Brilliant Blunders: From Darwin to Einstein - Colossal Mistakes by Great Scientists That Changed Our Understanding of Life and the Universe (11 page)

On April 28, 1862, Kelvin (then still Thomson) read to the Royal Society of Edinburgh a paper entitled
“On the Secular Cooling of the Earth.” This paper followed closely on the heels of another
article published just the month before, with the title
“On the Age of the Sun’s Heat.” Thomson made clear from the opening sentence that this was not going to be just another forgettable technical essay. Here was a hard-line attack on the geologists’ assumption about the unchanging nature of the forces that had shaped the Earth:

For eighteen years it has pressed on my mind, that essential principles of Thermodynamics have been overlooked by those geologists who uncompromisingly oppose all paroxysmal hypotheses, and maintain not only that we have examples now before us, on the earth, of all the different actions by which its crust has been modified in geological history, but that these actions have never, or have not on the whole, been more violent in past time than they are at present.

While the phrase “pressed on my mind” was somewhat of an overdramatized exaggeration, it was certainly true that
Kelvin’s first papers on the topics of heat conduction and the distribution of heat through the body of the Earth were written as early as 1844 (when he was a twenty-year-old student) and 1846, respectively. Even before his seventeenth birthday, Thomson succeeded in spotting a mistake in a paper on heat by an Edinburgh professor.

Kelvin’s point was simple: Measurements from mines and wells indicated that heat was flowing from the Earth’s interior to its surface, implying that the Earth was an initially hotter planet that was cooling. Consequently, Kelvin argued, unless some internal or external energy sources could be shown to compensate for the heat losses, clearly no steady state, or repeating, identical geological cycles, were possible. Charles Lyell was actually aware of this problem, and in his
Principles of Geology
he proposed a self-sustaining mechanism by which he believed that chemical, electric, and heat energy could be exchanged cyclically in the Earth’s interior. Basically, Lyell envisaged a scenario in which chemical reactions generated heat, which drove electrical currents, which in turn dissociated the chemical
compounds into their original constituents, thus starting the process anew. Kelvin could barely hide his contempt. He demonstrated unambiguously that such a process amounted to some sort of perpetual motion machine, violating the principle of dissipation (and conservation) of energy—when mechanical energy is transformed irreversibly into heat, as in the case of friction. Lyell’s mechanism therefore violated the basic laws of thermodynamics. To Kelvin, this was the ultimate proof that the geologists were completely ignorant of physical principles, and he remarked caustically:

To suppose, as Lyell, adopting the chemical hypothesis, has done, that the substances, combining together, may be again separated electrolytically by thermoelectric currents, due to the heat generated by their combination, and thus the chemical action and its heat continued in an endless cycle, violates the principles of natural philosophy in exactly the same manner, and to the same degree, as to believe that a clock constructed with a self-winding movement may fulfill the expectations of its ingenious inventor by going for ever.

At its core, Kelvin’s calculation of the age of the Earth was straightforward. Since the Earth was cooling, he explained, one could use the science of thermodynamics to calculate the Earth’s finite geological age: the time it took the Earth to get to its current state, since the formation of the solid crust. The idea itself was not entirely new;
the French physicist Joseph Fourier had developed the mathematical theory of thermal conductivity and of the Earth’s cooling process at the beginning of the nineteenth century. Realizing the theory’s potential, Kelvin engaged in 1849 in a series of measurements of underground temperatures (together with the physicist James David Forbes), and in 1855 urged that a complete geothermal survey be conducted, precisely to enable the calculation of the Earth’s age.

Kelvin assumed that the mechanism that transported heat from the interior to the surface was the same type of conduction that
transfers heat from an iron skillet on an open fire to its handle. Still, in order to apply Fourier’s theory to the cooling Earth, he needed to know three physical quantities: (1) the initial internal temperature of the Earth, (2) the rate of change in the temperature according to depth, and (3) the value of the thermal conductivity of the Earth’s rocky crust (which determines how fast heat can be transported).

