When it comes to Galileo Galilei (1564–1642) and his publications people tend to automatically think first of the Dialogo (1632) and the problems that it caused him with the Catholic Church or the Sidereus Nuncius (1610), which launched the age of telescopic astronomy, as his most significant scientific works. However, the Dialogo is deeply flawed and is, to a very large extent, polemic rather than science. The Sidereus Nuncius is somewhat better but is in fact closer to a good press report that a scientific publication, and as I have noted on more than one occasion if Galileo had never made a single telescopic observation, it would have made no difference to the history of astronomy, as all of his discoveries were made pretty much simultaneously by other observers. Galileo’s real scientific inheritance and that for which he should truly be feted is his Discorsi e Dimostrazioni Matematiche, intorno a due nuove scienze (Discourses and Mathematical Demonstrations Relating to Two New Sciences) published in 1638, the year that he went totally blind.
Up till now I have progressed chronologically with this series although going back and forth following one discipline through the sixteenth century then going back to its beginning to follow another one. I followed optics up to Kepler’s Dioptrice in 1611 and then dropped back to celestial mechanics in the sixteenth century before looking at Kepler’s new celestial mechanics in his Astronomia nova in 1609. So, why the leap to 1638, was there nothing in physics worth mentioning in between? There was indeed but the date of publication of the Discorsi is deceptive, Galileo carried out nearly all of the work it contains during his eighteen years as professor for mathematics in Padua from 1592 to 1610. He originally conceived the book in 1609 but life and fame got in the way.
In late 1609, he got his first telescope and began to make the astronomical discoveries that when he published them in early 1610 catapulted him from being an obscure North Italian mathematicus to become Europe’s star astronomer. It also took him from being a lowly university mathematicus to the appointment as court philosophicus and mathematicus in Florence, where he was expected to entertain his Medici patrons in battles of wit with the Aristotelian scholars of the group he cynically named the Pigeon League. At the same time, he developed ambitions to become the man who would prove the truth of the Copernican heliocentric system. This ambition brought him into conflict with the Inquisition leading to a slap on the wrist in 1616. In 1618, he took up cudgels against the Jesuit astronomer, Orazio Grassi (1583–1654), in an extended dispute about the nature of comets that peaked on Galileo’s side with his Il Saggiatore (1623), which was dedicated to his old friend Cardinal Maffeo Barberini (1568–1644), now freshly elected Pope Urban VIII. Barberini found much favour in Il Saggiatore, granted Galileo several audiences and gave him permission to write a book about the conflicting cosmological systems.
As more than richly documented, Galileo wrote and published his book. This resulted in him being tried by the Inquisition for breaching the injunction from 1616 not to hold or teach the Copernican doctrine and opinion, which he had very obviously done in his Dialogo. Found guilty of vehement suspicion of heresy he was sentenced to life imprisonment, which was immediately commuted by the pope to lifelong house arrest. Galileo spent the first six months of his house arrest as a guest of the Archbishop of Sienna in his palace and it was here that he finally found the time to begin writing the book that he had originally planned to write in 1609. It is an irony of history that we can in principle thank the Inquisition for forcing Galileo to withdraw from his turbulent life and find the peace and quiet that he needed to write his most important scientific work, on which his reputation as a scientist should actually rest.
Of course, given the Church’s ban on all of his publications when the book was finished in 1636, it proved somewhat difficult to get it published. Initial attempts were made in the Republic of Venice, always ready to cock a snook at Rome but in this case the Inquisition’s prohibition on publishing Galileo’s work proved too strong. The same happened to approaches made in Vienna and Prague. Feelers were put out in Germany and France without success and in the end it was the Protestant publisher Louis Elzevier in Leiden, who had already printed the, equally banned, Latin edition of the Dialogo as well as the bilingual edition (Italian/Latin) of his Letter to Grand Duchess Christina, who published the book giving it, much to Galileo’s annoyance, its title. Galileo had wanted to title it Dialogues on Motion and complained that the publishers had taken the liberty of changing it and substituting, “a low and common title for the noble and dignified one carried on the title page.”
I have several times already referred to the Discorsi, as Galileo’s finest scientific work, a judgement that others might disagree with, but not Galileo. In a letter to his friend, the Swiss lawyer, Elia Diodati (1576–1661) Galileo refers to the Discorsi as being, “superior to everything else of mine hitherto published”.
In order to avoid accusations from the Inquisition that he had gone behind their backs and published the work, Galileo presents a cock and bull story in the dedication of the work to the Count François de Noailles, who was a former student of Galileo’s and the French ambassador to Rome. In this dedication he expresses his surprise and also pleasure that the Count has given the manuscript of his book to the publishers:
Most Illustrious Lord:–
In the pleasure which you derive from the possession of this work of mine I recognise your Lordship’s magnanimity. The disappointment and discouragement I have felt over the ill-fortune which has followed my other books are already known to you: Indeed, I had decided not to publish any more of my work. And yet in order to save it from complete oblivion, it seemed to me wise to leave a manuscript copy in some place where it would be available at least to those who follow intelligently the subjects which I have treated. Accordingly I chose first to place my work in your Lordship’s hands, asking no more worthy depository, and believing that, on account of your affection for me, you would have at heart the preservation of my studies and labours. Therefore, when you were returning home from your mission to Rome, I came to pay my respects in person as I had already done many times before by letter. At this meeting I presented to your Lordship a copy of these two works which at that time I happened to have ready. In the gracious reception which you gave these I found assurance of their preservation. The fact of your carrying them to France and showing them to friends of yours who are skilled in these sciences gave evidence that my silence was not to be interpreted as idleness. A little later, just as I was on the point of sending other copies to Germany, Flanders, England, Spain and possibly some places in Italy, I was notified by the Elzivirs that they had these works of mine in press and that I ought to decide upon a dedication and send them a reply at once. This sudden and unexpected news led me to think that the eagerness of your Lordship to revive and spread my name by passing these works on to various friends was the real cause of their falling into the hands of printers who, because they had already published other works of mine, now wished to honour me with a beautiful and ornate edition of this work.[1]
Of course, there is no truth in the fairy tale that Galileo is dishing up here and Count de Noailles was not responsible for his manuscript reaching the printers. However, he must have agreed to being used for this deceptive dedication. It should be noted that although the Latin edition of the Dialogo, the printed edition of the Letter to Grand Duchess Christina, and now the publication of the Discorsi all breached the conditions of Galileo’s house arrest, the Inquisition took no action against him for these breaches.
After an overlong introduction setting it in its historical context we now turn to the book itself. As with the Dialogo it is presented as four days of discussions, in fact by the same three figure, Salviati, Sagredo, and Simplicio, although they now have different characters and roles. Days One and Two are dedicated to the study of the resistance or strength of materials and fall generally under to the area of statics. Days three and four are Galileo’s much better known studies of motion. These are, as Galileo says in his dedication, really two works obviously written separately. The first two days are in Italian and days three and four in Latin. In the following I shall sketch days one and two.
Day One:
The three men meet for their discussions at the Venice Arsenal the complex of shipyards and armouries clustered together in the city, where Galileo was employed at times as a consultant.
It is interesting to note that, although Galileo is often presented, falsely, as the first experimental scientist, the discussion on the first two days are centred on experience and not experiment. The third day, of course, containing his famous inclined plane experiments to determine the laws of fall. The natural philosophers in this period lived in a transitional phase where scientific facts go from being based on experience with eyewitness accounts offered as proof, to being based on repeatable experiments. In fact, the term experiment originally meant experience.
Day One covers a wide range of, at times seemingly unrelated, topics starting out with the problem of scaling up from models to real objects, a practice used in shipbuilding. Here Galileo makes very clear that this process has inherent problems. Galileo also notes that scale matters giving as example, a horse falling from a height of 3 or 4 cubits will break its bones whereas a cat falling from twice the height won’t, nor will a grasshopper falling from a tower. A very simple example of a scaling problem is that if one doubles all three dimensions of a beam one automatically increases the volume and also the weight eight fold. Starting with the problems of scaling up harks back to Galileo’s very earliest scholarly work the two lectures he presented by invitation to the Florentine Academy On the Shape, Location, and Size of Dante’s Inferno in 1588, in the period between dropping out of university in 1585 and his appointment to the mathematics’ lectureship at the University of Pisa in 1589. In these lectures Galileo determined the thickness of the roof of hell by scaling up from the dome of Florence Cathedral and concluded the roof must be 600 kilometres thick. On this early occasion he made an error in his scaling up.
