Galileo is praised for his work on falling bodies, but his arguments were dishonest and his trifling discoveries were not new.
Opinionated History of Mathematics
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In 1971, Apollo 15 astronauts conducted a famous experiment on the moon. Here’s a bit of the original recording:
“In my left hand I have a feather. In my right hand a hammer. And I’ll drop the two of them here and hopefully they will hit the ground at the same time. How about that? Mr Galileo was correct.”
Actually, no. Mr Galileo was not correct. What the astronauts should have said is: Mr Galileo was wrong. According to Galileo, the moon has an atmosphere like the earth. So the feather should fall more slowly then, just like on earth. Galileo even claimed that this is “obvious” that the moon has an atmosphere. Obvious! That’s his word. This is in the Sidereus Nuncius, one of his famous published works. It is “obvious” that “not only the Earth but also the Moon is surrounded by a vaporous sphere.” Those are Galileo’s own words.
So if the astronauts wanted to test Galileo’s theory they should not have dropped a hammer and a feather. They should have taken off their helmets and suits and tried to breathe. That would have showed you how “right” Galileo really was.
But ok, let’s put the issue of the moon’s atmosphere aside. Heavy objects fall as fast as light ones, if we ignore air resistance. We are often told that this is one of Galileo’s most fundamental discoveries, and also that he supposedly destroyed the Aristotelian theory of physics on this point by simply dropping some objects of different weight from the Leaning Tower of Pisa. That was allegedly an eye-opening moment in which the world realised that empirical science is more reliable than philosophy and the words of ancient authorities. So goes the story-book version. Let’s see how much truth there is to these things. If any.
Galileo indeed often portrays himself as defeating obstinate philosophers who would rather cling to the words of Aristotle than believe empirical evidence and experimental demonstration. He imagines his enemies to say things like: “You have made me see this matter so plainly and palpably that if Aristotle’s text were not contrary to it, I should be forced to admit it to be true.” That’s a quote from one of Galileo’s dialogues. Galileo likes to pretend that his enemies are like that. It makes life easy for him. But in reality Galileo’s “anti-Aristotelian polemics were directed only at straw men.” Galileo concocted these caricature Aristotelians in order to “let them play the buffoon in his dialogues, and thus enhance his own image in the eyes of his readers,” as one historian has aptly put it.
Galileo’s ploy was well calculated. It tricks many of his readers to this day into believing the fairytale of Galileo the valiant knight singlehandedly fighting for truth in world beset by dogmatism. But “excessive claims for Galileo the dragon slayer have to be muted,” as one overly diplomatic historian puts it. Such ridiculous characterisations of Galileo should not only be “muted” but actively reversed.
This is clearly seen in the case of that famous question: do heavy objects fall faster than lighter ones? Aristotle had answered: yes. Twice as heavy, twice as fast. According to Aristotle.
Legend has it that Galileo shocked the world when he dropped some balls of different weight from the tower of Pisa and revealed them to fall at the same speed. But the notion that it required some kind of radical conceptual innovation by a scientific genius like Galileo to realise that one could test the matter by experiment is ludicrous and idiotic. Of course one can drop some rocks and see if it works: this much has been obvious to any fool since time immemorial. 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. This is just a plain fact. We have the source.
So if you want to believe that experimental science and empirical verification was a radical new insight then this puts you in quite a pickle. If that was a revolution, then why is it found for the first time in this extremely mediocre commentator from the 6th century? If these people had the key to science, then why did sit around and write commentary upon commentary on Aristotle? Their contributions to mathematics and science is otherwise zero. Do you really expect anyone to believe that the principles of scientific method escaped the many first-rate minds of the age of Archimedes, only to be discovered by utter nobodies in an age of vastly, incomparably lower intellectual quality? How likely is it that such elementary scientific principles eluded generations of the best mathematical minds the world has ever seen, only to be then discovered by derivative and subservient thinkers in an age where the pinnacle of mathematical expertise extended little further than the ability to multiply 3-digit numbers?
It doesn’t make any sense. So that’s a proof by contradiction that testing things empirically was never revolutionary. It is a trivial idea that any fool has always considered obvious.
Indeed Galileo was far from original in his own age either. Have you ever heard anyone calling Benedetto Varchi “the father of modern science”? Yet here is his statement of “Galileo’s” great insight, expressed two decades before Galileo was even born. Quote:
“The custom of modern philosophers is always to believe and never to test that which they find written in good authors, especially Aristotle. [But it would be] both safer and more delightful to descend to experience in some cases, as for example in the motion of heavy bodies, in which both Aristotle and all other philosophers without ever doubting the fact, have believed and affirmed that according to how much a body is more heavy, by so much more [speed] will it descend, the test of which shows it not to be true.”
