Friday, August 8, 2008

On Being The Right Size

Problem 28 of Chapter 2 in the 4th Edition of Intermediate Physics for Medicine and Biology asks the student to calculate the terminal speed of a spherical animal falling under the influence of gravity and air friction. After solving the problem, the student finds that large animals fall faster because the gravitational force increases with volume (as radius cubed) while the frictional force increases with surface area (as radius squared). At the end of the problem, Hobbie and I quote J. B. S. Haldane (1892-1964) from his essay "On Being The Right Size"

"You can drop a mouse down a thousand-yard mine shaft; and arriving at the bottom, it gets a slight shock and walks away. A rat is killed, a man is broken, and a horse splashes."

Haldane's essay addresses the general topic of scaling, which we discuss in Chapter 2. Another excerpt from "On Being The Right Size" provides insight into how scaling affects body shape:

"Consider a giant man sixty feet high--about the height of Giant Pope and Giant Pagan in the illustrated Pilgrim's Progress of my childhood. These monsters were not only ten times as high as Christian, but ten times as wide and ten times as thick, so that their total weight was a thousand times his, or about eighty to ninety tons. Unfortunately the cross-sections of their bones were only a hundred times those of Christian, so that every square inch of giant bone had to support ten times the weight borne by a square inch of human bone. As the human thigh-bone breaks under about ten times the human weight, Pope and Pagan would have broken their thighs every time they took a step. This was doubtless why they were sitting down in the picture I remember. But it lessons one's respect for Christian and Jack the Giant Killer."

According to wikipedia, the normal-sized Christian is "the protagonist in the First Part [of John Bunyan's Pilgrim's Progress], whose journey to the Celestial City is the plot of the story." I have found a picture of Pope and Pagan (sitting, of course), but I don't know if it is the one Haldane grew up with.

The copy of "On Being The Right Size and Other Essays" in the Oakland University library contains an introduction by John Maynard Smith, in which he describes Haldane:

"As a scientist, Haldane will be remembered for his contribution to the theory of evolution. Today, Darwin's theory of natural selection and Mendel's theory of genetics are so intimately joined together in 'neo-Darwinism' that is hard to image that, after the rediscovery of Mendel's laws in 1900, the two theories were seen as rivals. Haldane, together with R. A. Fisher and Sewell Wright, showed that they were compatible, and developed the theory of population genetics which still underpins all serious thinking about evolution. However, although it is not hard to identify Haldane's major contributions to science, he is in other respects somewhat difficult to classify. A liberal individualist, he was best known as a leading communist and contributor of a weekly article to the Daily Worker. A double first in classics and mathematics at Oxford, he made his name in biochemistry and genetics. A captain of the Black Watch who admitted to rather enjoying the First World War, he spent the end part of his life in India writing in defence of non-violence."

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