The Case Against Galileo

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

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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

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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

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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…

Episode #5: Galileo’s Errors on Projectile Motion and Inertia

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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….

Episode #6: Why Galileo is Like Nostradamus

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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.

Episode #7: Galileo’s Theory of Tides

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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.

Episode #8: Heliocentrism in Antiquity

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

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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!

27 thoughts on “The Case Against Galileo

  1. This all may be true, but it still makes me a little sad. It’s a little like I felt when I learned that Thomas Jefferson may not have truly believed that “All men are created equal.”

    1. Yeah, I feel that – though moral credibility is a very different thing than scientific credibility! It’s Jefferson’s soul on the line, whereas Galileo has only his C.V. to lose.

      On the brighter side, this revisionism lets us shift the focus to other scientific leaders, less famous than Galileo and perhaps worthier of discussion: Mersenne, Kepler, Cavalieri…

  2. The notion of “the Humanities” as opposed to “the Sciences” is a modern one, and would have baffled people at the time of Galileo (as would the distinction between philosophers and mathematicians). Galileo’s position as a populariser rather than an innovator has long been known — this seems simply to stir in modern Social-Media-style anger and bluster, and a lack of understanding of intellectual history. Better to read an actual book, peer reviewed, by someone who knows what she’s writing about — there are plenty out there. Podcasts… now rinse and spit.

    1. “Social-Media-style bluster” is certainly a fair charge! There’s plenty in the original, although my excerpts no doubt skew the bluster-to-history ratio further.

      Is “populariser rather than innovator” the consensus on Galileo among historians and philosophers of science? That view doesn’t seem to filter out into the popular literature (where he’s painted as Bacon’s peer in creating the foundations of empiricism, and Kepler’s in presaging Newtonian physics, plus more). But that would hardly be the first time that the popular literature missed the scholarly consensus!

      1. I’m a bit behind on the history-of-science literature, to be honest — the notion of Galileo as a populariser rather than an innovator was something I learnt as an undergraduate back in the early 1980s, gleaned from books such as Thomas Kuhn’s 1962(!) book “The Structure of Scientific Revolutions”. A more recent book, which is well worth reading, is Michael Sharratt’s “Galileo: Decisive Innovator” (Cambridge Science Biographies) — it presents him as a populariser of the new science, though is a lot more generous to him with regard to his own work. Incidentally, the notion of Galileo dropping rocks (or a cannon ball and a feather, or whatever) from a tower has long been exploded; the actual experiment involved an inclined plane, and Galileo wasn’t the first to perform it.

        1. Thank you – I’m reading a little of Kuhn’s discussion now! And I’ll seek out Sharratt’s writing before I pretend to have any notion of what words should complete the sentence “Galileo was a popularizer ___ an innovator.” (Is it “and”? “More than”? “Rather than”?)

          I do hope Viktor writes something on Galileo, too! I love podcasts, but they’ve got their limitations, of course.

  3. Personally, I’d rather read a paper on the subject than listen to a podcast, where in the latter, one could inadvertently (or not) be a little looser with sources and accuracy.

      1. I do love me some thonyc, and that is the format that I prefer, but I was more interested in the aspects of Galileo’s relationship with mathematics. Though I guess this does go to show that Galileo is supremely overrated.

        1. This is my first experience with thonyc! I’m impressed.

          I was just reading a 2010 post (can’t find the link now) in which thonyc gets more into the weeds on the “geocentrism vs. heliocentrism,” making a case that Galileo was pretty irrelevant to the scientific debate, in large part because he just wasn’t engaging at the appropriate level of mathematical technicality.

          Tried to find that piece by searching, but thonyc has a *lot* of Galileo-skeptical writing!

  4. I tend to celebrate Galileo in math history as the guy who mathematized science. He was a math fan boy, and his efforts to describe motion and position vs time were the start of something great. The reasons math became fashionable are connected to this need to describe nature with it.

    1. Yeah, this is more or less the history I’ve always heard, and never had any reason to question. Certainly the intellectual steps attributed to Galileo in this account seem very important!

      What this podcast brought to my attention (and what I hadn’t known before) was that there’s a serious strand of scholarship arguing that the steps attributed to him may not really be his. Like, maybe he brought these ideas (heliocentrism, principles of empiricism, the idea that math is the language of physical motion) to a wider literate audience, but didn’t really change the trajectory of science’s internal development.

      One thing I’m curious about: Blasjo makes a lot of the church’s censorship of heliocentrism, as a reason why other Copernicans were shy about coming forward. But I’ve seen others making exactly the opposite argument – that the church wasn’t super invested in geocentrism, and that Galileo’s alienation from the church was driven by other factors.

