“Mazzoleni, I am stupid.”
“I don’t know, maestro,” the old one objected. “Where does that leave the rest of us?”
“Ha-ha.”
Eventually, these moments he was trapped in now would also meld together and become all of a piece: the mornings splayed in the garden, the afternoons working on the new dialogues; the grief for Maria Celeste, infusing everything with its black light. Arcangela turning her head away when he visited, the look that was not a look, and thus worse than any look, which at the very least was a contact. His sister-in-law, Anna Chiara Galilei, moving into Il Gioièllo with three daughters and her youngest son Michelangelo, then all five of them promptly dying of the plague. More black light piercing all; all part of the one thing of this particular time.
People continued to write to him, and one morning that fall, he got up and stacked up all their letters and started writing back. He answered questions, and inquired about other people’s physical or mathematical investigations, and told people about the new dialogues he had begun. It was of course unlikely he could ever have these dialogues published. That he was using the same three characters only increased the difficulty. So when a correspondent he had never met, Elia Diodati, wrote from Holland asking him if he could help with publication of a new book, Galileo quickly agreed.
At first this seemed like a good thing; but we noticed that Galileo soon began to create more requirements for the book, so that it appeared he would never be able to finish it. It became obvious he didn’t want to finish it, that for him that would be like finishing his life. He was trying to fit in everything he had ever learned, or even thought to be possible—everything but the cosmological matters he was forbidden to discuss. Those in any case remained speculative matters, mysterious no matter how hard one tried to see into them—as was made clear by the confounding information coming in from correspondents about tide times in the Atlantic, which made his theory of how tides were formed seem clearly wrong, as he had to admit in his replies.
Whereas on the other hand, with these simple propositions about motion, force, friction and strength, he could stick to only those assertions that he had demonstrated by experiment. After all the guesses about comets and stars and sunspots, about buoyancy and magnetism and all the fascinating mysteries he did not have any basis for comprehending, that were in the end the equivalent of astrology, it was a tremendous pleasure to write down only what he had seen and tested. “This is the book I should have written all along,” he said one day as he finished writing. “This and only this. I should have avoided words and stuck to equations, like Euclid.”
Let AC be the inclined plane and AB the perpendicular, each having the same vertical height above the horizontal, namely, BA; then I say, the time of the descent along the plane AC bears a ratio to the time of fall along the perpendicular AB, which is the same as the ratio of the length AC to AB.
Space and time, in a relation. So satisfying! A little bell rings!
In the new book’s first day of dialogue, there in the pink ark of Sagredo’s palazzo on the Grand Canal in his mind, he had Salviati, Sagredo, and Simplicio discuss the following subjects: ratios of size to strength in machines; the strength of braided rope; a method for separating the action of the vacuum from other causes; the breaking point of a column of water, which was always eighteen cubits; the role of fire in liquefying hot metals; the paradox of an infinite within an infinite; the geometry of shrinking surfaces; an experiment that might determine the speed of light; problems and theorems in projective geometry; questions of buoyancy and the speed of falling objects; the question of why water beads up on some surfaces; what terminal velocity is, and air resistance, as well as water resistance and the resistance of a vacuum; results of attempts to weigh air, to find out the ratio of the weight of water to air (which was forty to one, not Aristotle’s ten to one); results from the experiments on inclined planes to measure the speed of falling objects; designs for pendulums made of different materials; questions of percussion and impact; and lastly, a long discussion of harmonies and dissonances in music, explained as functions of proportion in vibrations of a pendulum string, with speculations as to why such strong emotions could be created by such sounds.
On the second day, the three characters discussed the equilibrium and balance of beams, the longitudinal and latitudinal strength of beams, strength as a function of size, and strength as a function of shape.
On the third day, they discussed questions of motion, both local and uniform; questions of speed and distance; naturally accelerated motions, in which everything was said about gravity but the word itself; inclined plane experiments to test motion; pendulum experiments for same; and various inclined plane theorems of equal speeds, with comparisons to vertical fall.
On the fourth day the three discussed the motion of projectiles, as being a combination of uniform and naturally accelerated motion, thus leading to the theorem of the semiparabola, with lots of tables recording information from experiments to support these assertions, and to let the objects speak for themselves.
Early in the dialogue of the first day, Salviati said something that startled Galileo when he read it later:
And here I must relate a circumstance which is worthy of your attention, as indeed are all events which happen contrary to expectation—especially when a precautionary measure turns out to be a cause of disaster.
That was 1615, he suddenly saw; his precautionary measure had led to disaster. But how could you tell until after the fact? And so didn’t you have to try? You did. You could only try. You learn things that make you try.
He had done what he could with what he had. As he wrote on, thinking about this, he had Salviati defend his practice:
Our Academician has thought much upon this subject, and according to his custom has demonstrated everything by geometrical methods, so that one might fairly call what he does a new science.
“Who has demonstrated everything by geometrical methods!” Galileo said, reading it with a shake of the head. “Ha. If only you could. That would be a new science indeed.”
As the book continued to pile up, page after page, he kept writing down things that surprised him later—things he didn’t know that he knew.
The attributes “equal,” “greater,” and “less” are not applicable to infinite quantities.
Amazing the force which results from adding together an immense number of small forces. There can be no doubt that any resistance, so long as it is not infinite, may be overcome by a multitude of minute forces.
Infinity and indivisibility are in their very nature incomprehensible to us; imagine then what they are when combined. Yet that is our world.
Any velocity once imparted to a moving body will be rigidly maintained as long as the external causes of acceleration or retardation are removed … motion along a horizontal plane is perpetual; for if the velocity be uniform, it cannot be diminished or slackened, much less destroyed.
A body which descends along any inclined plane and continues its motion along a plane inclined upwards, will, on account of the momentum acquired, ascend to an equal height above the horizontal; and this is true whether the inclinations of the two planes are the same or different.
At times when he wrote it seemed as if Salviati and Sagredo were still alive somewhere and talking to him from that place, their minds as lively as ever. Sometimes he put into the book actual things he had heard them say in life, as when he included one of Salviati’s many fine offhand remarks: