The Pendulum
by ISABELLA YEAGER
The following is pulled from research conducted by mathematician and historian Tacitus Dune in preparation for the lecture he planned to give at the University of South Edinburgh's 1985 "Techniques in Visualization" conference. It is not known whether the lecture was given elsewhere, but it was not, in the end, presented at Edinburgh. One possible reason could have been Dune’s declining health at the time of the conference – in 1982 he was diagnosed with a small lesion of the brain stem, and died on June 3, 1984. Another explanation, arguably more troubling, could be the fact that a quantity of information presented as fact has not been confirmed as true.
The text below – an incomplete timeline of the pendulum's development – was found among Dune's extensive collection of three-ring notebooks, into which he inserted reams of pages written on typewriter.
CHINA, EASTERN HAN DYNASTY
The Chinese scientist Zhang Heng monitored the earth's stability with a seismograph comprising an urn, a lever, a ball, and eight frogs sitting open-mouthed at the eight points of the compass. Inside, an inverted pendulum that stirred with the earth struck the ball to rolling down, down a slope, into a gullet at the north, south, east, or west. The frogs waited while the earth slept, each dreaming of the day that his gaping throat might bear proof of the rod's tremblings and witness to the doom at hand.
photo by Marilyn Shea
17th CENTURY
Galileo Galilei came to understand that a small pendulum was a good visualization of regularity.
The time it takes a small pendulum to swing back and forth is its period and relies not at all on how far it has to go. So it is isochronous.
A part of the oscillator family alongside AC power, the pendulum operates in perfectly even time around a fixed point of stasis. Galileo and others found that this made a pendulum the ideal mechanism to keep musicians on tempo and to monitor the pulses of both anxious and unimpressed medical patients.
The regularity that Galileo made explicit with the pendulum clock anticipated another of the pendulum's known behaviors: the coupled oscillation that our Dutch colleague Christiaan Hyugens called "odd sympathy." Lying on his back in bed, at sea, in 1665, Hyugens observed two pendulum clocks strung from the same beam tend towards perfectly synchronized though opposing motion, and eventually guessed that this resulted from the accumulated influence of minute stirrings of the supporting beam. The pendulums became a mirror image of each other, each driving and being driven by the other. Under the influence of this same "odd sympathy," the two pendulums could fall still together, a phenomenon Hyugens, again slanting towards personification, called a "death state."
It was the realization that pendulum clocks swung at different speeds in different parts of the world that led to the discovery of Earth's oblatitude, or slightly elliptical shape. Records of gravity's strength collected at points along countless travelers' journeys combined to give us the correct dimensions of the earth. Via these measurements, Westerners came to understand lines of longitude and latitude (explicated in Isaac Newton's monograph Philosophiae Naturalis Principia Mathematica), and in so doing grasped the true meaning of the ancient Chinese expression "throwing a net over the world" – which they had until that point mistakenly used in conjunction with their own phrase, "The sun never sets on the British empire."
Galileo noted the pendulum's demonstration of simple harmonic motion, by which a system departs from and returns to equilibrium, and so determined that the pendulum performs both order and disorder. When this order-disorder relationship is visualized as a system acting in phase space, where all possible states of a system are shown, it yields this phase portrait:
18th CENTURY
Some say it is no coincidence that this portrait resembles a stylized map of the city of Paris: its dimensions, the assemblage of its arrondissements, and the placement of its main body of water. Using the same rationale that throughout literature attributes the presence of Indian burial grounds beneath remote American villages to sinister activity above, it's been well argued that the pendulum's model for departure from and return to equilibrium – more simply, for disorder – was built into the foundations of the city, and so can account for (and illuminate) some of Paris's major moments of political turbulence.
One writer, taking this theory further than most, even posits that the careful reader can locate the pendulum's model for disorder at the heart of some of the French Revolution's better-known texts. Robespierre, he asserts, stumbled upon the idea for his treatise "Terror Is the Order of the Day" while gazing upon the family pendulum clock sitting on his writing desk.
