Karl Marx remarked that all historical events occur twice, first as tragedy, the second time as farce. If Toscanini’s lapse was tragic (in the heroic sense), then I witnessed the farce just two hours ago. I listened while the ghost of Guy Lombardo missed a beat. For the first time in God only knows how many years, that smooth sound, that comfortable welcome to the New Year, fell apart for a mysterious moment. As I learned later, someone forgot to tell Guy about the special 61-second minute that ended 1978; he started too early and could not compensate with unnoticed grace.
This second, added for internal bookkeeping to synchronize atomic and astronomical clocks, received wide press coverage, virtually all of it in a jocular vein. And why not—good news is rare enough these days. Most reports pushed the same theme: they twitted scientists about their concern for consummate accuracy. After all, how can so trifling a span of time as a single second matter?
I then remembered another figure, 1/50,000 second per year. This figure, an ant before the behemoth of a full second, is the annual rate of deceleration in the earth’s rotation due to tidal friction. I will attempt to show just how important such an “insignificant” number can be in the fullness of geological time.
We have known for a long time that the earth is slowing down. Edmund Halley, godfather to the famous comet and Astronomer Royal of England early in the eighteenth century, noted a systematic discrepancy between the recorded position of ancient eclipses and their predicted areas of visibility based on the earth’s rate of rotation in his time. He calculated that this disparity could be resolved by assuming a faster rotation in the past. Halley’s calculations have been refined and reanalyzed many times, and eclipse records suggest an approximate rate of two milliseconds per century for rotational slowing during the past few thousand years.
Halley proposed no adequate reason for this deceleration. Immanuel Kant, a versatile fellow indeed, supplied the correct explanation later in the eighteenth century. Kant implicated the moon and argued that tidal friction had slowed the earth down. The moon pulls the waters of the earth toward it in a tidal bulge. This bulge remains oriented toward the moon as the earth rotates under it. From our point of view as earthbound observers, high tide moves steadily westward around the earth. This tide, moving continuously across land and sea (for continents have their minor tides as well), creates a great deal of friction. Astronomers Robert Jastrow and M. H. Thompson write: “A huge quantity of energy is dissipated in this friction each day. If the energy could be recovered for useful purposes, it would be sufficient to supply the electrical power requirements of the entire world several times over. The energy is actually dissipated in the turbulence of coastal waters plus a small degree of heating of the rocks in the crust of the earth.”
But tidal friction has another effect, virtually invisible on the scale of our lives, but a major factor in the earth’s history. It acts as a brake upon the spinning earth, slowing the earth’s rotation at the leisurely rate of about two milliseconds per century, or 1/50,000 second per year.
Braking by tidal friction has two correlated and intriguing effects. First, the number of days in a year should be decreasing through time. The length of a year seems to be essentially constant relative to the official cesium clock. Its invariance is affirmed both empirically, by astronomical measurement, and theoretically. We might predict that a solar tide should slow the earth’s revolution just as the lunar tide slows its rotation. But solar tides are quite weak, and the earth, hurtling through space, has such an enormous moment of inertia that the year increases by no more than three seconds per billion years. Here we finally have a figure that we can safely ignore—half a minute from the origin of the earth to its destruction by an exploding sun some five billion years hence!
Second, as the earth loses angular momentum in slowing down, the moon—obedient to the law of conservation of angular momentum for the earth-moon system—must pick up what the earth loses. The moon does this by revolving around the earth at a greater and greater distance. In other words, the moon has been steadily receding from the earth.
If the moon looks big now, low on the horizon on a crisp October night, you should have been around to see what the trilobites saw 550 million years ago. G. H. Darwin, noted astronomer and second son of Charles, first developed this idea of lunar recession. He believed that the moon had been wrenched from the Pacific Ocean, and he extrapolated its present rate of recession back to determine the time of this convulsive birth. (It does fit, but thanks to plate tectonics, we now know that the Pacific is not a permanent hole, but a configuration of the geological moment.)
In short, tidal friction induced by the moon entails two coupled consequences through time: slowing the earth’s rotation to decrease the number of days per year, and increasing the distance between earth and moon.
Astronomers have long known about these phenomena in theory; they have also measured them directly over geological microseconds. But until recently, no one has known how to gauge their effects over long stretches of geological time. A simple backward extrapolation of the current rate will not suffice because intensity of braking depends upon the configuration of continents and oceans. The most effective braking occurs when tides sweep across shallow seas; the least effective when tides move with comparatively little friction over deep oceans and land. Shallow seas are not prominent features of our present earth, but they covered millions of square miles at various times in the past. The high tidal friction of those times may be matched by very slow deceleration at other times, particularly when all the continents coalesced into a single Pangaea. The pattern of rotational slowing through time therefore becomes more a geological than an astronomical problem.
