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For most of his adult life, from about the age of 30 until his death at 78 in the year 1642, Galileo propounded his theory of how the tides work. Yet a lengthy summary of our understanding of the tides that the British physicist Lord Kelvin published in 1882 mentions Galileo only in passing.

Why the cursory treatment? Because Galileo's theory of the tides, while extremely well thought out and eminently reasonable considering the state of scientific knowledge at the time, was wrong. Indeed, it was the most significant stumble in an otherwise brilliant scientific career. A look back at Galileo's big mistake offers clues to how and why such a great thinker could have made it, and what lessons it can offer us today.

A planet like a barge

It was in 1595 when Galileo, just shy of his 30th birthday, first came up with his explanation for the tides. The idea occurred to him while traveling on a barge that was ferrying freshwater to Venice. (Galileo lived in nearby Padua and often visited Venice.) He noticed that whenever the barge's speed or direction altered, the freshwater inside sloshed around accordingly. If the vessel suddenly ground to a halt on a sandbar, for instance, the water pushed up towards the bow then bounced back toward the stern, doing this several times with ever decreasing agitation until it returned to a level state.

Galileo realized that the Earth's dual motion—its daily one around its axis and its annual one around the sun—might have the same effect on oceans and other great bodies of water as the barge had on its freshwater cargo. The key, as Galileo saw it, was that even though we don't sense it, different parts of our planet move at different speeds depending on the time of day. It's as if the Earth were a barge, which sped up, slowed down, and periodically changed direction.

In his "Treatise on the Tides," a paper he wrote in 1616, Galileo used a diagram to explain why he thought this was true (see animated version at right above). In this animation, the Earth revolves in a counterclockwise direction both on its axis and around the sun.

Galileo demonstrated that the combination of the two motions—the so-called "absolute motion"—is always fastest on the part of the circle near A, because that part is moving in the same direction for both the daily and annual movements. And it is always slowest on the part of the circle near B, because that part is moving in opposite directions for the daily and annual movements. He determined that because the two absolute motions are additive on one side of the globe and subtractive on the other, the extreme ends of any sufficiently large basin of water, such as the Mediterranean Sea, would be moving at different speeds. The daily acceleration and deceleration of that body of water, he reasoned, effects a sloshing within it—the tides.

The chief objection to Galileo's argument was that his model should have called for only one high tide a day, whereas there are roughly two. Galileo explained this away by stating that many other factors play a role in creating a specific tidal situation. These include the length of a basin, its orientation, its depth, the shape of its coasts, the effect of winds, and so forth.

A sensible theory

Galileo thought he had discovered the correct explanation for the tides, one that would sink the other leading hypothesis of the day—namely, that the moon triggered the tides. In 1609, the German mathematician Johannes Kepler had written, "The sphere of influence of the attraction which is in the moon extends as far as the Earth, and incites the waters up from the torrid zone...." But because Kepler and other proponents of the moon theory could offer no scientific explanation for such influence, Galileo, who worked strictly on the basis of what he could see with his own eyes, found it impossible to believe; the theory smacked of the occult, he declared. (It wasn't until Sir Isaac Newton published his law of universal gravitation in 1687 that Kepler's "attraction" gained a firm scientific footing. Today, of course, most schoolchildren know that Kepler was right: the moon's gravitational tug gives rise to the tides.)

Galileo also thought his tidal theory provided powerful support for the notion that the Earth revolved around the sun (and not the other way around, as virtually everyone in the world then believed). This notion was first advanced in the mid-16th century by the Polish astronomer Nicolaus Copernicus, who maintained that our planet's rotation and revolution around the sun accounted for the apparent movement of the heavenly bodies. Galileo believed in the Copernican rather the Ptolemaic system, which had held sway ever since Aristotle and his successor Ptolemy. The Ptolemaic view, that the Earth was the center of the universe and all heavenly bodies revolved around it, was insinuated by Catholic teachings to be supported by the Bible and was therefore upheld by the Vatican.

