Galileo's Lost Message

by D. Allen Henry

  “It’s a plaque describing how Galileo dropped balls from the tower when he was a professore at The University of Pisa. That would have been perhaps around 1588.”

  “Would have been?” Antonietta asked.

  “Right. There seems to be a great deal of disagreement about whether or not he actually did drop balls from the tower.”

  “Too bad, it’s a good story,” she replied placidly.

  “Well, I have another one, if you are interested,” he proposed.

  “Okay,” she answered disinterestedly.

  “This one relates to the poem,” he replied.

  Brightening at the prospect of getting back on the trail of the puzzle, she responded, “Oh, well then, by all means, tell me!”

  “Excellent!” he rejoined, “But for that, we must enter the cathedral.” He headed over to the back entrance, and she followed. Once inside they took a few moments to let their eyes adjust to the dim lighting, and he took the opportunity to give his small speech.

  “Galileo is sort of the inventor of the pendulum clock, although the real credit goes to Christiaan Huygens, who came up with an effective design about fifteen years after Galileo died. But when Galileo was a very young man, he was apparently attending service one day right here in this cathedral when he noticed the lantern adjacent to the pulpit over there swinging to and fro. It was not uncommon for the lantern to be swinging to and fro during service, as the lantern was usually lit just beforehand by pulling it towards the pulpit with a long hooked bar and subsequently lighting the candles. By using his own heartbeat as a clock, Galileo noticed that the time of transit of one cycle of the swing of the lantern over there adjacent to the pulpit was more or less independent of the distance travelled. He apparently lost the thread of the sermon during the religious service, and his errant and inventive mind came up with what was the most common means of measuring time until well into the twentieth century.”

  “Ah, so that’s THE lantern, is it?” Antonietta replied happily.

  “No, it’s not,” Paul replied. “The lantern was replaced sometime after Galileo’s death, so that is not the lantern that he watched to discern the law of the pendulum.”

  “Hee hee…” she answered ecstatically. “I knew that! I meant the lantern in the poem!”

  “Oh! Right, right you are, that IS at the location of the lantern in the poem of course. But we already know what it refers to, don’t we, Antonietta!”

  “We do?” she glared at him dubiously.

  Smirking at his own superiority, he replied, “We know that the directions will lead us to The Leaning Tower. Here, give me the poem.”

  She handed him the poem from her purse, and he read aloud, “Seventh stanza:

  Thenceforth find Leonardo, count his way

  Eighty paces toward the tilt

  And left (from lantern) eighty more

  The tilt shall be found in the way,

  And falter on the selfsame day?

  “Sooo, we start from the tomb of Leonardo in the Camposanto, walk eighty paces south, then…”

  “Why south?” she interjected.

  “I already explained that,” he responded impatiently. “The tower leans directly south.”

  “Oh, right,” she replied.

  Continuing, he said, “Where was I? Oh, right. Eighty paces south brings us directly to the lantern. From there we turn left and go eighty paces directly east. And voila, we arrive at The Leaning Tower.”

  “Got it,” she answered laconically. “So let’s go check out Leonardo’s tomb. I want to see the starting point.”

  “Do I detect a note of skepticism?” he asked with good humor.

  “Not at all,” she answered noncommittally. “I just want to go inside the Camposanto.”

  “Ooh, me too!” he replied with boyish charm. They exited the cathedral and crossed over to the Camposanto. Stepping inside, both stood frozen in their footsteps, the silent serenity pervading their senses.

  "Oh, this is wonderful, Paulo. I love this cemetery. It is absolutely gorgeous."

  "Yes, and we are fortunate to still have it, after the terrible bombings in World War II," he replied.

  "So where is he buried?" she asked as they began to walk.

  "At the other end, but first let us see the frescoes, I especially like The Last Judgment, The Hell, and The Triumph of Death, by Buffalmacco." They stepped into the room and they found themselves all alone, surrounded by fabulous medieval frescoes. "They've done an unbelievable job of restoring them, don't you think, Antonietta?"

