Galileo Galilei!

Galileo Galilei!

Dialogue Concerning the Two Chief sistemiIn that same 1624 Galileo began his new job, a dialogue that, when comparing the different views of the audience would allow him to expose the various current theories on cosmology - and therefore the Copernican - without showing commitment personally in favor of any of them. Reasons of health and family Porunga the drafting of the work: he had to take care of the large family of his brother Michael, while his son Vincenzo, who graduated in law at Pisa in 1628, she married the following year with Sestilia Bocchineri, sister of Geri Bocchineri, one of the secretaries of Duke Ferdinand, and Alexander, which will take some part in the last years of our life. To fulfill the desire of his daughter Maria Celeste, a nun in Arcetri, to have closer, he rented the house near the convent, "The Jewel".

It was expected that the dialogue, whose title should have been the ebb and flow, was published in Rome by the Accademia dei Lincei and Galileo, the work completed in January 1630, went there in March to get the imprimatur of ecclesiastical . Departed from Rome on June 26, with insurance assessors, the Dominicans and Nicholas Riccardi Raffaello Visconti, authorization to print a few non-substantive changes.

On August 1, but died Federico Cesi, the patron of the Accademia dei Lincei, and this gave to publish the works, so that Galileo decided to publish it in Florence: here quickly got permission from the Dominican Giacinto Stefani, but also necessary ' authorization from Rome, which was slow to come. Finally, in July of 1631, Father Riccardi sent the inquisitor of Florence permission to print a draft preface and an order to change the title provided on the ebb and flow: the title, recalling that Galileo considered the evidence the correctness of the Copernican system was changed in Dialogue of Galileo Galilei Lincei, where neither the congress of four days, he talks on the Two Chief World Systems, Ptolemaic and Copernican, and the work could be published in Florence February 21, 1632 .

TolomeoI Two Chief World Systems is the Ptolemaic and Copernican - Galileo thus excludes from discussion the recent hypothesis of Tycho Brahe - and three are at the center of the Dialogue: two are real characters, friends of Galileo, and at that time already dead, the Florentine Filippo Salviati (1582-1614) and the Venetian Gianfrancesco Sagredo (1571-1620), in whose house pretending to be held conversations, while the third, Simplicio, in the name recalls a famous, ancient commentator on Aristotle, as well as imply its simple science. He is the supporter of the Ptolemaic system, while the opposition is supported by the Copernican Salviati, plays a more neutral the Sagredo, which ends, however, to sympathize with the Copernican hypothesis.

Dialogue takes place over four days: the first is criticized for the old thesis of Aristotelian physics, unfounded or insufficiently founded on observation and experimental verification, and lack a rigorous mathematical support: indeed, the human intellect can not remotely match the sum of the infinite divine knowledge, but even a few human knowledge of mathematics and geometry equal the divine knowledge by reaching the "objective certainty."

In the second and third day will refute the objections to the motion of Earth's rotation and revolution, "there is strength again exclaim and extol the admirable perspicuity of Copernicus and together compiagner his misfortune, since he does not live in our time when, tor via the apparent absurdity of the movement to preserve the Earth and the Moon, we see Jupiter nearly another Earth, not canned of the moon, but accompanied by four moons, go around the sun in 12 years. " [52]

The fourth day will expose the subject of the tides, as evidence of motion of the Earth: evidence wrong, especially since the dialogue is criticism about the right intuition of Kepler and other astronomers that the attraction was the cause of the lunar tides. Almost at the end are the words of Simplicius: "Your well thought parermi more ingenious than others I n'abbia heard me, but I respect him but not true and conclusive: indeed, considering always ahead of his mind's eye a steadfast doctrine, person who had been most learned and learned and Eminent which is under subside [...] God with His infinite power and wisdom could confer the mutual movement of the water element [...] and yet in many ways from ' [...] our intellect inescogitabili excessive boldness would be if others wanted to limit and coerce the divine power and wisdom to his particular fancy. " [53]

This was an exposure of the 'argument of the end' or 'topic of Urban VIII, "so called because he had brought, still a cardinal, Galileo, God," in his infinite power, can anything that does not contradict [...] and if God could have these things and he knew otherwise, as has been devised [...] we must not constrain in this way, the divine power and knowledge. " [54] In this way science is conceived, not in its value as an explanation of the phenomena on the basis of an absolute principle, but as descriptive of appearances sensitive traced to hypothetical principles, without expecting to achieve genuine knowledge of physical reality.

Certainly Galileo never shared such a position, but it was thought that those words made by Simplicio said they intended to be a mockery of the Pope: in fact, Galileo found it necessary that, just at the conclusion of the Dialogue, it shows the position of Urban VIII of the three main characters, logically only non-Copernican Simplicio, when pressed by his interlocutors, he could expose it, wanting to Galileo - according to the wording of the decree of 1616 - or at least mitigate, deny the feeling that the Copernican system was intended by him to be the 'only basis for each correct cosmological interpretation.

[Edit] The process, apostasy and condemnation Main articles: The trial of Galileo Galilei es: Judgement of condemnation of Galileo Galilei.

John CiampoliL'opera received many accolades, including those of Benedetto Castelli, Fulgenzio Micanzio, collaborator and biographer Paolo Sarpi, and Tommaso Campanella, in August, but already spread the rumors of a ban of the book: the Master of Sacred Nicholas Riccardi Palace on July 25 he wrote to the inquisitor of Florence Clement Egidi by order of the Pope's book was no longer to be widespread, Aug. 7 asking him to trace the copies already sold and seizure.

For his part, Ambassador Francesco Niccolini in Florence at the court on September 5 reported that he conferred with the Pope who "broke into a lot of anger, and suddenly I said ch'anche our Galilei had to enter warp where it ought, and materials in the most serious and most dangerous in these times we Had inspire. I replied that the Sr Galilei had printed without the approval of these [...] He said his ministers with the same theatrics he and Ciampoli [55] had worked around that in these subjects in the [...] S.to Office had no more than criticize, and then call to cancel. "

On September 23, urging the Roman Inquisition to Galileo the Florentine to notify the order to "appear in Rome before the end of October before the Commissioner-General of the Inquisition." Several were his attempts to avoid in Rome: on 1 January 1633, Cardinal Antonio Barberini Egidi Clement wrote to the inquisitor of Florence that the Holy Office would not "tolerate these fintioni, nor conceal his coming here," threatening " et take him take him to the prison of this Supreme Court, also linked with irons. " [56] Without the protection of the Grand Duke of Tuscany, who do not intend to shock with the Church, February 13, 1633 Galilei arrived in Rome.

Ambassador Niccolini was given permission to host the scientist, pending the trial began, and learned from the Pope himself to Galileo, 'well if it says it will treat the hypothetical movement of the earth, however, the actual arguments in the report, I talked and talked and then allegedly conclusively, and had ch'anche contravene the order given to her in 1616 by Cardinal Bellarmine Sr. [57]

For the first time you become aware of an order - or precept - that the notice would Bellarmine to Galileo quell'ormai far in 1616. Galileo did not seem worried indeed, as he wrote to Geri Bocchineri March 5, had the conviction that "the charges decreasing artifact, and some yet to be completely gone too obvious for their vanity, which you can believe that another reduction adversely that there are still standing, so I hope they still have to finish in the same way. " The ambassador had the opposite view and urged Galileo to not make the mistake of defending his views before the Court of Copernicus, "in order to finish it as soon as possible." [58]

Joseph-Nicolas Robert-Fleury: The process of GalileiIl trial began April 12, with the first examination of Galileo, which the inspector inquisitor, the Dominican Vincent spotted confronted him that he has received February 26, 1616, a "precept" [59] with which Cardinal Bellarmine would formally abandon the Copernican theory, not to support it in any way and do not teach it.

That rule, if it was actually shown to Galileo in February 1616 and if this is even a built in fake art, not contain any signature or of Bellarmine, or witnesses, or of Galileo himself, who denied having aware, but had only received a voice from Bellarmine notification of the Congregation, according to which the views of the motion of the Earth "to be repugnant to Holy Scriptures and only admitted ex suppositione 'and' ex suppositione could be detained and servirsen. In the following May he received the famous letter of Bellarmine in which "contains the doctrine attributed to Copernicus that the earth moves around the sun and the sun is in the center of the world without moving from east to west, is contrary to Holy Scriptures, and therefore we can not defend or hold. " The letter did not explicitly mention the prohibition against teaching the Copernican doctrine, even within the limits of a scientific hypothesis and strength of this indirect authorization, as well as the explicit, but only verbal, received in February, he wrote his Dialogue Concerning the Two Chief World Systems, is no coincidence that obtaining the required imprimatur of ecclesiastical authority.

The interrogator pressed, however, asking if there were witnesses present at the time of notification of the 'precept' and Galileo, responding not to remember the mistake of mentioning the word obligation, arguing that "not in any way contravene then precept. " The Inquisitor, verbalizing, he took to the notice of the alleged obligation and asked him if he remembered how and by whom he had been given notice and Galileo: "I was fitting that the precept that I could not hold or defend, and that there can be no Fusse still teach. "

For the interrogator it was time to establish that Galileo published Dialogue, had circumvented the order not to treat the Copernican theory, deceiving the ecclesiastical censors: the question of whether he had shown the precept of the Master of the Sacred Palace before being given 'imprimatur, Galileo not only admitted that he said "anything of sodetto precept" since to argue, "in that book I show the opposite of that opinion of Copernicus, and that the reasons for it are invalid and Copernicus inconclusive. " [60]

Galileo GoyaCon seen from this obvious falsehood, ended the first interrogation, Galileo was detained, "though under close surveillance," in three rooms of the palace of the Inquisition, "with large and free right to walk." [61]

The Congregation of the Holy Office, which met on April 21, stated that in Galileo's Dialogue "will defend, es'insegni riprouata opinion, and condemned by the Church, et, however, that the author makes yet suspicion of keeping it." [62] Galileo questioned again on April 30, said he had reread his Dialogue in those days, "almost like nova and writing of another author," admitting that a reader not intimately familiar with the author would have had the impression that he wanted to confirm the Copernican theory. Apologizing for the Inquisitor, "an error so alien to my intention," offered to "resume the arguments already made in favor of that false opinion and damage, and refute most effective in that way that God blessed me will be given." [63]

The full submission of the scientist and ill health made him get permission to leave the palace of the Inquisition and return to the embassy in Florence. In the next Costituto 10 May explained that the letter of Bellarmine - where the ban was not required to teach the Copernican doctrine - had made him forget the precept where instead the ban was ordered, and justified the "worsening" of his dialogue as due solely the "vain ambition to appear witty and welcomed addition to the common de 'popular writers, from the pen inavertentemente scorsomi', declaring once again ready to correct his book.

To conclude the process, the Inquisition was to examine the sincerity of the statement of Galileo's "do not hold the damned opinion" to this end, the Congregation on June 16 stated that "Galileo was questioned about his intention, and also imposed the torture if he had sustained, after abjuration de Vehement in front of the congregation, was sentenced to imprisonment at the will of the Holy Congregation, with the injunction not to treat more, no writing or verbally, the mobility of the Earth and the Sun on the property '. [64]

On June 21, Galileo was interrogated for the last time, when asked if still held, or had taken in the past, and for how long, the theory of the centrality of the sun, Galileo said that he had once considered the views of Ptolemy and Copernicus both "disputable, because either one or the other could be true in nature," but after the ban in 1616, claimed to hold, since then, and still is, "for most true and undoubted opinion of Ptolemy." Asked to explain why he had then defended the opinion of Copernicus in his Dialogue, Galileo said that he wanted only to explain why the two views, believing that no demonstration had strength, so that "to proceed with safety have recourse to the determination of the most sublime doctrines. " The insistence of the inquisitor to tell the truth, otherwise he would act "against him with the appropriate remedies in law and fact ', Galileo denied that he ever supported the opinion of Copernicus," moreover, I am here in their hands, little face that he likes. " Explicit threat of torture, Galileo said only: "I'm here to do the obedience, and I have held this opinion after the determination made, as I said." The minutes of Costituto concludes that "not being able to have anything else running the decree, had his signature, was sent back to his place." [65]

"Sun is the center of the world and imobile of local motion, the proposition is false and absurd in philosophy and formally heretical, to be expressly contrary to Holy Scripture;

that the Earth is not the center of the world or imobile, but it moves eziandio of diurnal motion, the proposition is equally absurd and false in philosophy, theology and considered to minus incorrect fide "

[Edit] Dialogues matematicheSe the legend of the sentence of Galileo, "and yet it moves", which was delivered just after the recantation, it serves to suggest his conviction intact the validity of the Copernican model, the conclusion of the process marked the defeat of his program at which the new scientific methodology, based on observation of the facts and their rigorous experimental test - against the old science that produces' experiences as made and satisfying their need without ever having seen or done or [70] - and against the prejudices of common sense, which often suggests any real appearance: a program of scientific renewal, which taught "not to have more confidence in their government, tradition and common sense," he wanted to "teach to think." [71]

Dialogues matematicheLa sentence included a prison term at the discretion of the Inquisition and the obligation to act for three years, once a week, the penitential psalms. The penalty was mitigated in the literal facts: in the living room consisted of forced captivity for five months at the Roman residence of the Grand Duke of Tuscany, Francesco Niccolini, in Trinita dei Monti and here in the house of the Archbishop Ascanio Piccolomini in Siena, at the request of these. As for the penitential psalms, Galileo undertook to recite, with the consent of the Church, his daughter Maria Celeste [72]. At the Siena Piccolomini Galileo favored allowing the city to meet with personality and scientific debate. Following an anonymous letter that denounced the actions of the archbishop and of Galileo himself, [73] the Holy Office provident, receiving the same request made earlier by Galileo, on the border in the isolated villa ("The Jewel") that the scientist had in the campaign of Arcetri [74].

The order of 1 December 1633 is formally called Galileo to "be alone, do not call or receive any, for the time at the discretion of His Holiness." [75] Only the family could visit him, with the prior authorization: even For this reason he was particularly painful loss of his daughter Sister Maria Celeste, the one with which he maintained ties, which occurred April 2, 1634.

He could, however, maintain correspondence with friends and admirers, even outside Italy: to Elia Diodati, in Paris, wrote March 7, 1634, of consoling her misfortunes that "envy and malice against me car" with the statement that " the shame lies above the traitors and made the most sublime degree of ignorance. " From the King James Version translation of the Latin he learned that Matt was doing in Strasbourg Bernegger of his Dialogue, which was released a year later in Holland, and told him to "such a peripatetic Antonio Rocco [...] pure, and very remote dall'intender nothing or mathematics or astronomy "he wrote in Venice" and sarcastic insults "against him.

This and other letters, show how little Galileo Copernicus had renounced their beliefs, but now he was involved in the drafting of a new work, which will be the last and his best, published in Leiden, the Netherlands [76] Discourses and mathematical demonstrations concerning two new sciences. It is still a dialogue that takes place between the same three protagonists of the previous Dialogue of Two Chief World Systems - Sagredo, Salviati and Simplicio - again in four days.

On the first day, Galileo is the strength of materials: the varying resistance should be linked to the structure of the particular matter and Galileo, while not claiming to arrive at an explanation of the problem, deals with the atomistic interpretation of Democritus, considering a hypothesis capable of to account for physical phenomena. In particular, the possibility of the existence of the vacuum - provided by Democritus - is considered a serious scientific hypothesis and a vacuum - that nell'inesistenza of any means capable of resisting - Galileo rightly maintains that all bodies' flows with equal speed, "in opposition to modern science believed that the impossibility of motion in a vacuum.

After treating the static and the lever on the second day, in the last two deals with the dynamics, establishing uniform laws of motion of naturally accelerated motion and uniformly accelerated motion.

Of 1640 is the decisive contribution of Galileo, who encouraged his pupil Bonaventura Cavalieri to develop ideas on the master and other indivisible assembling them in a geometric method (method of indivisible), to determine area and volume: This method represents a milestone for the future development of calculus.

In 1757, Giuseppe Baretti, in his reconstruction, he would have created the legend of a Galileo who once stood up and hit the ground and murmured: "And yet it moves!" [78]. This phrase is not contained in any contemporary document, but in time was considered true, probably because of its suggestive value, so that the Berthold Brecht in "The Life of Galileo", Galileo dedicated to theatrical work to which he devoted himself long.

Over the following centuries, the Church changed its position on Galileo: the Holy Office in 1734 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 to books that taught the Earth's motion, thereby formalizing what was already in fact had Pope Alexander VII in 1664 with the withdrawal of the decree of 1616. The final authorization to the teaching of motion of the Earth and the immobility of the Sun arrived with a decree of the Sacred Congregation of the Inquisition approved by Pope Pius VII September 25, 1822. In 1968 Pope Paul VI did start the review process.

Beyond the historical analysis on the legal and moral condemnation of Galileo, the epistemological questions and biblical hermeneutics that were at the heart of the process were the subject of consideration by many modern thinkers, who often cited the story of Galileo to illustrate - sometimes in deliberately paradoxical terms - their thoughts on these issues. For example, the Austrian philosopher Paul Feyerabend, a supporter of an anarchist theory of knowledge, wrote:

"The Church of Galileo was much more faithful to reason than Galileo himself, and took into consideration the ethical and social consequences of Galileo's doctrine. Its verdict against Galileo was rational and just, and only for reasons of political expediency can be legitimized the review [79] "

(P. Feyerabend, Wider den Methodenzwang, FrankfurtM / Main 1976, p. 206.)

In the opposite direction has been expressed in recent years, John Paul II:

"Like most of his opponents, Galileo makes no distinction between what is the scientific approach to natural phenomena and reflection on the nature of a philosophical, which it generally draws. That's why he rejected the suggestion that he had been given to present the Copernican system as a hypothesis, as long as it was not confirmed by irrefutable evidence. That was, however, a requirement of the experimental method of which he was the brilliant founder. [...] The problem is that the theologians of the time was then placed over the compatibility of heliocentrism and Scripture. Thus the new science, its methods and the freedom of research that they assume, obliged theologians to question the criteria for their interpretation of Scripture. Most could not do it. Paradoxically, Galileo, a sincere believer, showed himself on this point, most insightful theologians of his opponents. "

(John Paul II to the members of the Pontifical Academy of Sciences, October 31, 1992 [80])

[Edit] Galileo and science

Galileo's tomb in Santa CroceLa crucial importance that the figure of Galileo about his role in the recovery of the scientific method developed in the Hellenistic period and then almost forgotten, thanks to his careful study of several scientific works, particularly those of Archimedes.

Its importance for the rebirth of science in general and physics in particular is attributable to the discoveries made by testing, such as, for example, the principle of relativity, the discovery of the four main moons of Jupiter, called the Galilean satellites ( Io, Europa, Ganymede and Callisto), the principle of inertia and the speed of falling bodies is the same for all bodies, regardless of weight or the material (an idea, the latter, which actually dates back to John Philoponus, but had apparently been forgotten).

Galileo is also interested in the problem of measuring the speed of light: in fact, he sensed that this could not be infinite, but his attempts were fruitless to measure it.

Reflecting on the motions along inclined planes discovered the problem of minimum time in the fall of material bodies, and studied various trajectories, including the spiral paraboloid and the cycloid.

As part of his research he discovered the first mathematical properties of infinity: one part is equal to the whole.

Also led his student, Bonaventura Cavalieri, to study the indivisible, realizing the consequences of calculus in the study of motion.

On the issue of mathematics as an investigative tool of nature, wrote:

"... this great book [of nature], which stands continually open before our eyes (I mean the universe), it can not be understood without first learns to comprehend the language and know the characters or what is written. It is written in mathematical language, and its characters are triangles, circles and other geometric figures, without which means it is humanly impossible to understand a word without these one is wandering through a dark labyrinth. "

(Galileo Galilei, Opere VI)

To Galileo, mathematics is therefore the ultimate tool in the investigation of nature. In that regard, he distinguished between primary qualities of bodies, sharp objects of scientific inquiry as they apply to the mathematical calculation, and secondary qualities (eg. Smells, tastes, judgments of taste, etc..), Who can not be studied in a scientific manner.

The Galilean method consists of two main aspects:

meaningful experience, ie the experiment, which can be practically accomplished, or only the abstract ("mental experience"), but must always follow a careful theoretical formulation, which is a hypothesis that can guide the experience so it does not give arbitrary results;

required proof, which is a rigorous mathematical analysis of the results and experience, which is able to draw from this in any way necessary and therefore not debatable, and further evaluation, with further experience, or the so-called trial, which is the 'experiment with concrete which is always verified the findings of any theoretical formulation.

[Edit] Inventions between stars and bodies in motion

Phases of the Moon 1616Nel designed by Galileo in the course of his life, Galileo was originally proposed some inventions, useful not only in the study of stars, but also of bodies in motion:

the inclined plane to study the motion of bodies;

hydrostatic balance to measure the density of bodies;

the thermoscope to measure changes in air density as a function of temperature;

a car driven by animal power to raise water from deep wells;

the proportional compass to solve problems in mathematics and geometry;

the celatone, an instrument to measure longitude at sea using the satellites of Jupiter;

the jovilabe, a tool to calculate the relative positions of Earth and Jupiter;

the helioscope, a tool that allows you to observe the Sun

micrometer [81] [82] [83] a device mounted on the telescope can measure, simultaneously observing with a telescope, how far away each satellite from the planet.

[Edit] parabolic motions, circular motions and surface area of ​​the parabolic cerchioGli studies of the movements, commuter and long inclined planes allowed Galileo to discover the universality of the motion.

Studies on the movement of the polished stone ball along the inclined planes and measures such as moving objects increase and decrease their speed enabled Galileo to discover that their trajectories were parables. By processing the data with a mathematical method was discovered that, wanting to throw a cannon ball as far as possible, the inclination of the barrel should be 45 °. Varying up or down the slope, for the same values, the range is the same: the trajectory of 40 ° and 50 ° that have the same range.

Studying, again, as if the stones vary linked along a string, or falling as they move along an inclined plane, Galileo discovered that they were examples of the same physical quantity: the motion. Thus was born the first example of universality in physics: all movements of material bodies are due to a single source. It stems from the strength that gives life to the motion and friction that opposes it. The sum of these two forces come speed and acceleration, with strictly conserved quantity such as, for example, the amount of linear motion.

The rectilinear and the circular can be composed and decomposed in different ways. It is then possible to produce a variety of parabolic motion: all examples of motion. The universality of the motion, however, undermines the squaring of the circle, a concept that has deep roots.

The circle is the perfect geometric figure and was associated with the sky, while the lines and then the geometric shape of the square to the natural world: it was so obvious, before Galileo, feel unable to get a square from a circle and vice versa. Galileo, however, designed the "proportional compass, the implementation of which is assigned to the artisan of his trust, Marcantonio Mazzoleni, with whom he can turn a circle of any length in the four sides of a square. The instrument consisted of two rulers connected by a metal hinge.

The obvious conclusion was that there was nothing in the circular movement of the privileged and no difference from all other types of motion, Galileo was nevertheless convinced that the planetary orbits were not circles and ellipses, as Kepler discovered - God to make the world, has chosen for the orbits perfect geometric shapes: circles and these are not ellipses. Material bodies are moving because there is a resultant force acting on them. The speeds and accelerations are determined by the sum of the forces positive and negative ones, usually the friction, which, taking account of all the conservation laws, determines the motion said.

[Edit] The principle of inerziaFacendo experiments with the pendulum and inclined plane, Galileo arrived at the discovery of the role of friction in the motion of bodies and the formulation of the principle of inertia, then codified by Isaac Newton in the first law of motion: a body in motion a constant velocity remains in this state in the absence of friction, or even in a system without friction, a body will remain in its state of motion or rest if there are no external forces on it are involved.

[Edit] The pendulum

The chandelier that since 1587 has taken the place of the "lamp of Galileo" in the cathedral of Pisa.Un 'other discovery Galilean implemented in 1583 is the isochrone of small oscillations of a pendulum. On this issue there is also a legend that the idea would have occurred to observing the oscillations of a lamp suspended in the nave of the Cathedral of Pisa. The lamp is commonly referred to as the lamp of Galileo, it is not the view from the young scientist, as she was built in 1587 by Vincenzo Possenti Domenico, then a few years after Galileo's insight on the pendulum. The lamp instead was seen swinging, more spartan and small, is now kept in near Monumental Cemetery in the Chapel Aulla.

This tool is simply composed of a stone tied to a thin, inextensible, if this has a length of one meter, we obtain an oscillation period of approximately two seconds.

The periodicity in the motion of the pendulum was not the only observation of Galileo: he noticed, in fact, that for a given length of wire, and regardless of the weight of the stone, the oscillation takes the same amount of time to vary the amplitude, provided that this is not excessive.

The periodic law of the pendulum for small oscillations, and neglecting the effects of friction, is in fact:

where T is the oscillation period, the length of the wire and g the acceleration due to gravity. You may notice that the period of oscillation is independent of the mass (in the approximation valid for small oscillations) maximum amplitude of the oscillation itself, ie the angle between the initial position and the central minimum.

To swing a pendulum means the movement of small weights of the pendulum from the initial point of oscillation (from which the pendulum starts with zero speed) at the same point of departure through the other end, then the movement from one extreme to another is a half-swing.

[Edit] The scale idrostaticaLa Bilancetta was written by Galileo in 1586, when he was still awaiting the assignment at Pisa University.

The work, published posthumously, describes the invention of the hydrostatic balance:

o the scale for fabric, piglisi a straight edge at least two arms, and the more accurate will be longer than the instrument, and Divide in the middle, where the sheer is raised [the focus], then they're in the arms aggiustino ' balance, with the thin one that weighed more, and over the arms of a note the words [where territories] the counterweight of nano metals will be easier when weighed nell'aqqua, warning of the purest metals that weigh you are. (The Works)

It also describes how you get the specific gravity of a body of water as PS:

In The Bilancetta are then two tables showing thirty-nine specific weights of precious metals and genuine, which he determined experimentally with a rigorous mathematical method: The measurements are very accurate and comparable with modern values.

This is the first detailed list of specific gravities derived analytically and experimentally.

[Edit] Slopes, acceleration of gravity and conservation dell'energiaGalileo was able to determine the value of the acceleration of gravity, ie the size which governs the motion of bodies falling toward the center of the Earth, studying the fall of the long ball well-polished an inclined plane, also well polished. Since the motion of the ball depends on the angle of inclination of the plane, with simple measurements at different angles was able to get a value slightly lower than that known today (9.80665 m/s2), due to systematic errors due to friction which could not be completely eliminated.

Said v the velocity of the ball along the inclined plane, the velocity parallel to the horizontal plane is given by

v cos θ

while the perpendicular, which is useful for the determination of gravity, is

v sin θ

With these studies, Galileo discovered that a phenomenon is a direct consequence of conservation of mechanical energy: by putting another beside the first inclined plane on which to trace the ball, he discovered that in fact it stops at the same height to start. However, the concept of energy is still present in the physics of the seventeenth century and only with the development, over a century later, the classical mechanics of Newton arrives at the precise formulation of the concept.

[Edit] The speed of luceGalileo was certainly among the first to realize that the speed of light was not infinite, and devised an experiment to obtain the first measurement

His idea was to bring on a hill with a lantern covered with a cloth and then lift the cloth by launching a signal to a friend to post on another hill a mile away. His friend, as soon as he saw the signal, then raised his banner would allow Galileo to record the time taken by light to reach the next hill and go back. A precise measurement of this time would allow to measure the speed of light. However, the attempt was unsuccessful: it is considered that the light takes only one hundred thousandth of a second to travel a distance of 3 km.

The first measurement of the speed of light was the work, in 1675, Danish astronomer Rømer, based on accurate measurement of delays of the eclipses of Jupiter's moon Io.

[Edit] Science and teologiaGalilei in the early years of his astronomical discoveries, is not explicitly poses the question of the theological implications of the discoveries made with his telescope and how that universe immense, full of irregularities, corruptible, not perfect spheres and without no center could be in conflict with the vision of the world, defended by the Catholic Church. For example, notice how the "Starry Messenger," in which these findings were reported for the first time ever, the problem between science and faith was not even discussed or mentioned.

That question was posed to Galileo by the strong reactions and controversies that over the years were aroused by his discoveries and the way to investigate, based on direct reading of the book of nature, without recourse to authority, it was Aristotle or theological.

He was forced to intervene on the question of the relationship between science and faith, the concept of truth, with the main purpose of defending the autonomy of science and also to warn the Church of the harm that would come to the Christian religion if he insisted on using Holy Scripture in matters of natural science that scientific progress would show clearly false.

The first document in which Galileo addressed this question was his letter to Father Benedetto Castelli, written in 1613 it was also the episode where the biblical Joshua, who stopped the course of the sun. In this letter Galileo explained his position as a Christian and a scientist who claimed the autonomy of science from religion and concluded that science and faith does not interfere with each other, since they worked on separate floors, faith spoke and worked on the metaphysical plane, while science on the physical.

Astronomy has nothing to do with the Bible

"[...] Propositions which, even as, dettante the Holy Spirit in this way were proffered by the sacred writers to sit down to the ability of the common people very rude and unruly [...]. "

(Galileo Galilei, "Letter to Madame Christina of Lorraine Grand Duchess of Tuscany)

That is, Scripture, inspired by the Holy Spirit, which therefore can not lie, he spoke the ancient language of that time to understand. But

'[...] In the disputes of the natural problems are not expected to begin by the authority of places of Scripture, but from sense experience and the necessary proof, because, proceeding equally from the divine Word the Holy Scripture and nature, that as dictated by the Holy Spirit, as a very faithful executor of the orders of God [...]. "

(Galileo Galilei, "Letter to Madame Christina of Lorraine Grand Duchess of Tuscany)

So

"... It seems that the effects of natural or sense experience puts us before the eyes or the necessary proofs we conclude, should not in any account be undermined by place of Scripture that they had different words likeness, then that any of Scripture that is linked to such stringent obligations com'ogni effect of nature. [84] "

Hence, the Galilean vision according to which there are two "books" that are able to reveal the same truth that comes from God: one is the Bible, which has essentially the value of redemption and salvation of the soul, written in terms that match view widespread in the populace, and therefore requires careful interpretation as to the allegations relating to the description of natural phenomena that are described in it a little. The other is the "great book of Nature written in mathematical characters", [85] the universe, which should be read in a scientific manner and therefore should not be postponed to the first but to be properly interpreted, should be studied with the tools the same God of the Bible with us, "meaning", "discourse" and "intellect." [86]

'[...] I believe that the authority of Scripture had only intended to persuade the men to those articles and propositions, which are the needed requirements for their health, and overcoming all human speech, I could not for science or other for another half farcis credible, that the mouth of the same Holy Spirit. But that same God who has endowed us with senses, speech and intellect, has intended, by postponing the use of these, give us the news in any other way than for we can achieve, I think it is necessary to believe, and maximum in those sciences of which a small particle and split it into conclusions stated in the Scriptures, what exactly is astronomy, of which there is something so small part, that there are not even named the planets. But if the sacred writers were the first car thought to persuade the people and the provisions de'corpi celestial movements, not so little avrebero Treaty, which is nothing in comparison to the infinite high and admirable conclusions which are competing in this science. "

(Galileo Galilei, "Letter to Father Benedetto Castelli")

The letter to Father Castelli sparked controversy, however violent and sarcastic by the Florentine clergy, totally conservative, such that Galileo was forced to make public displays of Catholicism and even to hasten to Rome to defend his work in courtly circles of believing scientist . After decades of controversy and a process, the Church forced Galileo to recant, censured and condemned his findings to index the works of Copernicus and Galileo until 1823.

In 1757 the Congregation of the Holy Office rehabilitate the figure of Galileo Galileo recognizing true theories. Only in 1992 Pope John Paul II, who had requested in 1979 a review of "Galileo", withdrew his condemnation of the Catholic Church to the scientist, publicly acknowledged the validity and truth of scientific theories of Galileo Galilei and apologized, by the Church , for having unjustly condemned not only the founder of modern science but arguably one of the best minds, brilliant and sharp the last millennium.

[Edit] Galileo and the art

2000-Italian lire banknote in circulation from 1973 to 1983 depicting Galileo.Ludovico Cardi, said Cigoli, Florence, was a painter at the time of Galileo, at one point in his life to defend his actions, asked for help to his friend Galileo : was, in fact, to defend themselves from attacks of those who believed the sculpture than to painting, as has the gift of three-dimensionality, at the expense of simply two-dimensional painting. Galileo responded with a letter, dated June 26, 1612. He, first of all, it provides an incredible anticipation of the modern distinction between optical and tactile values: the statue, with its three dimensions, he deceives the sense of touch, while the painting in two dimensions, he deceives the sense of sight. From what gives the painter Galilei greater expressive power than the sculptor, since the former is capable of producing emotions much better than the second.

"To say that then that the sculptors, that nature makes men of sculpture and painting, I would say that she is no less carved paintings, because she's carved and colored, ... "

(Works XI)

He adds:

"For, as the means, co 'which mimics, are far from things to imitate, imitation is the more wonderful. "

(Works XI)

In art, as in poetry and music, said Galileo, that the emotional power that can be transmitted. And this description ignores the stark reality.

[Edit] musicaIl Galilei and Galileo's father was a musician (lute player and composer) and music theorist best known in his day. Indirectly, Galileo provided a fundamental contribution to the understanding of acoustic phenomena, having first understood the importance of oscillatory phenomena and the concept of frequency.

In the aforementioned letter of Galileo to Lodovico Cardi is this sentence:

"We do not admire a musician, who singing and representing the court and the passions of a lover we moved with compassion, much more than it did when crying? ... And much admired him, if silent, with only one instrument, with crudities and accents pathetic music, what did ... "

(Works XI)o understand the meaning, it must be held towards the end of the sixteenth century had opened in the Italian music a dispute between supporters of the "second circulation" or "new practice" of music that would later gave birth to the genre of melodrama and the oratory and the "first practical" in Palestrina was considered the most typical member. For these, the relationship between music and text was realized mainly in so-called madrigals, onomatopoeic effects or variously alluding to words like "murmur", "tremble," "down", "breath" and the like. According to the musicians of the second practice, however, the music itself was likely to evoke the emotions and the movements of the soul: each had a specific musical interval evocative, and between text and music had to exist a perfect matching of effects: correspondence much easier to be realized in monody and in polyphony. The sentence of Galileo would testify so his membership in the new musical aesthetics, according to which a melody (well made, and effectively enforced) is capable of arousing strong emotions in the listener even in the absence of a text. In fact, this position was supported by the circle of musicians that owned his father, Vincenzo Galilei. The idea that instrumental music should be just as expressive of vocal music was shown some years later by Girolamo Frescobaldi in the introduction to the First Book of Toccatas and Matches (1637).

It should be noted, however, that the authenticity of the letter to Lodovico Cardi, of which there is only one copy of a few decades back, is uncertain; also the occasional reference to the music serves only as an argument to support the argument that painting not less than the sculpture.