Natural Hearing (Aristotle's Physics)
Lecture 64: Time as the Number of Motion: Before and After

Transcript
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Each changing place, which that which goes before, okay, that's changing place, right? How closely connected those things are, time there with change and with what? Place, right? Okay, so, now the second sense of before was what? Yeah, this can be without that, but not vice versa, right? What's the example Aristotle gave there? Numbers. Yeah, and he said one can be without two, but two cannot be without one, right? Kevin Jones, he takes an example from Ritmetech, right? An example, therefore, of a before and after that is without motion, right? And without the, what? Continuous, right? I kind of, you know, my old teacher, Cassuric, used to say, you know, you can tell how well a man understands by the examples he chooses. And he kind of used to say, you know, when Aristotle or Thomas gives examples, he can always stop and say, hey, why does he give these examples? I mean, there's a significant choice of examples, huh? But he says, if a modern Thomas gives examples, I wouldn't bother to look for any reason why he does. And of course, modern philosophers, they like to give an example that kind of strikes your imagination, you know, like a firecracker or something, you know, or... But it doesn't really illustrate the point, huh? You see? Clearly. So, Aristotle's examples, so carefully chosen, right? And you know, it's like when Thomas comments on the text there of Aristotle, when he gives examples, say, of the efficient cause, the mover cause, right? And he gives the example of the father, right? And the advisor, right? And Thomas says, well, the significance, and he's choosing these examples. Because the father is an example of a mover by nature, right? And the advisor by, what? Reason, right? And the two main movers in the world around us are nature and reason, huh? And he's choosing the father and the mother we saw for other reasons, but significant, huh? Because the mother is more associated with matter, huh? Mater, materia. But the father is the mover, the maker, and that's why we call God-father rather than mother, huh? Because he's a cause in the third sense, huh? So you see how carefully chosen are the examples of Aristotle, huh? And then he comes to the third sense of before, which is before in what? Recy. Yeah, the discourse of reasoning, huh? And in some ways it's more like the second, right, than the first. But because we start at the first, we compare the later things to that, right? And you can see that, you know, even in mathematical philosophy, where, you know, Euclid will call the, what we call the factors, he'll call those the, what? Sides, right? The sides of six are two and three. Now, you have some background in education there, but, you know, in the academic world today, if someone said, what are, you know, two and three to six, they'd probably say what? Factors. Factors, yeah, that's what I, you know. But, you know, it's much more concrete to say they're the sides, right? And of course, we still keep the words, what, square number, cube number, right? But the word square there is obviously, what, equivocal in arithmetic and in, what, geometry. But there's a likeness between the two, huh? Yeah. A likeness between the two, huh? It's kind of marvelous that, you know, in a way, it's false in a way, but in other ways marvelous that geometry is named from measuring the earth, right? Because it shows that it began with something very concrete and sensible, right? Or if we take it as much more abstract, huh? And so Euclid starts with the geometry and then he goes to the, what, science of numbers in books seven, eight, and nine. But the language reflects that, right? Where we speak of the sides of a number or the square number or cube number, or we speak of this, you know, continuous proportion and so on, huh? And so we do the same thing with thinking there. We carry the word road, right? Okay? But when we speak of a road in our knowledge, the continuous carry to the road is not the reason for carrying that word over. It's the, what, before and after, right, huh? In the road, right? We speak of a road in our knowledge because there's an order in our knowledge, a before and after in our knowledge, huh? But not a before and after in something, start to be speaking, continuous, right? Otherwise, you have to go through an infinity of things to know anything, etc. Okay? So. So notice in the second paragraph of the 17th reading, he's pointing out that the continuous is, what, first found in the magnitude. And because the magnitude is continuous, the motion over the magnitude is continuous. And consequently, the time the motion takes is, what, continuous, huh? And now he's saying something similar to that about before and after. The before and after is first in place. They're in position. Since there is a before and after in the magnitude, necessarily, there is a before and after in motion proportional to these, to those there, right? Okay? And notice what he's saying there, proportion to those, right? See? So. You know, I always follow Euclid's way of using the word proportion, as opposed to Thomas Aquinas' way of using the word proportion, right? And Thomas is taking into account that people tend to use the word proportion for, what? Ratio, right? Okay? But Euclid uses the word proportion, or analogy, I think it's a Greek word, right? For a likeness. Okay? So, you'd be an example of a ratio, right? 3 to 4 would be another example of a ratio. 4 to 6 would be another example of a ratio. Again, three separate ratios there, right? And then you come back upon these ratios and you see, well, 2 is to 3, not as 3 is to 4, right? As 8 is to 12, like 9 is to 12, is it? But 2 is to 3, and it's what? 4 is to 6. So now, we have four terms, right? And the first is to the second, as the third is to the fourth, right? And then you find out that you can alternate the proportion, right? And say the first is to the third, as the second is to the fourth. But anyway, that's basically what you mean by proportion. So, if you have a distance here, speed, and you start, you're starting at this place here. So, AB, that part of the road, comes before BC, right? Okay? Now, when I go down the road from A to what? C, right? The motion from A to B is also before the motion from B to C, right? Okay? So, as AB is to BC, so the motion over AB is to the motion over what? BC, right? And then further on, you take the time it takes, right? That's the same, right? Now, if you get complicated, you go faster in the store, but I mean, basically that's what you're doing. Right? Okay. So, that's why that first sense of before, that first sense of before, Yerastava gives, you'd reduce the other senses, huh? The first sense he gives of before is before in time, right? But to that you'd reduce before in motion and before in what? Distance, huh? Or magnitude, huh? And that's the way I show that that is the first meaning of before. Because it's tied up with the before and after in motion. And as Shakespeare says, or this he says in his play, Taurus and Cressida, Things in motion, sooner catch the eye than what not stirs, right? So motion is what, you know, my little childhood, you have a little thing, you screw it up and what? It plays music and goes around like that, right? Well, there's a double motion, the music and the, what? The little animals moving around over her head and it kind of, you know, distracts them, right? Things in motion, sooner catch the eye than what not stirs, huh? You know? Yerastava talks about the rattle there, you know, and the baby needs a rattle. You know, they can't be quiet. Of course, their arms and legs are always kind of moving, in fact, when they're awake. I suppose their muscles are developing, right? Eventually, they'll be able to stand up, you know, and run around. And you turn around, everyone's running, you know, the one that I saw in Omaha is running around now, or standing up anyway. And this one will be the next time I see you're probably shooting. So, since we name things as we know them, right, it's a before and after in motion that comes to mind first, right? And the sense in which one is before two is much more abstract, right, and not as concrete to the senses, huh? So, he's saying now, in the third paragraph, the before and after is first in place, they're in position, huh? And there's kind of a firm position there, because one place is not moving, right? Since there is the before and after in magnitude, necessarily there is a before and after in motion proportional to those there. But also, in time, there is a before and after, because always one of these follows the, what, other. Is that clear enough? Yeah? Now, you might ask, you know, why did Aristotle make the first sense of before, that in time, right? To give that as a central sense. When he's saying here that before and after is first found in the, what, place, right? Well, let's wait until we see the definition of time, right, to see why. But you'll see when you get to the definition of time, that before and after isn't the very definition of time, huh? And, well, in the definition of motion, we didn't use before and after, did we, see? So, there's some reason for why he makes time, the central sense, and then attaches the before and after in motion, and the before and after in the magnitude to that sense, right? Yeah. Well, in the case of the word in, he takes the central sense, in place, right? And then, in time, right, he attaches to that, right? But soon he's more clear to us, right, the sense in which things are in place than they're in time, right? Mm-hmm. See? Since which things are in time is at first a little bit obscure, right? You know? But I'm in this room, that's kind of, stands out, right? Okay. But in the case of before and after, you know, it's much more explicit in the definition, in the understanding of time than it is, and that of magnitude. It's going to be in the very definition of it. And you can see that in daily life, when you use the word before and after, we tend to think, first of all, of time, huh? If I say, I'm going to do this before I do that, right? You think in time, don't you, right? Not thinking of the place, but of time, right away. You know, we speak of afternoon, that's a very common word, afternoon, right? But, you know, you also speak of forenoon sometimes, huh? It comes up more immediately, right? Mm-hmm. Okay. When you take the before and after and the magnitude, you might think that you're kind of presupposing the other before and after, because why is A, B before B, C? Yeah. Not thinking of emotion. That's true, too, yeah. Yeah. I mean, it's just a little more arbitrary, you know, to see. Is this the beginning and that's the end, or vice versa, right? You know? Well, in the case of time, time seems to be, like, even the physicists wonder about that, right? Time seems to be one-directional, right? You'll say, by a way of distance, I can, you know, go here and come back again, right? I don't know. Well, I can't do that in time, at least I haven't been able to manage it myself. You know, even going the wrong direction. I can't go back and get younger, right? Except I can do it in the movies, right? By the way, you're too late. Thank you. Now, what does he mean here in the fourth paragraph? The before and after in motion, as regards that which it is, is motion. But to be that is other and not motion, huh? What the heck does he mean there? Make the distinction that the thing is the same. There's not a different thing, motion, and the motion is before and after. No, right. But it's