The Science of Shakespeare

by Dan Falk

  That’s a lot of threes (and I haven’t listed them all). Were these triads as important to Shakespeare as they are to McAlindon, or is he reading into the plays a subtext that the author never intended? McAlindon insists that these number patterns “tell us something important about Shakespeare’s beliefs and motivation.” His findings show that Macbeth, for example, is “a far more intricate and artful play than has customarily been thought” and provide us “with firm clues as to its meanings. Its special relevance in this context lies, of course, in the fact that number symbolism is part of the language of cosmology.…”

  Another scholar struck by Shakespeare’s use of numbers is Shankar Raman at the Massachusetts Institute of Technology. In a paper titled “Specifying Unknown Things: The Algebra of The Merchant of Venice,” he examines Bassanio’s and Portia’s argument over the status and value of unknown things—a quarrel that “parallels a shift in the history of algebra.” He says that “the language of proportionality and algebraic equations permeates in particular Bassanio and Portia’s responses to the ‘hazard’ of choosing the right casket.” The play expresses “a fundamental connection between law and mathematics.” In another paper, “Death by Numbers: Counting and Accounting in The Winter’s Tale,” Raman focuses on a “deep and abiding … connection between the language of Renaissance arithmetic and the (at first glance) unmathematical world of Shakespearean romance.” The most important numbers in the play, he says, are zero and one, with much of the drama rooted in an “overarching tension” between the two: “The difference between the zero and the one in The Winter’s Tale bespeaks a tension between the two different numbering systems, Arabic and Roman, to which the early modern era is heir,” and offers the playwright a chance to create “dense ruminations on the finititude of existence.”†

  * * *

  These highly analytic studies of Shakespeare’s use of numbers are certainly intriguing, and no doubt Shakespeare knew what he was doing in his use of numbers most of the time. But occasionally he seems to have been downright sloppy. In Hamlet, the prince ponders the imminent battle between Norwegian and Polish forces, and the “two thousand souls” (4.4.25) that will likely perish; a few dozen lines later it is “twenty thousand men” who will die (4.4.60).* In Henry V (1.2), the archbishop of Canterbury rattles off a long list of names and dates in order to justify the English king’s claim to France, and Shakespeare—repeating an error in Holinshed’s arithmetic—subtracts 426 from 805 and gets 421 (rather than 379). In Julius Caesar, Octavius laments Caesar’s “three and thirty wounds” (5.1.52), although Plutarch clearly has the number at twenty-three, not thirty-three. In The Winter’s Tale, both Leontes and the Chorus (“Time”) give the duration of the gap between the third and fourth acts as sixteen years, but Camillo gives it as fifteen (4.2.4). These few examples may not prove that, as Harold Jenkins has put it, Shakespeare “was often lax with numbers”; still, we should perhaps be cautious about attaching a deep significance to every number in the canon.

  As we’ve seen, Usher is not the first to focus on Shakespeare’s use of numbers; nor is he the first to look for hidden treasure in the curious words and phrases that one finds throughout the canon. Consider, for example, that peculiar line from Hamlet that we looked at earlier, about knowing a hawk from a handsaw. Recall that Usher’s explanation involved geography, and in particular the relationship between Elsinore, Tycho Brahe’s island of Hven, and the German university city of Wittenberg. It may have sounded like a stretch—but consider this explanation, offered by a nineteenth-century critic. After a reminder that “handsaw” may refer to a kind of bird, we are told that

  The meaning generally given to this passage is, that birds generally fly with the wind, and, when the wind is northerly, the sun dazzles the hunter’s eye, and he is scarcely able to distinguish one bird from another. If the wind is southerly, the bird flies in that direction, and his back is to the sun, and he can easily know a hawk from a handsaw. When the wind is north-north-west, which occurs about ten o’clock in the morning, the hunter’s eye, the bird, and the sun, would be in a direct line, and with the sun thus in his eye he would not at all be able to distinguish a hawk from a handsaw.