  "Yes, they were in really bad shape after the fire. Someday they hope to transfer all of them back from the Sinopie, you know, Paulo."

  "Yes, it is truly an incredible setting, don't you think?"

  "Oh yes," she replied with obvious fascination, "But frankly, all of these good and bad Angels make these paintings appear rather menacing to me."

  "Well, it was the Church's way of advertising in the Middle Ages, I expect. They were trying to herd the sheep, and they were using every means available to keep the masses in line."

  Antonietta shivered and said, "That reminds me of that horrible Last Judgment by Vasari in the Dome at Santa Maria del Fiori."

  "Yes, there are plenty of those still around. Actually we will see a really interesting one in Siena, perhaps tomorrow."

  Antonietta moved towards the portal to the room, and walked out into the portico. As she did so she noticed a man in the antechamber who was studying the photos depicting the restoration of the frescoes after World War II. Somewhat incongruously, the man was wearing a black business suit.

  "This is my favorite part," she said, stepping into the courtyard of the Camposanto. "Tis sacred soil, you know, Professore. It was brought here from Golgotha during the crusades. Imagine carting all of this dirt across the Mediterranean. Those people were dedicated, weren't they!"

  "Yes, I suppose that they were. And we are the beneficiaries of their toils. And now, let us go see Signore Leonardo. This way, please." The walk to the other end within the Camposanto was solemn, punctuated by their passing of Roman sarcophagi, monuments, and carvings of various shapes and sizes, almost all cut from marble. They eventually arrived at the far end, where stood a magnificent statue of Leonardo do Pisa.

  "Wonderful!" Antonietta said excitedly. "I've seen this statue before, but I never read the inscription. "I had no idea it was Fibonacci."

  "Yes, it is nice. And after all, we owe him a great deal today."

  "Exactly what do we owe him, Professore?"

  "Well, he was a great mathematician. He wrote a book called Liber Abaci, which utilized Hindu numbers. Today we often call those numbers Arabic numerals, but historians have been able to trace them back to India, so they are actually Hindu numerals."

  "But why are they so important, Paulo?"

  "The simplest way I can explain that is by asking a question: how would you like balancing your checkbook using Roman numerals?"

  "Oh, I see, when you put it that way..." she replied. "So Fibonacci didn't actually invent the numbers, he just translated them to the western world, right?"

  "Right, but his book really helped to drive the Renaissance."

  “Amazing,” Antonietta replied with little interest, “But what sort of clue are we looking for here, Paulo?"

  "Frankly, I don't know, Contessa. But I do have a hunch."

  "I thought that you might..."

  "I think that the clue has to do with numbers."

  "Why do you say that, Paulo?"

  "Well, the poem says 'then onward to the tomb of numbers'. As we discover more and more from this riddle, I am more and more convinced that Galileo labored long and hard to use very few words to impart an enormous amount of information. Thus, whereas I initially thought that 'tomb of numbers' referred uniquely to the tomb of Fibonacci, I now think that it may in fact be a double entendre."

  "Meaning?"

  "I don't know...something else having to do with numbers," was all Paul could
think of to say. "I need to think some more about it. Let’s go check out the Baptistery. I like the acoustics in there.”

  “Okay,” Antonietta said thoughtfully. They walked onwards a few paces, and she suddenly said, “Galileo played the lute, didn’t he?”

  “Yes. Yes, he did,” Paul replied. “His father was one of the great musical talents of his age. Actually, there is much extant literature today describing Vincenzo Galilei and his influence on Galileo. He taught his son the lute, and he also taught him something much more important – to never accept the voice of authority out of hand.”

  “In what way?” Antonietta queried.

  “Vincenzo Galilei instilled in his son Galileo an extraordinarily deep seeded passion to seek the truth. This quality that is today taken for granted as essential to all scientific advancement was spurned by all academics and clerics in Galileo’s time. Thus, we owe much to Galileo’s parentage.”