Even as he published his tidal theory in 1616, however, Galileo may have had some lingering doubts about it. At the end of the "Treatise," he says he hopes his idea "does not turn out to be delusive, like a dream which gives a brief image of truth followed by an immediate certainty of falsity. This I submit to the judgment of intelligent investigators." Such scientific investigators would not appear for some time, and then, alas, they would judge him wrong.

In deep water

In the meantime, Galileo had to face investigators of a different stripe: inquisitors. Within two months, the Inquisition placed Copernicus's book on the Index of Prohibited Books. Called before the Pope's theological adviser, Roberto Cardinal Bellarmino, Galileo was forced to agree not to defend or hold Copernicus's doctrine.

For years, Galileo kept his thoughts on the matter close to his chest, but eventually he could contain himself no longer. He fervently believed Copernicus was right, and he would tell the world. In 1632, Galileo published his Dialogue Concerning the Two Chief World Systems. During the six years he had labored on it, Galileo's working title for the book had been On the Flux and Reflux of the Sea, and indeed, he reprised his 1616 argument in the last of the book's four sections.

All the old arguments were there. At one point, for example, one of the book's three main characters, Salviati, who is a thinly disguised stand-in for Galileo, says, "Among all the famous men who have philosophized [about the tides], I wonder more at Kepler than any of the rest. Though he is a free and acute genius, he has lent his assent to the moon's dominance over the oceans and to other occult happenings and other such trifles."

In a dramatic way, Galileo also broke his promise to obey the Church's mandate not to espouse the Copernican system. The Dialogue represents, as another superior thinker, Albert Einstein, put it in a foreword to a 1953 edition of the book, "a downright roguish attempt to comply with this order in appearance and yet in fact to disregard it. Unfortunately, it turned out that the Holy Inquisition was unable to appreciate adequately such subtle humor." Galileo was placed under house arrest and the Dialogue banned.

A strenuous quest

Einstein had keen insights on why Galileo acted so rashly. First of all, it was Galileo's longing to find a mechanical proof of the Earth's motion, Einstein felt, that misled him into not only formulating but clinging so tenaciously to his flawed theory on the tides. The planet's motion accounts for the tides, Galileo posited, and the tides account for the planet's motion—it was all so neat. Moreover, all Galileo's astronomical observations convinced him that Copernicus was correct, and he wanted desperately to prove that fact scientifically. As Einstein put it, "His aim was to substitute for a petrified and barren system of ideas the unbiased and strenuous quest for a deeper and more consistent comprehension of the physical and astronomical facts."

Even Galileo's greatest blunder reveals his greatest strength as a scientist. Referring to the tidal theory, Stillman Drake, a leading Galileo scholar, once wrote, "The prime source of Galileo's effectiveness was his bringing together of mathematics, astronomy, and physics in an inseparable relationship. Hence even a questionable example of such a relationship given by him was still capable of revealing to others what sort of thing should be sought after in constructing a scientific explanation." For another view of Galileo's contribution, see His Place in Science.)

That is, even though Galileo was wrong in this instance, he was right about the direction of science (and showed it by example): away from a more speculative, deductive approach and towards a more empirical, experimental method. Galileo didn't make it into Lord Kelvin's seminal paper on the tides. But for all his work, including his tidal theory, he secured a place in history as the first modern scientist.

"Galileo's Discourse on the Tides," by Galileo Galilei. In The Galileo Affair: A Documentary History, edited by Maurice A. Finocchiaro (Berkeley, Calif: University of California Press, 1989). Dialogue Concerning the Two Chief World Systems: Ptolemaic and Copernican, by Galileo Galilei (New York: The Modern Library, 2001). "The Tides" [Evening Lecture to the British Association at the Southhampton Meeting, Friday, August 25th, 1882], by Sir William Thomson (Lord Kelvin). See www.bartleby.com/ 30/16.html

His Life An illustrated chronology of Galileo's life.   His Place In Science Why Galileo is the father of modern science. His Telescope (and Sir Isaac's) On Galileo's refractor and Newton's reflector.   His Big Mistake How and why Galileo got it wrong about the tides. His Experiments Falling objects, inclined planes, and more.

Peter Tyson is editor in chief of NOVA online.