of time because no particular care was taken to protect them,” said Morrison, as a preliminary to his next question: “What’s so special about this one to have warranted such extraordinary precautions to preserve it?”
For the first time during the interview, Galway hesitated. He took off his glasses and rubbed his eyes before replying, looking as if he were carefully choosing his words.
“Actually, that’s still a bit of a mystery for us. But we’re working on it.”
Later, back in his office, Galway reflected on how close to (or far from) the truth was the story he had told the journalist from The Times—and others who had asked him essentially the same questions about the discovery of the papyrus. He had only lied by omission, he told himself, for the story was strictly true, except for the fact that his Italian colleague became involved only at the end, and not from the beginning.
On his return to Oxford after his successful Roman adventure, Galway had contacted Antonio Marcheggiano, a well-known Italian archaeologist and director of Rome’s Capitoline Museums. He had told the Italian he was on the trail of a papyrus scroll supposedly written by Pythagoras and had lately come across certain records pointing to its possible location, somewhere in the center of Rome. And then he had made his offer: Would Dottore Marcheggiano be interested in becoming his partner in the search for the manuscript in exchange for helping him to obtain the necessary excavation permits from the Italian authorities?
It was the best thing to do, he had thought then and he still did; going at it alone was too risky. Even if he were the one to discover it, the scroll would be immediately seized as belonging to the Italian cultural heritage and he would lose control over it. He doubted the Italians would allow a foreign archaeologist to be the first to study the papyrus, let alone publish a translation of it. To be sure, by getting Marcheggiano on board as co-discoverer he would have to share the glory, but it would guarantee him first-hand access to the precious scroll from the start. Sharing the catch had appeared to him as the only way of securing a piece of it for himself—and a non-negligible one at that.
His plan worked just as he had imagined. The “discovery” of the scroll took place in the presence of Marcheggiano and his team, under powerful lights and in front of video cameras. With appropriate precautions, the papyrus was removed from its metal container, placed in a special protective case and sent to the Capitoline Museums restoration laboratory, where it was carefully unrolled in optimal temperature and humidity conditions, digitally scanned, and subjected to various tests and analyses. A press conference was held, press releases in various languages issued, and a party thrown to celebrate the momentous discovery. Throughout it all, Galway shared the spotlight with the Italian archaeologists: his gamble had paid off.
A three-person team headed by Galway was set up to translate and analyze the ancient text. Fully unrolled, the papyrus measured 24 by 96 centimeters. The scroll was written in columns of about 7 centimeters, continuously, without breaks between words; a space of about 1 centimeter was left between columns. As was customary in ancient times, there was no title at the beginning of the manuscript, and a blank space was left to protect the first part of the roll. It was not signed, and the author did not identify himself either, but it was clear from the style and the quality of the language that whoever wrote it belonged to the elite of highly educated persons. Moreover, the extent and depth of the mathematics suggested that its author was well versed in that science. All in all, and considering also the clues that led to its discovery, the members of the team strongly felt that they had come into possession of an extremely rare jewel, one which until then they had thought did not exist: a manuscript written by Pythagoras himself.
It began with an exhortation:
All inhabitants of cities or country should in the first place be firmly persuaded of the existence of divinities as a result of their observation of the heavens and the world, and the orderly arrangement of beings contained therein. These are not the productions of chance or men.
This divine “orderly arrangement,” the author claimed, was ruled by the pervasive presence of “Number,” not only in “the heavens and the world” but also in all human activities and creations. Of the universe, the text said that “it has existed from all eternity and will remain eternally,” and that it is made of five “mathematical” solids. These solids are at the origin of the four elements (earth, fire, air, and water) of which everything is composed: earth arose from the cube; fire, from the tetrahedron; air, from the octahedron; water, from the icosahedron; and the “sphere of the All” from the dodecahedron. Therefore, what the author called “mathematical” solids are the five regular solids, also known as Platonic solids. These are defined as convex polyhedra whose faces are congruent regular polygons, such as triangles, squares, or pentagons.
