Philosophy 167: Class 6 - Part 6 - Galileo's Science of Local Motion- the Parameters, the Historical Notion of 'Momenta'

Smith, George E. (George Edwin), 1938-


  • Synopsis: Galileo's concept and definition of motion is different from the modern

    Segment: Class 6, Part 6.

    Opening line: 'What are his parameters, Galileo's parameters, for local motion?'

    Duration: 12:13 minutes.
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What are his parameters, Galileo's parameters, for local motion? Well this is fairly striking. What we're talking about is local motion here is uniform motion, naturally accelerated motion both free and constrained in vile and projectile motion. That's what we're gonna be studying and he says in the absence of resisting media, that's a key phrase here.
The only relevant parameters are distance, height of descent or ascent, time and speed. In particular the weight of a body does not matter, the shape of a body does not matter. All bodies behave in the exactly same way. It's an extraordinary point. So irrelevant parameters, in the absence of a resisting medium, weight, shape, density of the body, density of the resisting medium.
The very parameters that show up most prominently. If a resistance force is present. Disappear entirely when you drop the resistance and you go to the initial ones, okay? Now, that's a fairly radical idea. What's radical here is not the ones at the top, other than singling out the height of descent or assent but time, speed and distance are not radical but they claim that none of these others, all these others can be ignored.
Flies in the face of everything you see around you all the time and it is a quite radical proposal going back to this question Leon asked, he's doing something quite extraordinary. Question? Okay, what's his basis for separating those? Well, there's the famous thought experiment that gets repeated in the discourse about weight.
I'll just, it's in the dialogue as well and I can't remember whether I assigned that part of the dialogue. It's quoted so often. So here is a rectangular slab and it's falling. Now you put another body on top of it, make it fall faster. Well if that's right, if you put another body below it, it's gonna resist the motion, right?
The smaller body, cuz it falls slower and it's gonna resist. Now, the thought experiment is the little body on top of the bottom makes no bloody difference, and therefore, the weight doesn't make any difference. That's a thought experiment. He gives other thought experiments, that's the one I single out, on page 108.
Then there's the claim he, of course, is famous for dropping objects from the tower of Pisa It's one of those things he's famous for that he surely never did and never anywhere claims to have done it. Okay, so this is one of these that is like Newton's apple, it's taking something.
It appears that people did drop objects off the Leaning Tower of Pisa and he might ha've even been present when somebody did it. Some sort of experiment, but there's no claim by him that he did it. But what he does claim is that if you take bodies of different weight, the heavier does, invariably, land sooner than the lighter.
But not proportional to the weight, as Aristotle requires. Aristotle says the time is proportional to the weight. Then his third basis for the claim is the effects of resistance on a falling body are smaller the the less density of the medium. So you start in water the effects are very large, the effects can be large enough that it sits on the top buoyantly but if its falling, the effects are much more dramatic than the same object in the air.
And now he argues take that to the limit of no resisting medium and weight's gonna disappear. And then there's the fourth, the two pendulums one with a cork bob the other with a lead bob remain synchronous with equal periods even though resistance affects the former more and I'm gonna deal with that in a moment.
I want to pause with this. Because I want you to realize that at this moment. The moment he says these are the parameters that count and these are the parameters that do not, a very large part of the exercise has been completed. So the basis for claiming that has to be empirical in one way or another it can't be mathematical.
That's why it's not presented mathematically as part of the academicians treatise, but has to be argued for quite separately. And then there's a question whether these arguments are really adequate. Okay. And I will raise questions about that. I want to say one other thing before we go on.
Speed for him is not our notion. The word he uses is velocitas, velocitatis. In Latin, I didn't bother to look at the Italian but I know what it is in Latin. It is not a vector quantity and just to try to drive that point home Cameron will laugh at this.
Vector quantities came into existence around 1900 before or after they were invented by Willard Gibbs as a teaching device at Yale trying to make electromagnetism easier to do than it had been without them, and you'll agree, it's easier to do. He's been writing about Maxwell without them and it's not easy.
And when the book got published, one of his students named Wilson, intervene and said, can I write my notes up and we publish a book on what became vector analysis and the first four pages are going in great detail making the following point. I won't do it here, but I can picture it.
