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inclined planes a thousand ways to derive the rate of acceleration in free fall—in whatever time he could sparebetween meeting teaching obligations and running a cottage industry in military compasses. Later, as courtphilosopher at Florence in 1618, with the promise of more leisure for such pursuits, he reopened the labeledfolders of his Paduan notes—only to be waylaid first by illness and then by comets. He returned once more to theproject early in 1631, while awaiting permission to publish the Dialogue. Now, detained at the archbishop’spalace, Galileo revisited his ideas about the way everyday objects move, bend, break, and fall.“There is perhaps nothing in Nature older than MOTION,” Galileo noted of the humdrum topic for his nextbook, “about which volumes neither few nor small have been written by philosophers.” But all of those earliertexts had concerned themselves with pinning down the cause of motion. Galileo proposed to strike out on adifferent course—to drop all Aristotelian talk of why things moved, and focus instead on the how, throughpainstaking observations and measurements. In this fashion, he had discovered and described phenomena thatgenerations of earlier philosophers had not even noticed. For example, the shape of the path traced through spaceby a hurled or fired missile, Galileo showed, was not just “a line somehow curved,” as his predecessors had said,but always precisely a parabola. And when lemons dropped from treetops, or cannonballs from towers, each onepicked up speed in the same characteristic pattern tied to the elapsed time of its fall: Whatever distance the objectcovered in one instant—measured as a pulse beat, a sung note, the weight of water that dripped from Galileo’stiming device—by the end of two such instants it would travel four times as far. After three instants, it wound upat nine times the initial distance of descent; after four instants, sixteen distance units—and so on, alwaysaccelerating, always arriving at a distance determined by the square of the time passed.Aristotle had ruled out any such mathematical approach to physics, on the grounds that mathematicians ponderedimmaterial concepts, while Nature consisted entirely of matter. And Nature, furthermore, could not be expectedto follow precise numerical rules.Galileo argued against this stance: “Just as the accountant who wants his calculations to deal with sugar, silk,and wool must discount the boxes, bales, and other packings, so the mathematical scientist, when he wants torecognize in the concrete the effects he has proved in the abstract, must deduct any material hindrances [such asfriction or air resistance]; and if he is able to do that, I assure you that things are in no less agreement than arearithmetical computations. The trouble lies, then, not in abstractness or concreteness, but with the accountantwho does not know how to balance his books.”Galileo envisioned the experimental, mathematical analysis of Nature as the wave of the future: “There will beopened a gateway and a road to a large and excellent science,” he predicted, “into which minds more piercingthan mine shall penetrate to recesses still deeper.” *While Galileo devoted his time at Siena to writing, Ambassador Niccolini in Rome tirelessly pursued his fullrepatriation. The pope, however, would not be pressured into a promise, thus leaving the final sentence an openquestion. Rumors spoke of Galileo’s possible confinement after Siena at the Certosa, a vast hilltop monasterybuilt in the fourteenth century to the south of Florence, where the twelve resident monks produced a locallyfamous wine. Such a move would bring Galileo even closer to Arcetri, facilitating the exchange of letters withhis daughter, while ruling out any chance of his seeing her.MOST BELOVED LORD FATHERWhen I wrote to you about your coming home soon, Sire, or your otherwise remaining where you are for a whilelonger, I knew of the petition you had made to his lordship the Ambassador, but was not yet aware of his answer,which I since learned from Signor Geri when he came here last Tuesday, just after I had written yet another letterto you, enclosing the formulation of the pills that by now must surely have reached you. My motive foraddressing you in that seemingly distant fashion had grown out of my frequent discussions with SignorRondinelli, who all through this period has been my refuge (because, as practical and experienced as he is in theways of the world, he has many times alleviated my anxiety, prognosticating for me the outcome of situationsconcerning your affairs, especially in cases that seemed more precipitous to me than they later turned out to be);once during those discussions he told me how people in Florence were saying that when you departed fromSiena, Sire, you would have to go to the Certosa, a condition that displeased every one of your friends; yet hesaw some good in going along with those orders, as I understand the Ambassador himself did, too, for they both