In another sense, though, my sports timer confirms the twofold accuracy of a much earlier chronometer: the hourglass. Although an hourglass cannot measure an accurate second, it can gauge a fairly accurate minute and get close to measuring an exact hour. Yet there is something even more exact about it. An hourglass is a perfect functional symbol; it both symbolizes time and measures it. The sand rushes through the present moment, the waist of the hourglass, on its way to the past, the heap of sand at the bottom, in a rushing, dry waterfall. The resemblance between my sports clock and the hourglass deepens here. Just as hundredths of seconds flow faster than tenths of seconds, the speed of the falling sand is faster in the centre of the flow than at the edges, where it is slowed by its contact with the glass. The speed of “now,” in both chronometers, seems infinitely divisible into ever-faster increments.
There is a further parallel, not with my sports clock, but between the hourglass and time. Beyond the hourglass’s direct representation of time’s flow is the correspondence between the shape of the hourglass and the division of time into past, present and future. The reservoirs of future and past, the upper and lower bulbs respectively, are connected by the waist of the present. Perhaps the present moment, our “now,” is more exactly like the waist of the hourglass than we know. “Now” is unmoving, and instead, time rushes through it, giving us the illusory sense that the present moment races from the past towards the future, or that the future flows through it towards the past. Maybe the present moment is more like the lens of a projector that the film of time is playing through.
The hourglass has a final deep parallel with time. If, at the end of time, time reverses and the universe runs backwards, as an astophysicist named Thomas Gold has proposed, then turning the hourglass upside down after the “future” has run out is a perfect allegory. Perhaps the process repeats endlessly, the universe inverting like an egg timer in a kitchen morning after morning, or like the demon that Nietzsche wrote about (who, like Thomas Gold, we will encounter later on in this book). Finally, there is the analogy between mortality and time running out. The Grim Reaper doesn’t brandish his hourglass idly.
Mechanical clocks had, and still have, an element of mortality to them. Their measured ticks seem to dole out our lives. I remember how, when my mother was in her final days, she would keep glancing at her bedside clock. It was her compass, an absolute within the delerium that slowly overtook her. It was also a solace of sorts. I think the last control she could exercise over the world was to keep track of her daily calendar of events, of impending visits by her home-care nurse and the lonely hours of the night. Clocks are not the enemy, of course. They only measure our mortality. (Though neither are they our friend.) But the connection between clocks and mortality is strong nonetheless. It sometimes seems as if time stalks us, like the ticking clock in the stomach of the crocodile in Peter Pan.
I doubt that associations of mortality were a factor when clocks were a brand-new technology, when the chiming of the hours became a theme song to the cultural awakening of Europe in the sixteenth century. Still, the measurement of minutes was centuries away. Although the church had already instituted St. Bede the Venerable’s division of the hour into sixty minutes and the minute into sixty seconds, at least on paper, it wasn’t until Christiaan Huygens invented the pendulum clock in 1665 that accurate minutes became a reality and Bede’s abstractions became practicable. Huygens, the son of the famous Dutch poet Constantijn Huygens, was a mathematician, physicist and astronomer. His invention of the pendulum clock was more of a practical necessity than an end in itself; he wanted to measure the motion of the planets and their moons as precisely as possible. Eleven years later Ole Römer used Huygens’ pendulum to calibrate the occlusion of the moons of Jupiter and came up with the first quantitative estimate of the speed of light: 136,000 miles per second, which although 26 percent lower than the currently accepted speed, was nonetheless very close. It was to be another half-century after Huygens’ pendulum that clocks could measure seconds with any precision.
SECONDS
Your average day of 1,440 minutes consists of 86,400 seconds. If the average thirty-day month, then, has 2,592,000 seconds and hence the average year consisting of twelve thirty-day months would consist thereby of 31,104,000 seconds, I have then, in fact, lived (since I am approaching my thirty-sixth year) but 1,088,640,000 seconds.
—Glenn Gould
When I was a child our family camped every summer in the wilds of northern Ontario. They were idyllic months, canoeing by day and setting up camp in the late afternoon, on an island in the middle of a lake to avoid the mosquitoes that were thicker on the mainland shores. Most of these lakes were so pure you could dip your cup in them and drink. The weather was usually sunny, but on hot afternoons, convection storms would build and cruise over the landscape—brooding cloud-towers with lightning at their bases. Inevitably there were occasional night storms, some of which were terrifically violent. A sleeping bag and a canvas tent don’t feel like much protection in a severe lightning storm, and my father, to allay my fears, taught me how to calculate how far away the storm was by timing the thunderclaps. You just count the seconds between flash and thunder. Five seconds equalled a mile. For “seconds” we counted out “steamboats,” stopping as soon as we heard the thunder.
Sometimes the storm would miss us, never getting closer than four steamboats, but more often the storm would score almost a direct hit. It was hard to concentrate on counting when the tent was flapping in the wind and the rain drummed down so hard that it sounded like the campsite was being washed away. It was even more difficult to concentrate when there was no delay between the brilliant violet flash of lightning and the bedrock-shaking explosion of thunder. But as the first steamboats began to emerge between the flashes and the thunder, I knew, to my relief, that the storm was finally leaving.
