Great theories are expansive; failures mire us in dogmatism and tunnel vision. I do not know the actual context of Goethe’s famous dying words. Perhaps he was only asking for another candle, all the better to view the faces of his beloved one last time. But perhaps he was begging the Almighty for the greatest gift that fruitful theories can provide—Mehr Licht! (more light!).
Time in Newton’s Century
11 | On Rereading Edmund Halley
MY DEAR COLLEAGUE Sewall Wright saw the comet in 1910 while working on the railroads in South Dakota—and then, as he so strongly wished, lived to witness its return in 1986. Mark Twain born under the comet’s waning light in 1835, died at its next passage seventy-six years later. But the vast majority of us get only one chance—or none at all. So we celebrate and, if intellectually inclined, we also cerebrate. If any natural happening ever received more than its merited share of written attention, we can only nominate the return of Halley’s comet in 1986, especially since that miserable iceball mocked our long anticipation by putting on such a poor show. I therefore fully intended to ignore both Mr. Halley and his cursed comet in the monthly essays that form the basis for this series of books.
But, as good intentions so often succumb to pervasive temptation, I confess that I was drawn to the man by a curious omission or underplaying that I detected in the flood of articles written about Halley in the light (hmm!) of his namesake’s return. We are all parochial at heart and tend to view wide-ranging geniuses like Halley as members of our own fraternity, even for limited contributions. I insist that Thomas Jefferson was primarily a paleontologist, and insurance salesmen surely view Charles Ives as a compatriot who occasionally dabbled in composition (as they, no doubt, appropriate Edmund Halley, who devised some of the first actuarial tables).
In my parish, Edmund Halley ranks as a geologist who occasionally looked upward. We claim him for a five-page article published in the Philosophical Transactions of the Royal Society of London. Its title exhausts a good part of page one: “A short account of the cause of the saltness of the ocean, and of the several lakes that emit no rivers; with a proposal by help thereof, to discover the age of the world.” In short, Halley wrote one of the finest and most influential papers with a testable proposal for that primum desideratum of our discipline—the earth’s age. Moreover, his method, though ultimately flawed, engendered much fruitful research and was, before the development of radioactive dating, among the two or three leading contenders for addressing this fundamental question.
Yet this paper and its interesting idea, so central to my profession and its history, got lost in the popular articles on Halley. Discover magazine abandoned its tradition of contemporaneity and named Halley their scientist of the year—but gave his geological work less than a paragraph. Carl Sagan and Ann Druyan’s Comet awarded just a few lines more. John Noble Wilford’s long article in the New York Times science section (October 29, 1985) omitted this work entirely from a long listing of Halley’s achievements.
This veil of silence forced me back to my old Xerox of Halley’s original, lovingly made in my graduate student days at the American Museum of Natural History, from a beautifully bound set of this oldest scientific journal in English. I had often assigned its offspring to students but had not read the original for several years. Perhaps if I encountered something intriguing, I might actually find a chink of difference and be able to add, rather than merely reiterate, if I chose to write about Halley after all. I plunged in and read with mounting disappointment. Nothing unremembered, nothing unusual. Oh, I did manage a tiny contribution to the great issue that seemed to obsess press commentators—the spelling and pronunciation of the man’s name. We were instructed so often to say “Edmond” (not “Edmund”), that “o” became an insider’s badge of sophistication. But he is Edmund in this article (and the indifferent spelling of Halley’s time probably made either quite acceptable to him). As to the other vexatious mystery—why Americans, flagrantly disregarding one of the few decent guides that English spelling offers for pronunciation, insist on calling the man “Hayley”—I can only conjecture (as many others have) that our minds were poisoned by a certain Haley (properly “Hayley” by virtue of the single “I”) who made a lot of noise when I was a teenager and also called his group the Comets.
Reading long after midnight, I finally came to the last paragraph, having no fun at all as the clock struck one (and unable to get that wretched tune out of my head). Then I had a moment of discovery, that one instant in ten thousand that makes a scholar’s life so exciting, and that justifies the tedium and discipline accompanying any serious intellectual work (Edison’s old allocation of effort between perspiration and inspiration is just about right—ninety-nine to one). I realized, in short, that I, and every other comment I have ever read about Halley’s proposal for the earth’s age, have interpreted him precisely the wrong way round. I also think I know why. The difficulty lies not with anything Halley wrote. His meaning could not have been stated more explicitly. Rather, for concerns of our own, and by a traditional misreading of the history of science, we have simply passed over Halley’s own construction and imposed our preferences upon his reasoning. It’s a damned shame, too—for his intent is both interesting and instructive for us today.