Kelvin thought that he had a fairly good handle on two of these quantities. Measurements by a number of geologists have shown that while results varied from location to location, in the mean, the temperature toward the Earth’s center increased roughly by one degree Fahrenheit for every fifty feet of descent (this quantity is known as the temperature gradient). Concerning the thermal conductivity, Kelvin relied on his own measurements for two types of rocks and for sand to give him what he regarded as an acceptable average. The third physical quantity—the Earth’s deep internal temperature—was extremely problematic, since it couldn’t be measured directly. But Kelvin was not a man easily deterred by such difficulties. Putting his analytic mind to work, he was eventually able to deduce an estimate for the unknown internal temperature. The entangled intellectual maneuvering that he had to perform to achieve this result presented Kelvin at his best—and his worst. On one hand, his virtuosic command of physics and his ability to examine potential alternatives with a razor-sharp logic were second to none. On the other, as we shall see in the next chapter, due to his overconfidence, he could sometimes be completely blindsided by unforeseen possibilities.

Kelvin started his assault on the problem of the Earth’s internal temperature by analyzing a variety of possible models for the cooling Earth. The general assumption was that the Earth’s initial state was molten, as a result of the heat generated by some collision—either with a number of smaller bodies, such as meteors, or with one body of nearly equal mass. The subsequent evolution of this molten sphere depended on a property of rocks that was not known with certainty: whether upon solidifying, molten rock expanded (as in the case of freezing water) or contracted (as metals do). In the former case, one could expect the solid crust to float
over a liquid interior, just like ice on the surface of lakes in winter. In the latter, the denser solid rocks forming near the Earth’s cooler surface would have sunk down, eventually forming perhaps a solid scaffolding that could support the surface crust. While the empirical evidence was scarce, experiments with melted granite, slate, and trachyte all seemed to point in the direction of molten rock contracting both upon cooling and solidifying. Kelvin used this information to chart a new scenario. He proposed that before complete solidification took place, the cooler surface liquid had sunk toward the center, thus maintaining convection currents similar to those generated in the oil in a frying pan. In this model the convection was assumed to sustain a nearly uniform temperature throughout. Consequently, Kelvin assumed that at the point of solidification, the temperature everywhere was roughly the temperature at which rock melts, and he took that to be the Earth’s internal temperature (assuming that the core had not cooled by much since). This model implied that the Earth was nearly homogeneous in its physical properties. Unfortunately, even this ingenious scheme did not fully solve the problem, since the value of the fusion temperature of rock was not known in Kelvin’s time. He was, therefore, forced to adopt an educated guess of seven thousand to ten thousand degrees Fahrenheit for an acceptable range. (Seismic measurements performed in 2007 gave a temperature of about 6,700 degrees Fahrenheit for a region that is about 1,860 miles below the Earth’s surface.)

Putting together all of this information, Kelvin finally computed an age for the Earth’s crust: ninety-eight million years. Estimating the uncertainties in his assumptions and in the data available to him,
Kelvin believed that he could state with some confidence that the Earth’s age had to be somewhere between twenty million and four hundred million years.

In many respects, in spite of the insecure assumptions, this was a truly brilliant calculation. Who would have thought that one could actually calculate the age of the Earth? Kelvin took a seemingly insoluble problem and deciphered it. He used sound physical principles both in the formulation of the problem and in his method of
calculation, and he augmented those by the best quantitative measurements available at the time (some of which he performed by himself). Compared with his determination, the geologists’ estimates appeared to be nothing more than crude guesses and idle speculation based on poorly understood processes such as erosion and sedimentation.