  Who could have missed that? Still, if “handsaw” means “heron” in Hamlet, one might wonder why it appears to straightforwardly mean “handsaw” in Henry IV, Part 1. The relevant scene comes in act 2, where Falstaff claims to have been attacked by a horde of bandits. (The number of attackers grows with each telling of the tale, but in reality it was just two men—Prince Hal and his accomplice, Poins, in disguise.) After intentionally damaging his own sword to make it appear as though he had used it to fight off his assailants, Falstaff laments that his weapon is “hacked like a handsaw” (2.4.161). Maybe, just maybe, Hamlet’s handsaw was a handsaw all along. As Freud is supposed to have said, “Sometimes a cigar is just a cigar.”

  WHEN SHALL WE 1,250 MEET AGAIN?

  The Shakespeare Association of America is to Shakespeare studies what the American Astronomical Society is to astronomy. The SAA* is the world’s largest professional association for Shakespeare scholarship and allied studies, boasting some 1,250 members from 36 countries. I had the privilege of sitting in on a number of sessions at their annual conference in 2012, when it was held in Boston, and again in 2013, when it was held in Toronto. The breadth of topics tackled at a typical SAA conference is truly staggering, encompassing not only Shakespeare’s writings but also those of Marlowe, Jonson, and any other writers active in early modern England, as well as analyses of the rapidly changing material, social, and intellectual environment in which these writers lived and worked.

  Scholars come to present their papers, listen to other scholars’ papers, and to discuss research areas of mutual interest. That much it probably has in common with any other arts or humanities conference. But one difference stood out: In each seminar room, some fifteen or twenty chairs are placed around a central table, as in a corporate boardroom; people actually presenting a paper in the session are invited to sit in this “inner circle.” Surrounding them one finds another thirty or forty chairs lined up against the outer perimeter of the room, facing inward. This is where the “auditors” sit—anyone who’s not presenting a paper. (These are often graduate students, but they’re just as likely to be tenured professors who are attending the session to listen rather than to present.) This arrangement, which one senses hasn’t changed in many, many years, is clearly seen as normal by the attendees—but it seems to create an unnecessarily harsh divide between the presenters and the auditors. (The view from the auditors’ circle is a bit odd, as one peers at the faces of half of the presenters, and the backs of the heads of the other half. Even when you can see a speaker’s face, it is always partially obscured by the back of someone else’s head.)

  Topics that came up for discussion in 2012 and 2013 ranged from the predictable to the esoteric. A seminar titled “Reading Shakespeare and the Bible” is hardly surprising; in the twenty-first century, neither is “Early Modern Queer Colonial Encounters” or “iShakespeare: New Media in Research and Pedagogy.” For myself, on the lookout for science-related topics, a panel on “‘The Famous Ape’: Shakespeare and Primatology” was a highlight of the 2012 conference; so was a seminar on “Matter, Perception, and Cognition in the Renaissance.” (I tried not to worry too much when a seminar leader referred to philosopher and cognitive scientist Daniel Dennett as “David Dennett”; I suppose anyone can make a one-time slip.) Sometimes what seem like minor things become major discussion topics: The question of how many people have to be able to see a dagger before it should be considered “real”; how sleep deprivation affects Macbeth’s cognitive abilities; whether the names of Shakespeare’s characters have scatalogical significance, reflecting (as one scholar suggested) “aspects of anality and flatulence.” At the 2013 conference, I was intrigued by a listing for a two-hour session on The Tempest, one of my favorite plays. As the seminar unfolded, the presenters pondered questions that l
ikely escaped casual readers of the play. For example: What language, exactly, does Prospero teach to Caliban? Should we think of Caliban and Miranda as grammar-school students, with Miranda the more advanced pupil? And is Caliban still a student of Prospero’s, or was he expelled for attempting to rape Miranda? And why is Alonso so certain that he will never see his daughter again, just because she’s moved from Milan to Tunis—when there was already a centuries-old trade route established between the Italian city and the North African port? Later, someone made a case for interpreting Caliban’s log gathering as a symbol for deforestation and environmental destruction. An older gentleman along the outer perimeter of auditors chimed in: “Or at least for log gathering,” he said dryly.

  For anyone not up to speed on twenty-first-century Shakespeare scholarship, some of the topics covered may seem to come from somewhere just beyond the left-field wall. Some sample titles from the last two conferences:

  1. “Diagnosing Hamlet: The mad prince and the autism spectrum.”

