Galileo's Revolution

— Ansar Fayyazuddin

THIS YEAR MARKS the 450th anniversary of Galileo’s birth. Modern telescopes, which make visible the far reaches of the universe and take us back in time to the moments when the universe was still small, are related by direct lineage to Galileo, who first turned the telescope heavenward and started asking questions that continue to stir us.

What is the relevance of Galileo today? Why remember him so prominently when so many other important scientists are not? Einstein identifies one set of reasons in his foreword to Galileo’s Dialogue Concerning the Two Chief World Systems:

“A man is here revealed who possesses the passionate will, the intelligence, and the courage to stand up as the representative of rational thinking against the host of those who, relying on the ignorance of the people and the indolence of teachers in priest’s and scholar’s garb, maintain and defend their positions of authority. His unusual literary gift enables him to address the educated men of his age in such clear and impressive language as to overcome the anthropocentric and mythical thinking of his contemporaries...(1)

Einstein wrote the Foreword from his American exile, having escaped one authoritarian regime to find himself having to stand up to another, albeit one of a much different character. Bertolt Brecht, also having escaped the same murderous Nazi regime, found himself hounded by the HUAC during his American sojourn, and, increasingly unable to abide by the stultifying dogmas and authoritarianism of the Communist parties. Brecht, who wrote a play chronicling Galileo’s condemnation, saw Galileo as a kindred spirit.

The Prevailing Dogmas

Galileo Galilei was born in 1564 in the Tuscan city of Pisa. In traditional periodization, this corresponds to the late Renaissance or, more generally, the Early Modern Period.

Soon after Galileo’s birth, his family moved to Florence, where he grew up. Florence, a major center of the Renaissance had by this stage combined with other smaller city states, including Pisa, to form the relatively large Republic of Tuscany.

The Catholic Counter-Reformation was in full swing, policing the Catholic dominions to the extent that it could through the Roman Inquisition and the Censor. The Censor produced the so-called Index specifying proscribed texts and ideas.

While the Counter-Reformation tried to exert Catholic orthodoxy in the kingdoms of Italy, another set of dogmas held sway at the universities. By the mid 16th century, the ancient texts that had sparked the intellectual revival of the Renaissance formed the basis of a new secular orthodoxy. Intellectual life at the universities was confined largely to interpreting and transmitting these texts.

Knowledge was considered to be that which could be extracted from these texts rather than from material experience. Aristotelian philosophy reigned supreme. Some aspects of Aristotelian philosophy were even incorporated into Catholic dogma. Thomas Aquinas had inducted the Ptolemaic synthesis of Aristotelian astronomy into Church doctrine.

Thus Ptolemaic astronomy had the imprimatur of both the Church and the secular philosophers based at the universities. It may be useful to briefly linger on some key features of Aristotelian physics and astronomy.

Aristotle conceived of terrestrial matter and heavenly bodies as possessing fundamentally different natures.(2) Terrestrial matter, according to Aristotle, is composed of four elements: fire, air, water, and earth. These elements have basic properties, chief among them being natural motion.

All natural motion is vertical: light elements rise while heavy ones fall. Fire is the lightest of the elements, earth the heaviest, while air and water are intermediate on this scale. Horizontal motion is not “natural” and requires the application of external force (“violent motion”).

The natural properties of any object, according to Aristotle, are determined by the proportions of the basic elements in the composition of the object in question. Heavenly bodies, on the other hand, are composed of aether, which is supposed to be “incorruptible,” i.e. unchanging and permanent.

Aristotle conceived the universe as earth-centric, with the static (non-rotating and unmoving) earth occupying the geometric center of the universe. Concentric, uniformly rotating spherical shells on which the sun, moon, and planets were affixed accounted for various observed cyclic phenomena — such as the daily cycle of night and day through the purported rotation of the sun’s spherical shell.

The outermost shell of this system was fixed and held the stars in place. The stars were fixed in space and eternal. All heavenly bodies and the rotating concentric shells were perfect spheres.