  5. You point out that ancients had already got to some of the ideas attributed to Galileo: pause to remember, though, that Galileo’s contemporaries were likely unaware of those ancients. They knew a select few of the ancients and regarded only some of them as trustworthy sources. An ancient they’d never heard of, or that wasn’t taken seriously, isn’t relevant to Galileo’s significance: what matters is that he got more folk to take some ideas seriously. Whether what he was saying was original is far less important than the fact that he managed to get it listened to.

    Our culture likes myths of heroes and genius, so tends to paint a few people as such, exaggerating their achievements while ignoring all the other folk who made their (actual) achievements possible. Inevitably, the popular myth of Galileo thus grew beyond the reality, ignoring his deficiencies along the way. Scholarship usually has a rather toned-down view of figures that culture has magnified in this way; the reality is usually that plenty of their contemporaries were having thoughts along similar lines, some of them taking them further and closer to what we’ve later settled on, but the ones who are remembered managed to get public attention, for one reason or another, so they’re who gets the credit. Occasionally two have to share, as Newton and Leibniz with the calculus, but even then the popular account makes it sound like it came out of the blue – ignoring the well-established work that surely contributed to the idea behind it.

    (Aside: polynomial f(x) = sum a_i x^i; chord gradient (f(u) -f(v)) / (u – v); for each power i, (u^i -v^i)/(u -v) is the usual sum of i terms, u^{i-1} +u^{i-2}.v +… +u.v^{i-2} +v^{i-1}; multiply by a_i and sum over i to get the gradient of the chord (f(u) -f(v))/(u -v). Since the numerator did have the denominator as a factor, we’re rid of that pesky denominator and can now let u and v get arbitrarily close without having to think too hard about what the gradient’s going to be; when they coincide, it’ll be sum i a_i u^{i-1}, and its value for v close enough to u will necessarily (as the polynomial is continuous) be close to this. Although you might have qualms about using the value at u=v as a gradient of anything, we get a polynomial in two free variables that does give exact chord gradients and does make it entirely natural to interpolate the u=v value as the gradient of a tangent. Newton and Leibniz managed to formalise this without relying on f being a polynomial; which *is* an important leap; it just doesn’t come out of nowhere.)

    Myths of heroes and genius give us a simple story to anchor new ideas to, that helps culture assimilate the idea; during the course of doing so, it distorts the truth of whence the idea came because that’s less important than getting the lesson assimilated. Later we can go back and fix up the reality of those historical figures who don’t quite match the myths that got attached to them. The same goes for demons, for that matter – The Spanish Inquisition was grossly misrepresented by protestants (particularly in Holland and the North American colonies), building up a myth that barely resembles the historical reality. This is how cultures mangle their past; fortunately, we’ve had writing for a few millennia now, so we often have contemporary sources historians can consult to rediscover the original. Which is worth doing, so I hope you enjoy the podcasts.

    1. … and I neglected to say: so, rather than “the case against Galileo”, think in terms of “the case against the mythology that has accreted around Galileo” and, putting all that mythology aside, take some time to learn what Galileo actually did and to appreciate him for who he actually was. Far more mortal and flawed than the myth, but an interesting and worthy chap, none the less. Try Dava Sobel’s “Galileo’s Daughters” for a sympathetic-ish picture of him.

  6. Worry I don’t have the intellectual rigor of some of the posters, and can’t cite sources. However, I’d heard/read that Arabs already had much more significantly evolved mathematics (and astronomy) long before the Greeks. I probably read it in one of the more scholarly and less sensational articles on the Antykethera device.

    1. Well, the ancient Greek civilisation’s heyday came long before that of the Arabic civilisation, so I suspect there’s some garbling there; but Europe got its Greek learning from the Arabs, who’d improved it and enhanced it in various ways along the way, including merging it with some important learning from India (which was probably a source for the Greeks also), notably the better system for representing numbers. An Arab (after whom algorithms are named) was responsible for the invention of algebra and the reinterpretation of lots of geometry in terms of it. (Arabs also worked out how to square Greek philosophy (coming from a polytheistic culture) with a monotheistic religion; the resulting synthesis was then taken over wholesale, with minor adaptations, by Thomas Aquinas and others to give Christianity a philosophical rationale. Meanwhile Arab alchemists invented the alembic with which to purify an essence that came to be known as alcohol. You’ll notice a lot of words starting with “al” here; it means “the” in Arabic, IIRC.) Christians appropriating all this learning weren’t always eager to credit the Arabs with it, but crediting the Greek precursor sources (where there were any) was totally cool. All of which is roughly why the Renaissance happened.

      So *after* the Greeks (and with input also from India and possibly elsewhere), Arabs did indeed significantly advance mathematics (and astronomy); and it’s on the result of the Arabs’ work (and that of some intervening Europeans) that Galileo was building.

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