All of that is a quote from a run-of-the-mill humanist writing in 1544, long before Galileo. That just goes to show what an obvious idea it was.
It is not clear whether Galileo did in fact carry out such an experiment from the tower of Pisa when he was teaching at the university there, as legend would have it. Personally I find the story plausible since a field day throwing rocks surely had great appeal to a professor who wasn’t very good at thinking. But be that as it may. It is in any case perfectly clear that many people carried out such experiments around that time, independently of Galileo. Simon Stevin, for example, in the Netherlands, certainly did, and published his results years before Galileo made his experiment, if indeed he ever did. Stevin used lead balls of different weights. He dropped them from a height of 30 feet. And on the ground he had placed some metal sheet or something that would make a lot of noise. So you could hear whether they banged down at the same time or not. So again a way of avoiding the need for stopwatches or high-speed cameras by relying on our natural hearing which is pretty good at this. And Stevin was not the only one. In Paris, Mersenne was doing the same thing. He was dropping weights out out Parisian chamber windows before he ever heard of Galileo.
Here’s a quote from Butterfield: “To crown the comedy, it was an Aristotelian who in 1612 claimed that previous experiments had been carried out from too low an altitude. In a work published in that year he described how he had improved on all previous attempts—he had not merely dropped the bodies from a high window, he had gone to the very top of the tower of Pisa. The larger body had fallen more quickly than the smaller one, and the experiment, he claimed, had proved Aristotle to have been right all along.”
Galileo himself once cited another Aristotelian philosopher who conducted similar experiments. In order to investigate whether lead falls faster than wood, “we took refuge in experience, the teacher of all things,” says this author, and hence “threw these two pieces of equal weight from a rather high window of our house at the same time. The lead descended more slowly. Not only once but many times we tried it with the same results.” That’s a work from 1575.
So much for Aristotelians hating experiments. On the contrary, appeal to experiments were commonplace long before Galileo. But these guys got the result wrong, you say. Maybe they didn’t experiment at all, or if they did they messed it up somehow.
Well, so did Galileo. You remember how he got the wrong value for the area of the cycloid? So also for falling bodies. He messed that up too at first. In his earlier notes on this he writes: “If an observation is made, the lighter body will, at the beginning of the motion, move ahead of the heavier and will be swifter,” but if the fall is long enough the heavier body will eventually overtake it. Galileo devotes a full chapter to following this up, in which, in his words, “the cause is given why, at the beginning of their natural motion, bodies that are less heavy move more swiftly than heavier ones.”
So when Galileo started experimenting on this he got the wrong result, and he also believed himself to a have a good theory “explaining” those false results. We now know that the true cause for the erroneous results was not a theoretical one like Galileo imagined, but more likely a more pedestrian circumstance. Namely, that we are not good at dropping one object from each hand at the same time. Modern experiments show that people tend to drop the lighter object sooner, even though we feel that we have dropped them at the same time. This is why Galileo and others ended up thinking that lead balls started out slower than lighter bodies and only then picked up speed.
With experiments being so inconclusive, then, it is no wonder that Galileo relied more on a theoretical argument in his published account. His supporters would have us believe that “Galileo showed that Aristotle’s rule could be refuted by logic alone.” His argument is supposedly a “splendid and incontrovertible” model example of “cast-iron reductio ad absurdum reasoning.” Those are quotes from Galileo scholars. And they are all wrong.
Here is the quote from Galileo: “By a short and conclusive demonstration, we can prove clearly that it is not true that a heavier moveable is moved more swiftly than another, less heavy. If we had two moveables whose natural speeds were unequal, it is evident that were we to connect the slower to the faster, the latter would be partially retarded by the slower. But the two stones joined together make a larger stone; therefore this greater stone is moved less swiftly than the lesser one. But this is contrary to your assumption. So you see how, from the supposition that the heavier body is moved more swiftly than the less heavy, I conclude that the heavier moves less swiftly.”
“From this we conclude that both great and small bodies, of the same specific gravity, are moved with like speeds.” Furthermore, “if one were to remove entirely the resistance of the medium, all materials would descend with equal speed.”
All of that is Galileo, his celebrated argument. With this argument Galileo allegedly exposes a fundamental logical inconsistency in the Aristotelian theory of fall. Except he doesn’t. Aristotle is perfectly clear: heavier objects fall faster. So when you put the heavy and the light together they will fall faster. The inconsistency arises only when one inserts the additional assumption that when you put two bodies together the lighter will retard the heavier and slow it down. But there is no basis whatsoever for this latter assumption in Aristotle. It is a fiction that Galileo has made up. Only by dishonestly misrepresenting the view he is trying to refute in this way is he able to draw his triumphant conclusion.