  2. “Dis-Eating Macbeth: Macbeth’s indigestion and the matter of milk.”

  3. “The Ecology of The Tempest: Was Prospero’s island carbon-neutral?”

  4. “‘Exhalations Whizzing’: Meteorology, melancholy, and moral action in Julius Casear.”

  5. “The Georgic Contract: Agrarian bioregionalism and eco-cosmopolitanism in Henry IV, Part 2.”

  6. “Head in the Clouds: Historicism, Hamlet, and neurophenomenology.”

  7. “Shakespeare’s Quantum Physics: The Merry Wives of Windsor as a feminist ‘parallel universe’ of Henry IV, Part 2.”

  8. “The Unbearable Lightness of Being Ariel: Is Prospero’s little helper a hologram?”

  Okay, I confess: Three of these eight titles are made up. But can you tell the fake titles from the real ones? It’s not easy, is it? (The answers can be found at the end of the chapter.)

  I mentioned that Usher devotes nine pages to the famous “Exit, pursued by a bear” stage direction in The Winter’s Tale. Perhaps his interpretation wouldn’t have been too wildly out of place at the 2013 conference, where a paper examined “the bear’s disruptive (and even desirable) queer effects that destabilize binary systems of difference. Shakespeare’s onstage bear—whether live in the flesh or represented by a bearskin (made of bear-that-once-was)—materializes ‘transspecies’ connections that refuse the (false) separation between human/animal and nature/culture, preferring inter-actions and inter-dependence to autonomy and antagonism.”

  When scholars like Peter Usher pick over a Shakespeare play line by line, looking for nuggets of hidden meaning that have slipped by unnoticed over the years, they are hardly alone. They are merely the latest in a long line of scholars who have reached as far as plausibility may allow—or perhaps slightly farther—in discerning a hidden meaning in Shakespeare’s centuries-old words.* They have mastered the peculiar blend of art and science that allows one to bend Shakespeare’s words perilously close to the breaking point in search of a fresh insight, a novel interpretation. If nitpicking each line of a Shakespearean passage were a crime, the last SAA conference would have to have been held in the Don Jail rather than the Royal York hotel.

  * * *

  Whatever one may think of Usher’s more extravagant claims, his work touches on a number of areas where the Shakespeare community is—gradually, perhaps—beginning to see things his way: More and more scholars are acknowledging that the connections between Shakespeare and Thomas Digges have been neglected, and that there is some sort of link between the characters and setting of Hamlet and the Danish astronomer Tycho Brahe. If his book manages to push a handful of researchers to more closely examine those issues, he will likely be satisfied. If they happen to embrace his other claims, I’m sure he’d be delighted—but he does not seem to be betting on it, or to be in any rush. “I think that good wine sells itself,” he says. “I’m retired, and I’m not in a hurry. After all, the canon has been around for four hundred years; another couple of centuries is not going to make a difference.”

  As it turns out, from among Usher’s myriad claims about Shakespeare and science one particular idea is gaining traction. It involves astronomy and one of the late plays, and it resonates particularly well with both Scott Maisano and John Pitcher. In fact, it seems that the three men all came upon the same idea, at about the same time, by chance. The play in question is Cymbeline, dating from the final few years of Shakespeare’s career. It also involves the development of modern astronomy, and the invention of the telescope in particular. That’s a subject that we have touched on only briefly, in connection with Usher’s provocative claims regarding Leonard Digges, who purportedly used such a device in the mid-1500s. Now we must examine the work of the Italian scientist who quite definitely did aim such an instrument skyward, more than half a century later. And so we are ready to meet that other great mind who came into the world in 1564.

  Answers to the quiz: Titles 1, 3, and 8 are fake. Paper number 7, which imagines Henry IV, Part 2 and The Merry Wives of Windsor as taking place in parallel universes, is quite real. As noted in the paper’s abstract, it invokes not only quantum theory but also string theory: “I posit that the parallel universe is one that contemporary quantum physics has demonstrated as a logical product of string theory.” The essay notes, with explanations from quantum theory, how the transportation from one universe to another occurs, and it argues that Shakespeare’s purpose in the creation of Merry Wives was to demonstrate “that female-determined justice against male abuses could indeed ultimately or even simultaneously transpire.” (http://www.shakespeareassociation.org/abstracts/41.pdf) The author issued a caveat during the seminar, admitting that Shakespeare may not have been “consciously thinking of string theory” when he wrote the plays.

