Just a Moment, Galileo

Bruce Vojak’s wonderful piece on innovation and the minds of Newton and Goethe got me thinking about another 17th century innovator. Like Newton, Galileo was a superstar in his day – a status he still holds. He was the consummate innovator and iconoclast. I want to take a quick look at two of Galileo’s errors, one technical and one ethical, not to try to knock the great man down a peg, but to see what lessons they can bring to the innovation, engineering and business of this era.

Less well known than his work with telescopes and astronomy was Galileo’s work in mechanics of solids. He seems to have been the first to explicitly identify that the tensile strength of a beam is proportional to its cross-sectional area, but his theory of bending stress was way off the mark. He applied similar logic to cantilever beam loading, getting very incorrect results. Galileo’s bending stress illustration is shown below (you can skip over the physics details, but they’re not all that heavy).

Galileo's beam bending diagram

For bending, Galileo concluded that the whole cross section was subjected to tension at the time of failure. He judged that point B in the diagram at right served as a hinge point, and that everything above it along the line A-B was uniformly in horizontal tension. Thus he missed what would be elementary to any mechanical engineering sophomore; this view of the situation’s physics results in an unresolved moment (tendency to twist, in engineer-speak). Since the cantilever is at rest and not spinning, we know that this model of reality cannot be right. In Galileo’s defense, Newton’s 3rd law (equal and opposite reaction) had not yet been formulated; Newton was born a year after Galileo died. But Newton’s law was an assumption derived from common sense, not from testing.

It took more than a hundred years (see Bernoulli and Euler) to finally get the full model of beam bending right. But laboratory testing in Galileo’s day could have shown his theory of bending stress to make grossly conservative predictions. And long before Bernuolli and Euler, Edme Mariotte published an article in which he got the bending stress distribution mostly right, identifying that the neutral axis should be down the center of the beam, from top to bottom. A few decades later Antoine Parent polished up Mariotte’s work, arriving at a modern conception of bending stress.

But Mariotte and Parent weren’t superstars. Manuals of structural design continued to publish Galileo’s equation, and trusting builders continued to use them. Beams broke and people died. Deference to Galileo’s authority, universally across his domain of study, not only led to needless deaths but also to the endless but fruitless pursuit of other causes for reality’s disagreement with theory.

So the problem with Galileo’s error in beam bending was not so much the fact that he made this error, but the fact that for a century it was missed largely for social reasons. The second fault I find with Galileo’s method is intimately tied to his large ego, but that too has a social component. This fault is evident in Galileo’s writing of Dialogue on the Two Chief World Systems, the book that got him condemned for heresy.

Galileo did not invent the sun-centered model of our solar system; Copernicus did. Galileo pointed his telescope to the sky, discovered four moons of Jupiter, and named them after influential members of the Medici family, landing himself a job as the world’s highest paid scholar. No problem there; we all need to make a living. He then published Dialogue arguing for Copernican heliocentrism against the earth-centered Ptolemaic model favored by the church. That is, Galileo for the first time claimed that Copernicanism was not only an accurate predictive model, but was true. This was tough for 17th century Italians to swallow, not only their clergy.

For heliocentrism to be true, the earth would have to spin around at about 1000 miles per hour on its surface. Galileo had no good answer for why we don’t all fly off into space. He couldn’t explain why birds aren’t shredded by supersonic winds. He was at a loss to provide rationale for why balls dropped from towers appeared to fall vertically instead of at an angle, as would seem natural if the earth were spinning. And finally, if the earth is in a very different place in June than in December, why do the stars remain in the same pattern year round (why no parallax)? As UC Berkeley philosopher of science Paul Feyerabend so provocatively stated, “The church at the time of Galileo was much more faithful to reason than Galileo himself.”

At that time, Tycho Brahe’s modified geocentric theory of the planetary system (Mercury and Venus go around the sun, which goes around the earth), may have been a better bet given the evidence. Brahe’s theory is empirically indistinguishable from Copernicus’s. Venus goes through phases, like the moon, in Brahe’s model just as it does in Copernicus’s. No experiment or observation of Galileo could refute Brahe.

Here’s the rub. Galileo never mentions Brahe’s model once in Dialogue on the Two Chief World Systems. Galileo knew about Brahe. His title, Two Systems, seems simply a polemic device – at best a rhetorical ploy to eliminate his most worthy opponent by sleight of hand. He’d rather fight Ptolemy than Brahe.

Likewise, Galileo ignored Johannes Kepler in Dialogue. Kepler’s work (Astronomia Nova) was long established at the time Galileo wrote Dialogue. Kepler correctly identified that the planetary orbits were elliptical rather than circular, as Galileo thought. Kepler also modeled the tides correctly where Galileo got them wrong. Kepler wrote congratulatory letters to Galileo; Galileo’s responses were more reserved.

Galileo was probably a better man (or should have been) than his behavior toward Kepler and Brahe reveal. His fans fed his ego liberally, and he got carried away. Galileo, Brahe, Kepler and everyone else would have been better served by less aggrandizing and more humility. The tech press and the venture capital worlds  that fuel what Vivek Wadhwa calls the myth of the 20-year old white male genius CEO should take note.


  1. #1 by Simon on October 29, 2013 - 3:55 am

    Hi – I’ve been really enjoying your series of blogs and also been checking out the links too. One book you may be interested in is “The Wholeness of Nature: Goethe’s Way of Science”. It is written by the late philosopher, physicist and historian of science Henri Bortoft, who as well as Goethe also explains the mode of thinking of Galileo and Newton. This way of thinking, seeing and knowing is extremely important in understanding the process of creativity and innovation in business.

  2. #2 by Tillman Dickson on March 27, 2014 - 9:28 pm

    Two minor things:
    Newton’s first law of motion is a simple restatement if Galileo’s.

    You are, understandably, too kind regarding GG’s ego. While the formal charge was heresy GG hadn’t really said anything in his Dialogue that the Jesuits didn’t know and hadn’t discussed intellectually w GG in the past( it was published w approval if I remember right). Rather, in this particular Dialogue he made a very thinly veiled and brutal mockery of his long-time friend and admirer now pope Urban VIII(?). One should remember that the pope was not only the bishop of Rome, he was also a secular prince with all that entails: fief, army… GG was lucky to not be strangled.

    A very smart man who undertook an exceptionally foolish endeavor.

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