Dialogues Concerning Two New Sciences

by Galileo Galilei

September 27th, 2008

This book has been sitting on my bookshelf for a long time -- at least 300 years, and I'm glad I finally got around to reading it. This is not the book that got Galileo in so much trouble; that was Dialogues Concerning the Two Chief World Systems, in which Galileo pitted the Ptolemaic system favored by the Church against the Copernican system, and had the Ptolemaic system come out looking pretty stupid. The Pope had asked him to write the book, but asked him to make it "fair and balanced". Well, Galileo got the fair part down, but it wasn't balanced, and they very nearly killed him for that. As it was, they put him under house arrest for the rest of his life, banned all his books, and forbade him to write any more books. He wrote this book in secret and had the manuscript smuggled out of Italy. It was published in Northern Europe, where they weren't so persnickety about this sort of thing.

I read the book as part of my ongoing investigation into the process whereby we learned to think logically. And I truly came to understand the meaning of Newton's quote "If I have seen farther, it is because I stand on the shoulders of giants." Galileo was the most important giant.

The crucial innovation that Galileo made was a willingness to combine physical observation with geometric thinking. Here is a striking example of his approach:

As I was scraping a brass plate with a sharp iron chisel in order to remove some spots from it, and was running the chisel rather rapidly over it, I once or twice during many strokes heard the plate emit a rather strong and clear whistling sound.

Mystified by this experience, Galileo proceeded in the best scientific form to try variations on the scraping, and soon saw some interesting patterns. From this he began to draw some conclusions, which he tested and refined by further experiment. This was the scientific method as recommended by Roger Bacon centuries earlier. Why was Galileo the first to actually use scientific method? I think it was because he was willing to get his hands dirty. You would never have caught Greek or Chinese intellectuals actually soiling their hands in the real world. To them, an intellectual was somebody who confined himself to the world of pure thought. But the Italian Renaissance had replaced this model with something entirely different. The ancient Greek and Chinese thinkers were independently wealthy aristocrats or court retainers who were subsidized by rulers solely because they were educated. They were free to explore whatever they wanted. But the potentates of the Italian Renaissance weren't so open-minded. They didn't want scientists, they wanted engineers -- people who could build useful machines for them. Leonardo da Vinci always presented himself as first and foremost a military engineer. That's where the money was. Besides, Italian society was dominated by the merchant class, which had little time for abstruse theories. They developed mathematics, but not out of intellectual curiosity. Their interest lay in better calculations of financial operations. By Galileo's time (the early 1600s), the Renaissance was over, but the Italian intellegentsia had become imbued with the notion of practical learning. Even though Galileo was a professor, he had no reservations about rolling up his sleeves and getting his hands dirty.

Galileo combined this reality-based science with the geometrical analysis that was common among classical Greek thinkers. A good example of this is Euclid's proof of the Pythagorean Theorem. The basic method is to draw geometric figures, mark points on the figures, construct lines, and present rigorous deductions concerning the relationships between those elements.

Several Greek thinkers took the idea a bit further by applying these geometric methods to real-world problems. Eratosthenes used simple geometric calculations to determine the diameter of the earth. Much later, Copernicus used even more sophisticated geometric methods to determine that the Sun, not the Earth, was the center of the solar system. But the jump from geometry to science was in these cases small; both Eratosthenes and Copernicus were still thinking in terms of basic geometry. Galileo used their abstract geometry on real-world problems.

Galileo extended the same geometric reasoning to real-world problems. Here's an example:

Here Galileo draws the standard geometric figure with the salient points marked with letters, just as the Greeks did it. But this analysis doesn't concern lines or geometric figures; Galileo uses it to analyze the forces on the beam and prove this proposition:

A solid cylinder of glass, steel, wood, or other breakable material that is capable of supporting a heavy weight applied longitudinally is easily broken by the transverse application of a smaller weight in proportion as the length of the cylinder exceeds its width.

And then he proceeds to prove his point with rigorous logic. This application of rigorous geometric logic to physical objects was Galileo's big contribution to Western thinking. A few decades later, Newton took Galileo's ideas, added calculus, and made the breakthrough that launched the Enlightenment.