Halley’s article makes a simple and elegant proposal. (The bare bones of the method have not been misinterpreted, only Halley’s view of its meaning.) He assumes that the oceans were originally fresh and have become progressively more salty through an influx of dissolved materials transported by rivers. Since rivers flow in, but nothing flows out, salt must accumulate steadily. (Evaporation returns ocean waters to rivers in the earth’s hydrologic cycle, but evaporated waters are fresh and leave their salts behind.) We usually regard river water as fresh, but Halley recognized correctly that streams carry tiny (and untasteable) amounts of dissolved salts:
But the rivers in their long passage over the earth do imbibe some of the saline particles thereof, though in so small a quantity as not to be perceived, unless in these their depositories [that is, lakes and oceans] over a long tract of time.
Halley recognized that this argument for the source of oceanic salt suffered one grave methodological defect. The world ocean is a sample of one. How can the ocean, by itself, prove the general proposition that basins with riverine inlets, but no outlets, become progressively more salty with time? Perhaps the ocean is just a special case proving nothing but its individuality, not the largest representative of a general process.
The cleverness of Halley’s argument lies in his recognition that lakes, properly classified and divided, serve as smaller systems representing the same process he proposed for oceans. So he sorted large lakes into those—most of them—that have both inlets and outlets, and the few that, like the oceans, receive waters from rivers but provide no exit beyond evaporation.
He could find only four in this second category comparable with oceans—the Caspian Sea, the “Mare Mortuum” (Dead Sea), “the lake on which stands the City of Mexico,” and Titicaca in Peru. All are salt to varying degrees, while all freshwater lakes fell into his first category. Halley’s taxonomy of lakes had confirmed his theory for the origin of salt in oceans—a fine example of the methodological principle that sample sizes can often be increased only by recognizing proper analogues in other classes of objects.
Halley now felt ready to advance his argument for the age of the earth (or at least for its oceans):
Now if this be the true reason of the saltness of these lakes, ’tis not improbable but that the ocean it self is become salt from the same cause, and we are thereby furnished with an argument for estimating the duration of all things, from an observation of the increment of saltness in their waters.
If we could measure the salinity of modern oceans, then determine the amount of salt brought in by rivers each year, we could extrapolate back to an initial time of no salt at all and estimate the age of the oceans. Halley recognized that his method required a set of
simplifying assumptions that might not be strictly true—rough constancy of annual influx, no appreciable loss of salt in buried sediments, for example. But he felt that his method might give a reasonable first-order estimate.
Halley realized that he could not hope to measure the annual influx accurately—too much variation among too many rivers and probably too small a total compared with the amount of salt now in the oceans. But we could, for the benefit of posterity, make accurate measurements of salt now in oceans and lakes; for, a few centuries hence, the total increase should be palpable enough to permit a good estimate of average annual increment. Halley advised:
This argument can be of no use to ourselves, it requiring very great intervals of time to come to our conclusion…. I recommend it therefore to the Society, as opportunity shall offer, to procure the experiments to be made of the present degree of saltness of the ocean, and of as many of these lakes as can be come at, that they may stand upon record for the benefit of future ages.
The geological literature contains a “standard” interpretation of Halley’s contribution. It points out, first of all and quite correctly, that Halley’s method was wrong—a good try to be sure, but ultimately based on a false premise. Halley assumed that since salt entered the oceans every year, yet the sea was not saturated (as the greater salinity of the Dead Sea attested), newly entering salt must be added to the amount already present. But many of nature’s cycles are maintained in dynamic balance between influxes and outflows, long before most components reach some theoretically maximal level. Our atmosphere could maintain a lot more carbon dioxide, but until we began messing with an old balance by burning massive amounts of fossil fuel, carbon dioxide had remained relatively steady at percentages much smaller than the atmosphere can hold (as we may discover to our great sorrow if current rises lead to a runaway greenhouse effect).
Most components of the atmosphere and ocean are in such dynamic balance on our ancient earth. (In a sense, such equilibria must exist, for the earth is so old that any directional increment, however small, would lead to saturation in a fraction of historical time.) Oceanic salt persists at its current level in a dynamic balance, or steady state, between influx from rivers and numerous processes, including burial in sediments and biological uses, that constantly remove about the same amount that enters. Perhaps, right at the beginning of things, an originally fresh ocean accumulated salt in Halley’s manner. But that process of initial increase ended long ago, and Halley’s method cannot reach so far back into the abyss of time.
This usual presentation of Halley’s crucial error is then balanced in traditional accounts by warm praise—for two main reasons. First, Halley wins kudos for making the first serious quantitative proposal to determine the earth’s age. Moreover, though Halley felt that he could not apply the method himself, his suggestions were followed by later scientists, particularly toward the end of the nineteenth century by the great Irish geologist John Joly who used the accumulation of salt to propose a date of 100 million years for the earth. Although Joly’s estimate was vastly too small—the earth is some 4.5 billion years old—his work represented a great advance on previous speculative traditions that had led to little but hot air and had rarely dared to imagine dates even so old as Joly’s.