Years later I discovered that not only could you tell how far away the lightning was, you could also, using the same method, map out the lightning branches, particularly the horizontal ones that run parallel to the ground. Now when I hear thunder begin, especially the low, rippling thunder from deep in the clouds, I start counting, and by timing the length of the thunder’s peal I can calculate the length of the lightning branch. Sometimes they are more than a mile long. Using time to measure phenomena is precisely why accurate timepieces became a necessity, and why the second, something that is now so ubiquitous in our vocabulary and experience, was also necessary to quantify.
It turned out that the relationship between time and space, or in this case time zones and longitude, became the incentive to begin measuring precise seconds, and it fell to a carpenter from Yorkshire named John Harrison to devise a clock that could measure them. By the early eighteenth century, Britain was a maritime superpower in command of thousands of oceangoing ships. The difficulty of determining accurate position at sea was one of the greatest dilemmas facing the nation. Faulty navigation led to the loss of ships, lives and valuable cargo, and as more and more ships plied the sea, the losses mounted. It took the great maritime disaster of 1707 to galvanize England into action. Four Royal Navy ships sailed off course near the coast of the Scilly Isles and ran aground, costing the lives of fourteen hundred sailors. In an act of Parliament in 1714 Britain offered a price of £20,000 (equivalent to US $7 million today) to anyone who could accurately calculate longitude at sea.
Determining latitude had always been easy for sailors. By measuring the angle of the Pole Star and referring to an almanac of sun and star positions, they could judge their latitude exactly. But longitude posed another problem. To measure that you had to have an accurate clock, because you had to subtract your local time from the time at the prime meridian, which runs through Greenwich. A reckoning accurate within a minute would give you your position to within a mile. But there were no clocks capable of doing this at sea, since the wave-induced rolling motion of boats stymied their workings. It was such a long-standing problem that many ships’ navigators simply
sailed due south until they reached the correct latitude, then sailed due west or east. Needless to say these were not direct routes.
John Harrison took up the challenge, not just because of the extraordinary prize but also to save lives. He laboured for twenty-seven years, building successively more accurate clocks until his crowning achievement: the No. 4 Chronometer, which was tested on a voyage between Britain and Jamaica in 1761. It was able to maintain its accuracy during the entire voyage. He won the prize.
As a practical monument to his achievement, the Greenwich Observatory in England installed its famous time ball at the top of a tower visible to all boats in the adjacent harbour. When the ball dropped, it marked the precise hour, and maritime navigators would synchronize their ship’s clock with the Greenwich master clock. Knowing where you were depended on knowing what time it was.
MILLISECONDS, NANOSECONDS AND COASTLINES
The clock, not the steam-engine, is the key machine of the
modern industrial age.
—Lewis Mumford
Imagine that you have been hired to measure a small nation’s coastline. It’s a big job, but you have enthusiastic assistant surveyors, an unlimited budget and a whole summer ahead of you. You begin the survey one sunny May morning at the southernmost point of the coast, right at the border. The guards on the other side wave to you, and seagulls cry as they hover on a brisk, onshore breeze. The ocean is deep blue and dotted with whitecaps. North of you is a long, white beach. You begin your work.
The beach is relatively straight and quick to measure. It turns out to be almost two miles long. You break for an early lunch. The survey crew is talkative and excited. You decide that one summer should be ample time to measure the whole shoreline.
After lunch you begin to survey the point that shelters the beach’s north end. Here you realize that you will have to simplify your measurements. Instead of measuring the gradual curve of the point, you take a series of locations around it and measure the distance between them. It’s sort of cheating, but then again, how far off the actual distance could it be? Probably not a significant amount. Measuring the point takes up the early part of the afternoon, and as you and your crew come around to the other side, you see that the shoreline extending north is nowhere near as straight as the beach you measured in the morning. It is a long series of successive points, bays and inlets, some large, some small.
The first bay is simple, though it contains a small point that, after a brief conference, you and your assistants elect not to measure. “It’s too small,” you say. The next point has a little bay in it, perhaps only twenty feet across. If you measure the bay, it will extend the length of the shoreline by almost a hundred feet. But a decision has to be made. In the end you decide that all smaller features will be ignored. If you begin to measure every little bay and inlet, the job might take all year.
When you’ve finished for the day, you and your crew set up camp on the beach. After dinner, under the stars and around a driftwood fire, everyone talks about the day’s work. The conversation is lively and friendly at first, but then the discussion turns into an argument. One of the surveyors, a philosophy student, insists that the survey has to be done as conscientiously as possible. She didn’t like the decision to skip smaller features. “Every little bay and inlet has to be measured,” she insists. “There is an absolute length to the shoreline, and we’re being paid to measure it.”