There followed what amounted to a list of mathematical results furthering the notion of order and harmony and usually attributed to the Pythagorean school: properties of various classes of numbers, “perfect,” “triangular,” and “square” numbers;* theorems about triangles, polygons, and circles, the famous Pythagorean theorem among them, and a method for constructing right-angled triangles with any given odd number n as the smallest side, which, in modern notation, is expressed by the formula n2 + [(n2–1)/2]2 = [(n2 + 1)/2]2 (for example, when n = 3, one obtains the well-known 3, 4, 5 triangle).
The manuscript also mentioned “the most perfect proportion, consisting of four terms, and properly called musical,” and illustrated it with the numbers 6, 8, 9, 12. The author was probably referring to the fact that the ratio 6 : 12 between the extremes represents the octave ( = 1 : 2); both 6 : 8 and 9 : 12 represent the perfect fourth (= 3 : 4), and 6 : 9 and 8 : 12, the perfect fifth ( = 2 : 3). Moreover, 9 is the arithmetic mean of the two extremes (9 = (6 + 12)/2) and 8 their harmonic mean. (Given two numbers a, b, their harmonic mean is the number c equal to 2ab/( a+ b)—or, equivalently, 1/c is the arithmetic mean of their reciprocals 1/a and 1/b).
The scroll ended with an enigmatic warning against “the coming of a false prophet seeking to deceive and mislead men by preaching the preponderance of chaos over order and harmony, and the rejection of Number as the unifying principle through which a perfect knowledge of all that exists can be attained. He must be stopped, and with the help of the Gods, he will.”
The meaning of this last part remained obscure to the team that studied the papyrus. If one were to ignore it, they argued, the ancient manuscript could be considered a kind of compendium of Pythagorean principles and discoveries, which the famous philosopher had taken great pains to preserve for the benefit of future generations.
Galway reluctantly rallied to this interpretation, which was the one favored by the two other members of the team, but he had the nagging feeling that something wasn’t entirely right, that a piece of the puzzle was missing.
On a dreary, chilly morning in late November 1998, after Galway had come back from his morning walk with Slipper and was about to get in the shower, the doorbell rang. He wasn’t expecting any visitors, especially at such an early hour.
With Slipper barking at his side, Galway looked through the peephole and saw a short, rather young man with a pleasant looking face wearing a blue parka and gray trousers. The notion that the stranger was calling at the wrong place crossed his mind but it was quickly dispelled. No sooner had he half opened the door than the man said, with an eager voice:
“Professor Galway? Please forgive me for imposing myself on you like this but I’m sure you’ll be interested in what I have to tell you about Pythagoras.”
Something in the man’s appearance—the intelligent look in his clear green eyes, perhaps—was reassuring enough for Galway to open the door completely and invite him in.
“Please come in, Mister . . . ?
“Davidson. Jule Davidson.” The unexpected visitor stepped inside and immediately became the object of a thorough sniffing inspection on the part of Slipper. Galway, clad in a red-and-white striped bathrobe, led the way down the hall and into the living room. He said, without turning his head: “Have a seat, Mr. Davidson, please. I’ll be back with you in a few minutes,” and disappeared, leaving the dog behind as if to keep watch over the stranger.
Jule sat down in a battered leather sofa facing the fireplace and studied the room. It was dark, the only light coming through a window that opened on the front garden, since Galway had not turned on the lights. The walls were covered with framed photographs, mostly groups of people; there were a couple of paintings and a series of brightly colored African masks. Furniture was sparse—an armchair and two small tables beside the sofa—but there were plenty of objects crowding the room, from small ivory statuettes to a large Egyptian sarcophagus standing in one corner. Artificial lighting was provided by a table lamp, a floor lamp, and a crystal chandelier.
