Galileo’s Perspective

Our family lived in France for the last six months and at the end of that time we had the chance to visit family in Florence. Since we drove to Florence we could stop at Pisa along the way.  I found Galileo all around me.

Dava Sobel’s book, Galileo’s Daughter, once drew me in and brought new life to the story of the physicist who was right and the Church that condemned him. Galileo had a daughter who loved him, wrote to him after his arrest, and she was a nun. The book makes us privy to this very human, albeit extraordinary, story.  And it locates his home while under house arrest in Florence not far from the convent. We got the address, set out to find it and we did. When you visit such places, you try to get as close as you can to the lives you can’t touch, or the time outside your reach – to see something of the story’s three-dimensional reality.

IL Gioiello of Galileo

Galileo’s life in these cities is even more highlighted at the moment because August marks the 400th anniversary of his first telescope observations. We mostly imagine him as a physicist, but it was mathematics that captured his attention and was his profession. His affinity for mathematics is likely some consequence of the way he was poised to see. He is quoted as having said, “Where the senses fail us, reason must step in.” When we can’t see our way through something, we can shift our attention inward and reason our way through it. Reason builds on what the senses perceive, by opening a path and directing us when we can’t just watch where we’re going.

Looking closely at the abstract, this experimentalist had an insight about the notion of infinitely many things that foreshadowed work to come some 250 years later. In his book Two New Sciences, a conversation between Simplicio and Salviati (the Galileo character) outlines what is now called Galileo’s paradox – that there are the same number of perfect squares as there are whole numbers despite the fact that not every whole number is a perfect square. When Salviati describes the situation to Simplicio, he hints at the notion of one-to-one correspondence which will be invoked for the first time in 1874 by Georg Cantor. Salviati concludes that the attributes equal, greater or less do not apply to the infinite. When presented with lines of different lengths, Salviati tells us that it cannot be said that one line has more or less points than the other but simply that they both have an infinite number of them.

I imagine Galileo breathing in the fresh air of the Renaissance and breathing out ideas of the future. His role in our history seems an inevitable consequence of his nature, of the way he watched and reasoned. And he lived in a time when Western Europe may have been looking inward instead of just outward, across mysterious seas, to extend their reach or to move their horizon.

Galileo used what artists then understood about perspective to confirm that the spots he saw on the sun were, in fact, spots and not, as had been argued, other planetary spheres in front of the sun. He could see that their shape changed when viewed from different angles because they became foreshortened in precisely the way the mathematics of perspective required. And the word perspective is from the Latin perspicere, to see clearly.

Galileo’s work is his perception of the world, very directly and it makes sense that we often use the telescope, the mechanical extension of sight, to symbolize his effectiveness. The sense that he was a vital individual, who was just looking, is captured in the legend that his thoughts on pendulum motion began during a service in the Pisa Cathedral. A swinging lamp caught his attention and he timed its swings with the beat of his pulse. His body was his clock.

A good look at Galileo renders a very human, natural view of science and mathematics. And I think he says it best with this:  “In my opinion, nothing occurs contrary to nature except the impossible, and that never occurs.”