The number that Kelvin produced—roughly one hundred million years—was broadly consistent with an earlier estimate he had made of the age of the Sun. This was significant, since even some of Kelvin’s contemporaries realized that the strength of his argument about the age of the Earth derived at least part of its credibility from his solar calculation. Kelvin’s basic premise in the paper “On the Age of the Sun’s Heat,” and in a few similar later papers, was not very different from his central thesis in his analysis of the age of the Earth. The key assumption was that the
only
source of energy that the Sun had at its disposal was the mechanical
gravitational energy.
This was supposed to be supplied either by the falling-in of meteors, as Kelvin originally thought, but later rejected, or, as Kelvin proposed later and forcefully reiterated in 1887, by the Sun continually contracting, and dissipating its gravitational energy in the form of heat. Since, however, the energy supply was clearly not infinite, and the Sun was unceasingly losing energy by radiation, Kelvin concluded justifiably that the Sun could not remain unchanged indefinitely. To calculate its age, he borrowed elements from theories for the formation of the solar system proposed by the French physicist Pierre-Simon Laplace and the German philosopher Immanuel Kant. He then supplemented those with important insights on the Sun’s potential contraction gained from the work of his contemporary German physicist Hermann von Helmholtz. Weaving all of these ingredients into one coherent picture,
Kelvin was able to obtain a rough estimate of the Sun’s age. The last paragraph in Kelvin’s paper reflected his acknowledgement of the many uncertainties involved:

It seems, therefore, on the whole most probable that the sun has not illuminated the earth for one
hundred million years, and almost certain that he has not done so for five hundred million years. As for the future, we may say, with equal certainty, that inhabitants of the earth can not continue to enjoy the light and heat essential to their life for many million years longer unless sources now unknown to us are prepared in the great storehouse of creation.

As I shall describe in the next chapter (and explain in detail in chapter 8), the last sentence proved to be truly farseeing.

The fact that the calculated ages of the Sun and the Earth turned out to be comparable—even though the estimates were determined independently—made Kelvin’s calculation more compelling, since there was every reason to suspect that the entire solar system had formed around the same time. Still, quite a few British geologists remained unconvinced. It almost seemed as though, for some of them, it was more convenient to explain everything not by the laws of physics but rather by what the American geologist Thomas Chamberlin cynically termed in 1899 “reckless drafts on the bank of time.” The best illustration of the skeptical attitude toward Kelvin’s findings is a fascinating exchange Kelvin had in 1867 with the Scottish geologist Andrew Ramsay. The occasion was a lecture by the geologist Archibald Geikie on the geological history of Scotland.
Kelvin later described the conversation he had with Ramsay immediately following the talk, noting that almost every word of it remained “stamped on my mind”:

I asked Ramsay how long a time he allowed for that history. He answered that he could suggest no limit to it. I said, “You don’t suppose geological history has run through 1,000,000,000 [one billion] years?” “Certainly I do!” “10,000,000,000 [ten billion] years?” “Yes!” “The sun is a finite body. You can tell how many tons it is. Do you think it has been shining for a million million years?” “I am as incapable of estimating and understanding the reasons which you physicists have for limiting geological time as you are incapable of understanding the geological reasons
for our unlimited estimates.” I answered, “You can understand the physicists’ reasoning perfectly if you give your mind to it.”

Kelvin was absolutely right. Ignoring for a moment the question of how solid his physical assumptions were and the mathematical details of his calculations, Kelvin’s main point was accessible. Since the Sun and the Earth are both losing energy, and they don’t possess any known sources that could replenish the losses, he argued, the Earth’s geological past must have been more active than the present. A hotter Sun would have caused more evaporation, with the associated higher rate of erosion by precipitation. At the same time, a hotter Earth would have experienced heightened volcanic activity. Consequently, Kelvin concluded, the uniformitarian assumption of an Earth in an almost indefinite quasi–steady state was untenable.

It wasn’t surprising, then, that in 1868,
when Kelvin delivered an address before the Geological Society of Glasgow, he chose as the target for his acrimonious criticism the first text that had brought the principle of uniformitarianism (formulated by James Hutton) to the attention of a wide audience. This was the 1802 book
Illustrations of the Huttonian Theory of the Earth
by the Scottish scientist John Playfair. From this book, Kelvin cited the following stunning passage, which to him represented the epitome of the orthodox opinion of the geologists of the day: