 So this talk will be about Garristotle's views on falling bodies and in particular about whether he really thought that heavier bodies fall faster than light ones. So many people have heard about all the mistakes made by Garristotle. For example, he not only was supposed to have said that heavy bodies fall faster than light ones but also that men are more teeth than women and so on. Now if you stop and think about some of these claims you'll realise there's something a bit fishy about them because many of these things Garristotle is supposed to have said are not just wrong but it's trivial to show they're wrong. So the internet is something called an evil overdo list of rules that you should follow if you're trying to conquer the universe. One of which says you should show your master plan to an eight-year-old child and if the eight-year-old child can see something wrong with it maybe you should revise your plan. We should apply this rule to these statements that Garristotle is supposed to have made. If we think Garristotle made a statement that an eight-year-old can see is wrong in three seconds then just maybe Garristotle didn't actually make that statement or maybe we misunderstood or something. So let's have a look at these claims that Garristotle said heavy bodies fall faster than light bodies. Everyone who has taken a physics class has heard the story that Galileo disproved the claim that heavy bodies fall faster by dropping a couple of walls off a tower. It's not entirely clear if Galileo really did this. He may well have done because he was really good at self-publicity. And in any case the experiment became so popular afterwards that you get the impression that one of the main hazards of walking around Italian cities was being hit on the head by balls dropped by philosophers. Anyway Galileo certainly did do experiments with balls rolling down inclined planes to slow them down so he would see how fast they went and he definitely discovered that heavy balls roll at much the same speed as light balls and was able to show the acceleration was constant and pretty much invented experimental physics. However you don't need to do such complicated experiments to show that heavy bodies fall at the same speed as light bodies. You don't need to climb towers or do inclined planes. Anyone can do this experiment in two seconds. Here we go. I pick up the small rock and the big rock and I drop them at the same time and I can see that they're going at the same speed within a few percent and it's completely absolutely obvious that the stone that is 10 times heavier does not fall 10 times as fast when you drop this. So not only is it stupid to believe that freely falling bodies fall at a speed proportion to their weight but it's also stupid to believe that Aristotle thought this because Aristotle wasn't a complete moron and couldn't possibly have believed this. Well, okay. Well, let's see what Aristotle did actually say. Let me just get this camera working. Okay, so we have a section from Aristotle here where he says, if we look here, he says a given weight moves a given distance in a given time, a weight which is as great and more moves the same distance in less time the time is being in inverse proportion to the weights. So this is his book on the heavens, book one chapter six if you want to check. So he says, for instance, if one weight is twice another it will take half as long to fall over a given movement. So that seems to be pretty unambiguous. Aristotle was saying that heavy bodies fall faster than light bodies. On the other hand, if we look at this paper here, it's from nature January the 2nd 1914, page 584 if you want to look it up. There's a letter from a guy called Hard Castle who said this idea that Aristotle made this claim is just nonsense. So here he gives a story about a physics teacher claiming that Aristotle had said that a 10 pound weight would fall 10 times as fast as a one pound weight and the physics teacher was mocking Aristotle. And here, Hard Castle says the physics teacher was wrong. Hard Castle says explicitly that Aristotle never said this at all. Well, we seem to have something a bit puzzling going on. On the one hand, Hard Castle says that Aristotle never said this. I've said that Aristotle never said this. And on the other hand, I've just shown you a passage in Aristotle where Aristotle really seems to say it. So what is going on? Well, Hard Castle explains this. It's a problem of misinterpretation or mistranslation that the words that Aristotle used like speed or force which have been translated as speed and force don't have exactly the same meanings to Aristotle as they do to us. So let's have another look at a different section by Aristotle. If we look at this section here. Okay, he's talking about falling bodies. He says we see the same weight or body moves faster than another for two reasons, either because there is a difference in what it moves through as between water and earth or because the moving body differs owing to excessive weight or lightness. I think that's something to do with buoyancy, although it's a bit hard to tell. And he says a medium causes a difference because it impedes moving things. In other words, Aristotle is explicitly considering bodies moving in mediums and is explicitly not considering freely falling bodies. Furthermore, when he's talking about the speed of bodies, he's not talking about the speed of bodies the moment you drop them. It's exactly clear what he is talking about. But one rather obvious possibility is that when he was talking about the speed of a body falling in the medium, he was discussing the terminal velocity. So this is at least consistent with what he said in his book. So if he's talking about the terminal velocity of a body moving in water, then it is indeed true that heavier ones will tend to fall faster than light ones. You can test this yourself by taking a big stone and a small stone and dropping them in a puddle of water. And although Aristotle has a reputation for not doing experiments, this is absolute nonsense. If you read his book, they are full of experimental observations and he almost certainly did drop a couple of stones in a puddle of water to see what happened. So the exact speed with which things fall in water is complicated because you've got the Navier-Stokes equation which is highly nonlinear. But to a first approximation, the terminal velocity is indeed roughly proportional to the weight. And it also depends on lots of other things, you know, viscosity in the shape of the body and buoyancy in heaven knows what else. But Aristotle's claim that the terminal velocity of falling bodies in water is proportional to the weight is simply correct. One of the problems of trying to sort this out is that Aristotle was really considering at least three different effects all at once. The force on the body due to gravity, the force caused by buoyancy. He distinguishes a lot between light bodies and heavy bodies where a light body is one that tends to go upwards and a heavy body is one that tends to go downwards. And finally, there's the resistance caused by the air or water that it falls through. So Galileo had this really brilliant idea of eliminating two of these complications by rolling balls down inclined planes which makes things much simpler. Incidentally, there's one extra complication with balls rolling down inclined planes that the ball is actually rotating. So it actually ends up going slightly slower than you might expect because some of the kinetic energy gets converted into rotational energy rather than translational energy. So let's take a look at another famous passage in Aristotle where he seems to prove that there is no vacuum. So if we take this book here and look at this passage, he says that bodies which have a greater weight or lightness move faster over an equal space. Well, what does that mean? Well, as I said, I think it means the terminal velocity of a heavier body will be larger. And therefore, he says, therefore they will also move through a vacuum at this ratio. Then he says a very interesting sentence, but that is impossible for why should one move faster. So what he seems to be saying here is that in a vacuum, heavy bodies will move at the same speed as light bodies. And that's kind of remarkable because it's pretty much exactly what Galileo claimed a thousand or 2,000 years later, that if bodies are in a vacuum, then their speed doesn't depend on their weight. So Aristotle seems to make a brilliant insight but then completely grabs the wrong end of the stick and deduces from this that you can't have a vacuum. And this argument seems to be in a vacuum, a heavy body would go at the same speed as a light body, but we know that heavy bodies always go faster than light bodies in a medium if you're talking about their terminal velocity and deduces from that contradiction that you can't have a vacuum. I think the error here is that instead of deducing that you can't have a vacuum, you should have deduced that you can't have a terminal velocity in the vacuum, which is subtly different. So he's not making a stupid mistake. He's making a rather subtle error. So what's the conclusion? Well, so our conclusion is that we can't really say whether Aristotle was wrong or not about falling bodies because there is so much uncertainty about what he meant. So we've said that when he talked about speed he was talking about the terminal velocity of something in a medium and that's plausible, but we can't really be certain about this. My only opinion is that when he was talking about speed he was quite often referring to the terminal velocity rather than the instantaneous speed and that with this interpretation most of his statements about falling bodies are roughly correct, at least for common cases such as stones falling in water. And his implicit claim that in a vacuum bodies move in the same way under a force is, of course, also correct if that's what he was saying. Well, of course, his conclusion that a vacuum can't exist is a bit fishy and his argument just seems unsound and I can't see any way to make it correct. So in other words, he's correct about most things when interpreted properly, but was sometimes either rather unclear about what he was talking about or just occasionally makes, made a minor mistake. I mean, Aristotle was basically trying to invent physics, biology, politics, law, logic all at the same time and of course he made a few small errors. Any pioneer does. And there's very little justification for the widespread claims that he made rather stupid and obvious errors about falling bodies.