Galileo Galilei Supports Atomism, Part II

People change over time, and so do their ideas. The “public” Galileo who published the Sidereus Nuncius (Starry Messenger¹) in 1609, Il Saggiatore (The Assayer²) in 1623 and the Dialogo sopra i due massimi sistemi del mondo (Dialogue Concerning the Two Chief World Systems³) in 1632 was very different from the Galileo who published in 1638, while under house arrest, his last work, the Discorsi e Dimostrazioni Matematiche, intorno a due nuove scienze (Discourses and Mathematical Demonstrations Relating to Two New Sciences⁴).

The same three characters (Simplicio, Sagredo and Salviati) appear in both the Dialogue and Two New Sciences. However, they play different rôles in the two works. In the Dialogue, Simplicio is a complete simpleton, representing the Aristotelean cause, with every utterance on his part being complete nonsense; Sagredo is the sometimes overly enthusiastic interested bystander; and Salviati represents the completely self-confident Galileo. See the numerous posts about the Dialogue in my archive.

On the other hand, in the Two New Sciences, the three characters can perhaps be better understood as representing three stages in Galileo’s life: Simplicio the young Galileo who was still studying Aristotelian texts; Sagredo the public Galileo who wrote the Sidereus Nuncius, the Assayer and the Dialogue; and Salviati the older, mature Galileo.

Galileo’s perspective on atomism also changed over time. The structure he proposed in his Assayer, outlined in my post Galileo Galilei Supports Atomism, Part I, was seemingly reminiscent of the atomism of the ancient Greek and Roman worlds, which I presented in my post Lucretius's Of the Nature of Things: Atoms and the Void.

The atomism presented in the First Day of Two New Sciences, the subject of this post, is something else. Here Galileo discusses extensionless point-atoms interacting with extensionless voids (vacua), where “extensionless” means not taking up space. In other words, any given volume is made of an infinite set of infinitely small particles, separated by infinitely small voids. The intuition of Galileo was of a fluid, with infinitely fine particles, where the infinitely fine voids allowed for rarefaction and compression. As for solids, once heated, the fire particles would enter the infinitely fine voids, and separate the solids into some kind of fluid:

Sometimes, in considering how heat [fuoco, fire] goes snaking among the minimum particles of this or that metal, so firmly joined together, and finally separates and disunites them; and how then, the heat departing, they return to reunite with the same tenacity as before, without the quantity of gold being diminished at all, and that of other metals very little, even though these remain disunited for a long time, I have thought that this may come about because of very subtle fire-particles. Penetrating through the tiny pores of the metal, between which (on account of their tightness) the minimum [particles] of air and other fluids could not pass, these [fire-particles] might, by filling the minimum voids distributed between these minimum particles [of metal], free them from that force with which those voids attract one [particle] against another, forbidding their separation. And being thus able to move freely, their mass [massa] would become fluid, and remain so until the fire-particles between them depart. But when these go, leaving the pristine voids, the usual attraction returns, and consequently the attachment of the parts. [Two New Sciences, p.27]

What is interesting is that once one understands the model of atomism in the Two New Sciences, rereading the relevant passages in the Assayer, one can see that the same intuition was already there, even if the idea was not fully developed:

To sum up, the operation of fire by means of its particles is merely that in moving it penetrates all bodies by reason of its great subtlety, dissolving them more quickly or more slowly in proportion to the number and velocity of the fire-corpuscles (ignicoli) and the density or rarity of the material of these bodies, of which many are such that in their decomposition the major part of them passes over into further tiny corpuscles (ignei), and the dissolution goes on so long as it meets with matter capable of being so resolved. [Assayer, p.312]

It is important to remember that Galileo was writing just as the first steps of development in Europe of the infinitesimal calculus were taking place. So reading the above passages, one can intuit that Galileo was conflating the physical universe and the mathematical universe, as in the following passage from the Assayer:

And as the four senses considered here are related to the four elements, I believe that vision, the sense which is eminent above all others, is related to light, but in that ratio of excellence which exists between the finite and the infinite, the temporal and the instantaneous, the quantity and the indivisible; between darkness and light. Of this sense and the matters pertaining to it, I pretend to understand but a trifle, and since a long time would still not suffice for me to explain that trifle—or even to hint at its explanation in writing—I pass this over in silence. [Assayer, pp.311-312, my emphasis]

Galileo himself did not write about this new mathematics, but one of his students, Bonaventura Cavalieri, did write about the indivisibles in mathematics in a text entitled Geometria indivisibilibus continuorum nova quadam ratione promota (Geometry, developed by a new method through the indivisibles of the continua). I do not know of any English translation, but Lucio Lombado-Radice did publish in 1966 an Italian translation.⁵ Cavalieri wrote this work in 1627, but it was only published in 1635, three years before Galileo published the Two New Sciences.

From this post, we can see that there are two natural streams to follow. The first pertains to the different proposals about the structure of matter, be it using atoms or a plenum; in particular, we can consider Galileo’s vision as a precursor of Boskovich’s atoms, which I discussed in the post The Point-atoms of Ruđer Josip Bošković: The Key to the Fields of Michael Faraday. The second pertains to the developments of the infinitesimal calculus. The choices made in each of these two streams, of course, affected the understanding of motion, and I intend to study both.

As I was reading Two New Sciences, I have found that some of the writings of Gregorio Baldin⁶ and Carla Rita Palmerino⁷ have been very instructive and insightful. I can recommend the work of each of these researchers.

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1. Galileo Galilei. The Sidereal Messenger and a part of the Preface to Kepler's Dioptrics Containing the Original Account of Galileo's Astronomical Discoveries. A Translation with Introduction and Notes by Edward Stafford Carlos. London: Rivingtons, 1880.

2. Galileo Galilei. The Assayer. In Galileo Galilei, Horatio Grassi, Mario Guiducci, Johann Kepler. The Controversy on the Comets of 1618. Translated by Stillman Drake and C.D. O’Malley. University of Pennsylvania Press, 1960.

3. Galileo Galilei. Dialogue concerning the two chief world systems — Ptolemaic and Copernican. Translated by Stillman Drake, foreword by Albert Einstein. University of California Press, 2nd ed., 1967.

4. Galileo Galilei. Two New Sciences, Including Centers of Gravity & Force of Percussion. Translated by Stillman Drake. University of Wisconsin Press, 1974.

5. Bonaventura Cavalieri. Geometria degli Indivisibili. A cura di Lucio Lombardo-Radice. Unione Tipografico-Editrice Torinese, 1966.

6. Gregorio Baldin. Hobbes e Galileo: Metodo, materia e scienza del moto. Firenze: Leo S. Olshki Editore, 2017. English translation: Gregorio Baldin. Hobbes and Galileo: Method, Matter and the Science of Motion. Cham, Switzerland: Springer Nature Switzerland, 2020.

7. Carla Rita Palminero. Galileo's and Gassendi's Solutions to the Rota Aristotelis Paradox: A Bridge between Matter and Motion Theories. In Christoph Lüthy, John E. Murdoch, William R. Newman, editors. Late Medieval and Early Modern Corpuscular Matter Theories. Leiden, Boston, Köln: Brill, 2001, pp.381-422.