Galileo Galilei

gigatos | May 26, 2022

Summary

Galileo Galilei (Pisa, Feb. 15, 1564 – Arcetri, Jan. 8, 1642) was an Italian physicist, astronomer, philosopher, mathematician, writer and academic, considered the father of modern science.A key figure in the scientific revolution for explicitly introducing the scientific method (also called the “Galilean method” or “experimental method”), his name is associated with important contributions in physics and astronomy. Also of primary importance was his role in the astronomical revolution, with his support for the heliocentric system

Its main contributions to philosophical thought derive from the introduction of the experimental method in scientific inquiry through which science abandoned, for the first time, that metaphysical position that had hitherto predominated, to acquire a new, autonomous perspective, both realist and empiricist, aimed at privileging, through the experimental method, more the category of quantity (through the mathematical determination of the laws of nature) than that of quality (the result of the past tradition directed only to the search for the essence of entities) in order to elaborate now a rational objective description

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Youth (1564-1588)

Galileo Galilei was born on February 15, 1564, in Pisa, the eldest of seven children of Vincenzo Galilei and Giulia Ammannati. The Ammannati family, originally from the area of Pistoia and Pescia, boasted important origins; Vincenzo Galilei, on the other hand, belonged to a more humble lineage, although his ancestors were part of the good Florentine bourgeoisie. Vincenzo had been born in Santa Maria a Monte in 1520, by which time his family had fallen into decline and he, a musician of worth, had to move to Pisa, combining the practice of the art of music with the profession of commerce out of a need for greater earnings.

Vincenzo and Giulia”s family, counted in addition to Galileo: Michelangelo, who was a musician to the Grand Duke of Bavaria; Benedetto, who died in infancy; and three sisters, Virginia, Anna, and Livia, and possibly a fourth named Lena.

After an unsuccessful attempt to include Galileo among the forty Tuscan students who were being housed free of charge in a boarding school at the University of Pisa, the young man was hosted “without charge” by Muzio Tebaldi, customs officer of the city of Pisa, godfather of Michelangelo”s baptism, and such a friend of Vincenzo”s that he provided for the family”s needs during his long absences for work.

In Pisa, Galileo Galilei met his young cousin Bartolomea Ammannati, who looked after the household of the widowed Tebaldi, who, despite the marked age difference, married her in 1578 probably to put an end to the malicious rumors, embarrassing to the Galilei family, that were being made about his young niece. Thereafter the young Galileo made his first studies in Florence, first with his father, then with a master of dialectics and finally in the school of the convent of Santa Maria di Vallombrosa, where he wore the habit of novice until the age of fourteen.

Vincenzo, on September 5, 1580, enrolled his son in the University of Pisa with the intention of having him study medicine, to make him retrace the tradition of his glorious ancestor Galileo Bonaiuti and, above all, to set him on a career that could provide lucrative earnings.

Despite his interest in the experimental advances of those years, Galileo”s attention was soon drawn to mathematics, which he began to study from the summer of 1583, taking advantage of the opportunity of his acquaintance in Florence with Ostilio Ricci da Fermo, a follower of the mathematical school of Niccolò Tartaglia. Characteristic of Ricci was the approach he gave to the teaching of mathematics: not of an abstract science, but of a discipline that served to solve practical problems related to mechanics and engineering techniques. It was, in fact, the “Tartaglia-Ricci” line of study (a continuation, in turn, of the tradition headed by Archimedes) that taught Galileo the importance of precision in the observation of data and the pragmatic side of scientific research. It is likely that in Pisa, Galileo also took physics courses taught by the Aristotelian Francesco Bonamici.

During his stay in Pisa, which lasted until 1585, Galileo arrived at his first, personal discovery, the isochronism of the pendulum”s oscillations, which he would continue to deal with throughout his life, trying to perfect its mathematical formulation.

After four years the young Galileo gave up his medical studies and went to Florence, where he deepened his new scientific interests, working on mechanics and hydraulics. In 1586 he found a solution to Hieron”s “crown problem” by inventing an instrument for the hydrostatic determination of the specific weight of bodies. The influence of Archimedes and Ricci”s teaching can also be detected in his studies on the center of gravity of solids.

In the meantime, Galileo was looking for a regular financial settlement: in addition to giving private mathematics lessons in Florence and Siena, in 1587 he went to Rome to ask for a recommendation to enter the Studio of Bologna from the famous mathematician Christoph Clavius, but to no avail, because in Bologna they preferred the Paduan Giovanni Antonio Magini to the chair of mathematics. At the invitation of the Accademia Fiorentina he gave two Lectures in 1588 about the figure, site and size of Dante”s Inferno, defending the hypotheses already formulated by Antonio Manetti about the topography of Dante”s imagined Inferno.

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Teaching in Pisa (1589-1592)

Galilei then turned to his influential friend Guidobaldo Del Monte, a mathematician known through an exchange of letters on mathematical matters. Guidobaldo was instrumental in helping Galilei advance in his university career when, overcoming the enmity of Giovanni de” Medici, a natural son of Cosimo de” Medici, he recommended him to his brother Cardinal Francesco Maria Del Monte, who in turn spoke with the powerful Duke of Tuscany, Ferdinando I de” Medici. Under his tutelage, Galileo was given a three-year contract for a chair in mathematics at the University of Pisa in 1589, where he clearly expounded his pedagogical program, immediately garnering some hostility in the Aristotelian-educated academia:

The fruit of Pisan teaching is the manuscript De motu antiquiora, which collects a series of lectures in which he attempts to account for the problem of motion. The basis of his research is the treatise, published in Turin in 1585, Diversarum speculationum mathematicarum liber by Giovanni Battista Benedetti, one of the physicists who advocated the theory of “impetus” as the cause of “violent motion.” Although the nature of such an impetus imparted to bodies could not be defined, this theory, first elaborated in the 6th century by John Philoponus and later supported by Parisian physicists, while unable to solve the problem, opposed the traditional Aristotelian explanation of motion as a product of the medium in which the bodies themselves move.

In Pisa, Galilei did not limit himself to scientific pursuits alone: in fact, his Considerations on Tasso date from this period, which would be followed up with Postille all”Ariosto. These are scattered notes on sheets of paper and annotations in the margins in the pages of his volumes of Gerusalemme liberata and Orlando furioso where, while he reproaches Tasso for “the paucity of imagination and the slow monotony of image and verse, what he loves in Ariosto is not only the fluttering of beautiful dreams, the rapid change of situations, the lively elasticity of rhythm, but the harmonious balance of this, the coherence of the image the organic unity – even in variety – of the poetic phantasm.”

In the summer of 1591 his father Vincenzo died, leaving Galileo with the burden of supporting the entire family: for the marriage of his sister Virginia, who married that same year, Galileo had to provide a dowry, incurring debts, just as he would later have to do for the marriage of his sister Livia in 1601 to Taddeo Galletti, and more money he would have to spend to succor the needs of his brother Michelangelo”s large family.

Guidobaldo Del Monte stepped in to help Galilei again in 1592, recommending him to the prestigious Padua Studio, where the chair of mathematics was still vacant after the death in 1588 of Giuseppe Moleti.

On September 26, 1592, the authorities of the Republic of Venice issued the decree of appointment, with a contract, extendable, of four years and a salary of 180 florins a year. On December 7, Galilei gave his introductory speech in Padua and after a few days began a course destined to have a large following among students. He would stay there for eighteen years, which he would call “the best eighteen years of all my age.” Galilei arrived in the Republic of Venice only a few months after Giordano Bruno”s arrest (May 23, 1592) in the same city.

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The Padua period (1592-1610)

In the dynamic environment of the Padua Studio (also a result of the climate of relative religious tolerance guaranteed by the Venetian Republic), Galileo maintained cordial relations even with personalities with philosophical and scientific orientations far from his own, such as the professor of natural philosophy Cesare Cremonini, a strictly Aristotelian philosopher. He also frequented the cultured circles and senatorial circles of Venice, where he befriended the nobleman Giovanfrancesco Sagredo, whom Galilei made the protagonist of his Dialogo sopra i massimi sistemi, and Paolo Sarpi, a theologian and expert also in mathematics and astronomy. Contained in the very letter addressed on October 16, 1604, to the friar served is the formulation of the law of falling bodies:

Galileo had lectured on mechanics in Padua since 1598: his Treatise on Mechanics, printed in Paris in 1634, is supposed to be the result of his courses, which had originated from Aristotle”s Questioni meccaniche.

In the Studio in Padua Galileo equipped, with the help of Marcantonio Mazzoleni, an artisan who lived in his own house, a small workshop in which he performed experiments and made instruments that he sold to supplement his salary. The machine for bringing water to higher levels, for which he obtained a 20-year patent from the Venetian Senate for public use, dates from 1593. He also gave private lessons-his pupils included Vincenzo Gonzaga, the prince of Alsace Giovanni Federico, and future cardinals Guido Bentivoglio and Federico Cornaro-and obtained salary increases: from the 320 florins he received annually in 1598, he rose to the 1,000 obtained in 1609.

