Roots of Unity

Roots of Unity

Mathematics: learning it, doing it, celebrating it.

Lord Kelvin and the Age of the Earth


William Thomson, 1st Baron Kelvin. Image: Smithsonian Libraries, via Wikimedia Commons. This image is in the public domain in the United States because its copyright has expired.

Today is the 189th anniversary of the birth of William Thomson, better known as Lord Kelvin. I don't usually make a big deal about 189th birthdays, but I've been thinking a lot about Lord Kelvin recently. Yesterday I came across this quote of his on Pat Ballew's blog, which reminded me that it's his birthday: "When you measure what you are speaking about and express it in numbers, you know something about it, but when you cannot express it in numbers your knowledge about it is of a meagre and unsatisfactory kind."

Kelvin is probably most famous for his contributions to thermodynamics, including the temperature scale that bears his name. My recent interest in Kelvin is due to his attempts to use thermodynamics to figure out how old our planet is. Earlier this year, I helped compile a Scientific American Classics issue called Determining the Age of the Earth. Classics issues are collections of articles from the Scientific American archives on one topic. In this case, I found several 19th- and early 20th-century articles about the advances in geology and physics that eventually led to our current understanding that the Earth is about 4.5 billion years old.

As chemist and author Paul Braterman (who, full disclosure, taught me chemistry for a semester in 1999 and is my Facebook friend) wrote in the introduction to Determining the Age of the Earth, "It is a drama consisting of a prologue and three acts, complex characters, and no clear heroes or villains. We, of course, know the final outcome, but we should not let that influence our appreciation of the story as it unfolds. Even less should we let that knowledge influence our judgment of the players, acting as they did in their own time, constrained by the concepts and data then available."

One of the "three acts" Braterman refers to is Kelvin's attack on the idea held by some 19th century geologists that the earth had been around forever. Primarily basing his estimates on heat transfer within the earth itself and from the sun to the earth, Kelvin believed that the earth was between 20 and 100 million years old. His estimates were only as good as the mathematical models he used to make them, and unfortunately these models were not aware of plate tectonics, the nuclear fusion that creates the heat of the sun, or radioactivity. Mario Livio includes Kelvin's determination of the age of the earth as one of the greatest mistakes in the history of science in his recent book Brilliant Blunders.

Mathematician Gil Kalai discussed Kelvin's mistakes in May on his blog Combinatorics and more, going deeper into the exact ways in which Kelvin's calculations failed to yield correct results. After detailing the shortcomings of Kelvin's work in the area, Kalai wrote, "It is rather impressive that this genius of physics was opposed by a bunch of geologists (high boots, shorts, field hammers, limited perspective) and that the latter turned out right, but it is also true that Kelvin showed two important points: The first is that the age of the earth is NOT INFINITE as many thought in the 19th century, and the second is that the age of the earth is calculable from physical principles. At that time, several geologists claimed that 'physics cannot be applied to geology,' and in this they were wrong! We owe him much for teaching us these two points."

I thoroughly enjoyed working on the Determining the Age of the Earth issue. It is riveting to read about scientific progress as it unfolds, especially when Ernest Rutherford himself is writing about it! The two other Classics issues I've put together are also fascinating reads.

The Quest for the Periodic Table, as the title implies, chronicles the development of the periodic table as a way of organizing and understanding the properties of the chemical elements. Not only is it fascinating to see how many different ways Mendeleev was spelled in the late nineteenth century (I counted five), I love the way the periodic table almost sneaks up among the discoveries of new elements. The first mention is a mere paragraph from 1876 that notes that the newly discovered element gallium may fill a gap in "the system of known elements" recently proposed by "Mendeleef."

Polio: Pushed to the Brink contains several articles from the 1950s about the study of polio and eventual development of the enormously successful polio vaccines. As we get closer to global polio eradication, it is fascinating to read about the early days of the struggle against the disease. The highlight of the issue is probably the 1955 article by Jonas Salk himself about the killed-virus vaccine he developed.

Along with Determining the Age of the Earth, these issues are available as pdf downloads for about $10 from Scientific American. I usually try to link to free stuff on this blog, but I'm rather proud of these compilations, and if you're interested in the history of science, I think they are worthwhile additions to your library.

The views expressed are those of the author and are not necessarily those of Scientific American.

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