“Where are you from, Mr. Davidson?” The question startled Jule, who instinctively got up, only to be motioned to remain seated by Galway, who had changed into a tweed jacket and corduroys.
“I’m from the eastern United States; New Hampshire, to be exact.”
“And you came all this way to tell me something about our common friend Pythagoras,” said Galway in a faintly amused tone. He was sitting in an armchair across the room and seemed to be enjoying the company of his unannounced American visitor.
“Actually, I’m traveling through Europe on a kind of sabbatical. I have plenty of time. By the way, I owe you an apology.” Jule leaned forward and fixed Galway: “A few months ago someone broke into your house and stole your computer. I feel partially responsible for that and I’ll explain why. Please accept my sincere regrets for the intrusion and the theft.”
Galway hadn’t expected the conversation to take such a turn. He became a little tense and it showed in his voice.
“You’re not the person who broke in, I gather.”
“No, that person is now dead.”
An awkward silence followed. It was broken by Jule: “Let me start from the beginning. I don’t suppose you know an American,” he hesitated, “pseudo-religious organization called ‘The Beacon.’ ”
“No, I don’t. What about it?”
“They are in fact a sect of Neo-Pythagoreans who worship Pythagoras as their master.”
“Esoteric sects of that kind existed during the Roman Empire, but I wasn’t aware of any contemporary Neo-Pythagorean group. Are you a member of that sect?”
“No, but I worked for them. They hired me to help them find Pythagoras.”
Galway almost jumped from his seat.
“I beg your pardon.”
“Yes, that’s precisely what they wanted.”
“Are we talking about the same Pythagoras?”
“We are. But let me explain. The leaders of the sect claimed to have found reliable evidence in some obscure Middle Eastern libraries that Pythagoras would be reincarnated in the middle of the twentieth century.” Jule paused and observed Galway’s reaction. The professor remained expressionless, waiting for him to go on.
“I think it was more of an act of faith on their part,” Jule resumed. “Whatever the case, they hoped to find Pythagoras reincarnate and convince him to become their master and guide.”
“Do you believe in reincarnation?”
“I didn’t at the beginning, but . . . some things happened; I don’t know what I believe anymore. I was part of the search team. When we learned that a medieval book with references to Pythagoras was for sale in London, we wanted to know what was in it. Since we couldn’t afford to buy it, we—I mean, a member of our team—stole your computer, hoping to find the translation among your files.”
“And so you did. Congratulations,” interrupted Galway, with an edge of sarcasm.
“Yes, but it didn’t help our search for Pythagoras.”
“And in the end, did you find him?” Galway asked point-blank. He was of course expecting an unqualified “No,” but Jule’s answer was far from categorical and certainly not in the negative.
“For a while, I thought we had found him, but I’m no longer so sure.”
Galway couldn’t hide his puzzlement. He moved forward to the edge of his seat.
“What do you mean?” he asked, fixing Jule intently.
Jule then told him about what they had thought was overwhelming evidence that Norton Thorp was the reincarnation of Pythagoras. He didn’t mention the tragic kidnapping episode and simply said that, sadly, Thorp had died in a car accident before they could talk to him. In any case, the police had never traced the kidnapping to Trench or the Neo-Pythagorean sect. The death of such a high-profile scientist had prompted a huge federal investigation, but the FBI had concluded that Rocky, already known to the police, had kidnapped Thorp for ransom with the help of an accomplice.
Galway did not say anything for a while. He seemed to be struggling between the impulse to dismiss outright any possibility of reincarnation and acknowledging that perhaps there was something more than simple coincidences in Jule’s story.
“You said that you’re no longer sure that Thorp was Pythagoras reincarnate. Why?” he asked at long last.
