Book Review: A Tenth of a Second
By Jimena Canales
I spend a lot of time thinking about time. It’s at the center—or buzzes the center on some tangential course—of everything I write. We are born into its flow and are carried along on its current, but it stretches so far beyond the measure of our lives that both past and future are, comparatively, infinite and incomprehensible. It is not, itself, a physical thing, but its passage gives play to the forces that transform the physical, from the millennia of water and wind that crumble cliffs to the decades during which we morph from child to adult before the physiological equivalent of the second law of thermodynamics kicks in and has seemingly overnight rendered me unable to haul my middle-aged ass off the carpet without performing a pathetic parody of an Olympic floor exercise that involves a lot of rolling and tumbling before, at last, I am upright again. It’s like the advice Dick Van Dyke used to give us in case we ever found ourselves on fire—stop, drop and roll—only in reverse.
Unlike me, time’s arrow, alas, moves ever forward, and if the topology of our universe is flat and/or the cosmological constant is sufficiently high (damn you, dark energy) and the first and second laws of thermodynamics have universal application—all of which seem to be true according to current data—the whole shebang is headed toward a depressing end (i.e., the heat death of the universe or, as those of us with a bent toward gallows humor sometimes refer to it, “the Big Chill”). The good news is that we will all be long dead before this becomes an issue. Meanwhile, we will continue to mark time’s passage on a variety of human scales: as seasons in the year; as days on our calendars; as minutes on our watches; as a second during which, if you want to get all technical about it, 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of a cesium 133 atom occur.
I include that bit of info about the second not to be a smarty pants (because, truth be told, I barely understand it myself) but to illustrate the precision with which the International System of Units (SI) defines what we call a second. If you noodle around with the math a little, you can determine that a second is 1/86,400th of a day (multiply 60 seconds by 60 minutes by 24 hours, and you get 86,400 seconds in a day—and if you’re me, you’ve also got “Five hundred twenty-five thousand six hundred minutes” now on an endless tape loop bouncing through your brain). The math is the easy part. Using that measure to keep every clock and watch and computer in the world in sync is the hard part. Even if we strive to build our instruments with the precision of a Swiss watch, each instrument is unique and will tick off its “seconds” in a little less or a little more than 1/86,400th of a day. The amount of time lost or gained by most modern instruments over the course of a year is so miniscule that we don’t notice it and it doesn’t make a real difference in our daily lives. But those small differences become really big really fast when you think about how much we have come to rely on systems that need to be synchronized by time across space. It’s amusing/annoying when the audio and video tracks get out of sync on television and the performers’ lips are a few tenths of a second ahead of their words. But consider the consequences if a global positioning system (GPS) gets out of sync.
GPS navigation relies on satellites, and per special relativity, time dilates—i.e., slows down—for a satellite in earth orbit due to the satellite’s relative motion around the planet. General relativity, though, also kicks in, and earth’s mass pulls on the satellite. Taken together, the 7 microseconds per day lost because of special relativity and the 45 microseconds a day gained due to general relativity result in the satellites gaining approximately 38 microseconds per day. That’s thirty-eight millionths of a second. No biggie to us, but in terms of its impact on GPS accuracy, that tiny little loss causes errors in positioning to accumulate at a rate of roughly 54 kilometers (33.5 miles) per day. No matter whether you’re bringing a ship into port or backpacking in the middle of nowhere or just using Waze to find a quicker route home on your commute, those 54 kilometers/33 miles can clearly make a damn big difference as to whether you dock safely, go around the mountain instead of over it, or make it home in time for dinner. To negate this problem, clocks on GPS satellites are reset every day, and it is to the time as measured by that uber-precise cesium clock (which loses one nanosecond in 30 days—i.e., one billionth of a second over the course of a month) noted above that they are calibrated. Banks, stock exchanges, communications companies and a host of other enterprises rely on this clock as well to ensure accuracy in transactions, transmissions, observations, etc.
If the accuracy of an observation made by a human is dependent on a precise measurement of time, there is, unlike the constant cesium second, a margin of error inherent in such an observation. Some amount of “processing time” is required for the nervous system to transmit the stimulus to the brain, for that stimulus to be processed and for the nervous system to transmit the brain’s response so that the measurement can be recorded. This amount of time is unique to each individual and is, thus, inherent in his or her observations. This margin of error came to be known in the mid-19th century as the personal equation, and it is explored in depth in Jimena Canales’s A Tenth of a Second: A History.
Canales draws on psychologist and historian of psychology Edwin G. Boring’s 1929 text A History of Experimental Psychology to locate the first recorded instance of what would come to be called the personal equation in 1796 when Royal Astronomer Nevil Maskelyne of the Royal Observatory Greenwich fired his assistant, David Kinnebrook, because Kinnebrook’s observations systematically differed from his own. By the late 18th century, both timekeeping and the charting of the heavens had reached sufficient precision for observational differences of Canales’s titular tenth of a second to become evident—and troublesome—in astronomy.
As noted in the GPS example above, a very small difference in the measurement of time can result in a significant difference in the measurement of space. One outstanding problem for astronomers well into the late 19th century was obtaining an exact measurement of the solar parallax. To explain what that is, I’m going to punt to Canales’s footnote:
“Parallax” generally refers to the angular change of an object when it is observed from two different positions. If the distance between two observational positions is known, it can be considered the base of a triangle that when combined with measurements of the direction of the object as seen from both points can be used to determine the distance to the object. The solar parallax can be determined using [Edmond] Halley’s method, which consisted in observing the transit of Venus across the sun. This was done either through the method of durations or the method of [French astronomer Joseph-Nicholas] De l’Isle. In the method of durations the times of the transit as viewed from two different stations was determined, the lengths of the chords were deduced, and from these the least distance between the centers of the sun and Venus was found. However, since the method of duration required the observation of the whole transit, the method of De l’Isle was proposed. De l’Isle’s method required the precise determination of the time of contact between Venus and the sun at two different stations, which were either time coordinated or whose difference in longitude was accurately known. (89-90)
The value of the solar parallax was used “to determine the distance from the earth to the sun, set the dimensions of the solar system, and, using Newton’s law, deduce the masses of the planets” (90), so determining this value precisely was not small potatoes. The value of the solar parallax based on observations of transits of Venus in 1761 and 1769 ranged from 8.5 to 9.1 arc seconds, which rendered the distance between the earth and the sun somewhere between 145,000,000 kilometers and 155,000,000 kilometers (or, for us Americans, between 90,098,823 miles and 96,312,535 miles). Because of the importance of this measurement (the distance from the earth to the sun is called an astronomical unit [AU], and it’s used by astronomers to determine other distances within the solar system), 10 million kilometers/6 million miles matter. To give you some idea, the average distance between the earth and the moon is 238,900 miles. If Waze operated with this “precision” and sent me 6 million miles off course, I’d be about a tenth of the way to Mars.
“So, okay,” you say, “small differences make big differences down the line. That’s chaos theory in a bottle. What the hell does that have to do with the personal equation?” It’s the personal equation that, to some degree, accounts for these differences in measurement by the different observers. The discipline that would become known as experimental psychology had identified a differential between stimulus and response its practitioners labelled reaction time that was also consistently measured to be around one tenth of a second. While each discipline held to its own terminology, many astronomers came to believe that the personal equation was a manifestation of reaction time:
Different astronomical observers assessed time differently, and while these assessments showed a remarkable constancy within the same person, when individuals were compared against each other, results often varied by a few tenths of a second. Many astronomers believed that one reason why observers differed in these estimations was due to their different times of reaction. (22)
In fact, astronomers conducted observations for the sole purpose of determining their own personal equations so they would know and could share with others (like their bosses, to avoid poor Kinnebrook’s fate) the standard variance inherent in their observations (again, usually around a tenth of a second). Think about De l’Isle’s method of observing the transit of Venus: the key to the measurement is for an astronomer, peering through his telescope, to mark the exact instant in time when the edge of Venus touches the edge of the sun and then compare that with the exact instant another astronomer, whose clock is synchronized to that of the first astronomer and is observing from a known distance away, recorded that same instant of Venus-sun contact. The difference in time and the difference in distance are the essential components needed to calculate the solar parallax, so if the first astronomer has a known personal equation of .08 seconds and the second astronomer has a known personal equation of .13 seconds, the variance inherent in their measurements is, on average, .05 seconds—and this doesn’t factor in the difficulty in synchronizing the chronometers these 19th-century chaps were using to record their measurements. A .05 second difference represents a .75 arc second difference, greater than the difference between 8.5 to 9.1 arc seconds measured by astronomers recording the 1761 and 1769 eclipses. Yeesh. (And a big shout out to F. Mignard whose paper, “The Solar parallax with Gaia,“ provides, on page 17, a handy dandy chart that shows the history of measurements of the solar parallax throughout time; see https://dms.cosmos.esa.int/COSMOS/doc_fetch.php?id=1265128.)
Canales devotes a goodly chunk of her book to describing how scientists and technologists from a variety of disciplines sought to reduce or eliminate the personal equation through the development of instruments and observational techniques throughout the 19th century. Many of these innovations were developed with an eye toward more accurately measuring the solar parallax during the 1874 and 1882 transits of Venus. However, accuracy for accuracy’s sake was by no means the primary driver for many of the men seeking precision, and Canales records a long history of bitter rivalries founded in ego, disciplinary chauvinism and/or national pride. The upshot is that the 1874 transit was pretty much a bust, but observations from 1882 provided a range of 8.79 to 8.88 arc seconds. The latter estimate is in keeping with today’s accepted measurement of 8.794 143 836 arc seconds, leading to an AU of 149,597,870.700 kilometers or 92,955,807.273 miles, a measure the International Astronomical Union (IAU) declared to be the defining constant in 2012.
Of course, this 2012 constant was not defined by astronomers peering through telescopes and punching telegraph keys to record the instant of contact between Venus and the sun. Technology has relegated the consideration of the personal equation in measurement a quaint artifact of history. We no longer have to rely on our senses but have, instead, augmented them with instruments that are far more sensitive and are not plagued by the innate lag time of our nervous system. So why write a whole book about a tenth of a second if this former limitation is no longer relevant? Canales is not so much concerned with the concept of the personal equation as with its measurement:
Instead of focusing on local political and social aspects of modernity that affected the place of numbers in society, this book is centered on the moment of measurement (author’s emphasis). All measurements (including “measurements of distance”) require a “making present” that is intimately connected to problems of a temporal order. Instead of studying the tenth of a second in modernity, my aim is to understand the tenth of a second as modernity (author’s emphasis). (14)
Canales laboriously lays the groundwork necessary to achieve this aim in the book’s first seven chapters. She demonstrates her bona fides as an historian of science by evincing an encyclopedic knowledge not only of the tenth of a second problem but also of the social and political context in which science was practiced in the 19th and early 20th centuries—and, as importantly, of the science itself. This may be more a reflection of the reader than the writer, but I often felt as though I was reading fact upon fact with little in the way of narrative to unite them. Or to return to the construction metaphor, I was handed brick after brick after brick, but it was not always clear where in the edifice they should be placed—and lord only knows if I got them anywhere near the right spot I realize this is not a work necessarily intended for the general reader, so narrative may well matter less than evidence, and there is an assumption of some depth of knowledge around the subject which I admittedly do not bring to the table (for example, Canales and I do not share the same definition of famous: neither Sigmund Exner (23) nor Henri Victor Regnault (36) nor Louis Berman (41) nor Karl Pearson (42) are famous in my world; I was relieved to find, on page 45, the adjective applied to Max Weber, someone with whose work I have at least a passing familiarity; moreover, if a person or paper is famous, do you really need to call that out?). So I’ll just say that the first seven chapters are dense with facts and that the reader’s failure to grasp and assemble those facts into a coherent narrative evinces a different kind of density that is likely located squarely in the reader’s head.
It is in Chapter 7, “Reacting to Relativity,” that Canales really starts cooking with gas. The disagreement between Henri Bergson and Albert Einstein over the nature of time is ground Canales covers in greater depth in her 2016 work The Physicist and the Philosopher: Einstein, Bergson and the Debate that Changed Our Understanding of Time, but the chapter she devotes to it here is the high point of this book for me. Canales tidily boils the argument down as follows:
[Einstein] considered two ways of understanding [short moments of time]. The first was in terms of physics, as they were revealed by numerous laboratory instruments. The second was psychologically, as they were imperfectly captured because of our sensorial limitations. For Bergson, in contract, Einstein’s views were excessively simple and ignored evident complexities behind these short moments. Yes, instruments had demystified them to some degree. However, we still needed to think about how instruments achieved this. For Bergson, a philosophy of science and technology was just as important as science and technology themselves. (181)
Einstein believed that Bergson did not understand relativity, while Bergson believed that Einstein did not understand his philosophical concerns, and so two great minds talked past one another. After reading the chapter, I find myself at the very least more intrigued by Bergson’s views, and I tend to agree with him: he was not, as he frequently repeated, discussing physics when he talked about time but rather philosophy, and it seems that Einstein was simply unable to engage him and his ideas in that sphere. It would have been quite interesting had he done so, but that discussion, alas, did not occur.
Bergson was fascinated by cinematography (though not in a positive way) and how it creates the illusion of movement by projecting still images one after another, 24 in the space of a single second, so quickly that the human eye cannot perceive them as singular snapshots but they are, instead, blurred into one another by the brain. This is not, however, true motion, for some bit of movement must be lost in the framelines between each frame as a movie camera shoots is subject. Bergson emphasizes movement over form, arguing in a quote Canales lifts from Creative Evolution, that “’there is no form, since form is immobile and reality is movement. What is real is the continual change of form: form is only a snapshot view of transition (emphasis in original).’” (186) From a later work, The Two Sources of Morality and Religion, Canales finds Bergson arguing that “’the conception of movement as a gradual diminution of the space between the position of the moving object, which is immobility, and its terminal point considered as reached, which is immobility also’” is an illusion, “’whereas positions are but mental snapshots of the indivisible movement’” (201). I, too, am fascinated by the change of form over time, primarily the change of the self, and I read Bergson’s formulation as a sort of differential calculus of time, graphing changes in form against a constant axis of portions of seconds. Bergson, however, tied this movement to something he called dynamic morality, defining it as the opposite of static morality—i.e., morality that “’has become ingrained in customs, ideas, and institutions; its obligatory character is to be traced to nature’s demand for a life in common’” (201). This taste only makes me want to read more Bergson.
In her final chapter, Canales examines the personal equation through the lens of contemporary thinkers on the history and philosophy of science. Even though it was removed as a factor in measurement, the personal equation could not, argue Karl Popper and Michael Polanyi, be removed from the enterprise of science:
The personal equation appeared as an example illustrating the social nature of science—as embodying the moment when the scientific community agreed about what should count as “direct experience.” For Popper it proved “that what we call ‘scientific objectivity’ is not a product of the individual scientist’s impartiality, but a product of the social or public character of scientific method.” He derived two lessons from the personal equation. First, it revealed that the moment at which scientists stopped questioning their observations was neither absolutely final nor permanently fixed. Second, it showed the inherently intersubjective character of science.
To Polanyi the personal equation brought an additional lesson. It proved the inescapable presence of personal judgment in science, that is, the “essential personal participation of the scientists even in the most exact operations of science.” (213-214)
I am reminded of Heisenberg and Schrodinger and wave equations that collapse at the instant of observation, but it’s after 4 p.m. on a Sunday afternoon, and I don’t feel like going there. I guess if form is an illusion and there is only movement, I’m going to get up, do a few chores then pour myself a glass of wine and raise a glass to Bergson since it’s a little past five o’clock somewhere.
Learn more about Jimena Canales and her work.