A “new star” was observed on October 9, 1604, by the astronomer Fra” Ilario Altobelli, who informed Galilei about it. Very bright, it was later observed on October 17 also by Kepler, who made it the subject of a study, De Stella nova in pede Serpentarii, so that star is now known as Kepler”s Supernova.

Galileo gave three lectures on that astronomical phenomenon, the text of which is not known to us, but against his arguments a pamphlet was written by a certain Antonio Lorenzini, a self-styled Aristotelian originally from Montepulciano, probably at the suggestion of Cesare Cremonini, and the Milanese scientist Baldassarre Capra also intervened in turn with a pamphlet.

From them we know that Galileo had interpreted the phenomenon as proof of the mutability of the heavens, on the basis that since the “new star” presented no change in parallax, it should be beyond the Moon”s orbit.

In favor of Galilei”s thesis, a caustic booklet in the Pavia dialect entitled Dialogo de Cecco di Ronchitti da Bruzene in perpuosito de la Stella Nuova by an author under the pseudonym Cecco di Ronchitti was published in 1605. The writing defended the validity of the parallax method for determining distances (or at least the minimum distance) even of objects accessible to the observer only visually, such as celestial objects. The attribution of the writing remains uncertain, that is, whether it is the work of Galilei himself or of his pupil Girolamo Spinelli, a Paduan Benedictine (c. 1580 – 1647). It is also likely, according to Antonio Favaro, that the work was written by both.

Around 1594 Galilei composed two treatises on fortification works, the Short Introduction to Military Architecture and the Treatise on Fortification; around 1597 he fabricated a compass, which he described in the pamphlet Le operazioni del compasso geometrico et militare, published in Padua in 1606 and dedicated to Cosimo II. The compass was an instrument already known and, in different forms and for different uses, already used, nor did Galileo claim to give himself special credit for his invention; but the usual Baldassarre Capra, a pupil of Simon Mayr, in a pamphlet written in Latin in 1607 accused him of plagiarizing an earlier invention of his. On April 9, 1607, Galileo overturned Capra”s accusations and obtained his condemnation by the Reformers of the Paduan Studio and published a Defense against the calumnies et impostures of Baldessar Capra from Milan, where he also returned to the earlier issue of the Supernova.

The appearance of the supernova created great consternation in society, and Galileo did not disdain to take advantage of the moment to draw up personal horoscopes on commission. Moreover, in the spring of that same year, 1604, Galilei had been placed under indictment by the Padua Inquisition following a complaint from one of his former collaborators, who had accused him precisely of making horoscopes and claiming that the stars determine man”s choices. The proceedings, however, were vigorously blocked by the Senate of the Venetian Republic, and the case file was buried, so that no news of it ever reached the Roman Inquisition, that is, the Holy Office. The case was probably also abandoned because Galileo had dealt with natal astrology and not forecasting.

“His fame as an author of horoscopes brought him requests, and no doubt more substantial payments, from cardinals, princes, and patricians, including Sagredo, Morosini, and some who were interested in Sarpi. He exchanged letters with the grand duke”s astrologer, Raffaello Gualterotti, and, in the most difficult cases, with an expert from Verona, Ottavio Brenzoni.” Among the natal themes calculated and interpreted by Galileo are those of his two daughters, Virginia and Livia, and his own, calculated three times: “The fact that Galileo devoted himself to this activity even when he was not paid to do so suggests that he attached some value to it.”

It does not appear that, during the years of the “new star” controversy, Galilei had already publicly come out in favor of the Copernican theory: it is believed that he, while intimately convinced Copernican, thought he did not yet have sufficiently strong evidence to invincibly win the assent of the universality of scholars. He had, however, privately expressed his adherence to Copernicanism as early as 1597: in that year, in fact, he wrote to Kepler-who had recently published his Prodromus dissertationum cosmographicarum “I have already written many arguments and many refutations of the adverse arguments, but so far I have not dared to publish them, afraid of the fate of Copernicus himself, our master.” These fears, however, would vanish precisely because of the telescope, which Galileo first pointed at the sky in 1609. Optics had already been dealt with by Giovanni Battista Della Porta in his Magia naturalis (1589) and De refractione (1593), and by Kepler in Ad Vitellionem paralipomena, of 1604, works from which it was possible to arrive at the construction of the telescope: but the instrument was first constructed independently of those studies in the early 17th century by the craftsman Hans Lippershey, a German optician naturalized Dutch. Galileo then decided to prepare a lead tube, attaching two lenses to the end of it, “both with one full face and with the other spherically concave in the first lens and convex in the second; then, approaching the eye to the concave lens, I perceived the objects to be quite large and close, inasmuch as they appeared three times nearer and nine times larger than they turned out to be looked at by natural sight alone.” On August 25, 1609, Galileo presented the apparatus as his own construction to the government of Venice, which, appreciating the “invention,” doubled his salary and offered him a life-long teaching contract.The invention, rediscovery and reconstruction of the telescope is not an episode that can arouse great admiration. The novelty lies in the fact that Galileo was the first to bring this instrument into science, using it in a purely scientific way and conceiving of it as an enhancement of our senses. Galileo”s greatness in regard to the telescope was precisely this: he overcame a whole series of epistemological obstacles, ideas and prejudices, using said instrument to strengthen his own theses.

Through the telescope, Galileo proposed a new view of the celestial world:

The new discoveries were published on March 12, 1610 in Sidereus Nuncius, a copy of which Galileo sent to the Grand Duke of Tuscany Cosimo II, already his pupil, together with a specimen of his telescope and the dedication of the four satellites, christened by Galileo at first Cosmica Sidera and later Medicea Sidera (“Medici planets”). Galileo”s intention to earn the gratitude of the House of Medici is evident, most likely not only for the purpose of his intent to return to Florence, but also to obtain influential protection in view of the presentation, before the scholarly public, of those novelties, which certainly would not have failed to raise controversy. Also in Padua, following the publication of Sidereus Nuncius, while observing Saturn Galileo discovered and drew a structure that would later be identified with the rings.

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In Florence (1610)

On May 7, 1610, Galileo asked Belisario Vinta, First Secretary of Cosimo II, to be hired at the Studio of Pisa, specifying, “as to the title and pretext of my service, I would desire, in addition to the name of Mathematician, that S. A. add to it that of Philosopher, professing I have studied more years in philosophy, than months in pure mathematics.”

On June 6, 1610, the Florentine government informed the scientist that he had been hired as “Primary Mathematician of the Studio of Pisa et di Filosofo del Ser.mo Gran Duca, without the obligation to read and to reside either in the Studio or in the city of Pisa, et con lo stipendio di mille scudi l”anno, moneta fiorentina” Galileo signed the contract on July 10 and in September reached Florence.

When he arrived here, he took care to give Ferdinand II, son of Grand Duke Cosimo, the best optical lens he had made in his organized workshop when he was in Padua where, with the help of the master glassmakers of Murano, he made ever more perfect “spectacles” and in such quantity that he exported them, as he did with the telescope sent to the Elector of Cologne who in turn lent it to Kepler who made good use of it and who, grateful, concluded his work Narratio de observatis a sé quattuor Jovis satellitibus erronibus of 1611, thus writing: “Vicisti Galilaee,” acknowledging the truth of Galilei”s findings. Young Ferdinand or someone else broke the lens, and then Galilei gave him something less fragile: a “weaponized” magnet, that is, one wrapped in a sheet of iron, suitably placed, which increased its force of attraction in such a way that, while weighing only six ounces, the magnet “lifted fifteen pounds of iron worked in the form of a tomb.”

On moving to Florence, Galilei left his cohabitant, the Venetian Marina Gamba (1570-1612) he had met in Padua, by whom he had had three children-Virginia (1600-1634) and Livia (1601-1659), never legitimized, and Vincenzio (1606-1649), whom he recognized in 1619. Galileo entrusted his daughter Livia in Florence to his grandmother, with whom his other daughter Virginia was already cohabiting, and left his son Vincenzio in Padua in the care of his mother and then, after her death, to a woman named Marina Bartoluzzi.

Later, having made it difficult for the two girls to live with Giulia Ammannati, Galileo had his daughters enter the convent of San Matteo, in Arcetri (Florence), in 1613, forcing them to take vows as soon as they turned the ritual age of sixteen: Virginia took the name Sister Maria Celeste, and Livia that of Sister Arcangela, and while the former resigned herself to her condition and remained in constant correspondence with her father, Livia never accepted her father”s imposition.

The publication of Sidereus Nuncius aroused appreciation but also several controversies. In addition to the accusation that the telescope had taken possession of a discovery that did not belong to him, the reality of what he claimed to have discovered was also questioned. Both the famous Aristotelian from Padua, Cesare Cremonini, and the Bolognese mathematician Giovanni Antonio Magini, who would be the inspiration behind the anti-Galilean libel Brevissima peregrinatio contra Nuncium Sidereum written by Martin Horký, while accepting Galilei”s invitation to look through the telescope he had built, believed that they did not see any supposed satellites of Jupiter.

Only later did Magini recant, and with him also the Vatican astronomer Christoph Clavius, who had initially believed that the satellites of Jupiter identified by Galilei were merely an illusion produced by the telescope”s lenses. It was, the latter, an objection difficult to refute in 1610-11, consequent both to the low quality of the optical system of Galilei”s first telescope and to the assumption that lenses could not only enhance vision but also distort it. Very important support was given to Galileo by Kepler, who, after initial skepticism and once a sufficiently efficient telescope had been built, verified the actual existence of Jupiter”s satellites, publishing in Frankfurt in 1611 the Narratio de observatis a sé quattuor Jovis satellitibus erronibus quos Galilaeus Galilaeus mathematicus florentinus jure inventionis Medicaea sidera nuncupavit.

Because the Jesuit professors at the Roman College were considered among the leading scientific authorities of the time, Galileo traveled to Rome on March 29, 1611, to present his discoveries. He was received with full honors by Pope Paul V himself, by Cardinals Francesco Maria Del Monte and Maffeo Barberini, and by Prince Federico Cesi, who enrolled him in the Accademia dei Lincei, which he had founded eight years earlier. On April 1, Galileo could already write to the ducal secretary Belisario Vinta that the Jesuits “having finally known the truth of the new Medicean Planets, have been making continuous observations of them from two months onward, which are going on; and we have matched them with my own, and they are answered most justly.”

Galilei, however, did not yet know at that time that the enthusiasm with which he was spreading and defending his discoveries and theories would arouse resistance and suspicion in ecclesiastical circles.

On April 19, Cardinal Robert Bellarmine instructed Vatican mathematicians to prepare a report for him on the new discoveries made by “a valiant mathematician per mezo d”un istrumento chiamato cannone overo ochiale,” and the Congregation of the Holy Office, on the following May 17, precautionarily asked the Inquisition in Padua if any proceedings had ever been opened locally against Galilei. Evidently, the Roman Curia was already beginning to glimpse what consequences “these singular developments of science might have on the general conception of the world and thus, indirectly, on the sacred principles of traditional theology.”

In 1612 Galileo wrote the Discorso intorno alle cose che stanno in su l”acqua, o che in quella si muovono, in which leaning on Archimedes” theory he demonstrated, against Aristotle”s, that bodies float or sink in water according to their specific weight not their shape, provoking the polemical response of the Apologetic Discourse d”intorno al Discorso di Galileo Galilei by the Florentine scholar and Aristotelian Ludovico delle Colombe. On Oct. 2, at the Pitti Palace, in the presence of the grand duke, Grand Duchess Christina and Cardinal Maffeo Barberini, then a great admirer of his, he gave a public experimental demonstration of the assumption, definitively refuting Ludovico delle Colombe.

In his Discourse, Galilei also mentioned sunspots, which he claimed to have already observed in Padua in 1610, but did not report: he wrote again, the following year, the Istoria e dimostrazioni intorno alle macchie solari e loro accidenti, published in Rome by the Accademia dei Lincei, in response to three letters from the Jesuit Christoph Scheiner, which, addressed in late 1611 to Mark Welser, duumvir of Augsburg, patron of the sciences and friend of the Jesuits of whom he was banker. Apart from the question of the priority of the discovery, Scheiner wrongly claimed that the spots consisted of swarms of stars rotating around the Sun, while Galileo considered them fluid matter belonging to the surface of the Sun and rotating around it precisely because of the star”s own rotation.

Observation of the spots thus enabled Galileo to determine the Sun”s rotation period and to demonstrate that heaven and earth were not two radically different worlds, the former only perfection and immutability and the latter all variable and imperfect. In fact, on May 12, 1612, he reiterated to Federico Cesi his Copernican vision by writing how the Sun turned “in itself in a lunar month with revolution similar to the others of the planets, that is, from west to east around the poles of the ecliptic: which novelty I doubt is intended to be the funeral or more properly the extreme and last judgment of pseudophilosophy, signs having already been seen in the stars, moon and sun; and I am waiting to see great things spring forth from the Peripatos for the maintenance of the immutability of the heavens, which I do not know where it will be saved and concealed.” Observing the rotational motion of the Sun and planets was also very important: it made the Earth”s rotation, due to which the velocity of a point at the equator would be about 1700 km less improbable

Galileo”s discovery of the phases of Venus and Mercury, observed by Galileo, was not compatible with Ptolemy”s geocentric model, but only with Tycho Brahe”s geo-heliocentric model, which Galileo never considered, and Copernicus” heliocentric model. Galileo, writing to Giuliano de” Medici on Jan. 1, 1611, asserted that “Venus necessarily turns around the sun, as also Mercury and all the other planets, a thing well believed by all the Pythagoreans, Copernicus, Kepler and myself, but not sensibly proved, as now in Venus and Mercury.”

Between 1612 and 1615 Galileo defended the heliocentric model and clarified his conception of science in four private letters, known as “Copernican letters” and addressed to Father Benedetto Castelli, two to Monsignor Pietro Dini, and one to Grand Duchess Mother Christina of Lorraine.

According to Aristotelian doctrine in nature, emptiness does not exist since every earthly or heavenly body occupies a space that is part of the body itself. Without a body there is no space and without space there is no body. Aristotle argues that “nature shuns emptiness” (every gas or liquid always attempts to fill every space, avoiding leaving empty portions of it. An exception to this theory, however, was the experience whereby it was observed that water sucked into a pipe did not fill it completely but inexplicably left a portion that was thought to be completely empty and therefore should be filled by Nature; but this did not occur. Galilei responding to a letter sent to him in 1630 by a Ligurian citizen Giovan Battista Baliani confirmed this phenomenon by claiming that “the repugnance of emptiness on the part of Nature” can be overcome, but partially, and that, indeed, “he himself has proved that it is impossible to make water rise by suction for a difference in height of more than 18 fathoms, about 10 and a half meters.” Galilei therefore believes that horror vacui is limited and does not question whether in fact the phenomenon was related to the weight of air, as Evangelista Torricelli will show.

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The dispute with the Church

On Dec. 21, 1614, from the pulpit of Santa Maria Novella in Florence, the Dominican friar Tommaso Caccini (1574 – 1648) hurled against certain modern mathematicians, and in particular Galileo, the accusation that they were contradicting Scripture with their astronomical conceptions inspired by Copernican theories. Arriving in Rome on March 20, 1615, Caccini denounced Galileo as an advocate of the motion of the Earth around the Sun. Meanwhile, a book by the Carmelite theologian Paolo Antonio Foscarini (1565-1616), Lettera sopra l”opinione de” Pittagorici e del Copernico, dedicated to Galileo, Kepler and all the academicians of the Lincei, had been published in Naples, which intended to accord the biblical passages with the Copernican theory by interpreting them “in such a way that they do not contradict it at all.”

Cardinal Roberto Bellarmino, already a judge in the trial of Giordano Bruno, stated in his letter of reply to Foscarini that it would be possible to reinterpret the passages of Scripture that contradicted heliocentrism only in the presence of a true demonstration of it, and, not accepting Galileo”s arguments, he added that so far none had been shown to him, and argued that in any case, in case of doubt, sacred scripture should be preferred. Galileo”s refusal to accept Bellarmine”s proposal to replace the Ptolemaic theory with the Copernican theory-as long as Galileo acknowledged it as a mere “mathematical hypothesis” suitable for “saving appearances”-was an invitation, albeit unintentional, to have the Copernican theory condemned.

The following year Foscarini would be, briefly, imprisoned and his Epistle forbidden. Meanwhile, the Holy Office ruled, on November 25, 1615, to proceed with the examination of the Letters on sunspots, and Galileo decided to come to Rome to defend himself personally, supported by Grand Duke Cosimo: “Comes to Rome the mathematician Galileo,” Cosimo II wrote to Cardinal Scipione Borghese, “et comes spontaneously to give an account of himself of some imputations, or more properly calumnies, which have been laid upon him by his emuli.”

On Feb. 25, 1616, the pope ordered Cardinal Bellarmine to “summon Galileo and admonish him to abandon the said opinion; and if he refused to obey, the Father Commissary, before a notary and witnesses, to precept him to abandon that doctrine altogether and not to teach, defend or treat of it.” In the same year Copernicus” De revolutionibus was placed on the Index donec corrigatur (until it was corrected). Cardinal Bellarmine nonetheless gave Galileo a statement denying abjuration but reiterating the prohibition against supporting Copernican theses: perhaps the honors and courtesies he received in spite of everything made Galileo fall under the illusion that he was allowed what others were forbidden.

In November 1618 three comets appeared in the sky, a fact that attracted the attention and stimulated the studies of astronomers throughout Europe. Among them the Jesuit Orazio Grassi, a mathematician at the Roman College, successfully delivered a lecture that was widely echoed, Disputatio astronomica de tribus cometis anni MDCXVIII: with it, on the basis of some direct observations and a logico-scholastic procedure, he supported the hypothesis that comets were bodies located beyond the “sky of the Moon” and used it to corroborate Tycho Brahe”s model, according to which the Earth is placed at the center of the universe, with the other planets orbiting instead around the Sun, against the heliocentric hypothesis.

Galilei decided to reply to defend the validity of the Copernican model. He responded indirectly, through the writing Discourse of Comets by his friend and disciple, Mario Guiducci, but in which the master”s hand was probably present. In his reply Guiducci erroneously claimed that comets were not celestial objects but pure optical effects produced by sunlight on vapors raised from the Earth, but he also pointed out the contradictions in Grassi”s reasoning and his erroneous deductions from observations of comets with the telescope. The Jesuit responded with a paper entitled Libra astronomica ac philosophica, signed with the anagrammatic pseudonym Lotario Sarsi, directly attacked Galilei and Copernicanism.

Galilei responded directly at this point: it was not until 1622 that the treatise Il Saggiatore was ready. Written in letter form, it was approved by the academicians of the Lincei and printed in Rome in May 1623. On August 6, after the death of Pope Gregory XV, under the name Urban VIII Maffeo Barberini, a longtime friend and admirer of Galileo, ascended to the papal throne. This mistakenly convinced Galileo that “hope is resurrected, that hope which was now almost entirely buried. We are on the verge of witnessing the return of precious knowledge from the long exile to which it had been forced,” as written to the pope”s nephew Francesco Barberini.

The Assayer presents a theory later revealed to be erroneous of comets as appearances due to solar rays. In fact, the formation of the comet”s crown and tail, depend on the exposure and direction of solar radiation, so Galilei had a point and Grassi a reason, who being opposed to the Copernican theory, could only have a sui generis idea of celestial bodies. However, the difference between Grassi”s arguments and Galileo”s was mainly one of method, as the latter based his reasoning on experience. In the Saggiatore, Galileo in fact wrote the famous metaphor that “philosophy is written in this very large book that continually stands open before our eyes (I say the universe),” putting himself at odds with Grassi, who relied on the authority of past masters and Aristotle for ascertaining the truth on natural matters.

On April 23, 1624, Galilei arrived in Rome to pay his respects to the pope and wrest from him the concession of the Church”s toleration of the Copernican system, but in the six audiences granted to him by Urban VIII he obtained no definite commitment from the latter to that effect. Without any assurance but with the vague encouragement that came from being honored by Pope Urban-who granted a pension to his son Vincentius-Galileo felt he could finally respond, in September 1624, to Francesco Ingoli”s Disputatio. Paying formal homage to Catholic orthodoxy, in his reply Galileo was to refute Ingoli”s anti-Copernican arguments without proposing that astronomical model or responding to the theological arguments. In the Letter Galileo enunciates for the first time what will be called the Galilean principle of relativity: to the common objection brought by the supporters of the Earth”s immobility, consisting in the observation that graves fall perpendicularly on the Earth”s surface, rather than obliquely, as they apparently should if the Earth were moving, Galileo responds by bringing the experience of the ship in which, whether it is in uniform motion or is stationary, the phenomena of falling, or, in general, of the motions of the bodies contained in it, occur in exactly the same way, because “the universal motion of the ship, being communicated to the air and to all those things which are contained in it, and not being contrary to the natural inclination of those things, is indelibly preserved in them.”

In the same 1624 Galilei began his new work, a Dialogue, which, by comparing the different opinions of the interlocutors, would enable him to expound the various current theories on cosmology, and thus also the Copernican theory, without showing any personal commitment to any of them. Health and family reasons prolonged the writing of the work until 1630: he had to take care of his brother Michelangelo”s large family, while his son Vincenzio, who graduated in law from Pisa in 1628, married the following year Sestilia Bocchineri, sister of Geri Bocchineri, one of Duke Ferdinand”s secretaries, and Alessandra. To fulfill the wish of his daughter Maria Celeste, a nun at Arcetri, to have him closer, he rented the small villa “Il Gioiello” near the convent. After not a few vicissitudes in obtaining ecclesiastical imprimatur, the work was published in 1632.

In the Dialogue the two greatest systems compared are the Ptolemaic and Copernican systems (Galileo thus excludes Tycho Brahe”s recent hypothesis from the discussion) and three are the protagonists: two are real characters, friends of Galileo”s, and at the time already deceased, the Florentine Filippo Salviati (1582-1614) and the Venetian Gianfrancesco Sagredo (1571-1620), in whose house the conversations are pretended to be held, while the third protagonist is Simplicio, a fictional character whose name recalls a well-known, ancient commentator on Aristotle, as well as implying his scientific simplicism. He is the proponent of the Ptolemaic system, while the Copernican opposition is supported by Salviati and, playing a more neutral role, Sagredo, who ends up, however, sympathizing with the Copernican hypothesis.

The Dialogo received much praise, including those of Benedetto Castelli, Fulgenzio Micanzio, Paolo Sarpi”s collaborator and biographer, and Tommaso Campanella, but by August 1632 rumors were already spreading of a ban on the book: the Master of the Sacred Palace Niccolò Riccardi had written on July 25 to the inquisitor of Florence Clemente Egidi that by order of the Pope the book should no longer be circulated; on August 7 he asked him to track down copies already sold and seize them. On Sept. 5, according to the Florentine ambassador Francesco Niccolini, the angry pope accused Galileo of deceiving the ministers who had authorized the publication of the work. Urban VIII expressed all his resentment as one of his theses had been treated, according to him, clumsily and exposed to ridicule. Discussing the theory on the tides advocated by the Copernican Salviati – and which was supposed to be the definitive proof of the Earth”s mobility – Simplicio propounded “a most steadfast doctrine, which already by a most learned and eminent person I learned, and to which it is force to be quieted” (clear reference to Urban), according to which God, thanks to his “infinite wisdom and power,” could have caused the tides in very different ways, and one could not be sure that the one proposed by Salviati was the only correct one. Now, regardless of the fact that the Galilean theory of the tides was wrong, Salviati”s ironic comment, calling Simplicio”s proposal “an admirable and truly angelic doctrine,” must surely have seemed outrageous. Finally, the work closed with the assertion that men are “granted to dispute about the constitution of the world” as long as they do not “find the work fabricated” by God. This conclusion was nothing more than a diplomatic ploy contrived to get into print. Which had infuriated the Pontiff. On September 23, the Roman Inquisition urged the Florentine one to notify Galileo that he was ordered to appear in Rome by October before the Commissioner General of the Holy Office.” Galileo, partly because he was ill, partly because he hoped the matter could somehow be settled without the opening of the trial, delayed his departure for three months; in the face of the Holy Office”s threatening insistence, he left for Rome on January 20, 1633 in a litter.

The trial began on April 12, with the first interrogation of Galileo, to whom the inquisitorial commissioner, Dominican Vincenzo Maculano, disputed that on February 26, 1616, he had received a “precept” in which Cardinal Bellarmine allegedly enjoined him to abandon the Copernican theory, not to support it in any way and not to teach it. In the interrogation Galileo denied that he had any knowledge of the precept and claimed that he did not remember that the words quovis modo (in any way) and nec docere (not to teach) were in Bellarmine”s statement. Pressed by the inquisitor, Galileo not only admitted that he had not said “anything of the said precept,” but rather went so far as to claim that “in the said book I show the contrary of the said opinion of Copernicus, and that the reasons of it Copernicus are invalid and inconclusive.” Once the first interrogation was concluded, Galileo was detained, “albeit under very close surveillance,” in three rooms of the Inquisition building, “with ample and free faculty to walk about.”

On June 22, the day after Galilei”s last interrogation, in the chapter house of the Dominican convent of Santa Maria sopra Minerva, with Galileo present and kneeling, the sentence was issued by Cardinals Felice Centini, Guido Bentivoglio, Desiderio Scaglia, Antonio Barberini, Berlinghiero Gessi, Fabrizio Verospi and Marzio Ginetti, “inquisitors general against the heretical pravity,” in which they summarized the long history of the contrast between Galileo and Church doctrine, which began in 1615 with the writing Delle macchie solari and the opposition of theologians in 1616 to the Copernican model. The judgment then claimed that the document received in February 1616 was an effective admonition not to defend or teach the Copernican theory.

Imposing the abjuration “with a sincere heart and unfeigned faith” and forbidding the Dialogue, Galilei was sentenced to “formal imprisonment at our discretion” and the “salutary penalty” of weekly recitation of the seven penitential psalms for three years, reserving the Inquisition to “moderate, change or levar in whole or in part” the penalties and penances.

If the legend of Galileo”s phrase, “E pur si muove,” uttered just after his abjuration, serves to suggest his undiminished belief in the validity of the Copernican model, the conclusion of the trial marked the defeat of his program to spread the new scientific methodology, based on rigorous observation of facts and their experimental verification-against the old science that produces “experiences as made and responsive to its need without ever having made or observed them”-and against the prejudices of common sense, which often leads one to believe any appearance to be real: a program of scientific renewal, which taught “no longer to trust authority, tradition and common sense,” which wanted to “teach how to think.”