  “So how does that play into Galileo’s later life?”

  “Excellent question,” Paul replied. “As it turns out, it didn’t take long for that to take root. Within a few years Galileo designed and built a bilancetta, a balance for measuring relative weights of objects, right here in Pisa. That was a harbinger of his lifelong obsession with mechanics, especially experimental mechanics. Of course, he had already begun to suspect that Aristotle was wrong about many things, including the fall of heavy objects, but the bilancetta paid homage to Galileo’s hero Archimedes.”

  “I am very much afraid that I am in need of a glass of something stronger than water,” Antonietta replied perfunctorily. “All of this is making my head spin.”

  “Ha!” Paul replied. “Excellent suggestion. We should have no trouble locating a good ‘watering hole’ adjacent to the Piazza.”

  1589

  Galileo sat patiently listening to the Sunday sermon. As the sermon wore on, his mind drifted to other more interesting subjects. He thought of that other time, when he had noticed the swinging lantern right here in this place. That had led to his discovery of a medical device for measuring pulse rates.

  Then he thought on his time in Siena, when he had calculated the volume of Hell using the text of The Inferno by Dante Alighieri. That had been little more than theatrics, but it had at least led to his current position as the Chair of Mathematics at the University. True, this was a backwater place when compared to where the great universities of the world were, but he was confident that he would rise to greater heights as his fame grew.

  The sermon droned onwards, his mind wandering still further astray. He pondered his recent readings on the works of Archimedes. Surely here was an intellect to match his own. In his mind he imagined how a chance meeting would go if he could but meet the greatest scientist from antiquity.

  “Good day, Professore Galileo,” Archimedes would say.

  “And a pleasant day to you as well, Signore Archimedes,” he would respond.

  “How is the development of your bilancetta proceeding?” Archimedes would ask with interest.

  “Oh, excellent. I must say, quite excellent indeed,” he would answer agreeably.

  At this pronouncement Archimedes would clap his hands in glee, saying, “Wonderful! Wonderful! You must demonstrate it to me!” In Galileo’s dreams true scientists sought only truth - disagreements fueled by personal jealousy simply were not possible among great men of science.

  “Sir, I would be most happy to demonstrate it for you. I believe it to be in all ways superior to your balance,” Galileo would respond. “Of course, the theory of the lever that it is based on must be credited to you. My invention lies in the realm of application rather than fundamental concept such as you yourself have been so fortunate to give the world. The principle of buoyancy, the principle of the lever, the center of mass of a cylinder intersected by a plane, and the astronomical clock – these are all fundamental laws of nature invented by you, The Great Archimedes, that must be accorded the highest respect by mankind.”

  “That is most kind of you, Professore Galileo, most kind indeed. Nonetheless, my work, however useful, is done. On the other hand, you - Galileo - you have the ability to change the world far more than did I. I must entreat you – Reach high, my son. Look farther than those before you. Change the world as no one before you has done.”

  Galileo was suddenly snapped away from his reverie by the ringing of the bell announcing the Eucharist. As he arose to take his turn in line, he revisited his daydream. He resolved to spend more time studying The Great Archimedes, and to work especially hard to understand the principle of the lever more profoundly. Perhaps in time he might even be able to expand on this important concept in a way that approached the level of a fundamental principle. There indeed was a challenge worthy of his talents.

  The mass ended and Galileo departed the Basilica, heading back towards his house. As he did so, he passed The Leaning Tower. He suddenly stopped dead in his tracks, an epiphany coming over him. The words of Archimedes were ringing in his ears, “Reach high, my son.”

  Yes, of course, here was a sign indeed, as high above him stood The Leaning Tower, as if entreating Galileo to think on another even higher plane. Up to now he had envisioned the tower as little more than an expedient platform for performing experiments on balls of different sizes and weights. But now it seemed that Archimedes had sent him a message, and that message was to reach for the tower itself. Struck by this realization, he stood dumbfounded before it, imagining the tower to be supported on a balance. Such a monumental problem! How would he attack it? He resolved to take on Archimedes’ challenge – to reach high, and in so doing, to solve the problem of The Leaning Tower.

