Brilliant Blunders: From Darwin to Einstein - Colossal Mistakes by Great Scientists That Changed Our Understanding of Life and the Universe (13 page)

You might have thought that these enormous gains to geology, combined with Kelvin’s other myriad contributions to science (he published more than six hundred papers), would have exalted him to the rank of those who have had an everlasting impact—the likes of Galileo and Newton. Sadly, the reality is rather different, and even the fact that Kelvin was equally comfortable in the academic and technical worlds did not help. In 1999
Physics World
magazine and
Physics Web
(an internet publication by the British Institute of Physics) conducted polls in which they asked one hundred leading physicists
to name the ten greatest physicists of all time. Kelvin’s name did not feature on either list. At least one of the reasons for this subsequent deterioration in Kelvin’s status concerns the debate over the age of the Earth:
We know today that the age of the Earth is about 4.54 billion years.
This is about fifty times longer than Kelvin’s estimate!
How could he have blundered so badly in a calculation supposedly based on the laws of physics?

Science becomes dangerous only when it imagines that it has reached its goal.

—GEORGE BERNARD SHAW

T
he debate on the age of the Earth between Kelvin and Thomas Huxley generated considerable scientific and public interest. Few disagreed with the assessment that, if anything, Kelvin’s position had been strengthened somewhat by this war of words. Huxley did raise one point, however, which proved to be particularly perceptive. In effect, it identified the crux of Kelvin’s blunder:

Mathematics may be compared to a mill of exquisite workmanship, which grinds you stuff of any degree of fineness; but, nevertheless, what you get out depends upon what you put in; and as the grandest mill in the world will not extract wheat-flour from peascod, so pages of formulae will not get a definite result out of loose data.

Indeed, Kelvin had such an exceptional command of mathematics that it was essentially guaranteed that if he had made any mistake,
it would not have been in the actual calculations. It was his set of
assumptions
that provided the input for those calculations that had to be scrutinized.

The first person who, albeit reluctantly, took a stab at searching for a loophole in Kelvin’s original postulates was Kelvin’s former pupil and assistant,
the engineer John Perry. By happenstance, Perry studied engineering under James Thomson, Kelvin’s older brother, but later he spent a year in Kelvin’s Glasgow laboratory. While most of Perry’s scientific output focused on electrical engineering and applied physics, he is perhaps best known today for his brief foray into geology.

In August 1894, Robert Cecil, the Third Marquis of Salisbury, delivered a presidential address at the sixty-fourth meeting of the British Association for the Advancement of Science. Salisbury used Kelvin’s estimate of the age of the Earth (one hundred million years)
to argue that evolution by natural selection could not have taken place. As is often the case with messages that are too dogmatic, however, this speech achieved precisely the opposite effect to its intentions, at least with John Perry. Salisbury’s denial of the theory of evolution convinced Perry that there had to be something wrong with Kelvin’s calculations. Impressed by the accumulation of geological and paleontological data,
Perry wrote to a physicist friend that “once it became clear to my mind that there was necessarily such a flaw [in Kelvin’s estimates], its discovery was no mere question of chance.”

Perry completed the first version of his investigation of the problem of the cooling Earth on October 12, and during the following weeks,
he diligently sent copies of the paper to a number of physicists (including Kelvin) for comments. Respectful even in his criticism, Perry signed his letter to Kelvin “Your affectionate pupil.” While about a half dozen physicists expressed support for Perry’s conclusions, Kelvin himself did not bother to respond. Perry was
given a second chance when he was invited to a dinner party at Trinity College in Cambridge, a dinner that Kelvin was also supposed to attend. The opportunity to talk to Kelvin in person was too good to be missed. Perry excitedly described the event to a friend the following day:

I sat beside him [Kelvin] last night at Trinity and he had to listen. I knew beforehand that he would not read my documents and he hadn’t but I gave him a lot to think of and his pitying smile at my ignorance died away in about 15 minutes. I think he will now really begin to consider the matter. Geikie [the geologist Archibald Geikie] was opposite, his eyes gleaming with delight.

The scientific journal
Nature
eventually published Perry’s article on January 3, 1895. The report started in an apologetic tone: “I have sometimes been asked by friends interested in geology to criticize Lord Kelvin’s calculation of the probable age of the earth. I have usually said that it is hopeless to expect that Lord Kelvin should have made an error in the calculation.” Perry then went on to express his personal reservations about the methodology used in geology at the time: “I dislike very much to consider any quantitative problem set by a geologist. In nearly every case the conditions given are much too vague for the matter to be in any sense satisfactory, and a geologist does not seem to mind a few millions of years in matters relating to time.” Finally, Perry explained what had nevertheless convinced him to take on the daunting task of challenging Kelvin: “His [Kelvin’s] calculation is just now being used to discredit the direct evidence of geologists and biologists, and it is on this account that I have considered it my duty to question Lord Kelvin’s conditions.”