It is not impossible to imagine a connection between the constant state of potential maintained in the pendulum and the potential energy (and a demand for the kinetic) found in statements like these:
Danton: . . . You have just proclaimed to all of France that it is still in a real and active state of revolution. Well, this revolution must be consummated....I therefore ask that you decree at least 100 million [francs] to produce all kinds of weapons because, had we all had arms, we would all have marched.
Despite steps taken towards grasping the nature of the pendulum as a timekeeper, scientists did not discover until 1721 that climate had the ability to interrupt the regular motion of the pendulum, as the rod expanded and shrank in response to changes in ambient temperature. It is believed that this margin of error may be the key to the odd circumstances surrounding the London-based Italian romantic painter Agostino Brunias and his three-year disappearance in the West Indies. Painting in the tradition of verité éthnographique, departed in 1770, after a spat with a fellow painter, for the West Indies, where it is presumed he remained until he made his sudden reappearance in Europe in 1773, bearing with him a great many oil depictions of Caribbean life and people, including the now-infamous "Barbados Mulatto Girl" and "Washing Clothes In a River."
Not long after Brunias's return to the continent, however, it became clear that he was himself quite disoriented, believing that only a few months had passed since his departure, and alarmed at the changed state in which he found his old haunts and the altered appearance of his friends. Thanks to the discovery of Brunias's journals, we now know that the painter kept track of time while traveling using an outdated pendulum clock that was not temperature-compensated, whose stem, in the damp heat of the Caribbean, warped and allowed almost two-and-a-half years to pass Brunias by unawares. With this information, it seems possible that any number of his contemporaries may have experienced similar phenomena, and that texts of the period ought to be examined closely for odd anachronisms that could indicate reliance on an uncompensated timekeeping device.
19th CENTURY
Edgar Allen Poe published his short story "The Pit and the Pendulum" in the 1840 edition of The Gift: A Christmas and New Year's Present. His interest in pendulums has to do not only with their narrative quality (as we see in "The Pit", the pendulum is the perfect prop for a slow-building horror tale), but also with their aesthetic relationship to duality and mirroring, of the sort present in Hyugens’ work. In the short story "William Wilson", in which a man kills his doppelgänger only to have his bloody reflection in the mirror inform him that he has slain himself, the partnership, or odd sympathy, that we find in Hyugens occurs in Poe’s use of the Double. Both William Wilson and the Double are mentioned in Borges's Book of Imaginary Beings. Borges writes, "Suggested or inspired by mirrors, the surface of still water, and twins, the concept of the Double is common to many lands." He goes on:
It seems likely that statements such as Pythagoras’ “A friend is another myself” and Plato’s “Know thyself” were inspired by it. In Germany, it is called the Doppelgänger; in Scotland, the fetch, because it comes to fetch men to their death. Meeting oneself was, therefore, most ominous; the tragic ballad “Ticonderoga” by Robert Louis Stevenson recounts a legend on this theme. We might also recall that strange painting by Rossetti called “How They Met Themselves” – two lovers meet themselves at dusk in a forest. One need only mention other instances in Hawthorne, Dostoyevsky, and Alfred de Musset.
For the Jews, on the other hand, the apparition of the Double was not a foreshadowing of death, but rather a proof that the person to whom it appeared had achieved the rank of prophet. This is the explanation offered by Gershom Scholem. A tradition included in the Talmud tells the story of a man, searching for God, who met himself.
In Poe’s story “William Wilson”, the Double is the hero’s conscience; when the hero kills his double, he dies. In the poetry of William Butler Yeats, the Double is our “other side”, our opposite, our complement, that person that we are not and shall never be.
Plutarch wrote that the Greeks called the king’s representative the “other I”.
-Jorge Luis Borges, The Book of Imaginary Beings
The Double appears both as a catalyst of motion and development (Scholem) and as a herald of death (Stevenson, Poe). This tension recalls the symmetry of the coupled oscillator, which can both drive and halt the motion of its doppelgänger. If we label the two parts of the Double’s respective motion and stop with Hyugens's terms "odd sympathy" and "death state," the coupled oscillator seems like a perfect mechanical incarnation of the Scottish “fetch,” coming to fetch others to their death.
