Galileo's Daughter

by Dava Sobel

  The heavy rain made it impossible to set the broad beans in his garden, she said, but fair weather must come again, and with it his return. “I send you no pills because desire makes me hope that you must soon arrive here to claim them in person: I am all eagerness to hear the resolution that will reach you this week.”

  The resolution did not come, however. Galileo grew cranky with waiting, and so dependent on his daughter’s letters that he scolded her when they failed to arrive often enough to soothe him.

  “If only you could fathom my soul and its longing the way you penetrate the Heavens, Sire,” she began on November 5, “I feel certain you would not complain of me, as you did in your last letter; because you would see and assure yourself how much I should want, if only it were possible, to receive your letters every day and also to send you one every day, esteeming this the greatest satisfaction that I could give to and take from you, until it pleases God that we may once again delight in each other’s presence.”

  Then she told him how she had secured his coveted ortolans after all—through a bird keeper in the service of the grand duke. Any moment now she would dispatch Geppo to the game-rich acres of the Boboli Gardens behind the Pitti Palace, armed with a floured box in which to pack the delicate birds and deliver them straight away to Signor Geri. But when Galileo thanked her for them a few days later, he said nothing of his own flight from Siena.

  “I must tell you first how astounded I was,” she wrote the following Saturday, November 12, “that you made no mention in your most recent letter of having received any word from Rome, nor any resolution regarding your return, which we had so hoped to have before All Saints’ Day [November 1], from what Signor Gherardini led me to believe. I want you to tell me truly how this business is progressing, so as to quiet my mind, and also please tell me what subject you are writing about at present: Provided it is something that I could understand, and you have no fear that I might gossip.”

  Suor Maria Celeste necessarily understood the semisecret nature of her father’s works in progress. In fact, some of the materials removed from II Gioiello during Galileo’s trial concerned his writing on motion, including the manuscript for the third day of Two New Sciences, which he had roughed out before he left for Rome. Although Galileo would not have deemed these particular documents incriminating, he had reason to fear their needless destruction.

  Day Three’s treatment of uniform and accelerated motion bears witness to the untold number of Paduan hours Galileo spent tracking the course of a small bronze ball down the groove of an inclined plane to probe the mystery of acceleration. Unable to experiment fruitfully with freely falling objects, Galileo built his inclined-plane apparatus so he could control fall, stopping the action at will, making precise measurements of time and distance all the while. Salviati, who claims in Two New Sciences to have assisted Galileo occasionally in these efforts, describes them to Sagredo and Simplicio:

  We rolled the ball along the channel, noting, in a manner presently to be described, the time required to make the descent. We repeated this experiment more than once in order to measure the time with an accuracy such that the deviation between two observations never exceeded one-tenth of a pulse-beat. Having performed this operation and having assured ourselves of its reliability, we now rolled the ball only one-quarter the length of the channel; and having measured the time of its descent, we found it precisely one-half of the former. Next we tried other distances, comparing the time for the whole length with that for the half, or with that for two-thirds, or three-fourths, or indeed for any fraction; in such experiments, repeated a full hundred times, we always found that the spaces traversed were to each other as the squares of the times, and this was true for all inclinations of the plane . . . along which we rolled the ball.

  Just as Copernicus had discerned the configuration of the solar system with no telescope to guide him, Galileo arrived at this fundamental relationship between distance and time without so much as a reliable unit of measure or an accurate clock. Italy possessed no national standards in the seventeenth century, leaving distances open to guesstimate gauging by flea’s eyes, hairbreadths, lentil or millet seed diameters, hand spans, arm lengths, and the like. Even a braccio differed in dimension depending on whether it was measured in Florence, Rome, or Venice, and so Galileo delineated his own arbitrary units along the length of his experimental apparatus. As long as these units matched one another, he could use them to establish fundamental relationships.

  To clock the rolling time of the balls, Galileo literally weighed the moments. “For the measurement of time,” Salviati continues in his experimental description, “we employed a large vessel of water placed in an elevated position; to the bottom of this vessel was soldered a pipe of small diameter giving a thin jet of water, which we collected in a small glass during the time of each descent, whether for the whole length of the channel or for a part of its length; the water thus collected was weighed, after each descent, on a very accurate balance [against grains of sand]; the differences and ratios of these weights gave us the differences and ratios of the times, and this with such accuracy that although the operation was repeated many, many times, there was no appreciable discrepancy in the results.”

  Artistic rendition of Galileo’s incline plane

  Although this account reveals stunning experiments that promise to open a new window on philosophy, Salviati cannot be shaken from his recently acquired pedantic monotone, which threatens to establish an irreparable split, if not between science and religion, then between science and poetry.

  The ball-and-plane trials provided the tedious yet triumphant prelude to the truth about falling, which Galileo expressed in Two New Sciences as a series of theorems. He did not use the convention of algebraic analysis that later allowed his rules to be pared down to a few letters and symbols, but expressed his findings as geometric ratios, and wrote out his proofs in dense prose accompanied by letter-labeled line drawings in the style of the ancient Greek mathematicians.