A more honest form of the argument, which doesn’t depend on misrepresenting Aristotle, is the following.
Consider two identical bricks. If you drop them at the same time they would fall side by side. Of course. If a loose string connected them that wouldn’t make any difference. What if you glued the bricks together? According to Galilean logic, “no reason appears why this double brick of double weight should fall faster than two bricks tied together—or either one alone.”
Galileo was aware of this form of the argument, it’s in some notes of his. Although he decided to use the more dishonest version in his published work.
Anyway, what this shows, then, is that the real crux of the argument is the claim that two bricks held side by side should behave the same way in terms of fall whether they are glued together or not. This is not a bad argument, but it is not a matter of “logic alone” as the Galileo fans would have us believe. For instance, imagine you are taking a basketball free throw. You can choose between trying to hit the hoop with either two bricks glued together or two bricks merely held side by side as you throw them. Would you really say that “no reason appears” why nature should treat the two cases differently, so you might as well go with the loose bricks? I don’t think so. Then why accept this assumption in Galileo’s case?
So, if we’re being honest, we are back to having to rely on experiment after all. Galileo indeed discusses the experimental side of the matter too in his treatise. He admits that actual experiments do not come out in accordance with his law because of air resistance. But, he says, the fit is much better than for Aristotle’s law. He gives specific numbers for this. Exact measurements of how much the slower ball lags behind the heavier one. But this is fake data. He cooks the numbers to sound much more convincing in favour of his theory. The actual lag or difference between the two bodies is more than 20 time greater than the fake data Galileo reports in his published so-called masterpiece. “In no case could Galileo have consistently achieved the results he reported,” as one scholar says.
Nevertheless it remains true that Galileo’s law doesn’t fare as poorly as that of Aristotle in this experiment. So wow, what a hero, the great Galileo. He managed to improve on a two-thousand-year-old claim, made by a non-mathematician, which not a single mathematician ever believed. And which Aristotle himself obviously did not intend as quantitative science. Aristotle only introduced his so-called law very passingly and parenthetically as a stepping-stone toward making the philosophical point that there can be no such thing as an object of infinite weight. That’s one paragraph buried somewhere in the middle of his voluminous metaphysics, never to be used again.
Aristotle did not claim or intend his law as a definitive or quantitative treatment of falling bodies. Only later fools who clung to his words like gospel because they could not think for themselves made a big thing of this so-called law of fall. Kind of like some people seized upon some obscure remark in the Bible and gave it all kinds of significance beyond the apparent intent of the text.
Nobody was so foolish in antiquity as far as we know. As we saw, even people like Philoponus, who were so obsessed with Aristotle that they wrote long commentaries on his every word, even people like that rejected the law. In fact, “Galileo’s” discovery, so-called, that in the absence of air resistance, all objects fall at the same speed regardless of weight—that law is in fact not first stated by Galileo, as so many people believe. Rather it is explicitly stated by Lucretius, well over a thousand years before Galileo. “Lucretius was correct”; that’s what the astronauts should have said. As ever, Galileo gets credit for elementary ideas that are thousands of years old. In his own time too, a number of people discovered “Galileo’s” law of fall independently of him: certainly Thomas Harriott and Isaac Beeckman; arguably Descartes as well.
So we see how dependent Galileo is on the framing of him versus Aristotle. No wonder he clings to this and uses it as the trope of his dialogues. Galileo’s entire case rests on his readers considering Aristotle to be a great authority. If we admit the truth—that Aristotle’s law had been refuted more than a thousand years before, and that the ridiculous idea of relying on Aristotle for quantitative science would never have entered the mind of any mathematically competent person in Galileo’s time or in antiquity—then what does Galileo have to show for himself? An unproven claim that doesn’t even fit the fake data Galileo has specifically concocted for the purpose, let alone the many experiments that proved the opposite, including his own before he knew which way he was supposed to fudge the data. Galileo likes to portray himself as doing the world a great service by defeating the rampant Aristotelianism all around him. The truth is that he is rather doing himself a great service by pretending that these Aristotelian opinions are ever so ubiquitous, so that he can inflate the importance of his own contributions, the feebleness of which would be all too evident if he addressed actual scientists instead of straw men Aristotelians.
So, with all these arguments we have done quite a bit of damage to Galileo’s claim to credit for his law of fall, I believe. But we’re only getting started. There’s plenty more to come, including several howlers Galileo made when he tried to apply his law. But that’s for another day.