I am delighted to report that my own brand of geology has yielded, albeit ambiguously, the required information—for some fossils record in their patterns of growth the astronomical rhythms of ancient times. The haughty and high-riding mathematicians and experimentalists of modern geophysics do not often take a bow toward a lowly fossil. Yet one prominent student of the earth’s rotation has written: “It appears that paleontology comes to the rescue of the geophysicist.”
For more than a hundred years, paleontologists had occasionally noted regularly spaced growth lines on some of their fossils. Some had suggested that they might reflect astronomical periods of days, months, or years—much like tree rings. Yet no one had done anything with these observations. Throughout the 1930s Ting Ying Ma, a somewhat visionary, highly speculative, but infallibly interesting Chinese paleontologist, studied annual bands in fossil corals to determine the position of ancient equators. (Corals living at the equator in regimes of nearly constant temperature should not show the seasonal bands; the higher the latitude, the stronger the bands.) But no one had studied the very fine laminations that often occur by the hundreds per band.
In the early 1960s, Cornell paleontologist John West Wells realized that these very fine striations might record days (slow growth at night versus faster growth during daylight, much as trees produce annual bands of alternating slow winter and rapid summer growth). He studied a modern coral with both coarse (presumably annual) and very fine banding, and he counted an average of about 360 fine lines to each coarse band. He concluded that the fine lines are daily.
Wells then searched his collection for fossil corals sufficiently well preserved to retain all their fine bands. He found very few, but they enabled him to make one of the most interesting and important observations in the history of paleontology: a group of corals about 370 million years old had an average of just under 400 fine lines per coarse band. These corals had witnessed a year of nearly 400 days. Direct, geological evidence had finally been found for an old astronomical theory.
But Wells’s corals had affirmed only half the story—increasing length of day. The other half, recession of the moon, required fossils with daily and monthly banding; for if the moon had been much closer in the past, it would have revolved around the earth in a much shorter time than it does today. The
ancient lunar month should have contained fewer than the 29.53 solar days of the present month.
Since Wells published his famous paper on “Coral Growth and Geochronometry” in 1963, several claims have been entered for lunar periodicities as well. Most recently, Peter Kahn, a paleontologist from Princeton, and Stephen Pompea, a physicist from Colorado State University, have argued that the key to lunar history lies with one of everybody’s favorite creatures, the chambered nautilus. The nautilus shell is divided into regular internal partitions called septa. These same septa, and the beauty of their construction, inspired Oliver Wendell Holmes to exhort us, by analogy, to do better with our internal lives:
Build thee more stately mansions, O my soul,
As the swift seasons roll!
Leave thy low-vaulted past!
Let each new temple, nobler than the last,
Shut thee from heaven with a dome more vast,
Till thou at length art free,
Leaving thine outgrown shell by life’s unresting sea!
I am happy to report that nautiloid septa may have extended their utility beyond Holmes’s musings on immortality and O’Neill’s cribbing of a title for a play. For Kahn and Pompea counted the finer growth lines on the exterior of Nautilus’s shell and found that each chamber (the space between successive septa) contains an average of thirty fine lines, with little variation either among shells or on successive chambers of single shells. Since Nautilus, living in deep Pacific waters, migrates daily in response to the solar cycle (it moves towards the surface at night), Kahn and Pompea suggest that the fine lines record days. The secretion of septa may be entrained to a lunar cycle. Many animals, including humans of course, have lunar cycles, usually tied to breeding.
Nautiloids are quite common as fossils (the modern chambered nautilus is sole survivor of a very diverse group). Kahn and Pompea counted lines per chamber in twenty-five nautiloids ranging in age from 25 to 420 million years. They argue for a regular decrease in lines per chamber from thirty today, to about twenty-five for the youngest fossils, to only nine or so for the oldest. If the moon circled the earth in only nine solar days 420 million years ago (when the day only contained twenty-one hours), then it must have been much closer. Cranking through some equations, Kahn and Pompea conclude that these ancient nautiloids saw a gigantic moon slightly more than two-fifths its current distance from the earth (yes, they had eyes).