Perry focused most of his attention on one of Kelvin’s basic assumptions: that the Earth’s conductivity was
the same
at all depths. In other words, Kelvin assumed that heat was transported with uniform efficiency, be it at a depth of one mile or a thousand miles. This hypothesis was crucial. Just as a forensic investigator can determine
the time of death by measuring the temperature of the corpse, Kelvin used this assumption to determine the cooling age of the Earth, by measuring by how much the temperature within the Earth increased with each foot of depth. Kelvin’s calculation showed that if the Earth were older than about one hundred million years, then the temperature would rise with depth more slowly than was actually observed, since the cooled skin would be thicker.

Perry wondered, what if instead of being the same everywhere, heat transport in the deep interior were more effective than near the surface? Clearly, in that case, the bottom of the Earth’s outer skin could be kept warmer for much longer. In particular, Perry showed that if the Earth’s interior happened to be partly fluid, then, just as with water heated
in a deep pot, heat could be
convected
to the surface crust so efficiently (by the fluid itself) that the age estimate could be extended even to three billion years. He then concluded his article by addressing the arguments based on the age of the Sun and on the Earth’s spin, but there was nothing really new in his discussion of these topics. Regarding the question of the tidal retardation of the Earth’s rotation rate, Perry called attention primarily to George Darwin’s demonstration that even a solid Earth could still alter its shape.

At first, Perry’s article (in its prepublication circulated form) drew a response not from Kelvin himself but from his self-appointed “bulldog”: Peter Guthrie Tait. In an offensively dismissive letter, Tait wrote to Perry on November 22, 1894:

. . . my entire failure to catch the
object
of your paper. For I seem to gather that you don’t object to Lord Kelvin’s mathematics. Why, then, drag in mathematics at all, since it is absolutely obvious that the better conductor the interior in comparison with the skin, the longer ago must it have been when the whole was at 7000°F [Kelvin’s assumed melting point for rocks]: the state of the skin being as at present? I don’t suppose Lord Kelvin would care to be troubled with a demonstration of
that
.

Tait appears to have missed the point entirely. Since no one at the time could tell with any certainty what the conditions at great depths really were, what one
assumed
for the purpose of the calculation was a matter of mere conjecture. Perry’s intention was simply to show that if one made a different assumption from Kelvin’s about the Earth’s interior—that at the bowels of the Earth heat was transported more easily than in the Earth’s outer skin—then calculations based on physical principles could be made compatible with the old age that the geologists and biologists were requiring. Kelvin’s blunder was in
not realizing that the latitude allowed by the existing observations could introduce a much larger uncertainty into his estimated age than he was willing to acknowledge.

In his response to Tait, Perry attempted to be polite, noting,
“You say I am right, and you ask my object. Surely Lord Kelvin’s case is lost, as soon as one shows that there are
possible
[emphasis added] conditions as to the internal state of the earth which will give many times the age which is your and his limit.” In language probably reflecting the admiration of a former assistant, he then added, “What troubles me is that I cannot see one bit that you have reason on your side, and yet I have been so accustomed to look up to you and Lord Kelvin, that I think I must be more or less of an idiot to doubt when you and he were so ‘cocksure.’ ”

Figure 10

The conciliatory tone was apparently lost on Tait, since he continued to retort disparagingly: “
I should like to have your answers to
two
questions: (1) What grounds have you for supposing the inner materials of the earth to be better conductors than the skin?” The second “question” was not really a question but a contemptuous remark about the insatiable expectations of the geologists: “(2) Do you fancy that any of the
advanced
geologists would thank you for the ten billion years instead of one hundred million? Their least demand is for a trillion:—for
part
of the mere secondary period!” (Figure 10 shows a copy of his note.) But Perry did not give up:
“It is for Lord Kelvin to prove that there is not greater conductivity inside,” he insisted.

It goes without saying that Perry was correct in his assessment. In the absence of any definitive experimental evidence as to the Earth’s precise internal conditions, the fact that he was able to show that Kelvin
could
be wrong by a large factor was sufficient.

When he finally decided to respond, Kelvin was much less aggressive than Tait. While he stated,
“I feel that we cannot assume as in any way probable the enormous differences of conductivity and thermal capacity at different depths which you [Perry] take for your calculations,” he also remarked in an uncharacteristically appeasing style, “I thought my range from 20 millions to 400 millions was probably wide enough, but it is quite possible that I should have put the superior limit a good deal higher, perhaps 4000 instead of 400.” Perhaps at no other time did Kelvin show such respect for opinions that contradicted his own. Most likely this magnanimity expressed his sense of obligation to empathize with a former student. He hastened to insist, however, that his estimate of the Sun’s age was still
“refusing sunlight for more than a score or a very few scores of million years of past time.” As we shall see later in this chapter, Kelvin had no reason at the time to revise his calculation for the age of the Sun.