“I recently came across a paper of Thorp’s that was published post-humously, a sort of mathematical testament. By the way, you never asked me what I do for a living. I’m a mathematician, so I can fully appreciate the significance of Thorp’s landmark result: randomness and chaos, and not predictability and order, are at the heart of mathematics. And this has far-reaching consequences for other sciences as well, physics in particular, for if you can’t make connections, you cannot solve or prove things. Such a state of affairs is the exact opposite of the ideas advocated by Pythagoras, for whom it is numbers, and not chance, that rule the world, and by unlocking their secrets one can understand anything. According to Thorp, however, the secrets of numbers are for the most part impenetrable, so Pythagoras’ program is doomed from the start. To put it bluntly: if we compare Pythagoras to Christ, then Thorp is the Antichrist, so how could he be Pythagoras reincarnate?”
He paused and noticed Galway’s reaction to his words. The professor was overcome with excitement, his mouth open but producing no sound, until he finally said, talking to himself: “The missing piece of the puzzle. . . . ‘Beware of the coming of false prophets seeking to deceive and mislead by preaching the preponderance of chaos over order.’ ” He was quoting from the last part of Pythagoras’ papyrus, which now appeared to him in a new light.
“The prediction of Pythagoras’ reincarnation may have been right after all,” he said to Jule, who had no idea what was going through the professor’s mind.
Galway went on: “Let me tell you how the different pieces of the puzzle may, just may, fit together—reconstructing the past is not an exact science.
“Pythagoras somehow learns—an Oracle tells him, or he has a dream, I don’t know—that sometime in the future a man of unsurpassed intelligence, admired and respected throughout the world, will claim to have a proof that it is chance and chaos, and not the predictability and order of numbers, that actually rule the world. To Pythagoras and his school, such a person would personify the Anti-Pythagoras—or the Antichrist, as you called him—one who disseminates false and evil ideas to prevent men from comprehending the true nature of reality. This future heretic must be stopped at all costs. Such will be the mission of Pythagoras reincarnate.
“Pythagoras then writes down his most treasured results and the purpose of his mission as a message to himself reincarnate and sets up a mechanism for the preservation of this information, maybe through a chain of custodians, each passing on the document to the next. This may explain the extraordinary precautions taken to protect it. Some ancient historians, such as the third-century philosopher Porphyry, mention certain writings that later Pythagoreans left to their sons or wives to preserve within the family, a mandate that was obeyed for a long time.
“At some point, the precious scroll is hidden in the Neo-Pythagorean basilica, perhaps by a member of some esoteric sect who worshipped there, as the best way to protect it, and clues to its recovery and to the recognition of Pythagoras reincarnate are left behind—the letter of the Pythagorean, mentioning a manuscript in the Master’s hand; the drawing of the serpent bas-relief; the Tetraktys engraved in the stone; the Greek poem, and maybe others as well. Copies and translations of these documents—not always faithful or complete—circulate for centuries. Most of them are lost or destroyed, but one finds its way into the bowels of the Basilica of St. Francis, in Assisi. When the September 1997 earthquake exposes the medieval book, it sets in motion the chain of events leading to the discovery of the precious papyrus.”
Jule had been listening to the professor without daring to interrupt him. He had many questions, but there was one in particular he was anxious to ask: “So you believe that Thorp was probably the Antichrist, or rather the Anti-Pythagoras that Pythagoras so feared, right?”
“I didn’t say that. My story is at best a plausible guess and at worst wild speculation. Personally, I don’t believe in reincarnation, but if I did, I wouldn’t rule out the possibility that Thorp could have been both the Anti-Pythagoras and Pythagoras reincarnate, who, thanks to his exceptional intellect and equipped with the knowledge of twentieth-century science and mathematics, demolished the very foundations of his own doctrine.”
“If that’s the case. . . . What an irony! Being reincarnated as your worst enemy!” Jule shook his head and sat back in the soft, deep leather sofa. He felt tired.
It was already mid-morning, and neither of them had had anything to eat.
“I’m hungry,” said Galway getting to his feet. “What about you?” And before Jule had a chance to answer, he added: “Come to the kitchen, I’ll cook us some breakfast.”
*See appendix 5.