It was in Paris that Foucault suspended his pendulum from the dome of the Pantheon and showed the rotation of the earth in the first manner that didn't require celestial observation. Thousands flocked to see the device prove that the surface they stood on behaved in unseen ways.
20th CENTURY
In the late 1970s a progressive academy for advanced mathematics in upstate New York revised its assessment-based grading system in response to requests from students and parents. Until that point, the school had been using the simple pendulum formula devised by Galileo (see above) as means to appraise its students’ work, with T standing for the student's assessment result, 2π for the two-semester school year, L for ingenuity and g for net performance improvement. However, after pupils overwhelmingly complained that they felt unfairly limited by the use of a closed formula to judge the quality of their minds, the school issued a statement in their biannual newsletter to the effect that, considering the immeasurable and exponential capacities of the human brain, students should from that point forward be graded using an infinite series. Below is the infinite series developed by Galileo to represent the motion of larger pendulums, and adopted by the academy as an improved method for calculating its students' progress.
Here Dune’s timeline ends, and the entries following become highly disjointed. We can, however, gain a good deal of insight into his mental state from their content. Among the most coherent are these:
Tuesday, 5/29/84
In studying the pendulum I have come to appreciate in greater depth aspects that might fascinate anyone who stops to observe its regular motion, its elegant lines and its perfect, calculated weight; who considers its relationship to the eternal and the revelatory properties which have told us over time so much about the universe we inhabit. All these things drew me deeper into the study of its history but I cannot deny a growing alertness to a sinister quality that, when cast in a certain light, the pendulum might be said to possess. It is a generous instrument, providing much information to the onlooker about imminent disturbances in the earth, the passing of time, the shape of the globe on which we rest. It gives energy to its twin through the force of its own motion. It yields much. But in cases like that which Edgar Allan Poe illustrates so vividly in The Pit and the Pendulum, the device can also take a great deal from its viewer.
As the pendulum descends towards its victim in Poe’s short story, its destructive power lies as much in the blade fixed to its end as in its sapping the victim of sanity through its steady, repetitive motion. At its most extreme, hypnosis draws the watcher in, draining him of independent thought, of strength, and of motion. Oddly contrary to the mutually sustaining movement Hyugens described in his studies, this process is vampiric in the most classic sense. Considering this, I could not help recalling with some displeasure that Hyugens’ theories of were later disproved, and the two pendulums’ mirror movement attributed to other sources of energy, which, when sapped, caused them to fall still.
When I began delving into this history, I bought, for the purposes of research, a small pendulum that I placed on my desk and looked on daily. Seeing it there felt energizing, and my research and writing pushed ahead with a speed I had rarely felt. Soon I took to writing late into the night, having my meals at the desk, and finally to sleeping in my office, always with the pendulum angled so that even in sleep I faced it, since I discovered I slept more soundly – and often dreamlessly – this way.
Though was almost surely a result of close quarters and too many hours in front of the typewriter, I began to suspect my pendulum moved with a greater energy than it had in the past. But after a month or so of rarely leaving my study I myself began to experience a listlessness and, more disturbingly to me, an absentmindedness that made work difficult and sleep both appealing and unsatisfying. It was during this period that I reread Poe’s short story about the pendulum as a hypnotizing torture device and began to feel a sort of inexplicable chill when I looked at the one I had placed on my desk. I have now put it out of sight, on the bookshelf behind a row of books, but my energy goes on dwindling.
Saturday, 6/2/84
I cannot continue writing at this time. I have moved the typewriter to the bedside but will now pause for a few minutes to rest.
Sunday, 6/3/84
I have gotten out of bed finally to get some water from the kitchen. On my way back to bed I stopped at the bookshelf and moved aside some of the books I had placed in front of the pendulum. The pendulum has stopped.
Isabella Yeager is the senior contributor to This Recording. She is a writer living in Brooklyn. She twitters here and tumbls here. She last wrote in these pages about Rodin and Rilke.
"Hypnotized" - Spacemen 3 (mp3)
"Clamour" - Glasser (mp3)