  9. “Does the world go round?”

  SHAKESPEARE AND GALILEO

  While Shakespeare’s birthplace is a major tourist attraction, the house where Galileo entered the world—a four-story, pinkish-brown town house in the northern Italian city of Pisa—is to this day a private residence, marked only by a small plaque and an Italian flag. It stands on a quiet street in a neighborhood known as the San Francesco Quarter. In Galileo’s time, the area was home to artists, craftsmen, and shopkeepers. His father, Vincenzo Galilei, had settled there, with his wife, Giulia, just a year before the birth of their first son.

  Vincenzo was a skilled musician, teacher, and music theorist. In spite of his talents, money was tight, and he traded in wool to make ends meet. Giulia was an educated woman who could claim a cardinal among her relatives. Galileo was the first of their seven children; as was the custom in Tuscany at that time, he was given a Christian name that reflected the family name—hence the echo-like “Galileo Galilei,” the father of modern science, known to history simply as Galileo.

  Vincenzo had hoped his son would become a doctor, and the youngster was duly enrolled in the university at Pisa to study medicine. Instead, he developed an interest in mathematics. He left the university without a degree, although he would later return; it was at Pisa that he landed his first teaching job. To call Galileo a misfit might be too harsh, but from an early age he was known for his argumentative nature. We know that he irked some of the more senior faculty members by refusing to wear the school’s official robes, which he considered pretentious (and for which the university docked his pay).

  It was also in Pisa that Galileo first became fascinated by motion, and began to investigate the way that objects move in response to a steady force, like the force of gravity (although no one called it gravity at that time). One example of such movement is the swing of a pendulum. Galileo’s first thoughts on the matter are said to have been triggered by the sight of the massive chandelier in Pisa’s cathedral, gently swaying in the breeze; eventually, he worked out the mathematical formula for the duration of a pendulum’s swing. The movement of falling or rolling bodies intrigued him as well. One way to study such motion was to roll different kinds of objects down an inclined pl
ane, carefully measuring how far the objects moved in a given interval of time. He also wondered about the special case of objects falling straight down. Suppose you had a ball of iron, like a cannonball, and another ball of the same size and shape, but made of wood. You might guess that the cannonball would fall faster, just because it’s heavier. That’s what Aristotle thought. He said that the heavier body would fall faster than the lighter one, with a speed proportional to its weight. That certainly sounded plausible—but Galileo had his doubts. He would later give a detailed argument in what was to be his final book, the Discourses and Mathematical Demonstrations Relating to Two New Sciences (1638). Written in the form of a dialogue, Galileo’s line of reasoning is voiced by a character named Salviati:

  Aristotle declares that bodies of different weights, in the same medium, travel … with speeds which are proportional to their weights [and thus] a stone of twenty pounds moves ten times as rapidly as one of two [pounds]; but I claim that this is false and that, if they fall from a height of fifty or a hundred cubits, they will reach the earth at the same moment.… Aristotle says that “an iron ball of one hundred pounds falling from a height of one hundred cubits reaches the ground before a one-pound ball has fallen a single cubit.” I say that they arrive at the same time.

  According to his first biographer, Vincenzo Viviani, Galileo tested his hypothesis by dropping objects of varying weights from the top of the cathedral’s famous bell tower, the Leaning Tower of Pisa. Historians, however, suspect that the story may be more legend than fact. (Viviani’s account was driven largely by hero worship, and much is exaggerated—a common practice in biographies of the time.) Galileo certainly could have performed such an experiment; but he likely had already deduced the answer from his studies of motion on an inclined plane, in which the same principles are at work (in either case, the distance covered increases with the square of the elapsed time). Galileo also studied projectile motion, showing that a cannonball must follow a parabolic path. All of these findings contradicted Aristotelian physics, whose failings were becoming increasingly evident. Rather than relying on ancient wisdom, Galileo favored an experimental approach. At the same time, he was discovering the power of mathematics in describing the natural world. As he would put it in a short book called The Assayer (in Italian, Il Saggiatore), in 1623: