Galileo was born on on February 15th, 1564 in Pisa. Its childhood and its adolescence proceed between Florence and Pisa. His/her father, original and rather famous musician, author of a Dialog on the old and modern music, were interested in the rebirth of the musical forms inherited the Greek classicism. After having started into 1581 of the studies of medicine at the university of Pisa, Galileo under investigation devotes mathematics and philosophy; in 1585, it leaves the university, without diploma.

Science at the end of XVIe century

The university which is used as framework at the years of training of the Galileo young person functions on a largely widespread model in Europe, resting on a division of the knowledge in two fundamental branches: mathematics and philosophy.

Astronomy and mathematics
The purpose of the mathematical knowledge having been born with astronomy, the activity of the mathematician-astronomer is not the explanation of the celestial phenomena, but well rather their prediction. The ambition of the astronomer is limited to seek the combinations (more or less complicated) of circular motions which make it possible to describe the apparent movement of the stars, such as one observes it since the Earth. The activity of the mathematician rests on the idea that, under the apparent disorder of the phenomena, beyond the erratic course of planets (etymologically, the planets are “wandering stars”), it exists a quite particular hidden order, which can be represented using circular motions, images of a form of perfection.  

Philosophy
The teaching of this matter is also exempted by the European universities. “Natural philosophy” is the true science of the sky, charged to explain the phenomena. Based mainly on the doctrines of Aristote and, more precisely, on its theory of the movement, this discipline rests, very schematically, on the distinction between “natural” movement and “violent” movement.  

The world according to Aristote
Any body has a “natural” movement which is clean for him, expressing its tendency to join its “natural” place, which is entirely fixed by the nature of the body in question; having joined its natural place, the body remains motionless there. Thus the Earth has it for natural place, from its nature even of material body, the center of the Universe; its natural movement is to go towards this center, where it resides as much as nothing comes to dislodge about it. The natural movement of the celestial bodies, supposed to be of a nonmaterial species, is a circular motion around the center of the Universe. It is necessary to stress the importance of the part played in Aristotelian physics by the concept of “place”: each object occupies a place which is clean for him; Aristotelian space is not thus in no homogeneous way, since its various points can be indifferently occupied by any object. It will go from there differently in new physics, that of Galileo.  

To the “natural” movement, which does not require any external agent, is opposed the “violent” movement, opposite with the nature of the body which is animated by it and which can thus exist only by the effect of a driving agent. A cart, for example, which moves along a road has a contrary movement with its nature of material object (which would encourage it to join the center of the Universe); this movement is thus violent and it is the horse which is the driving agent. More precisely, the speed of an animated object of a violent movement is proportional to the “force” spent by the engine responsible for the movement. What one could call the “basic principle of Aristotelian dynamics” thus states as follows: a force produces a speed which is proportional for him; or: the speed of a body is worthy of the “force” that one prints to him. It should be noted that this basic principle, which will be given up by the new physics (where it is the acceleration and not the speed of a body which is proportional to the force which is exerted on him), is completely in conformity with the “common direction”: the more the horse draws on the cart, the more it goes quickly; in addition, the cart does not move if one does not exert any force on it!  

Critics of the Aristotelian system

It should not be believed that the physics of Aristote is universally accepted. Many are those which, at the beginning of the XVII E century, blame the Aristotelian teaching exempted by the University, taking again on their account certain objections formulated during the previous centuries.  

In XIVe century, the members of the school of Paris dispute already the cogency of this theory of the movement, and more particularly of the movement of the projectiles. At the same time, Nicole Oresme protests against the idea according to which the movement of planets can be induced of their apparent movement since the Earth, presumedly motionless: on the contrary, according to him, the stars would be motionless, and the Earth moving.  

The Church, guarantee of the aristotelism
For a long time these criticisms hardly find to be expressed elsewhere than in restricted circles, so much the authority of Aristote is large; more especially as the Church, principal political and cultural power of the western world, after having fought Aristotelian cosmology, finally endorsed it to the XIII E century. The idea that the Earth is in the center of the world grants very well with the fact that God was made man precisely in this place. To question the immobility of the Earth thus amounts fighting the Church and its dogma. It is only at the beginning of the XVII E century that the criticism of Aristote takes its true rise, mainly thanks to printing works and with the diffusion of the books which beat in breach the monopoly of the University as a source of knowing. Of aucuns then dare to formulate new assumptions, but it is that of Copernic which will play a fundamental role in the development of the new physics.  

The system of Copernic
In 1543 appears the work of Nicolas Copernic Of revolutionibus orbium coelestium, in which it exposes his heliocentric “assumption”. Copernic, which endeavoured to explain the movement of planets, within the framework of the Aristotelian theory of a motionless Ground, using combinations of circular motions, like wanted it the tradition, ends up losing courage in front of the mathematical complications met. He realizes whereas, while placing the center of the world not in the center of the Earth but in the center of the Sun, it is easier to bring back the movement of planets to combinations of simple movements.  

This work, initially unperceived past, in particular with the eyes of the Church, will be studied thereafter and taken with serious by a certain number of scientists, such Giordano Bruno, Tycho Brahe and Johannes Kepler, who, by developing the ideas of Copernic, will establish the tradition of what will be called the “system copernician”. However, the arguments which they presented in support of the heliocentric system rested not on a mathematical or experimental study of the movement of the bodies - as it will be the case in Galileo -, but on a design of the world whom one can describe as metaphysics, founded on the ideas of “central fire” or of “solar force”.

Galileo, which - his letters prove it - is informed of work of Copernic, however exempts a teaching of astronomy rigorously in conformity with the official programs. The Church not having yet openly taken position against the heliocentric assumption, this reserve is explained only in only one way: Galileo is not persuaded yet to hold a reasonable evidence of reality of the earthmoving. However, the things change radically starting from the publication, in 1610, of its work Sidereus Nuncius (the celestial Message or the Messenger of stars), in which it takes makes and causes for the partisans of Copernic, which it will not cease from now on making.  

A decisive discovery: glasses
The reversal of Galileo is indeed to put in keeping with its capital discovered of the telescope. According to the account that it makes some in the celestial Message, it had wind in 1609 of the invention, in the Netherlands, of an optical system able to make appear closer to the distant objects. It immediately realizes of the importance which it can have for the navigators; having obtained some information on the new object, he undertakes to build one of them, thinking of being able to extremely expensive sell it to the ship-owners of Venice. Thus at the end of the year 1609 it presents to the Senate of the city an instrument making it possible to distinguish from the ships, clearly and in detail, two hours before one can detect their presence with the naked eye. Its invention is not retained, and Galileo is tiny room to make his glasses a personal use, that of which it will not be deprived. On December 1st, 1609, it begins a series of observations of the Moon.  

He then sees, of his own eyes, that “the Moon is not surrounded by a smooth and polished surface , but that it is broken and unequal just like the surface of the Earth, covered with high rises and deep cavities and anfractuosities” (Sidereus Nuncius). Then “the seventh day of January, the year 1610, at 1 o'clock in the night, while I explored the sky, by means of the glasses, Jupiter was presented in my eyes: to me being built an instrument of utmost precision, I saw (what arrived never to me previously, in consequence of the weakness of the other glasses) three small stars”, in other words, the satellites of Jupiter in revolution around planet, just like the Moon around the Earth. Proof that the Earth is not the center of all the celestial movements and that its nature does not differ from that of Jupiter.  

End of the geocentrism
Such is well this “message” which the stars send: there is no difference in nature between the Earth and the celestial objects; those are not more, nor less, perfect that the Earth. The natural laws which are worth on Earth (in the sublunary world, as one says then) are also worth in the skies: nothing any more justifies the geocentrism, “privilege” which the Earth enjoys. What reveals the glasses is thus, on the one hand, in contradiction with the theory of the motionless Earth placed at the center of the Universe and, on the other hand, in accordance with the assumption according to which the Earth is only one planet among others, turning with them and like them around the Sun. The two assumptions, that of traditional physics and that of Copernic, are not from now on equivalent any more: only the heliocentric assumption is in conformity with the observation. The conviction of Galileo thus rests on the experimental obviousness and either, like that of the defenders of Copernic, on reasons metaphysics.

A new “system of the world”

At once, Galileo becomes a famous man. Its observations and the conclusions that it drew some are the subject of animated debates. He which, hitherto, had been held some with the most strict orthodoxy puts to teach the theory copernician - apparently without the Venetian authorities, which make the law with Padoue, not taking shade of it. But Galileo for a long time wishes to turn over to Florence, in his native area. Also, when a post of professor of mathematics at the university of Pisa is proposed to him in 1610, accepts it without realizing perhaps that the “liberalism” of the Venetian authorities does not have course in Tuscany.  

If Galileo accepts the offer, it is also that he hopes to lay out of more than time to write his “System of the world”, where it intends to expose work on the dynamics to which it was devoted during the eighteen last years to Padoue. The drafting of this book, unceasingly pushed back, became necessary after the publication of the celestial Message. Indeed, eager to convince his contemporaries of the veracity of the assumption copernician, Galileo must now render comprehensible and to explain why one could believe during so a long time that the Earth was motionless. That can be done only by studying the movement of the bodies, and by showing that the laws of the movement are thus made that it is impossible “to feel” and to observe that of the Earth. It is all in all a question of taking again in a critical way the talk of the bases of Aristotelian physics and advanced arguments by it in favor of the immobility of the sphere, then to oppose to this “system of the world” a new system which makes place with the mobility of the Earth and highlights the reasons for which the old one could pass for “truth”. From this concern is born, after one long period of gestation (of 1610 to 1632), Dialogo will sopra I due massimi sistemi LED mondo (Dialog concerning the two principal systems of the world). This text, intermingled with many digressions, presents, in particular, the new doctrines of the movement and constitutes the base of the modern physics, inaugurated by Galileo.  

The principle of relativity
This physics rests on a single principle, the principle of relativity, fundamental importance, since it is on him that is built modern physics. Salviati, spokesperson of Galileo in the Dialog, states it as follows: “For the objects which are driven of a uniform movement, this one is like null.” It hastens to illustrate it using an example: imagine - known as in Salviati substance - that, on a quay ship in Venice, you embark butterflies and small fish. Observe how, whereas the ship is motionless, the butterflies flutter die die and the fish, in their bottle, move with as much ease towards the prow of the boat than towards the poop. Observe them then, whereas the ship sails at its cruising speed on the Mediterranean: their movements are the same ones as when the boat is motionless; the fish and the butterflies provide an equivalent effort to move towards the back or it before boat; the uniform movement of the ship is, for fish and the butterflies which take part in it, “like no one”.  

One immediately conceives what this proposal has of revolutionist. According to the Aristotelian doctrines, a movement which is “as null” is a movement without speed, therefore only the rest is “like null”; to say that the movement of the animals is “as null” thus does not have strictly any direction. The situation is quite different in new physics, which, by affirming that certain movements (uniform movements) are like null, partly abolishes the radical distinction which Aristotelian physics between rest and movement establishes. The force and the fruitfulness of this principle come from what it is a principle of order. He affirms indeed that there exists on the phenomena of nature - and this, whatever their apparent complication - from the identical points of view: he is equivalent to observe the butterflies since the quay ship (in other words since the dry land) or since the ship moving uniform. The recognition of these homologies simplifies the study of the physical phenomena and makes it possible to make the share between what is essential and what is only business from point of view. Thereafter, physics will develop by stating several principles which, the such principle of relativity, stipulate under which operations the laws of physics are unchanged, or “invariant”. The evolution of the physique to the XX E century will be entirely guided by the search for principles of this type.  