“Hold on,” says the lead surveyor. He has a degree in mathematics and works for the department of national cartography. “Where do we stop? Let’s say we measure a small bay and it comes to forty-five feet. But what if there’s a big boulder embedded on the shore of this bay? We measure it and it adds another five feet. Do we include that?”
“Why not?” asks the philosophy student.
“Okay,” says the lead surveyor. “What if there’s an indentation in that boulder, a crack that measures a foot and a half on each side. Do we include those three feet?”
“Why not?” the philosophy student asks again.
“All right,” says the lead surveyor. “What if, in that crevice, there were a smaller crevice? Would we measure that?”
The philosophy student realizes where this is going.
“You’ve got me there,” she says. “Obviously there is no end.”
“That’s right,” says the lead surveyor. “If you measure ever smaller features on a shoreline, going from feet to inches to hundreths of an inch, you’ll soon discover that this nation’s coastline is infinitely long!”
Our little survey crew stumbled on a fact that has a profound implication for measuring time. One of the paradoxes of Zeno’s Arrow was that it could never reach its target because the distance it had to travel could be infinitely halved. Nearly three thousand years later, in the early half of the twentieth century, a British scientist by the name of Lewis F. Richardson continued Zeno’s quest. Coastlines and borders fascinated Richardson. Visiting countries that shared a common, zigzagging border, such as Holland and Belgium or Spain and Portugal, he found that the encyclopedias in each of these countries had estimates of their common borders that varied by as much as 20 percent. The discrepancy could be blamed on bad surveying, but Richardson didn’t think so. He thought there was something more profound going on, and he was right. But it wasn’t until years later that the French mathematician and physicist Benoît Mandelbrot, the father of chaos theory, picked up on Richardson’s interest in borders and coastlines and took it to its logical conclusion. Like our imaginary surveyors, he discovered that any irregular, natural coastline is endless.
You’d think that there would be a limit to this measurement. After all, coastlines exist in the real world. They are fixed, measurable. They don’t wiggle around or fade in and out of existence. But Mandelbrot discovered otherwise. Certainly if you were measuring something like a perfect rectangle lying on the ground, there would be a final value, an ultimate, fixed distance, but he found that with an irregular, natural shoreline there was no end to the bays and peninsulas. They simply got smaller and smaller until finally you were measuring them on the molecular and then the atomic scale. Perhaps on the atomic scale there might be an end to the measurement, a final length of the coastline. But that’s where, maddeningly, everything becomes fuzzy, because the quantum world is indeterminate.
Time, it appears, is the same. Like a shoreline, time is composed of ever smaller, divisible units of itself. A second then, at least hypothetically, ought to contain an eternity, and with the burgeoning pace of ever more accurate clocks, the second is indeed opening up into a new universe of time. After Harrison’s No. 4 Chronometer set a precedent for accuracy, it was inevitable that an even more accurate clock would be built. It happened in 1889. Siegmund Riefler of Germany constructed a clock that worked inside a partial vacuum to reduce the influence of air pressure on the moving parts. His device had an accuracy within a tenth of a second a day and could easily measure milliseconds, or thousandths of a second. It was at this point that clocks became capable of measuring actions that are beyond our ability to see…a housefly flapping its wings once every three milliseconds. But even Riefler’s preeminence was short-lived.
In the 1920s, William H. Shortt, an English railroad engineer, built the first electromechanical clock. It was based on two clocks: a “master” and a “slave.” The slave clock sent an electromagnetic impulse every thirty seconds to the pendulum master clock, which then, in turn, regulated the slave clock. This device was accurate to within one second a year, precise enough to measure microseconds, or millionths of a second. In a microsecond a sound wave will have moved only one-third of a millimetre.
Shortt’s timekeeper was usurped only eight years later, when Warren A. Marrison, an engineer at Bell Laboratories in the United States, designed the first quartz-crystal clock, using the vibrational frequency of an electrically charged quartz crystal. By the mid-1940s, quartz clocks had achieved a degree of accuracy within one second every thirty years. The world of th
e very small—the crystal lattice of silicon molecules that make up quartz—had become the new pendulum.
The pace of precision timekeeping continued to accelerate. In 1948 Harold Lyons created the first atomic clock, using the natural resonant frequency of an atom. By the mid-1950s this atomic clock had evolved into the cesium-beam atomic clock, which is still in use today to broadcast Co-ordinated Universal Time and which has an accuracy of about one nanosecond a day. A nanosecond is a billionth of second, the time it takes light to travel thirty centimetres in a vacuum. Computers take between two to four nanoseconds to process a single calculation. The children’s odyssey in C. S. Lewis’s The Lion, the Witch and the Wardrobe, where an imagined lifetime of adventure is crammed into a couple of seconds, must have been scaled to nanoseconds, each second in that world equalling a nanosecond of ours.
This kind of accuracy has allowed scientists to measure the duration of a second, long defined (somewhat tautologically) as the “sixtieth part of the sixtieth part of the twenty-fourth part of a day.” According to the cesium-beam atomic clock, a second is defined as the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium-133 atom at zero degrees kelvin. It’s not an elegant definition, but it’s absolute.
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