Secondly, Halley has been proclaimed a hero in the false view of history that sees light and truth locked in perpetual warfare with religion. Halley does begin his article by rejecting a literal interpretation of Genesis for the earth’s age. He accepts, because scripture so states, that humans have lived on earth for some 6,000 years but denies a creation of all things just five days before:
Whereas we are there told that the formation of man was the last act of the creator, ’tis no where revealed in scripture how long the earth had existed before this last creation, nor how long those five days that proceeded it may be to be accounted; since we are elsewhere told, that in respect of the almighty a thousand years is as one day, being equally no part of eternity; nor can it well be conceived how those days should be to be understood of natural days, since they are mentioned as measures of time before the creation of the sun, which was not till the fourth day.
But Halley writes these lines as a liberal theist, not as a scientist engaged in a conscious battle with religion. The word scientist didn’t exist in Halley’s day, and close ties between rational science and sensible religion were sought by most scholars engaged in work that we would now call scientific. Halley, in other words, speaks here for the liberal tradition of nonliteral interpretation.
The traditional literature usually unites these themes of praise in a single phrase: Halley ranks with the heroes of geology because his method, though flawed, does provide a minimal estimate of the earth’s age (the time of accumulation before oceans reached steady-state). The Discover man-of-the-year article concludes: “His effort was useful because, in arriving at a minimum age for the earth, it inspired others to look for better geological clocks.”
And so I have always read, and taught, Halley’s argument for the earth’s age—as a minimal estimate proposed to burst the bonds of a biblical literalism that made science impossible because ordinary causes could not produce the geological work required in only a few thousand years. And so I read it again last week—until I came to the last paragraph. Here Halley conveys one of the most important and subtle points of good scientific methodology—a lesson that ranks above all others in rules of procedure that must be purveyed to advanced students beginning their own careers in independent research.
In complex historical sciences like geology, few situations can be as well controlled as ideal laboratory experiments. Biases are unavoidably and intrinsically contained within available data. Since these biases cannot always be removed, researchers must follow one cardinal rule—they must be sure that recognized biases fall in a direction that will make confirmation of their hypothesis less likely (for if sources of bias tend to support favored views, how can you know whether a positive result records a preferred explanation or simply the inherent bias).
Halley begins the last paragraph by admitting a bias that he cannot correct:
If it be objected that the water of the ocean, and perhaps some of these lakes, might at the first beginning of things, in some measure contain salt, so as to disturb the proportionality of the encrease [sic] of saltness in them, I will not dispute it…
How lovely, I said to myself. He is about to state the principle that bias must lie against a favored outcome. I must note this and point it out to students. I read on and was not disappointed. Halley makes the argument with fine precision (continuing from the quotation above):
…but shall observe that such a supposition would by so much contract the age of the world within the date to be derived from the foregoing argument….
I smiled benignly, began to read on, and then experienced the moment of truth so like that classic scene of cartoon or comedy when the policeman sees a flying mouse or a walking snowman, smiles happily with a “how-nice, a-flying-mouse” look, then does a double take, drops whistle from mouth in astonishment, and says, “A flying mouse!” Wait a minute! Halley is supposed to be arguing for an age longer than tradition, an expansion of biblical limitations. But he actually says that a bias he can’t remove will make the earth seem older than it really is, the very kind of bias—one favoring your hypothesis—that must be avoided. (If a bag contains one hundred beans and you observe that one new bean is added each day, you will assume, by analogy with Halley’s argument about originally saltless oceans, that beans have been added for one hundred days. But if the bag started with twenty-five beans, the process will only be seventy-five days old, not one hundred as you estimated. In the same manner, if the oceans started with some salt, but you assume they began saltless, your age by Halley’s method will be greater than the true age.)
I then became seriously puzzled. Does Halley have his methodology backward? What is going on? How can he be trying to expand the earth’s age and then admit a bias
that will make it appear older? Either Halley was a methodological dunce or something must be desperately wrong with the traditional view that he was trying to set a minimal age for the earth. In fact, Halley is telling us that he has set a maximal age, and he is clearly damned pleased with himself. I read further (again continuing the last quotation):
…the foregoing argument, which is chiefly presented to refute the ancient notion, some have of late entertained, of the eternity of all things.
So Halley thought he was doing the exact opposite of what all posterity has attributed to him. He contends that he was establishing a maximal age to refute a notion of eternity. We say that he was seeking a minimal age to expand the literal biblical chronology. Why—given the admirable clarity of Halley’s words—have we so grievously misstated his intent?
Eight Little Piggies Page 17