Suppose I draw two equal length arrows on the blackboard, parallel to one another. Question, how many vectors have I put on the blackboard? And the point is, one. Vectors are quantities. It's like writing the numeral two up there. How many numbers have I put up? That's a very difficult concept, that's why it didn't show up until 1900.
That's way after physics became extraordinarily rich and complicated, we finally get the concept of a vector. Okay, so needless to say, he's very far removed from that. That's not a trivial notion. But on top of it, more peculiar from our point of view, he doesn't think of it as an extensive quantity.
Length, time, et cetera, those are extensive quantities. The heat, the hotness of a body what we would now call temperature. They didn't have a way of measuring temperature. But the heat of a body, the solidity of a body, those are intensive properties of a body. And he thought of speed as an intensive property of a body, something a body acquires as a property.
It allows it, when it impacts something, to do more and less damage. And associated with the notion of speed as, this he inherited from the middle ages, the word impetus. Which are little increments of adding speed to a given mass giving it added capability of doing damage when it hit something as in ballistically or his favorite word, momento.
My friend Paulo Galluzzi, whose name I've dropped two or three times from the IMSS. His first book was a 600 some page book on the meaning of momento in Galileo and that will give you a sense of how elusive that concept really is. It's obviously related to our notion of momentum but it's not it.
You are just thinking in a totally different way about these things. Particularly thinking intensively, which leads me to make the point I wanna make about this before I go on to start looking in more detail. There used to be a course at Princeton taught by for many years, when he taught it at MIT, I co-taught it with him cuz I did the Newton portion.
But what he would do was start back with Aristotle on motion. For those who don't know, Aristotle doesn't really distinguish motion,he distinguishes Kinesis. Kinesis is any form of change, and he has a general theory of change and treats motion as simply a species of all other forms of change.
Which means motion doesn't look like we think of it at all. And what Kun would do was show the history from Aristotle down to Newton of how our concept of speed- the relevant concepts tied to motion evolved during that time and the point he was making time and again.
and this is Kun's picture of science. What science is all about is forming a vocabulary that lets you conceptualize the world around you in a coherent way, and you can do that in multiple ways. Aristotle was perfectly coherent but he didn't do the things that were done later.
Increasingly you get to a point where you could solve certain kinds of problems with your reconceptualization. But the emphasis all the way through and it's a two fold emphasis. I'm telling you about this because I'm gonna make a key point here. The emphasis all the way through that course was teaching students to read.
Their way into the conceptualization that people had who wrote the books. And the real thrust of that course which used to be taught to a large number of undergraduates is you have to stop looking at things retrospectively if you're gonna understand these things. Okay, and then, you know, there are funny things about the way he taught Galileo, I'll mention it later.
But the point I'm making, that's one reason I'm having you read it and pay attention to it, because they really are thinking about speed, motion, et cetera in very different ways from us. And to really understand what he's doing is gonna take some effort. I'll get to that in a moment.
Ulitmately particularly about motion, it is changing very rapidly during the century. So by the time we get to Newton we something that looks an awful lot more like what we think of as motion. Not the same but much much closer. Fair enough? I mean, that's why this stuff about parameters is important.
You remember what I said about Apollonian parameters. The same parameters get reinterpreted time again, that's what happens with Galileo. The same parameters get reformed into hours and you don't even notice that you're doing violation to the text. What Kun would teach you to do was show you that the way you're reading the text has fierce anomalies in it.
And he would say and you think those anomalies are because the person didn't understand and then gradually make you realize what he had gone through to begin with when he first got into history of science. Learning to read Aristotle when it was coherent he was teaching that all over again to students.I'm not going to be teaching that but I'm going to spend the next roughly 20 minutes or so on the conceptualization and then start looking at questions of evidence.
Okay, maybe a half hour on conceptualization. But do hear me, they're not our concepts. I'll write algebraic expressions up there like S equals one-half AT square and I'm totally being anachronistic other than I can interpret each of those in his terms, but they're just not ours, okay?