Friday, April 9, 2010

Galileo's Daughter

Galileo's Daughter, by Dava Sobel, superimposed on Intermediate Physics for Medicine and Biology.
Galileo's Daughter,
by Dava Sobel.
As is my habit, I listen to recorded books when I walk my dog Suki each day. Recently, I listened to the book Galileo’s Daughter, by Dava Sobel. I was surprised how touching I found this story (like Galileo, I have two daughters). It is a biography of Galileo Galilei (1564–1642), the famous Italian scientist, but also tells the parallel story of Sister Maria Celeste (1600–1634), Galileo’s daughter who was a nun at the San Matteo convent near Florence. The book quotes Maria Celeste’s letters to Galileo, which Sobel herself translated from Italian. (Unfortunately, Galileo’s replies are lost.) Maria Celeste comes across as a loving, intelligent and extremely loyal daughter who played a central role in Galileo’s life. “She alone of Galileo’s three children mirrored his own brilliance, industry, and sensibility, and by virtue of these qualities became his confidante.”

I tend to see biological physics everywhere, and I found some in this story. Late in his life, Galileo published his final book, Two New Sciences. One of these sciences was the motion of projectiles, and the other was what we would now call the strength of materials. In the part about materials, Galileo addressed the issue of scaling in animals. I quote Sobel, who quotes Galileo:
I have sketched a bone whose natural length has been increased three times and whose thickness has been multiplied until, for a correspondingly large animal, it would perform the same function which the small bone performs for its small animal. From the figures here shown you can see how out of proportion the enlarged bone appears. Clearly then if one wishes to maintain in a great giant the same proportion of limb as that found in an ordinary man he must either find a harder and stronger material for making the bones, or he must admit a diminution of strength in comparison with men of medium stature.
Scaling: Why is Animal Size so Important? by Knut Schmidt-Nielsen, superimposed on Intermediate Physics for Medicine and Biology.
Scaling: Why is Animal
Size so Important?
by Knut Schmidt-Nielsen.
(You can find the picture of the two bones here.) This example of how the strength of bones must scale with animal size did not make it into the 4th edition of Intermediate Physics in Medicine and Biology, although I sometimes discuss it when I teach PHY 325 (Biological Physics) at Oakland University. It serves as an excellent example of how physics can constrain the structure of animals. I won’t hold it against Galileo that he didn’t get his drawing of the bones quite right; it was the 17th century after all. According to Knut Schmidt-Nielsen (Scaling: Why is Animal Size so Important)
The need for a disproportionate increase in the size of supporting bones with increasing body size was understood by Galileo Galilei (1637), who probably was the first scientist to publish a discussion of the effects of body size on the size of the skeleton. In his Dialogues [Two New Sciences was written in the form of a dialogue] he mentioned that the skeleton of a large animal must be strong enough to support the weight of the animal as it increases with the third power of the linear dimensions. Galileo used a drawing to show how a large bone is disproportionately thicker than a small bone. (Incidentally, judging from the drawing, Galileo made an arithmetical mistake. The larger bone, which is three times as long as the shorter, shows a 9-fold increase in diameter, which is a greater distortion than required. A three-fold increase in linear dimensions should give a 27-fold increase in mass, and the cross-sectional area of the bone should be increased 27-fold, and its diameter therefore by the square root of 27 (i.e., 5.2 instead of 9)).
Russ Hobbie and I discuss the issue of scaling in Chapter 2 of Intermediate Physics for Medicine and Biology. In Problem 28 of Chapter 2, we ask the reader to calculate the falling speed of animals of different sizes, taking into account air friction. The solution to the problem indicates that large animals, with their smaller surface-to-volume ratio, have a larger terminal speed (the speed of descent in steady state, once the acceleration drops to zero) than smaller animals. We end the problem with one of my favorite quotes, by J. B. S. Haldane
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, and man is broken, a horse splashes.
When listening to Galileo’s Daughter, I was surprised to hear Galileo’s own words on this same subject, which are similar and written centuries earlier.
Who does not know that a horse falling from a height of three or four braccia will break his bones, while a dog falling from the same height or a cat from eight or ten, or even more, will suffer no injury? Equally harmless would be the fall of a grasshopper from a tower or the fall of an ant from the distance of the Moon.
Of course, the climax of Galileo’s Daughter is the great scientist’s trial by the Catholic Church for publishing a book supporting the Copernican view that the earth travels around the sun. Although I was familiar with this trial, I had never read the transcript, which Sodal quotes extensively. Listening to the elderly Galileo being forced into a humiliating recantation of his scientific views almost made me nauseous.

Sobel is a fine writer. Years ago I read her most famous book, Longitude, about finding a method to measure longitude at sea. Galileo himself contributed to the solution of this problem by introducing a method based on the orbits of the moons of Jupiter, which he of course discovered. However, the longitude problem was not definitely solved until clocks that could keep time on a rolling ship were invented by John Harrison. I have also listened to Sobel’s book The Planets, which I enjoyed but, in my opinion, isn’t as good as Longitude and Galileo’s Daughter. I hope Sobel continues writing books. As soon as a new one comes out (and arrives at the Rochester Hills Public Library, because I’m too cheap to buy these audio books), Suki and I plan on taking some long walks. I can’t wait.

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