First steps of the laws of dynamics
Galileo distinguishes the quota from essence, i.e. what in the movement concerns the relation of causality. To say that a uniform movement is “like null”, it is to affirm that it is without cause; it can thus be maintained indefinitely without no “force” being exerted on the mobile - such is the base of the principle of inertia stated later by Newton, but already present in the various formulations of Galileo. That also supposes that the cause of a movement is not uniform; a “force” (a “engine”, to take again the Aristotelian terminology) thus produced a change of movement - an acceleration today would be said. For the proportionality force and speed, “fundamental law” of Aristotelian dynamics, is substituted that of the force and the variation of movement.  

The problem of the stone which falls
After having exposed the basic principle on which the new physics rests, Salviati undertakes to apply it to a seemingly formal problem, but of decisive importance in the debate to the copernicians and earthmoving which opposes Aristotelian. Its statement is the following: imagine a sailor who, from the top of mast of a ship, releases a stone, without him to communicate the least impulse; it is supposed that the boat sails at uniform speed. Question: does the stone fall ahead, with the foot, or behind mast?  

The answer that Simplicio, interprets the Aristotelian ones in the Dialog, hastens to provide is: the stone falls behind mast. Indeed, it reasons, while the stone traverse with the vertical the distance which separates the top from the mast of its foot, the boat (and the foot of the mast) advances; the stone, while arriving on the bridge, thus finds “behind” foot of the mast. This reasoning is false, retorts Salviati. Indeed, the stone, like the butterflies and fish of presently, falls under the movement of advanced ship; however, under the terms of the principle of relativity, this movement is “like null”. In other words, the things occur on board ship moving in the same way that if it were motionless: the two positions of the boat represent from the similar points of view on the course of the process; in both cases, the stone falls at the bottom of mast.

The Earth is not motionless any more
The importance of this problem is explained by the fact why it was traditionally used to justify the supposed immobility of the Earth. Indeed, one, this one said is like a ship; let us replace the mast of this ship by a high tower: a stone released from the top of this tower should, if the Earth is moving, fall “to the back” from the foot from the tower, just like the stone fall, for the Aristotelian ones, “with the back” of the foot of the mast. However each one can note that a stone released from the top of a tower falls exactly at the bottom of this one. This demonstration thus made it possible Aristotelian to conclude there that they had an irrefutable experimental proof of the immobility of the Earth.  

It is this reasoning which Galileo refutes by applying his principle of relativity. Indeed, the “experimental” fact of the fall of the stone at the bottom of the tower does not prove anything strictly; under the terms of the principle of relativity, that the Earth either or is not motionless, the things will occur always in the same way: the stone will fall at the bottom of the tower. The refutation is subtle. The argumentation primarily consists in showing that if the Earth turns, nothing enables us “to feel it”: any attempt to highlight this movement can only fail. Nothing astonishing under these conditions which the Earth could pass, during centuries, for motionless; but, known as Galileo, that prove by no means that it is it. In other words, the Aristotelian ones are free to deny the earthmoving, but they cannot advance more as proof of what they affirm the fact that a stone released from the top of a tower falls to its foot. In addition, since the observations carried out using the glasses obviously show that the Earth and the celestial bodies are not of a different nature, anything is not opposed more to than the Earth is it also moving.
 
Birth of the mathematical physics

The Dialog has this of remarkable that the arguments relating to the movement of the bodies (and in particular to their fall) there are deliberately mingled with cosmological considerations: the study of the laws which, on Earth, govern the movement of the butterflies and small fish is also used to think the cosmological structure of the world. Aristotelian distinction between sublunary world, reign of perishable and the liable to deterioration one, and lunar world, place of the imperishable and inalterable celestial bodies, lived, and with it the idea that the bodies can occupy of the “natural” places, determined by their intimate composition: the picturesque space of old physics replaced a homogeneous space, such as one conceives it today, where, for all the objects, all the places are equivalent.  

A mathematical vision of the world
The physics of Galileo also rings the knell of the distinction established by Aristote between mathematics and natural philosophy. Indeed, to say that the laws to which the celestial bodies are subjected are also those which govern the movement of the terrestrial bodies, it is to affirm that the astronomer cannot be satisfied any more to explain the phenomena using calculations resting on some absurd assumption: it should from now on here below justify bases of its calculations by confronting them with the reality of the observable phenomena, on the Earth. In the same way, the philosopher cannot be satisfied any more to explain why the things occur as they do it by calling upon “principles” inherent in their nature; it is necessary for him to subject the behavior of the terrestrial objects to calculation. The philosopher must be made mathematician, just like the mathematician must become philosophical. Galileo thus marks the moment when modern physics is born from the union of two disciplines before separate: natural philosophy and mathematics. Thus is necessary it to hear its famous sentence according to which the book of nature is written in mathematical language.  

The motion study uniformly accelerated
Well before the publication of the celestial Message, Galileo assigned for task to understand the fall of the bodies more geometrico, i.e. in mathematical terms. One finds in his last work, Discorsi E dimostrazioni matematiche intorno had nuove scienze (Speech concerning two new sciences), an echo of these concerns. At the beginning of the third day of the Speech (which is actually a dialog, putting in scene the same characters as those of the Dialog), Salviati, which holds in hand one of the first writings of Galileo (Of motu locali, published in Padoue in 1590), announces: “I propose to found a very new science relative on a very old subject . Surface observations were made, like the fact that the natural movement of a heavy body falling is continuously accelerated. But up to what point exact this acceleration occurs is what was not known as; in so far as I know, nobody until now pointed out that the distances crossed, during equal time intervals, by a body falling starting from the rest are between them in the same report as the successive odd numbers starting from the unit.”  

Galileo is thus in search of a quantitative representation of acceleration and, in a more general way, uniformly accelerated movement. Its famous definition instantaneous speed like passage follows then to the limit, starting from the “common” concept speed, while making tighten the time intervals towards zero - definition which, because it is based on the infinitely small, precedes the introduction of the infinitesimal calculus into Western science.  
 
The confrontation with the Church

If twenty-two years, from 1610 to 1632, separate the publication from the celestial Message of that of the Dialog, it is primarily for “political” reasons. Some time after his return to Florence, in 1611, Galileo, eager to give to his astronomical discoveries a greater glare, goes to Rome, where it is received paternally by the pope and the Roman College of the Jesuits. But such encouragements do nothing but poke the hatred of the adversaries of the “new system”, more perhaps than believes it Galileo himself. Always it is that, encouraged by the various supports of which it profits, it even dares to affirm that the biblical accounts must in no way of intervening in the debates relating to nature, which requires for its comprehension the knowledge of the language of mathematics.  

It is more than cannot support the party of the excessively pious people. Following various intrigues of court, Galileo is convened in Rome in front of the Holy Office, on on February 24th, 1616.  

The work of Copernic is put at the Index and Galileo receives the injunction to keep silent himself. Wounded morally, it takes refuge in the study and the drafting of the Dialog. He believes power to leave his retirement in 1623 when is elected pope the cardinal Maffeo Barberini, who until now always supported it. But, helping reason of State, the new pope convenes it to mean to him that, in spite of admiration that it carries to him, and taking into account the fact that the heretics are for most partisans of Copernic, the tolerance of the Church has limits. Galileo then negotiates the possibility of publishing his Dialog, where in all objectivity the two involved theses must be exposed. The work appears in 1632. But one points out with the pope whom his recommendations were not observed: in the Dialog, the beautiful role is given to Salviati-Galileo, whereas Simplicio, the Aristotelian one, is often turned into ridiculous. The pope sees himself constrained to inform the lawsuit of Galileo. Nevertheless, thanks to the many supports of which it lays out, this one “only” will be condemned to sign a retractation, then assigned with residence with Arcetri, village of the neighborhoods of Florence. It is there that, in spite of a growing blindness, it writes the Speech relating to two new sciences, that it succeeds in making publish in the Netherlands in 1638. Galileo dies on on January 9th, 1642.