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The last years (1633-1642)

The sentence of conviction included a period of imprisonment at the discretion of the Holy Office and the obligation to recite penitential psalms once a week for three years. The literal severity was mitigated in the facts: the imprisonment consisted of a forced stay for five months at the Roman residence of the ambassador of the Grand Duke of Tuscany, Pietro Niccolini, in Trinità dei Monti and from there, in the house of Archbishop Ascanio Piccolomini in Siena, at the latter”s request. As for the penitential psalms, Galileo instructed his daughter Maria Celeste, a cloistered nun, to recite them with the consent of the Church. In Siena, Piccolomini favored Galileo by allowing him to meet with city personalities and debate scientific issues. Following an anonymous letter denouncing the actions of the archbishop and Galileo himself, the Holy Office arranged, accepting the same request made earlier by Galilei, to confine him to the isolated villa (“Il Gioiello”) that the scientist owned in the Arcetri countryside. The order of Dec. 1, 1633, enjoined Galileo to “be alone, not to call or receive anyone, for the time at the will of His Holiness.” Only family members could visit him, with prior authorization: for this reason, too, the loss of his daughter Sister Maria Celeste, the only one with whom he had maintained ties, on April 2, 1634, was particularly painful to him.

He was nevertheless able to keep up correspondence with friends and admirers, even outside Italy: to Elia Diodati, in Paris, he wrote on March 7, 1634, consoling himself of his misfortunes that “envy and malignity have machinated against me” with the consideration that “infamy falls upon traitors and the constituted in the most sublime degree of ignorance.” From Diodati he learned of the Latin translation that Matthias Bernegger was making in Strasbourg of his Dialogue and reported to him of “a certain Antonio Rocco purissimo peripatetico, e remotissimo dall”intender nulla né di matematica né d”astronomia” who was writing in Venice “mordacità e contumelie” against him. This, and other letters, show how little Galileo had disavowed his Copernican beliefs.

After his trial in 1633, Galilei wrote and published in the Netherlands in 1638 a great scientific treatise entitled Discorsi e dimostrazioni matematiche intorno a due nuove scienze pertaining to mechanics and local motions, thanks to which he is considered the father of modern science. It is organized as a dialogue that takes place over four days between the same three protagonists of the earlier Dialogue of Maximum Systems (Sagredo, Salviati and Simplicio).

In the first day, Galileo deals with the resistance of materials: the different resistance must be related to the structure of the particular matter, and Galileo, while not claiming to arrive at an explanation of the problem, addresses Democritus” atomistic interpretation, considering it a hypothesis capable of accounting for physical phenomena. In particular, the possibility of the existence of a vacuum-predicted by Democritus-is held to be a serious scientific hypothesis, and in a vacuum-that is, in the nonexistence of any medium capable of resistance-Galileo rightly argues that all bodies would “descend with equal velocity,” in opposition to contemporary science, which held the impossibility of motion in a vacuum.

After dealing with statics and leverage in the second day, he deals with dynamics in the third and fourth, establishing the laws of uniform motion, naturally accelerated motion, and uniformly accelerated motion and pendulum oscillations.

In the last years of his life, Galilei engaged in an affectionate correspondence with Alessandra Bocchineri. The Bocchineri family of Prato had in 1629 given a young woman, named Sestilia, Alessandra”s sister, for wife to Galilei”s son Vincenzio.

When Galilei, in 1630, now 66 years old, met Alessandra, she was a 33-year-old woman who had honed and cultivated her intelligence as a lady-in-waiting to Empress Eleonora Gonzaga at the Viennese court where she met and married Giovanni Francesco Buonamici, an important diplomat who would become a good friend of Galilei.

In the correspondence Alessandra and Galilei exchanged numerous invitations to meet, and Galilei did not fail to praise the woman”s intelligence since “so rare are women found who so sensibly speak as she does.” With his blindness and worsening health, the Florentine scientist is forced at times to refuse invitations “not only because of the many indispositions that keep me oppressed in this most serious age of mine, but because I am still believed to be in prison, for those causes that are well known.”

The last letter sent to Alessandra in Dec. 20, 1641 of “unintentional brevity” only just precedes Galilei”s death, which would occur 19 days later on the night of Jan. 8, 1642 in Arcetri, assisted by Viviani and Torricelli.

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After death

Galilei was buried in the Basilica of Santa Croce in Florence along with other greats such as Machiavelli and Michelangelo, but it was not possible to raise him the “august and sumptuous repository” desired by his disciples because on Jan. 25 Urban VIII”s nephew, Cardinal Francesco Barberini wrote to the inquisitor of Florence, Giovanni Muzzarelli, to “put it through the ears of the Grand Duke that it is not good to fabricate mausoleums to the corpse of one who was penitentiary in the Tribunal of the Holy Inquisition, and died while the penance lasted; in the epitaph or inscription which shall be placed in the tomb, such words shall not be read as may offend the reputatione of this Tribunal. The same warning shall she also have with those who will recite the funeral oration.”

The Church also kept watch over Galileo”s students: when they started the Accademia del Cimento, it intervened with the Grand Duke, and the Accademia was dissolved in 1667. It was not until 1737 that Galileo Galilei was honored with a funeral monument in Santa Croce, which would be celebrated by Ugo Foscolo.

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Galilean doctrine of the two truths

Convinced of the correctness of Copernican cosmology, Galileo was well aware that it was believed to contradict the biblical text and the tradition of the Church Fathers, who supported instead a geocentric conception of the universe. Since the Church considered the Holy Scriptures to be inspired by the Holy Spirit, the heliocentric theory could only be accepted, until proven otherwise, as a mere hypothesis (ex suppositione) or mathematical model, with no bearing on the actual position of the heavenly bodies. On this very condition, Copernicus” De revolutionibus orbium coelestium had not been condemned by church authorities and mentioned in the Index of Forbidden Books, at least until 1616.

Galileo, a Catholic intellectual, entered the debate on the relationship between science and faith with his letter to Father Benedetto Castelli dated Dec. 21, 1613. He defended the Copernican model by arguing that there are two truths that are necessarily not contradictory or in conflict with each other. The Bible is certainly a sacred text of divine inspiration and of the Holy Spirit, but nonetheless written at a precise historical moment with the purpose of directing the reader toward an understanding of true religion. For this reason, as many exegetes including Luther and Kepler had already argued, the facts of the Bible were necessarily written in such a way that they could also be understood by the ancients and ordinary people. It is therefore necessary to discern, as Augustine of Hippo had already argued, the properly religious message from the historically connoted and inevitably narrative and didactic description of facts, episodes and characters:

The well-known biblical episode of Joshua”s request to God to stop the Sun in order to lengthen the day was used in ecclesiastical circles to support the geocentric system. Galileo argued instead that in that way the day would not be lengthened, since in the Ptolemaic system the diurnal rotation (day

For Galileo, the Holy Scriptures deal with God; the method for conducting investigations into Nature must be based on “sensible experiences” and “necessary demonstrations.” The Bible and Nature cannot contradict each other because they both derive from God; consequently, in case of apparent discord, it is not science that will have to take a step back, but rather the interpreters of the sacred text who will have to search beyond the superficial meaning of the latter. In other words, as Galilei scholar Andrea Battistini explains, “the biblical text conforms only ”to the common way of the vulgar,” that is, it adapts itself not so much to the skills of the ”connoisseurs,” but to the cognitive limits of the common man, thus veiling with a kind of allegory the deeper meaning of the utterances. If the literal message may diverge from the utterances of science, its “innermost” and more authentic content, which can be derived from the interpretation of the biblical text beyond its more epidermic meanings, never can. “Concerning the relationship between science and theology, famous is his phrase: “understood by an ecclesiastical person constituted in eminent degree, the intention of the Holy Spirit to be to teach us how to go to heaven, and not how to go to heaven,” usually attributed to Cardinal Cesare Baronio. It should be noted that, applying such a criterion, Galileo could not have used the biblical passage from Joshua to try to prove an alleged agreement between the sacred text and the Copernican system, and the supposed contradiction between the Bible and the Ptolemaic model.Instead, Galileo”s view that there are two sources of knowledge (“books”), which are capable of revealing the same truth that comes from God, derives precisely from such a criterion. The first is the Bible, written in terms comprehensible to the “vulgar,” which has essentially salvific and soul-redeeming value, and thus requires careful interpretation of statements about the natural phenomena described in it. The second is “this very great book that continually stands open before our eyes (I say the universe), which is to be read according to scientific rationality and is not to be postponed to the first but, in order to be well interpreted, must be studied with the instruments with which the same God of the Bible has endowed us: senses, speech and intellect:

Again in his letter to Grand Duchess Christina of Lorraine in 1615, when asked whether theology could still be conceived of as the queen of the sciences, Galilei replied that the subject matter of which theology dealt made it of primary importance, but that the latter could not claim to pronounce judgments in the field of the truths of science. On the contrary, if a certain scientifically proven fact or phenomenon does not agree with the sacred texts, then it is these that must be reread in the light of new advances and discoveries.

According to the Galilean doctrine of the two truths, there can ultimately be no disagreement between true science and true faith being, by definition, both true. But, in case of apparent contradiction on natural facts, the interpretation of the sacred text must be modified to bring it in line with the most up-to-date scientific knowledge.

The Church”s position in this regard did not differ substantially from Galileo”s: with much more caution, even the Catholic Church admitted the need to revise the interpretation of sacred scripture in the light of new facts and new knowledge that was solidly substantiated. But in the case of the Copernican system, Cardinal Robert Bellarmine and many other Catholic theologians reasonably argued that there was no conclusive evidence in its favor:

On the other hand, the failure to observe, with the instruments then available, stellar parallax (which should have been found as an effect of the Earth”s displacement relative to the sky of the fixed stars) constituted evidence against the heliocentric theory at the time. In this context, the Church thus admitted that the Copernican model was spoken of only ex suppositione (as a mathematical hypothesis). Galileo”s defense ex professo (knowledgeably and competently, purposefully and intentionally) of the Copernican theory as a real physical description of the solar system and the orbits of celestial bodies thus inevitably clashed with the official position of the Catholic Church. According to Galileo, the Copernican theory could not be considered a simple mathematical hypothesis for the simple reason that it was the only perfectly accurate explanation and did not use those “absurdities” constituted by eccentrics and epicycles. In fact, contrary to what was said at the time, Copernicus had needed more eccentrics and epicycles than those used by Ptolemy to maintain a level of accuracy comparable to that of the Ptolemaic system. The exact number of the latter is initially 34 (in his first exposition of the system, contained in Commentariolus), but reaches the figure of 48 in De revolutionibus, according to Koestler”s calculations. In contrast, the Ptolemaic system did not use 80, as claimed by Copernicus, but only 40, according to Peurbach”s 1453 updated version of the Ptolemaic system. Historian of science Dijksterhuis provides other data, believing that the Copernican system used only five fewer “circles” than the Ptolemaic system. The only substantial difference, therefore, consisted solely of the absence of equants in the Copernican theory. The aforementioned Koestler questioned whether this misjudgment could be attributed to Galileo”s failure to read Copernicus” work, or to his intellectual dishonesty. This opposition resulted initially in the placing of De revolutionibus on the Index, and finally, many years later, in the trial of Galileo Galilei in 1633, which ended in his conviction on “vehement suspicion of heresy” and the forced abjuration of his astronomical conceptions.

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Rehabilitation by the Catholic Church

Beyond the historical, legal and moral judgment on the condemnation of Galilei, the questions of epistemology and biblical hermeneutics that were at the heart of the trial have been the subject of reflection by countless modern thinkers, who have often cited the Galileo affair to exemplify, sometimes in deliberately paradoxical terms, their thinking on these issues. For example, Austrian philosopher Paul Feyerabend, an advocate of epistemological anarchy, argued that:

This provocation would later be taken up by Card. Joseph Ratzinger, resulting in public objections. But the real purpose for which Feyerabend had expressed such provocative statement was “only to show the contradiction of those who approve of Galileo and condemn the Church, but then toward the work of their contemporaries are as rigorous as the Church was in Galileo”s time.”

Over the centuries that followed, the Church changed its position toward Galilei: in 1734 the Holy Office granted the erection of a mausoleum in his honor in the church of Santa Croce in Florence; Benedict XIV in 1757 removed from the Index the books that taught the motion of the Earth, thereby formalizing what Pope Alexander VII had already in fact done in 1664 with the withdrawal of the 1616 Decree.

The final authorization to teach the motion of the Earth and the immobility of the Sun came with a decree of the Sacred Congregation of the Inquisition approved by Pope Pius VII on September 25, 1822.

Particularly significant is an 1855 contribution by British theologian and cardinal John Henry Newman, just a few years after enabling the teaching of heliocentrism and when Newton”s theories of gravitation were well established and experimentally proven. First, the theologian summarizes the relationship of heliocentrism to Scripture:

Interesting is the Cardinal”s reading of the Galileo affair as confirmation, not denial, of the divine origin of the Church:

In 1968 Pope Paul VI had the review of the trial initiated and, with the intention of putting a definitive word regarding these controversies, Pope John Paul II on July 3, 1981, called for interdisciplinary research to be undertaken into Galileo”s difficult relations with the Church and established a Pontifical Commission to study the Ptolemaic-Copernican controversy of the 16th and 17th centuries, in which the Galilei case fits. The pope admitted, in his Nov. 10, 1979 speech announcing the establishment of the commission, that “Galileo had much to suffer, we cannot hide it, from men and Church bodies.”

After a full thirteen years of hearing, on October 31, 1992, the Church cancelled the condemnation, which formally still existed, and clarified its interpretation on the Galilean scientific theological issue by acknowledging that the condemnation of Galileo Galilei was due to the obstinacy of both sides in not wanting to consider each other”s theories as mere hypotheses that were not experimentally proven and, on the other hand, to the “lack of perspicacity,” i.e., intelligence and foresight, of the theologians who condemned him, who were incapable of reflecting on their own criteria for interpreting Scripture and were responsible for inflicting much suffering on the scientist. Indeed, as John Paul II declared:

“The history of scientific thought in the Middle Ages and Renaissance, which we are now beginning to understand a little better, can be divided into two periods, or rather, because the chronological order corresponds only very roughly to this division, it can be divided, roughly, into three phases or epochs, corresponding successively to three different currents of thought: first Aristotelian physics; then the physics of impetus, begun, like everything else, by the Greeks and elaborated by the current of Parisian nominalists in the 14th century; and finally modern physics, Archimedean and Galilean. “

Among the major discoveries that Galilei made, guided by experiments, were an early physical approach to relativity, later known as Galilean relativity, the discovery of Jupiter”s four main moons, called Galilean satellites (Io, Europa, Ganymede and Callisto), and the principle of inertia, albeit partially.

He also made studies on the falling motion of graves and reflecting on motions along inclined planes discovered the problem of “minimum time” in the fall of material bodies, and studied various trajectories, including the paraboloid spiral and the cycloid.

As part of his research in mathematics, he approached the properties of infinity by introducing Galileo”s famous paradox. In 1640 Galilei encouraged his pupil Bonaventura Cavalieri to develop his master”s and others” ideas on geometry using the method of indivisibles to determine areas and volumes: this method represented a milestone in the development of infinitesimal calculus.

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The birth of modern science

Galileo Galilei was one of the leading figures in the founding of the scientific method expressed in mathematical language and posited experiment as the basic tool for the investigation of the laws of nature, in contrast to the Aristotelian tradition and its qualitative analysis of the cosmos:

Already in his third letter of 1611 to Mark Welser about the sunspot controversy, Galilei wondered what man in his quest wants to come to know.

And again: by knowledge do we mean coming to grasp the first principles of phenomena or how they develop?

The search for essential first principles thus involves an endless series of questions since each answer gives rise to a new question: if we were to ask what the substance of clouds is, a first answer would be that it is water vapor but then we would have to ask what this phenomenon is and we would have to answer that it is water, to ask immediately afterwards what water is, answering that it is that fluid that flows in rivers but this “news of water” is only “closer and dependent on more senses,” richer in different particular information, but it certainly does not bring us knowledge of the substance of clouds, about which we know exactly as much as before. But if, on the other hand, we want to understand the “affections,” the particular characteristics of bodies, we will be able to know them both in those bodies that are distant from us, such as clouds, and in those that are closer, such as water.

It is therefore necessary to understand the study of nature differently. “Some stern defenders of all peripatetic minutiae,” educated in the cult of Aristotle, believe that “philosophizing is nor can be anything but a making great practice over the texts of Aristotle” which they bring as the only proof of their theories. And unwilling “never to lift their eyes from those papers,” they refuse to read “this great book of the world” (i.e., from directly observing phenomena), as if “it were written by nature to be read by none other than Aristotle, and that his eyes should have to see for all his posterity. “Instead, “our discourses have to be around the sensible world, and not over a world of paper.”

Underlying the scientific method, then, are the rejection of essentialism and the decision to grasp only the quantitative aspect of phenomena in the belief that we can translate them through measurement into numbers so that we have mathematical knowledge, the only perfect knowledge for man who achieves it gradually through reasoning so as to equal the same perfect divine knowledge that possesses it entirely and intuitively:

Thus, the Galilean method is to be composed of two main aspects:

Summarizing the nature of the Galilean method, Rodolfo Mondolfo finally adds that:

This is the originality of the Galilean method: to have linked experience and reason, induction and deduction, exact observation of phenomena and elaboration of hypotheses, and this, not abstractly but, with the study of real phenomena and the use of appropriate technical instruments.

Fundamental was Galileo”s contribution to scientific language, both in mathematics and, in particular, in the field of physics. Even today in this discipline much of the sectional language in use derives from specific choices made by the Pisan scientist. In particular, in Galileo”s writings many words are taken from ordinary language and are subjected to “technification,” that is, the attribution to them of a specific and new meaning (a form, therefore, of semantic neologism). This is the case with “force” (albeit not in the Newtonian sense), “velocity,” “momentum,” “impetus,” “fulcrum,” “spring” (meaning the mechanical instrument but also “elastic force”), “rubbing,” “terminator,” and “tape.”

An example of the way Galileo names geometric objects is in a passage in the Discourses and Mathematical Demonstrations Around Two New Sciences:

As can be seen, in the text specialized terminology (“hemispheric,” “cone,” “cylinder”) is accompanied by the use of a term denoting an object of everyday life, namely “bowl.”

