Not long ago, Discover magazine ranked the ten greatest scientists of all time. Galileo came in at #6. Albert Einstein (who earned #1), dubbed him “the father of modern science.” Stephen Hawking agreed. An Italian contemporary declared that “God and Nature have joined hands and created the intellect of Galileo,” which is the kind of thing I’d love to hear in a job performance review.
There’s a time when I’d have heard this Galileo praise, and nodded along.
But lately I’ve been listening to Opinionated History of Mathematics, a podcast by historian of mathematics Viktor Blåsjö. The first season is a startling anti-Galilean polemic, with arguments range from the speculative to the devastating, and from the sassy to the hilariously sassy.
This is no frivolous hit job – there are real historical questions at stake here. How did science go from Ptolemy to Newton? What distinguished empiricism as an approach? Just how much did ancient Greeks know? You’ll find some of Blåsjö’s answers more persuasive than others, but he’s got the receipts, and if you embrace even a fraction of what he says, you’ll find your Galilean faith shaken.
I suggest you listen to the whole thing, but here’s an episode-by-episode teaser. (My apologies to Viktor for eschewing the more subtly argued passages in favor of juicy attacks. I couldn’t help myself.)
Episode #1: Galileo Bad, Archimedes Good
A classic math problem is to find the area of the cycloid. Blåsjö lays out what happened when Galileo attempted it: he floundered, failed, turned to crude trial-and-error, and still got the answer wrong. (Several of his contemporaries, meanwhile, calculated the precise answer.)
This, Blåsjö says, is typical of the fellow from Galilei:
He was not a pioneer of scientific method. He was not the father of modern science. He was not a heroic knight defeating dogmas and superstitions with the light of empirical truth…. Galileo was, first and foremost, a failed mathematician….
Episode #2: Mathematics Versus Philosophy, Then and Now
Galileo’s major works are, in effect, refutations of Aristotle. They’re dialogues between a foolish Aristotelian and a wise Galilean.
But according to Blåsjö, Aristotle was a straw man, whose shortcomings serious mathematicians had always known. Refuting Aristotle is shooting fish in a barrel, and impresses only those who don’t know any better.
Galileo’s books are “Science for Dummies”. He drones on and on about elementary principles of scientific method….
Galileo needs us to assume that… no one had ever heard of Archimedes. Only then do his so-called accomplishments come off looking any good.
Episode #3: Galilean Science in Antiquity?
Millennia before Galileo, were “Galilean” ideas already in circulation? Blåsjö’s says yes.
Either you are a cultural relativist and you think Galileo was a revolutionary… or you think mathematical thought is the same for you, me and everybody who ever lived, and then you think Galileo was just doing common-sense stuff.
(A possible counterargument: shouldn’t we credit Galileo for bringing these “common-sense” ideas to wider audiences? In my view, Blåsjö is too dismissive of popularization. But if the argument turns from “Galileo is the father of modern science” to “Galileo had a big impact as a popularizer,” then I think Blåsjö has already won.)
Episode #4: The Case Against Galileo on the Law of Fall
Among Galileo’s finest achievements: debunking Aristotle’s claim that heavier objects fall faster. (Legend holds, falsely, that he did this by dropping stones from the Tower of Pisa.)
But was the refutation really such an accomplishment? Aristotle makes the claim only once, in a paragraph-long aside; it does not seem central to his thinking. And isn’t the experimental verification a pretty straightforward idea?
Of course one can drop some rocks and see if it works…. In fact, Philoponus—an unoriginal commentator—had clearly and explicitly rejected Aristotle’s law of fall by precisely such an experiment more than a thousand years before Galileo…
Galileo gets a lot of credit for articulating a law of inertia that’s halfway to Newton’s. But he made several big errors; for example, he applied the rule only to objects whose initial motion was horizontal, waffling on whether it applied more broadly.
Calling this “halfway to Newton” is too generous, Blåsjö argues. Even poor, benighted Aristotle articulated a similar idea!
So take your pick. Here are the [two] options:
Option 1. Galileo’s understanding of inertia was very poor.
Option 2. Galileo’s understanding of inertia was pretty good, but so was Aristotle’s….
Galileo made a lot of striking errors. His gravitational constant is way off, because he inexplicably used made-up data. His theory of planetary speeds (that the planets “fell” into the solar system from a tremendous distance) fails the most basic mathematical test. And his “proof” that objects could never fly off the spinning earth is totally wrong (because if the earth spun fast enough, they absolutely could). He even tries to pass off one of his miscalculations as a “joke”!
Why so many mistakes? Blåsjö pulls no punches:
Galileo is another Nostradamus. He too threw a thousand guesses out there and hoped that one or two would stick. Like Nostradamus, Galileo’s reputation rests on his admirers having selective amnesia, and remembering only the rare occasions when he got something right.
Galileo rejected the true explanation of tides (which his contemporaries embraced) as “childish” and “occult.” His alternative theory contradicted all the data, as well as Galileo’s own scientific principles. Blåsjö explains:
Galileo’s theory implies that high and low [tides] should be twelve hours apart rather than six… The fact that everyone could observe two high and two low tides per day Galileo thus wrote off as purely coincidental….
Galileo even has some fake data to prove his erroneous point: namely that tides twelve hours apart are “daily observed in Lisbon,” he believes, even though that is completely false.
Galileo doesn’t just refute Aristotle. He also refutes the geocentric astronomy of Ptolemy.
But did Ptolemy really speak for all Greeks? Blåsjö argues otherwise, speculating that Archimedes’ pal Aristarchus had a well-reasoned heliocentric model.
Nowadays we are stuck with Ptolemy as the canonical source for Greek astronomy. But Ptolemy lived hundreds of years after the golden age of Greek science. It is likely that he was not the pinnacle of Greek astronomy, but rather a regressive later author who perhaps took astronomy backwards more than anything else.
Episode #9: Heliocentrism Before the Telescope
Galileo is remembered today as the greatest champion of Copernicus. But while other scientists filled the margins of Copernicus’s book with calculations and annotations, Galileo’s copy is bizarrely blank, as if he had not given the text a serious reading at all.
Blåsjö quotes another historian:
“…when I saw the copy in Florence, my reaction was one of scepticism that it was actually Galileo’s copy, since there were so few annotations in it. … This copy had no technical marginalia, in fact, no penned evidence that Galileo had actually read any substantial part of it. … Eventually, … I realized that my scepticism was unfounded and that it really was Galileo’s copy.”
There is no need for surprise, of course. Galileo was a poor mathematician.
More episodes are coming. (In an email, Blåsjö told me he’s barely halfway through his Galileo material!) I’m especially eager to hear the next one, which will tackle the discoveries Galileo made with his telescope.
Was Galileo a great scientist? A skilled popularizer? A talentless hack? I don’t honestly know. But the fact that we’re asking the question feels pretty darn radical to me.
EDIT: The first version of this post ran a little too snarky. I’ve toned it down because I find the historical question here – to what degree was Galileo a popularizer instead of an innovator, and how should we value that work? – genuinely interesting. And if you’re thinking, “Wait, this post was once even SNARKIER?” then you see why I changed it!