Wednesday, July 19, 2017

A Table in D'Arcy Thompson's "On Growth and Form" Has Some Inconsistencies

I was dipping into my 1992 edition of On Growth and Form, D'Arcy Thompson's magnum opus of mathematical biology, and I found some inconsistencies in one of the tables. These inconsistencies don't appear to be logged anywhere else, so I thought I'd note them here. They were present in the very first edition, published in 1917, and they're still in the newest edition, which was published in 2014.

Here is how the table looked in the 1917 edition, which is available online.

The point of the table is that the listed animals bear the majority of their weight on their front feet, not their hind feet. Weights are given in units of "cwt," which stands for "hundredweight." Unless I'm misunderstanding the data, the first three rows of the table all have inconsistencies. I don't see any inconsistencies in the last two rows.

First row (Bactrian camel)

The table says that a Bactrian camel puts 9.25 cwts on its fore-feet and 4.5 cwts on its hind-feet. One inconsistency I see is that 9.25 + 4.5 = 13.75, yet the table gives the gross weight of the camel as 14.25 cwts, not 13.75 cwts. The weight on the fore-feet plus the weight on the hind-feet should equal the gross weight.

The stated percentages, 67.3 and 32.7, have essentially the same ratio as the stated parts, 9.25 cwts and 4.5 cwts; but the parts don't agree with the whole.

Changing the gross weight from 14.25 cwts to 13.75 cwts would make the row self-consistent.

Second row (llama)

The inconsistency in the second row is of the same kind as the inconsistency in the first row. The table says that a llama puts 1.75 cwts on its fore-feet and 0.875 cwts on its hind-feet. Although 1.75 + 0.875 = 2.625, the table gives the gross weight of the llama as 2.75 cwts.

The stated percentages, 66.7 and 33.3, have the same ratio as the stated parts, 1.75 cwts and 0.875 cwts; but the parts don't agree with the whole.

Changing the gross weight from 2.75 cwts to 2.625 cwts would make the row self-consistent.

Third row (Indian elephant)

The inconsistency in the third row is of the same kind as the inconsistency in the first two rows. The table says that the elephant puts 20.5 cwts on its fore-feet and 14.75 cwts on its hind-feet. Although 20.5 + 14.75 = 35.25, the table gives the gross weight of the elephant as 35.75 cwts. (One ton = 20 hundredweight in this system.)

The stated percentages, 58.2 and 41.8, have essentially the same ratio as the stated parts, 20.5 cwts and 14.75 cwts; but the parts don't agree with the whole.

Changing the gross weight from 1 ton and 15.75 cwts to 1 ton and 15.25 cwts would make the row self-consistent.

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The inconsistencies are still being printed. Here is what the table looks like in the 2014 edition, according to a snippet from Google Books:

The data are unchanged from the 1917 edition. (This is also what my 1992 edition has.)

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On Growth and Form celebrates its centenary this year, with events in science and the arts being held all over the globe. It was a landmark work—Stephen Jay Gould called it "one of the great lights of science (and of English prose)." The book will be read (or at least dipped into) for another hundred years…maybe in a future edition somebody will add a footnote to the table.