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Physics, mathematics and philosophy

The figure of Galileo Galilei is also remembered in history for his reflections on the foundations and tools of scientific analysis of nature. Famous is his metaphor reported in The Assayer, where mathematics is defined as the language in which the book of nature is written:

In this passage Galilei connects the words “mathematics,” “philosophy,” and “universe,” thus beginning a long dispute among philosophers of science as to how he conceived and related these terms to each other. For example, what Galileo here calls “universe” should be understood, in modern terms, as “physical reality” or “physical world” since Galileo is referring to the mathematically knowable material world. Thus not only to the totality of the universe understood as the set of galaxies, but also to any of its inanimate parts or subsets. Instead, the term “nature” would also include the biological world, which is excluded from the Galilean investigation of physical reality.

With regard to the universe proper, Galilei, albeit in indecision, seems to lean toward the view that it is infinite:

He does not take a clear-cut position on the question of the finiteness or infinity of the universe; however, as Rossi argues, “there is only one reason that inclines him toward the infinity thesis: it is easier to refer incomprehensibility to the incomprehensible infinite than to the finite which is not comprehensible.”

But Galilei never explicitly considers, perhaps out of prudence, Giordano Bruno”s doctrine of an unlimited and infinite universe, without a center and consisting of infinite worlds among which Earth and Sun have no cosmogonic pre-eminence. The Pisan scientist does not participate in the debate on the finiteness or infinity of the universe and states that in his opinion the question is insoluble. If he appears to lean toward the hypothesis of infinitude, he does so on philosophical grounds since, he argues, the infinite is the object of incomprehensibility while that which is finite falls within the limits of the comprehensible.

The relationship between Galileo”s mathematics and his philosophy of nature, the role of deduction versus induction in his researches, have been brought back by many philosophers to the confrontation between Aristotelians and Platonists, to the recovery of the ancient Greek tradition with the Archimedean conception or even to the early development in the 17th century of the experimental method.

The issue was so well expressed by the medievalist philosopher Ernest Addison Moody (1903-1975):

Galileo lived at a time when the ideas of Platonism had spread again throughout Europe and Italy, and probably also for this reason the symbols of mathematics are identified by him with geometric entities and not numbers. On the other hand, the use of algebra derived from the Arab world in demonstrating geometrical relations was still insufficiently developed, and it was only with Leibniz and Isaac Newton that differential calculus became the basis of the study of classical mechanics. Indeed, Galileo in showing the law of falling bodies made use of geometric relations and similarities.

On the one hand, for some philosophers such as Alexandre Koyré, Ernst Cassirer, and Edwin Arthur Burtt (1892-1989), experimentation was certainly important in Galileo”s studies and also played a positive role in the development of modern science. Experimentation itself, as a systematic study of nature, requires a language with which to formulate questions and interpret the answers obtained. The search for this language was a problem that had interested philosophers since the time of Plato and Aristotle, particularly with respect to the nontrivial role of mathematics in the study of the natural sciences. Galilei relies on exact and perfect geometric figures that, however, can never be encountered in the real world, except at best as crude approximations.

Today mathematics in modern physics is used to build models of the real world, but in Galileo”s time this kind of approach was by no means taken for granted. According to Koyré, for Galileo, the language of mathematics allows him to formulate a priori questions before even confronting experience, and in doing so he directs the very search for the characteristics of nature through experiments. From this point of view, Galileo would thus follow the Platonic and Pythagorean tradition, where mathematical theory precedes experience and does not apply to the sensible world but expresses its intimate nature.

Other Galilean scholars, such as Stillman Drake, Pierre Duhem, and John Herman Randall Jr. have instead emphasized the novelty of Galileo”s thought compared to classical Platonic philosophy. In the Assayer”s metaphor, mathematics is a language and is not directly defined as either the universe or philosophy, but rather is a tool for analyzing the sensible world that was instead seen by the Platonists as illusory. Language would be the focus of Galileo”s metaphor, but the universe itself is the real target of his research. In this way, according to Drake, Galileo would definitely move away from the Platonic conception and philosophy, but without approaching the Aristotelian one, as argued by Pierre Duhem, according to whom Galilean science was rooted in medieval thought. On the other hand, the violent attacks launched by Aristotelians against his science make it difficult to consider Galileo one of them. Thus, for Drake, Galileo “had not cared to formulate a philosophy,” and in the third day of the Discourses he states, referring to philosophical conceptions, ” Similar deep contemplations are expected of higher doctrines than ours; and to us it must suffice to be those less worthy artisans who from the linings uncover and hollow out the marbles, in which then the illustrious sculptors make marvelous images appear which under rough and shapeless bark were hidden.”

According to Eugenio Garin Galileo, on the other hand, with his experimental method, wants to identify in the “Aristotelian” observed fact an intrinsic necessity, expressed mathematically, due to its connection with the “Platonic” divine cause that produces it by making it “live.”

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Motion studies

Wilhelm Dilthey sees Kepler and Galilei as the highest expressions in their time of “calculating thoughts” that were disposed to solve, through the study of the laws of motion, the demands of modern bourgeois society:

Indeed, Galilei was one of the leading figures in overcoming the Aristotelian description of the nature of motion. Already in the Middle Ages some authors, such as John Philoponus in the 6th century, had observed contradictions in Aristotelian laws, but it was Galileo who proposed a viable alternative based on experimental observations. Unlike Aristotle, for whom there are two “natural,” that is, spontaneous, substance-dependent motions of bodies, one directed downward, typical of bodies of earth and water, and one upward, typical of bodies of air and fire, for Galileo any body tends to fall downward in the direction of the center of the Earth. If there are bodies that rise upward, it is because the medium in which they are found, having a greater density, pushes them upward, according to the well-known principle already expressed by Archimedes: Galileo”s law of falling bodies, regardless of the medium, is therefore valid for all bodies, whatever their nature.

To achieve this, one of the first problems Galileo and his contemporaries had to solve was to find suitable tools to describe motion quantitatively. Resorting to mathematics, the problem was to figure out how to treat dynamic events, such as falling bodies, with geometric figures or numbers that as such are absolutely static and are devoid of any motion. To overcome Aristotelian physics, which viewed motion in qualitative and non-mathematical terms, as moving away and then returning to its natural place, it was therefore necessary first to develop the tools of geometry and in particular differential calculus, as Newton, Leibniz and Descartes, among others, later did. Galileo succeeded in solving the problem in the study of the motion of accelerated bodies by drawing a line and associating with each point a time and an orthogonal segment proportional to the velocity. In this way he constructed the prototype velocity-time diagram, and the space traveled by a body is simply equal to the area of the constructed geometric figure. His studies and research on the motion of bodies also paved the way for modern ballistics.

On the basis of motion studies, mental experiments and astronomical observations, Galileo intuited that it is possible to describe both events occurring on Earth and celestial events with a single set of laws. He thus also overcame in this way the division between the sublunar and supralunar worlds of the Aristotelian tradition (for which the latter is governed by laws different from those on Earth and by perfectly spherical circular motions, which were deemed impossible in the sublunar world).

Studying the inclined plane, Galilei dealt with the origin of the motion of bodies and the role of friction; he discovered a phenomenon that is a direct consequence of the conservation of mechanical energy and leads one to consider the existence of inertial motion (which occurs without the application of an external force). He thus had the insight of the principle of inertia, later included by Isaac Newton in the principles of dynamics: a body, in the absence of friction, remains in uniform rectilinear motion (at rest if v = 0) as long as external forces act on it. The concept of energy, however, was not present in seventeenth-century physics, and it was not until the development, more than a century later, of classical mechanics that a precise formulation of the concept was arrived at.

Galileo placed two inclined planes of the same base angle θ, facing each other, at an arbitrary distance x. By lowering a sphere from a height h1 for a distance l1 of that at SN he noticed that the sphere, having arrived on the horizontal plane between the two inclined planes, continues its rectilinear motion to the base of the DX inclined plane. At that point, in the absence of friction, the sphere ascends the inclined plane of RIGHT for a distance l2 = l1 and stops at the same height (h2 = h1) as it started. In present terms, conservation of mechanical energy dictates that the initial potential energy Ep = mgh1 of the sphere transforms-as the sphere descends the first inclined plane (SN)-into kinetic energy Ec = (1

Now imagine decreasing the angle θ2 of the inclined plane of DX (θ2 < θ1),and repeating the experiment. To succeed in rising-as the principle of conservation of energy dictates-to the same altitude h2 as before, the sphere will now have to travel a longer distance l2 on the inclined plane of DX. If we gradually reduce the angle θ2, we will see that each time the length l2 of the stretch traveled by the sphere increases in order to rise to the height h2. If you finally bring the angle θ2 to be zero (θ2 = 0°), you have in fact eliminated the inclined plane of RIGHT. By now bringing the sphere down from the height h1 of the inclined plane of SN, it will continue to move indefinitely in the horizontal plane with velocity vmax (principle of inertia) since, due to the absence of the inclined plane of DX, it can never rise to the height h2 (as the principle of conservation of mechanical energy would predict).