At this point, I must confess to some ambivalence about this large body of data on fossil growth rhythms. The methods are beset with unsolved problems. How do you know what periodicity the lines reflect? Consider the case of fine lines, for example. They are usually counted as though they record solar days. But suppose they are a response to tidal cycles—a periodicity that involves both the earth’s rotation and the moon’s revolution. If the moon revolved in a much shorter time in the past, then ancient tidal cycles were not nearly so close to the solar day as they are now. (You should now grasp the importance of Kahn and Pompea’s argument, made without direct evidence by the way, that the fine lines of Nautilus reflect day-night cycles of vertical migration rather than tidal effects. In fact, they explain their three exceptional cases by arguing that these nautiloids inhabited persistently shallow, nearshore waters and may have recorded the tides.)
Even if lines are a response to solar cycles, how do you assess the days per ancient month or year? Simple counting is not the solution because animals often skip a day but do not, so far as we know, double up. Actual counts generally underestimate the number of days (remember Wells’s original modern corals with an average of 360, not 365, daily bands—on very cloudy days, growth during the daytime may not exceed growth at night, and bands may not form).
Moreover, to pose the most basic question of all, how can we be certain that lines reflect an astronomical periodicity at all? Too often, little beyond their geometric regularity has inspired the assumption that they record days, months, or years. But animals are not passive machines, dutifully recording astronomical cycles in all their regularities of growth. Animals have internal clocks as well, and these are often keyed to metabolic rhythms with no apparent relationship to days, tides, and seasons. For example, most animals slow down their growth rates greatly as they advance in age. But many growth lines continue to increase in size at a constant rate. The distance between septa of Nautilus increases constantly and regularly throughout growth. Are septa really deposited once each month, or do later ones measure longer amounts of time? Nautilus may live by the rule: grow a septum after reaching a regularly increasing chamber volume, not grow a septum each full moon. I am, primarily for this reason, highly skeptical about Kahn and Pompea’s conclusions.
The result of these unsolved problems is a body of poorly synchronized data. Uncomfortably large differences exist in the literature. One study of supposedly lunar periodicities in corals suggests that, about 350 million years ago, the month contained three times the number of days that Kahn and Pompea would allow.
Nonetheless, I remain satisfied and optimistic for two reasons. First, despite all internal asynchrony, every study has revealed the same basic pattern—decrease in the number of days per year. Second, after an initial period of uncritical enthusiasm, paleontologists are now doing the required hard work to learn just what the lines represent—experimental studies on modern animals in controlled conditions. Criteria for the resolution of discrepancies in fossil data should soon be available.
Scarcely any geological subject could be more fascinating or more beset with juicy problems. Consider the following: if you extrapolate back through time the current recession of the moon as estimated from eclipse data, the moon enters the Roche limit about one billion years ago. Inside the Roche limit, no major body can form. If a large body enters it from outside, results are unclear but certainly impressive. Vast tides would roar across the earth and the lunar surface would melt, which, conclusively from dates on Apollo rocks, it did not. (And the recession rate estimated from modern data—5.8 centimeters per year—is much less than the average advocated by Kahn and Pompea—94.5 centimeters per year.) Clearly, the moon was not this close to us either a billion years ago or ever at all since its surface solidified more than four billion years ago. Either rates of recession have varied drastically, and were much slower early in the earth’s history, or the moon entered its current orbit a long time after the earth’s formation. In any case, the moon was once much closer to us, and this different relationship should have had an important effect on the history of both bodies.
As for the earth, we have tentative indications in some of our earliest sedimentary rocks of tidal amplitudes that would put the Bay of Fundy to shame. For the moon, Kahn and Pompea make the interesting suggestion that its closer position and the earth’s stronger gravitational pull at that time may explain why the lunar maria are concentrated on its visible, earthward side (the maria represent vast extrusions of liquid magma), and why the moon’s center of mass is displaced in an earthward direction.
Geology has no more important lesson to teach than the vastness of time. We have no trouble getting our conclusions across intellectually—4.5 billion years rolls easily off the tongue as an age for the earth. But intellectual knowledge and gut appreciation are very different things. As a sheer number, 4.5 billion is incomprehensible, and we resort to metaphor and image to emphasize just how long the earth has existed and just how insignificant the length of human evolution has been—not to mention the cosmic millimicrosecond of our personal lives.
The standard metaphor for earth history is a 24-hour clock with human civilization occupying the last few seconds. I prefer to emphasize the accumulated oomph of effects utterly insignificant on the scale of our lives. We have just completed another year and the earth has slowed down by another 1/50,000 second. So blinking what? What you have just read is what.
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