Ptolemy introduced two innovations to bring the Aristotelian system closer in line with observations. The first was “eccentricity,” which allowed the Aristotelian shells to be centered somewhat off the earth. The second, “epicycles,” allowed for more complicated planetary motion than uniform circular movement about the center of its spherical shell.

Epicycles are circular orbits about a fixed point on a rotating spherical shell — so an epicycle describes a circle around a point, which itself orbits the earth in a circle. Epicycles were to become a symbol of the complicated contortions that Ptolemaic astronomy was forced to introduce in order to remain observationally viable.

Skeptic and Inventor

Galileo’s early career was spent as a professor of mathematics at the universities of Pisa in Tuscany, and subsequently at Padua in the Venetian Republic, before finally moving back to Florence. His early university career was dominated by traditional Aristotelian preoccupations. Personal debt forced Galileo to seek other sources of income to supplement his university salary. He took on students to tutor, which besides augmenting his salary gave him a venue to explore ideas outside of the university.

It is in the notes that he prepared for his private tutorials that the first hints of his skepticism towards Aristotelian astronomy and mechanics appear. Besides tutoring, Galileo’s activities outside the university included consulting for the Venetian government on military matters.

He further supplemented his income by manufacturing and selling a series of inventions and other devices. The inventions included a calculator based on a proportional divider, and a thermometer. Later, he manufactured and sold telescopes and compound microscopes, after hearing of these Dutch inventions. His engagement in these more “applied” problems, as opposed to the rarefied preoccupations of the academy, probably contributed to Galileo developing a more practical approach to problem solving and confronting Aristotelian mechanics with the real world.

A pivotal year in Galileo’s life and for the history of science was 1609, when Galileo first got word of the telescope. Inspired by the reports he received of this Dutch invention, he tried to construct the instrument himself and, on successfully building one that made objects appear a third of the distance away and nine times as big, he immediately constructed one that made objects appear sixty times their size.

Galileo describes what happened next in his book The Starry Messenger:

“It would be superfluous to enumerate the number and importance of the advantages of such an instrument at sea as well as on land. But forsaking terrestrial observations, I turned to celestial ones, and first I saw the moon from as near at hand as if it were scarcely two terrestrial radii away. After that I observed often with wondering delight both the planets and the fixed stars, and since I saw these latter to be very crowded, I began to see (and eventually found) a method by which I might measure their distances apart.”(3)

What Galileo Observed

The book goes on to explain in plain language(4) Galileo’s observations and deductions about heavenly bodies that were subsequently largely confirmed and remain part of our accepted body of knowledge to this day. The Starry Messenger is a truly remarkable book that quietly sets aside the Aristotelian view of the special nature of celestial matter, and treats it as if it were no different from terrestrial matter.

This radical departure characterizes much of Galileo’s thinking — he showed a facility for discarding cumbersome received wisdom if he could do with a simpler, more plausible set of assumptions instead.

When Galileo observed the moon through his telescope, he did not see a perfect sphere but a body that was pockmarked and jagged. He wrote that from these observations “I have been led to the opinion and conviction that the surface of the moon is not smooth, uniform, and precisely spherical as a great number of philosophers believe it (and the other heavenly bodies) to be, but is uneven, rough, and full of cavities and prominences, being not unlike the face of the earth, relieved by chains of mountains and deep valleys.”(5)

He observed that the darkened and lit parts of the moon were divided not by a smooth line, but by a jagged one, and that the lit part of the moon contained darkened spots that shifted. He found all of this to be consistent with a rough lunar terrain containing mountains and craters. He argued that the glow of the moon is the reflected light of the sun, and that the dark spots in the lit part of the moon are the shifting shadows produced as the moon moves in relation to the sun.

Perhaps the most remarkable part of The Starry Messenger is the discussion of the secondary lighting of the moon. Galileo observes that there is a faint lighting of the moon’s surface that cannot be explained by the light emanating from the sun.

After discarding some possible explanations, he poses his own solution: sunlight reflected off the earth provides the secondary light on the moon. Galileo expresses this in beautiful prose: “The earth, in fair and grateful exchange, pays back to the moon an illumination similar to that which it receives from her throughout nearly all the darkest gloom of night.”(6)

The symmetry between the moon and the earth is stark. A little later, in two startling sentences a few paragraphs apart, Galileo asks the reader to consider what would be visible from Venus and from the moon — a far more radical departure than Copernicus’ quite literal decentering of the earth.

Copernicus places the earth away from the geometric center of the universe, but does not necessarily deny the privileged position of earth as the observation point. In Galileo’s text, we are asked to imagine what the universe would look like for observers from multiple possible positions, none of which enjoy an inherently privileged status.(7)

I cannot dwell much longer on this remarkable book, but I would be remiss not to mention some of its highlights. Throughout the book, the working assumption is that the earth rotates about its axis and orbits the sun, while the moon, in turn, orbits the earth.

Galileo explains the phases of the moon, computes the height of a lunar mountain, establishes the existence of four moons orbiting Jupiter based on his extended observations, and argues that the Milky Way is not a band of light but, in fact, composed of a multitude of stars. He also explains the difference between stars, planets and the moons of planets in terms of which produce their own light and which shine due to reflected light from the sun.

Dangerous Fame

Publication of The Starry Messenger brought Galileo instant fame. But along with his great celebrity came a barrage of criticisms, from both secular and religious sources.

Secular critics, upset by the inherent rejection of Aristotelian astronomy, questioned the efficacy of the telescope in revealing the nature of viewed objects without distortion. They also found Galileo’s explanations incomplete, since he didn’t explain how unattached heavenly bodies could fail to fall onto the earth and why the earth’s rotation does not result in vicious winds that would create havoc on earth.

Galileo had no doubt that the objects and phenomena he observed through the telescope had a consistency that was not compatible with hypothetical distortions produced by the telescope. He was also convinced that his hypothesis of untethered planets and stars was correct, and there would ultimately be a viable explanation for why they do not fall to earth. The lack of winds due to the rotation and motion of the earth was explained by Galileo (see below) by understanding sufficiently well what we now call the principle of inertia.

The religious criticisms centered on his adoption of the Copernican hypothesis of a heliocentric universe, a view counter to the doctrines of the Catholic Church.(8)

Physics was Galileo’s life-long intellectual preoccupation that predated his interest in astronomy. Today, astronomy is a subfield of physics. This was not the case in Galileo’s time when the Aristotelian distinction between corruptible (terrestrial) and incorruptible (heavenly) matter held sway.

Paradoxically, astronomy was always a subject rooted in detailed measurements, while physics was based on qualitative principles that were not tested in quantitative detail. Perhaps Galileo’s most important contribution to physics was to make measurement a central aspect of the practice of physics.

As Galileo started to bring measurement to bear on determining new physical laws and establishing the veracity of purported laws, the Aristotelian edifice started to crumble. During his Pisa years, Galileo was able to disprove Aristotle’s contention that objects of different masses fall differently under the influence of gravity.

While the story of Galileo dropping two objects of widely different masses from the tower of Pisa is probably apocryphal, it is the case that both theoretical considerations and everyday experience led Galileo to the law that two objects made of the same material but of different masses would fall in the same way and would hit the ground simultaneously if dropped from the same height.

Galileo went on to discover a number of remarkable regularities through observation, which he formulated in mathematical terms. For instance, he discovered the counterintuitive fact that a pendulum of fixed length takes the same amount of time to return to its original position independently of how far the pendulum is swung from its equilibrium position.

An even more impressive feat was to establish that projectile motion (the motion of an object under the influence of gravity) followed a parabolic trajectory. Galileo established this mathematical law by meticulous and ingenious experiments in which he studied the motion of objects on slightly inclined planes, effectively tuning the vertical acceleration down so he could measure accurately the position of an object as a function of time.

Another general law that Galileo formulated in a limited form was the law of inertia — that all observers travelling at constant velocities with respect to each other see the same physics.

To the question “where would an object dropped from a ship’s crows nest land on the deck of a ship moving at constant velocity?” Galileo answered unhesitatingly: the object would land at the bottom of the mast. In Galileo’s view, the dropped object is moving with the ship and one cannot, by conducting an experiment of this sort, distinguish between a stationary ship or a uniformly moving one.

In fact, the distinction between a moving and stationary ship is based on a convention that certain objects on earth (trees, say) are stationary. This powerful realization addressed (with some caveats) why the motion of the earth (both around its axis and around the sun) does not produce violent winds — the reason being that the air moves with the earth rather than remaining stationary with respect to the moving earth.

The centrality of quantitative measurements to Galileo’s physics meant that, for Galileo, mathematics was necessary in formulating physical laws. Yet Galileo was clear on the very different natures of mathematics and physics.

Galileo understood that mathematical knowledge could be perfect in the sense that mathematical statements could, in principle, be shown to be true or false by employing the rules of mathematics alone. This was not the case with physics: All measurements were necessarily approximate, and all confirmations of physical laws were perforce subject to caveats of precision of measurement, control over extraneous disturbances, etc.

On Trial

To this already complex epistemology, Galileo added considerations on the relationship between science and theology. As Galileo came under increasingly frequent attack for his heretical Copernican views, he addressed the general problem posed by the clash of scientific knowledge and the literal meaning of the Bible in his Letter to the Grand Duchess Christina.

In this manuscript, he asserts that observations and experience should always have priority as tests of the truth of propositions about nature. When the literal meaning of the Bible is in contradiction with observation, then the only available recourse to someone who believes in the sacred nature of the Bible is to reject the literal meaning in favor of another interpretation, whether one is readily available or not.

In this carefully argued book, Galileo wields his polemical powers to great effect in arguing against the devout extractors of “knowledge” about the natural world through reading the Bible: “But I do not feel obliged to believe that that same God who has endowed us with senses, reason and intellect has intended to forgo their use and by some other means to give us knowledge which we can attain by them.”(9) This book should be required reading for arguing against present day creationists.

Galileo’s attitude towards philosophers was similar to what he expressed against the biblical literalists — the authority of select philosophers could not outweigh observation. He poked fun at the philosophers by giving credence to the lived experiences of uneducated artisans and peasants over the bookish assertions of academicians.

The trial of Galileo by the Roman Inquisition is now a legend. Galileo was condemned for the ostensible offense of treating Copernican astronomy as fact in his Dialogue Concerning the Two Chief World Systems.

The Dialogue was an explication of Galileo’s theory of tides in the form of a dialogue among three interlocutors: Salviatti, Sagredo and Simplicio. Simplicio represented the Aristotelian view whose ideas were undercut by the more compelling Salviatti, while Sagredo, the neutral party, asked the two rivals questions pushing the conversation forward.

Galileo’s explanation of the phenomena of tides, now discredited, was based on the two forms of motion the earth executes — the daily rotation about its axis and the yearly revolution around the sun.

Belief in both forms of motion was considered to be heretical by the Inquisition. But it was probably the insult of treating the static earth as a ridiculous proposition and putting the words of the current Pope in Simplicio’s unconvincing mouth that must have really stung(10) and brought the matter to such an outrageous conclusion.

Galileo was brought to Rome in frail health in early 1633 and condemned by the Inquisition for the crime of heresy and sentenced to indefinite imprisonment. This devastating sentence was thankfully commuted to house arrest due to the intervention of an Archbishop, who was allowed to keep him in his custody in Siena.

By the end of 1633, Galileo was allowed to move to his villa in Florence but still kept under house arrest. Galileo was to remain there until his death in 1642.

Democratic Spirit of Science

Galileo, shattered though he was by the condemnation and the inordinately harsh sentence, managed, with the encouragement of friends, to return to his work on physics. In the resulting book, Two New Sciences, written between 1634 and 1637 and published in 1638, Galileo again adopted the dialogue form, keeping the same three interlocutors as those of his book on tides.

The subjects of this new book were what preoccupied him his entire life: motion and the physics of materials. It is considered to be his most important work, prefiguring many aspects of the continuum mechanics of Newton. But it is the science of materials that again illustrated how Galileo prioritized experience over logic.

The opening dialogue explains an idea that remains counterintuitive: an object made proportionately larger or smaller, does not become proportionately stronger or weaker. The central reference point of this dialogue is the lived experience of the artisan, who knows that columns that are proportionately enlarged are weaker than the smaller versions of themselves since they must withstand their own weight in addition to the weight of the structure they support.

Galileo explains what this implies about the strength of materials. That this remains a point of confusion to this day is illustrated by the fact that J. B. S. Haldane’s most famous essay “On Being the Right Size,” written in the first half of the 20th century, was written to dispel exactly the same set of wrong ideas as Galileo’s dialogue does. Yet Hollywood blockbusters continue unmoved to show humans shrunk to the size of ants and ants blown up to the size of elephants.

The democratic spirit of science — that the world can be understood not just by geniuses but by everyone — is evident everywhere in Galileo. This spirit is not just present unconsciously, but expressed quite explicitly:

“I wrote in the colloquial tongue because I must have everyone able to read it, and for the same reason I wrote my last book in this language [Italian]. I am induced to do this by seeing how young men are sent through the universities at random to be made physicians, philosophers, and so on; thus many of them are committed to professions for which they are unsuited, while other men who would be fitted for these are taken up by family cares and other occupations remote from literature. The latter are, as Ruzzante would say, furnished with ‘horse sense,’ but because they are unable to read things that are ‘Greek to them’ they become convinced that in those ‘big books there are great new things of logic and philosophy and still more that is way over their heads.’ Now I want them to see that just as nature has given them, as well as philosophers, eyes with which to see her works, so she has also given them brains capable of penetrating and understanding them.”(11)



  1. Albert Einstein, “Foreword” xxiii in Dialogue Concerning the Chief World Systems (2001) Modern Library paperback edition.
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  2. See, for instance, I. Bernard Cohen, The Birth of a New Physics, New York: W. W. Norton 1985, 13-15.
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  3. Galileo Galilei, The Starry Messenger, quoted 29 in Discoveries and Opinions of Galileo, translated with an introduction and notes by Stillman Drake, New York: Anchor Books, 1957.
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  4. The Starry Messenger was originally published in Latin. The language nevertheless has that vernacular quality that characterizes most of Galileo’s writings in Italian (or the Tuscan dialect).
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  5. The Starry Messenger, 31.
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  6. The Starry Messenger, 44.
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  7. Hannah Arendt in The Human Condition considers Galileo’s use of the telescope as a crucial moment in the transition to “modernity.” She writes, “Philosophically, it seems that man’s ability to take this cosmic, universal standpoint without changing his location is the clearest possible indication of his universal origin, as it were. It is as though we no longer needed theology to tell us that man is not, cannot possibly be, of this world even though he spends his life here; and we may one day be able to look upon the age-old enthusiasm of philosophers for the universal as the first indication, as though they alone possessed a foreboding, that the time would come when men would have to live under the earth’s conditions and at the same time be able to look upon and act on her from a point outside.”
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  8. Although we have come to associate the earth-centered Aristotelian view with the Catholic Church, the leading figures of the protestant Reformation were not much better in this regard. Martin Luther considered the belief that the sun was at rest to be contrary to Christianity. This view was central to the Protestant astronomer, Tycho Brahe, who reworked the Copernican system to retain its great simplicity but making it compatible with a stationary earth (see Pierre Duhem’s discussion in “Renaissance Physics” in Toward Modern Science vol. II, 123-124).
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  9. “Letter to the Grand Duchess Christina” in Discoveries and Opinion of Galileo, 183.
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  10. See J. L. Heilbron’s “Introduction” xvi in Dialogue Concerning the Chief World Systems (2001) Modern Library paperback edition.
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  11. Quoted by Stillman Drake in Discoveries and Opinions of Galileo, 84.
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July/August 2014, ATC 171

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