  All the motions discussed on the third day of Two New Sciences are “natural” ones, since the experimental objects simply roll or drop, instead of being thrown with force. Not until Day Four (which Galileo would complete several years later, in 1637) do the “violent” movements of bullets and other projectiles come up for discussion. Here Galileo displays his singular insight in breaking motions into their separate components. For he shows that any cannonball fired from a mortar, for example, or any arrow shot from a bow, combines two vectors: the uniform forward thrust of the propulsion and the downward acceleration of free fall.

  “One cannot deny that the argument is new, subtle, and conclusive,” remarks Sagredo, “resting as it does upon this hypothesis, namely, that the horizontal motion remains uniform, that the vertical motion continues to be accelerated downwards in proportion to the square of the time, and that such motions and velocities as these combine without altering, disturbing, or hindering each other, so that as the motion proceeds the path of the projectile does not change into a different curve.”

  Whatever the weight of the projectile or the force propelling it, Salviati explains on Galileo’s say-so, the path traced in space always assumes the curved shape of a parabola. Shooting straight up or down, however, constitutes a separate category, also taken into consideration by the participants.

  Mere mention of the parabola by Salviati instantly occasions a digression into the geometry of the cone, the parent body of the parabola, for the sake of Sagredo and Simplicio, who fear they may fail to follow a discussion promising such a plethora of parabolas. “Your demonstration proceeds too rapidly,” complains Simplicio, “and, it seems to me, you keep on assuming that all of Euclid’s theorems are as familiar and available to me as his first axioms, which is far from true.”

  But once the shape has been thoroughly examined to the satisfaction of the less mathematically inclined, the discussion continues easily and amicably. It even allows for an analysis of the efficiency of various angles
of elevation of heavy artillery, complete with a geometric proof showing why the forty-five-degree angle surpasses all others—because the parabola thus described has the greatest possible amplitude, and therefore the shot carries farthest.

  “The force of rigid demonstrations such as occur only in mathematics fills me with wonder and delight,” Sagredo exclaims at this revelation. “From accounts given by gunners, I was already aware of the fact that in the use of cannon and mortars, the maximum range, that is the one in which the shot goes farthest, is obtained when the elevation is 450 or, as they say, at the sixth point of the quadrant; but to understand why this happens far outweighs the mere information obtained by the testimony of others or even by repeated experiment.”

  This emphasis on the practical application and value of science, so far removed from the metaphysical consideration of causes, set Galileo apart from most philosophers of his time. While Aristotelian philosophers talked of essences and natural places, Galileo went after quantifiable entities such as time, distance, and acceleration. Other contemporary treatises in dialogue format typically situated the speakers around a university quadrangle. Two New Sciences takes place in a shipyard. Its characters simply dismiss the pursuit of ultimate causes that has passed for science until their time: “The cause of the acceleration of the motion of falling bodies is not a necessary part of the investigation,” declares Salviati. From now on, physics will never be the same.

  “The continuous rain,” Suor Maria Celeste wrote in a morning-after postscript to her weekly summary of Saturday, November 12, “has not allowed Giovanni (as the bearer of this letter is called) to leave this morning, which is Sunday, and this leaves me time to chat with you a little longer, and to tell you that recently I pulled a very large molar, which had rotted and was giving me great pain; but what is worse is that I have several others that soon will do the same.” She had begun extracting her own teeth years earlier—a self-treatment that must have required heroic determination—and described herself as prematurely toothless when she was only twenty-seven.

  “To respond to that personal detail you shared with me,” her postscript continued, “that you find occupations so salubrious, truly I recognize them as having that same effect on myself as well: so that even though the activities occasionally seem superfluous and intolerable to me, on account of my being a friend of tranquility, I nevertheless see clearly how staying active is the foundation of my health, and particularly in the time that you have been far away from us, Sire, with great providence did the Lord arrange it so that I never had what you might call an hour of peace, thus preventing the oppression of your absence from distressing me. Such grief would have been harmful to me, and given you cause for worry instead of the relief I have been able to provide.”

  As Suor Maria Celeste sat writing in the Sunday morning rain of November 13, Ambassador Niccolini again approached the pope for permission to send Galileo back to Arcetri. Urban withheld his judgment. He neither granted nor denied the request during this audience, but pointedly let on that he knew Galileo was enjoying the support, defense, companionship, and correspondence of like-minded men—all of whom, Urban assured Niccolini with undisguised disgust, were now under surveillance by the Holy Office. The archbishop of Siena himself numbered among this company.

  “If good luck had enabled you to find even one gray partridge,” Suor Maria Celeste filled the time writing as another week passed without news of her father’s homecoming, “I would have been thrilled to have it for love of that poor sick young girl, who craves nothing but wild game: at the last full moon she was so ill as to be anointed with holy oil, but now she has made such a comeback that we believe she will live to see the new moon. She speaks with great vivacity, and gulps her food readily, provided we give her tasty things. Last night I stayed with her all through the night, and while I fed her, she said: ‘I cannot believe that when one stands on the verge of death it is possible to eat the way I do, yet, for all that, I have no desire to turn back; only to see God’s will be done.’ “

  As many times as Suor Maria Celeste must have touched the back of her hand to Suor Maria Silvia’s feverish forehead, she had no way to measure the girl’s temperature.* She could gauge it only relatively, refining her reading by the flush of the patient’s complexion, the rapidity of her pulse, and the shallowness of her breathing.

  Before the week was out, just as the daylight in the infirmary was fading one afternoon at the twenty-fourth hour, a messenger arrived from Siena with a pannier full of game birds.

  Inside it were 12 thrushes: the additional 4, which would have completed the number you state in your letter, Sire, must have been liberated by some charming little kitten who thought of tasting them ahead of us, because they were not there, and the cloth cover had a large hole in it. How fortunate that the gray partridges and woodcocks were at the bottom, one of which and two thrushes I gave to the sick girl, to her great joy, and she thanks you, Sire. I sent another gift, also in the form of two thrushes, to Signor Rondinelli, and the remainder we enjoyed together with our friends.

  I have taken the greatest pleasure in distributing all this bounty among various people, because prizes sought after with such diligence and difficulty deserve to be shared by several, and as the thrushes arrived a little the worse for wear, it was necessary to cook them in a stew, so that I stood over them all day, and for once I truly surrendered myself to gluttony.

  [ XXXI]

  Until I have

  this from your lips

  The wednesday before the start of Advent, when Suor Maria Celeste went searching for the pears Galileo had requested, she briefly imagined saving them to present to him in person—before her doubts dispelled these pleasant thoughts. “Because I hear that this year the fruits do not last long, I wonder if it might be better, once I have them, to send them to you right away and not wait for your return, which could be delayed for several more weeks, or so my desire leads me to fear.”

  By Church tradition, the hopeful time of Advent commenced with the Sunday closest to the feast day of Saint Andrew the Apostle, November 30. In 1633, the nearest Sunday happened to fall on November 27—the earliest possible date for Advent to begin, and this stretched the period to its maximum duration of twenty-eight days. Everything that had anything to do with waiting dilated during the dark season Suor Maria Celeste spent anticipating her father’s return. In her Breviary she read the Advent Liturgy regarding “the Lord the King that is to come,” “the Lord already near,” and “Him Whose glory will be seen on the morrow.”

  Inside the tiny Church of San Matteo, Suor Barbera prepared the violet-colored candles, the seasonal violet altar hangings, and the special violet and rose vestments for the priest.

  “It does me good to hope, and also to believe firmly,” Suor Maria Celeste wrote to Galileo on December 3, “that His Lordship the Ambassador, when he departs from Rome, will be bringing you the news of your dispatch, and also word that he personally will conduct you here in his company. I do not believe that I will live to see that day. May it please the Lord to grant me this grace, if it be for the best.”

  Suor Maria Celeste’s fear of not living to see Galileo’s return might have stemmed from some morbid presentiment regarding her indifferent health, but more likely it arose from her frustration at the innumerable delays and rumors bearing false hope. "I understand everyone in Florence is saying you will soon be here,” she wrote the following week, “but until I have this from your lips, all I will believe is that your dear friends are allowing their affections and desires to give themselves voice.”

  This time, however, the hearsay held true. Urban had condescended at last to change Galileo’s place of imprisonment to Arcetri— not so much to commute his sentence as to make it harsher, since the ambience at Siena approached that of an exclusive salon. The pope’s recommendation to the Holy Office stipulated that Galileo be limited in his social contacts henceforward, and that he refrain everafter from all teaching activities. Under these c
onditions, he now would be allowed to go home.

  MOST BELOVED LORD FATHER

  ONLY A MOMENT before the news of your dispatch reached me, Sire, I had taken my pen in hand to write to Her Ladyship the Ambassadress to beg her once more to intercede in this affair; for having watched it wear on so long, I feared that it might not be resolved even by the end of this year, and thus my sudden joy was as great as it was unexpected: nor are your daughters alone in our rejoicing, but all these nuns, by their grace, give signs of true happiness, just as so many of them have sympathized with me in my suffering.

  We are awaiting your arrival with great longing, and we cheer ourselves to see how the weather has cleared for your journey.

  Signor Geri was leaving this morning with the Court [for the annual winter session at Pisa], and I made sure to have him notified before daybreak of your return, Sire; seeing as he had already learned something of the decision, and came here last evening to tell me what he knew.

  I also explained to him the reason you have not written to him, Sire, and I bemoaned the fact that he will not be here when you arrive to share in our celebration, since he is truly a perfect gentleman, honest and loyal.

  I set aside the container of verdea wine, which Signor Francesco could not bring along because his litter was too overloaded. You will be able to send it to the Archbishop later, when the litter makes a return trip: the citron candy morsels I have already consigned to him. The casks for the white wine are all in order.

  More I cannot say for the dearth of time, except that all of us send you our loving regards.