Finally, imagine flattening mountains, filling valleys and building bridges, so that an absolutely flat, uniform and frictionless rectilinear path is achieved. Once the inertial motion of the sphere descending from an inclined plane with constant velocity vmax has begun, it will continue to move along such a rectilinear path until it goes completely around the Earth, and then restarts its journey undisturbed. Here is realized a (ideal) perpetual inertial motion, occurring along a circular orbit, coincident with the Earth”s circumference. Starting from this “ideal experiment,” Galileo would seem to erroneously assume that all inertial motions must be circular motions.Probably for this reason he considered, for the planetary motions he (arbitrarily) believed to be inertial, always and only circular orbits, rejecting instead the elliptical orbits demonstrated by Kepler since 1609. So, to be rigorous, what Newton states in the “Principia” – thus misleading countless scholars – does not seem to be correct, namely that Galilei would have anticipated his first two principles of dynamics.

Galileo was able to determine the value he believed to be constant of the acceleration of gravity g at the Earth”s surface, that is, the magnitude that governs the motion of bodies falling toward the center of the Earth, by studying the fall of well-smoothed spheres along an inclined plane, also well-smoothed. Since the motion of the sphere depends on the angle of inclination of the plane, by simple measurements at different angles he was able to obtain a value of g only slightly less than the exact value for Padua (g = 9.8065855 m

Calling a the acceleration of the sphere along the inclined plane, its relation to g turns out to be a = g sin θ so that, from the experimental measurement of a, the value of the acceleration of gravity g can be traced. The inclined plane allows the value of the acceleration (a < g) to be reduced at will, making it easier to measure. For example, if θ = 6°, then sin θ = 0.104528 and thus a = 1.025 m

Guided by the similarity with sound, Galileo was the first to attempt to measure the speed of light. His idea was to take himself to a hill with a lantern covered by a drape and then remove it, thus throwing a light signal to an assistant placed on another hill one and a half kilometers away: the latter, as soon as he saw the signal, would then in turn raise the drape of his lantern and Galileo seeing the light would be able to record the time interval taken by the light signal to reach the other hill and return. An accurate measurement of this time would have made it possible to measure the speed of light, but the attempt was unsuccessful given the impossibility for Galilei to have such an advanced instrument that could measure the hundred-thousandths of a second it takes light to travel a distance of a few kilometers.

The first estimate of the speed of light was the work, in 1676, of the Danish astronomer Rømer based on astronomical measurements.

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Experimental and measuring equipment

Experimental apparatuses were fundamental in the development of Galileo”s scientific theories, who built various measuring instruments either originally or by reworking them based on preexisting ideas. In the field of astronomy, he built some telescope specimens himself, equipped with a micrometer to measure how far a moon was from its planet. To study sunspots, he projected the image of the Sun onto a sheet of paper with a helioscope so that he could safely observe it without damage to his eyesight. He also devised the giovilabium, similar to the astrolabe, to determine longitude using the eclipses of Jupiter”s satellites.

To study the motion of bodies, he used instead the inclined plane with the pendulum to measure time intervals. He also took up arudimentary thermometer model, based on the expansion of air as temperature changes.

Galileo discovered in 1583 the isochronism of the small oscillations of a pendulum; according to legend, the idea came to him while observing the oscillations of a lamp then suspended in the nave of Pisa Cathedral, now kept in the nearby Monumental Cemetery, in the Aulla Chapel.

This instrument is simply composed of a grave, such as a metal ball, tied to a thin, inextensible wire. Galileo observed that the oscillation time of a pendulum is independent of the mass of the grave and also of the amplitude of the oscillation, if it is small. He also discovered that the period of oscillation T{displaystyle T} depends only on the length of the wire l{displaystyle l}:

where g{displaystyle g} is the acceleration of gravity. For example, if the pendulum has l=1m{displaystyle l=1m}, the oscillation that carries the grave from one end to the other and then back again has a period T=2.0064s{displaystyle T=2.0064s} (having assumed for g{displaystyle g} the mean value 9.80665{displaystyle 9.80665}). Galileo exploited this property of the pendulum to use it as an instrument for measuring time intervals.

Galileo in 1586, at the age of 22 while still awaiting his university appointment in Pisa, perfected Archimedes” hydrostatic balance and described his device in his first vernacular work, La Bilancetta, which circulated manuscript but was printed posthumously in 1644:

How to obtain the specific gravity PS of a body with respect to water is also described:

In La Bilancetta there are then two tables showing thirty-nine specific weights of precious and genuine metals, determined experimentally by Galileo with accuracy comparable to modern values.

The proportional compass was an instrument used since the Middle Ages to perform even algebraic operations by geometry, perfected by Galileo and capable of extracting the square root, constructing polygons and calculating areas and volumes. It was successfully used in the military by artillerymen to calculate bullet trajectories.

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Literature

During the Pisan period (1589-1592), Galileo did not limit himself to scientific pursuits alone: in fact, his Considerations on Tasso date from these years, which would be followed up with Postille all”Ariosto. These are scattered notes on sheets of paper and annotations in the margins in the pages of his volumes of Gerusalemme liberata and Orlando furioso where, while he reproaches Tasso for “the paucity of imagination and the slow monotony of image and verse, what he loves in Ariosto is not only the fluttering of beautiful dreams, the rapid change of situations, the lively elasticity of rhythm, but the harmonious balance of this, the coherence of the image the organic unity – even in variety – of the poetic phantasm.”

From a literary point of view, The Assayer is considered the work in which his love for science, truth and his wit as a polemicist merge the most. However, even in Dialogo sopra i due massimi sistemi del mondo (Dialogue over the Two Greatest Systems of the World) one can appreciate pages of a remarkable level in terms of quality of writing, vividness of language, and narrative and descriptive richness. Finally, Italo Calvino stated that, in his opinion, Galilei was the greatest writer of prose in the Italian language, a source of inspiration even for Leopardi.

The use of the vernacular served a twofold purpose for Galileo. On the one hand it was aimed at the popularizing intent of the work: Galileo intended to appeal not only to the learned and intellectuals but also to less educated classes, such as technicians who did not know Latin but could still understand his theories. On the other, he contrasted this with the Latin of the Church and the various Academies, which were based on the biblical and Aristotelian principle of auctoritas, respectively. A break with the earlier tradition is also delineated in terms of terminology: Galileo, unlike his predecessors, does not draw cues from Latin or Greek to coin new terms but takes them, modifying their meaning, from the vernacular language.

Galileo also demonstrated different attitudes toward existing terminologies:

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Fine Arts

“The Accademia e Compagnia dell”Arte del Disegno” was founded by Cosimo I de” Medici in 1563, at the suggestion of Giorgio Vasari, with the intention of renewing and fostering the development of the first guild of artists formed from the ancient company of San Luca (documented since 1339). It counted among its first academicians such personalities as Michelangelo Buonarroti, Bartolomeo Ammannati, Agnolo Bronzino, and Francesco da Sangallo. For centuries the Academy represented the most natural and prestigious center of aggregation for artists working in Florence and, at the same time, fostered the relationship between science and art. It provided for the teaching of Euclidean geometry and mathematics, and public dissections were to prepare for drawing. Even a scientist like Galileo Galilei was appointed in 1613 as a member of the Florentine Academy of the Arts of Drawing.”

Indeed, Galileo also took part in the complex events concerning the figurative arts of his period, especially portraiture, delving into Mannerist perspective and coming into contact with illustrious artists of the time (such as Cigoli), as well as consistently influencing the naturalistic current with his astronomical discoveries.

For Galileo in figurative art, as in poetry and music, the emotion that can be conveyed applies, regardless of an analytical description of reality. He also believes that the more dissimilar the means used to render a subject from the subject itself, the greater the skill of the artist:

Ludovico Cardi, known as Cigoli, a Florentine, was a painter at the time of Galileo; at a certain point in his life, in order to defend his work, he asked his friend Galileo for help: he had, in fact, to defend himself from the attacks of those who considered sculpture superior to painting, since it has the gift of three-dimensionality, to the detriment of simply two-dimensional painting. Galileo responded in a letter, dated June 26, 1612. He provides a distinction between optical and tactile values, which also becomes a value judgment on sculptural and painting techniques: the statue, with its three dimensions, deceives the sense of touch, while painting, in two dimensions, deceives the sense of sight. Galilei thus attributes greater expressive capacity to the painter than to the sculptor because the former, through sight, is better able to produce emotions than the latter through touch.

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Music

Galileo”s father was a musician (lutenist and composer) and music theorist well known in his time. Galileo made fundamental contributions to the understanding of acoustic phenomena by scientifically studying the importance of oscillatory phenomena in the production of music. He also discovered the relationship between the length of a vibrating string and the frequency of the sound emitted.

In his letter to Lodovico Cardi, Galileo writes:

putting vocal and instrumental music on an equal footing, since only the emotions one can convey are important in art.

Countless types of objects and entities, natural or man-made, have been dedicated to Galileo:

Galileo Galilei is remembered with celebrations at local institutions on Feb. 15, ”Galileo Day”, the day of his birth

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Bibliographical

Sources

1. Galileo Galilei
2. Galileo Galilei