Every few years, for a handful of minutes or so, science shines while the sun goes dark.

A total eclipse of the sun is, for those who witness it, something like a religious experience. For those who understand it, it is symbolic of science’s triumph over mythology as a way to understand the heavens.

In ancient Greece, the pioneer philosophers realized that eclipses illustrate how fantastic phenomena do not require phantasmagoric explanation. An eclipse was not magic or illusion; it happened naturally when one celestial body got in the way of another one. In the fourth century B.C., Aristotle argued that lunar eclipses provided strong evidence that the Earth was itself a sphere (not flat as some primitive philosophers had believed). As the eclipsed moon darkened, the edge of the advancing shadow was a curved line, demonstrating the curvature of the Earth’s surface intervening between the moon and sun.

Oft-repeated legend proclaims that the first famous Greek natural philosopher, Thales of Miletus, even predicted a solar eclipse that occurred in Turkey in 585 B.C. But the only account of that prediction comes from the historian Herodotus, writing more than a century later. He claimed that during a fierce battle “day suddenly became night,” just as Thales had forecast would happen sometime during that year.

There was an eclipse in 585 B.C., but it’s unlikely that Thales could have predicted it. He might have known that the moon blocks the sun in an eclipse. But no mathematical methods then available would have allowed him to say when — except, perhaps, a lucky coincidence based on the possibility that solar eclipses occurred at some regular cycle after lunar eclipses. Yet even that seems unlikely, a new analysis posted online last month finds.

“Some scholars … have flatly denied the prediction, while others have struggled to find a numerical cycle by means of which the prediction could have been carried out,” writes astronomer Miguel Querejeta. Many such cycles have already been ruled out, he notes. And his assessment of two other cycles concludes “that none of those conjectures can be regarded as serious explanations of the problematic prediction of Thales: in addition to requiring the existence of long and precise eclipse records … both cycles that have been examined overlook a number of eclipses which match the visibility criteria and, consequently, the patterns suggested seem to disappear.”

It’s true that the ancient Babylonians worked out methods for predicting lunar eclipses based on patterns in the intervals between them. And the famous Greek Antikythera mechanism from the second century B.C. seems to have used such cycle data to predict some eclipses.

Ancient Greek astronomers, such as Hipparchus (c. 190–120 B.C.), studied eclipses and the geometrical relationships of the Earth, moon and sun that made them possible. Understanding those relationships well enough to make reasonably accurate predictions became possible, though, only with the elaborate mathematical description of the cosmos developed (drawing on Hipparchus’ work) by Claudius Ptolemy. In the second century A.D., he worked out the math for explaining the movements of heavenly bodies, assuming the Earth sat motionless in the center of the universe.

His system specified the basic requirements for a solar eclipse: It must be the time of the new moon — when moon and sun are on the same side of the Earth — and the positions of their orbits must also be crossing the ecliptic, the plane of the sun’s apparent orbital path through the sky. (The moon orbits the Earth at a slight angle, crossing the plane of the ecliptic twice a month.) Only precise calculations of the movements of the sun and moon in their orbits could make it possible to predict the dates for eclipsing alignments.

Predicting when an eclipse will occur is not quite the same as forecasting exactly where it will occur. To be accurate, eclipse predictions need to take subtle gravitational interactions into account. Maps showing precisely accurate paths of totality (such as for the Great American Eclipse of 2017) became possible only with Isaac Newton’s 17th century law of gravity (and the further development of mathematical tools to exploit it). Nevertheless Ptolemy had developed a system that, in principle, showed how to anticipate when eclipses would happen. Curiously, though, this success was based on a seriously wrong blueprint for the architecture of the cosmos.

As Copernicus persuasively demonstrated in the 16th century, the Earth orbits the sun, not vice versa. Ptolemy’s geometry may have been sound, but his physics was backwards. While demonstrating that mathematics is essential to describing nature and predicting physical phenomena, he inadvertently showed that math can be successful without being right.

It’s wrong to blame him for that, though. In ancient times math and science were separate enterprises (science was then “natural philosophy”). Astronomy was regarded as math, not philosophy. An astronomer’s goal was to “save the phenomena” — to describe nature correctly with math that corresponded with observations, but not to seek the underlying physical causes of those observations. Ptolemy’s mathematical treatise, the Almagest, was about math, not physics.

One of the great accomplishments of Copernicus was to merge the math with the physical realty of his system. He argued that the sun occupied the center of the cosmos, and that the Earth was a planet, like the others previously supposed to have orbited the Earth. Copernicus worked out the math for a sun-centered planetary system. It was a simpler system than Ptolemy’s. And it was just as good for predicting eclipses.

As it turned out, though, even Copernicus didn’t have it quite right. He insisted that planetary orbits were circular (modified by secondary circles, the epicycles). In fact, the orbits are ellipses. It’s a recurring story in science that mathematically successful theories sometimes are just approximately correct because they are based on faulty understanding of the underlying physics. Even Newton’s law of gravity turned out to be just a good mathematical explanation; the absolute space and invariable flow of time he believed in just aren’t an accurate representation of the universe we live in. It took Einstein to see that and develop the view of gravity as the curvature of spacetime induced by the presence of mass.

Of course, proving Einstein right required the careful measurement by Arthur Eddington and colleagues of starlight bending near the sun during a solar eclipse in 1919. It’s a good thing they knew when and where to go to see it.

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