From scaling the three move on to problems concerning the strength of materials, comparing the breaking points of ropes, wooden cylinders and stone cylinders.
This leads into a discussion of the cohesion of materials and from there to vacuum, natures abhorrence of the vacuum not being adequate to hold material together. This is followed by an observation that a suction pump can only pump water to a height of eighteen cubits.
From the vacuum our trio move onto the subject of infinity and it is here that Galileo notes a paradox of infinity, in that he observes that the set of counting numbers is the same size as the set of square numbers although the former contains the whole of the latter. He was not the first to notice this paradox. For example, Duns Scotus (c.1265–1308) had already noted at the start of the fourteenth century that the set of natural numbers equals the set of positive numbers. However, the paradox is known as Galileo’s Paradox.
The discussion of infinity leads into a discussion of the difference between a fine dust and a liquid. He presents an atomist view of matter with the claim that liquids are matter dissolved into their ultimate, indivisible, and infinitely small components. Concentrated sunlight melting metals leads to a discussion on the nature of light and his failed attempts to measure the speed of light.
Measuring the speed of light assumes that light has motion, this leads on to a discussion dismissive of Aristotle’s theories of motion and the question, whether he every actually observed or tested his theory. We get Aristotle’s rejection of the vacuum because it would lead to infinite motion according to his theory. Here, Galileo goes into the theory that the rate of fall depends on the density of the medium through which the objects fall and the statement that in a vacuum all objects would fall at the same speed. This then leads to the problems of measuring small increments of time, when trying to measure the speed of fall and a discussion of the isochron behaviour of pendula.
The discussion of pendula leads onto the subject of vibrating strings, possibly Galileo’s very first area of research inherited from his father, the musician and music theorist Vincenzo Galilei (1520–1591). Galileo argued that there where three ways to raise the pitch of a string. To make it sound an octave higher, its length must be halved, or its tension quadrupled, or its cross-section reduced to one-quarter.
This brief sketch of some of the principle themes discussed on Day One of the Discorsi, this discussion covers sixty pages in the original, displays the wide spectrum of scientific topics that occupied the mind of Galileo in his years as professor in Padua.
Day Two:
The second day of discussions in much more closely focussed on a single theme the resistance or strength of materials, this statics of a rigid body. Like his medieval and sixteenth century predecessors, Galileo frames his discussion around simple machines, the lever and the balance.
His lever is novel in that the two arms are perpendicular to each other. This he illustrates in the form of a beam with a weight at the end jutting out from a wall.
He considers the strength of cylinders stating that:
In prisms and cylinders of equal length, but of unequal thicknesses, the resistance to fracture increases in the same ratio as the cube of the diameter of the thickness, i.e. of the base.
Throughout Day Two we see Galileo not merely discussing his cases as on Day One but analysing them mathematically. His analysis is not always correct but provide a basis for other in the future to correct and improve on his work.
Up next is a discussion on the breaking point of a rope with a weight suspended on one end. Followed by more cases of load bearing of prism and cylinders when increased in length or diameter. Galileo moves from the abstract to the concrete with a discussion of what happens when one increases the length of bones.
After more discussions of prisms and cylinders Galileo turns his attention to a beam supported at both ends and loaded with weights.
He moves on to a beam supported at one end and bearing a weight at the other. He proves that the optimum shape for such a beam is parabolic.
Although they are a significant contribution towards the modern concept of material engineering, which actually align Galileo more with the Renaissance artist-engineers* than with modern scientists, they do not loom as large in general discussions of Galileo’s contributions to the evolution of science as Days Three and Four on motions, which we will look at in the next post.
[1] Galileo Galilei, Dialogues Concerning Two New Sciences, Translated by Henry Crew and Alfonso de Salvio, Dover, 1954
* A good analysis of Galileo viewed as an engineer rather than as a scientist is Matteo Valleriani, Galileo Engineer, (Boston Studies in the Philosophy and History of Science Book 269), 2010