  1997

  The following morning, Paul stumbled into the breakfast room bleary eyed but nonetheless absurdly jovial.

  At the sight of his incongruous smile, Antonietta volunteered matter-of-factly, “You look like hell. Want some coffee?”

  Undeterred by her admonition, he ignored its implication and begged,“Yes, please! I am in desperate need of caffeine, and a lot of it!”

  As she poured him a cup, she stated the obvious, “Were you up all night?”

  “Pretty much. I caught a couple of hours sleep when I ran out of steam, but I have good news.” Seeing her peering over the rim of her cup with obvious anticipation, he volunteered boldly, “I believe I have solved a major piece of the puzzle!”

  She placed the cup before him and said, “Cream?” but otherwise showed no reaction to his revelation.

  “Did you hear me, Antonietta?” he growled his pointed reply.

  “Yes, of course I did,” she replied with little interest.

  Suddenly deflated by her unexpected lack of enthusiasm, he responded, “I thought you’d be excited.”

  She flashed him a smile and exclaimed, “I am!” but then she added, “I am, and then again, I’m not.”

  “But why?” he asked quizzically.

  “I suppose I have enjoyed the chase…perhaps too much. I shall be saddened to see it come to an end.”

  “Ah, I see your point,” he replied. “Okay, then. I won’t tell you,” and, buoyed by her explanation, he grinned broadly.

  Suddenly brightening, she exclaimed, “Not on your life, Professore! Not after all we’ve been through. Tell me. Tell me everything.”

  “Right, but you needn't get all teary eyed just yet. I've only solved a part of the puzzle. There's still plenty more to go,” and taking a long drag from his cup, he proffered, “I suppose that we should start with this.”

  “Va bene,” she responded but, unsure as to his meaning, she suggested, “Please continue, Professore.”

  At this he pulled the poem from his valise and commenced with, “Okay, let's review the seventh stanza -

  Thenceforth find Leonardo, count his way

  Eighty paces toward the tilt

  And left (from lantern) eighty more

  The tilt shall be found in the way,

  And falter on the selfsame day?

  "As
we now know, this stanza refers to The Leaning Tower.”

  "Yes, of course,” she replied impatiently, “But what pray tell does the last line mean?"

  "Right!" Paul expounded in evident accord. “You see, I couldn’t sleep last night. Our conversation about fundamental laws of nature yesterday kept coming back to me. To put it more appropriately, I was unbalanced by Galileo’s bilancetta. That little balance kept getting into my head and saying, ‘Think like Galileo’! Thus challenged by his little toy, I asked myself, ‘How would he think?’ Galileo was clearly taken with Archimedes, with the law of the balance, or more appropriately, the principle of the lever, which today we call ‘summing moments’.” He paused, took another long sip of coffee, and at this point he covertly placed the following page of calculations before Antonietta.

  Silently examining the page, she inquired diffidently, “Is this what you stayed up all night doing - some big homework problem? I haven’t a clue what all of this means. But you know that, you fool!”

  “Yes, of course I know that,” he responded pleasantly, which seemed somehow incongruous given his seriously disheveled appearance. “And no, I didn’t stay up all night doing this. This page only took a couple of hours. Unfortunately, my travails over the remainder of the night produced little of value.”

  “Okay, Professore,” she announced, making it clear that she would countenance no further prevarication on his part, “Please explain.”

  “Yes,” Paul responded, signaling that he understood the implied warning in her tone. Thus, rushing onward, he now offered, “Take a careful look at the parchment that we removed from the telescope, Antonietta. It shows The Leaning Tower, and there are arrows on the drawing. I deduced from the arrows that Galileo was trying to work out some explanation of the forces acting on the tower. Here is my more detailed version of his drawing, at which he shoved yet another piece of paper before her.