not the same as maybe... Not the same as the definition of motion, right? Yeah. See? Definition of motion was the act of what is able to be, right? As such, right? It wasn't before and after, right? So though before and after is the same, the before and after in motion is not something other than the motion, right? It's not what motion is by definition, huh? What he's trying to point out here, or why he's leading up to here, is that time is something of motion, right? But it's something of the before and after in motion, right? Rather than something of the definition of motion, although it's connected to the definition of motion, right? But it's something of the before and after in motion. And that's why it's more explicit, the reference to the before and after in time, which is not in the definition of motion. But we know time, he says, when we divide the motion, separating the before and after. And then we say time has been when we have sensation of the before and after in motion. And that's true even if you talk about the now, right, huh? Unless you realize that this now is not the now in which I fell asleep, right? The one is before and the one is after, right? Unless you see a before and after in motion, you're not aware of what? Time. Time, yeah. Okay? For we divide, he says, in taking these as other, and something other in between them, huh? So we're dividing by the now, and when we number the now, right, there's something in between there, huh? For when we understand the extremities of the middle to be other, and the soul says the nows are two, the one before and the other after, then we say this to be time, right? Okay? For what is divided by the now seems to be time, and let this be supposed, huh? The now is to time, a bit like the point is to the line, right? Okay? So just as if you say, you know, that this point is not that point, right? Then you have some distance in between them, right? So if this now is not that now, but this now is before and that's after, then you must have a time in between, right? So you've got to see a number, because two is the first. That's number, right? When then we sense the now as one, and not as the before and after in motion, or as the same of the before and something after, neither time nor motion seems to have been. Whenever we see them as before and after, and therefore as two, then we speak of time. For this is time, the number of motion according to the what? Before and after. Time therefore is not motion, but as motion has a number. But as you number what? The before and after in the motion. Okay? Now, let's make it a little more concrete here in a sense. Would you say I was gone for some time? Massachusetts? Yes. Yeah. I was gone, I don't know, I left on Friday, and I came back on Monday, not Monday. So how many days was I gone? Okay? Now, so ten days is the time I was gone. Okay? Now, there's a number there, right? Ten, right? And how do we, what does that mean, ten days I was gone? Um, more than one time around. Yeah. See? Goes around, okay? Now, you know, if I was, even in a primitive state, like I'm Robinson Crusoe and I've been stranded on the island, right? And I want to keep track of the passage of time, right? And I get a nice smooth piece of wood or something like that, right? Put it in my cave. And what? Every sunset, or every sunrise, whatever I do, I, what? Make a mark in that, right? Okay? And so, one sunset is before, and another sunset is after, right? Mm-hmm. And after one sunset, there comes another one after that, right? Okay? So, I'm numbering the before and after, right? Of a motion, in this case, the motion of the sun around the earth, right? Or the apparent motion of the sun around the earth, right? Okay? Now, we've got to see how fast you can run this distance, right? Okay? So, I have my watch, right? And it goes around once. I say, one minute. It's gone by. Two minutes, right? And you're not back yet. Three minutes. You know? So, I'll be back in five minutes. You sure about that? Four minutes. And five minutes is it, right? Okay? What I'm doing, I'm, this in a sense, is imitating the, what? Movement of the sun around the earth, it's singular. But I'm counting the, what? The circulations, right? Mm-hmm. One of which is before, and the other is after, right? So, time is ten days, or I could take ten hours, right? But again, if I take hours, in a way, I'm dividing one circulation of the sun around the earth, kind of arbitrarily into 24 parts, right? But the motion from here to here is before the motion from here to here, and so on, right? And so, I'm numbering the before and after in the, what? Motion of the sun around the earth, right? Okay? So, it's gone three hours, or whatever it might be, right? Okay? So, any amount of time is, what? Really a number of some motion according to what? The before and after in that motion. Okay? And notice the difference there, you know, the kind of used to sometimes talk about, you know, how the modern physicist doesn't ask the question, what is time? He asks, what time is it? So, you know, we're asking the question, not what time is it, it's what? 3.33, but we're asking, what is time, right? And time is always a what? A number, right? But it's a number of a before and after in some motion. We take, man has often taken the motion of the sun around the earth, and we'll see why he takes that particular motion, right? But that's what it is. Okay? A sign is, he says, huh? That we judge more and less by number, but motion more and less by time, right? Therefore, time is some number, huh? This is what John St. Thomas calls the vulgar distinction, right? Between numbering number and numbered number, right? My teacher Kosirik, he wrote his doctoral thesis has something to do with number and math, and he said, he first began reading, you know, John St. Thomas says, we suppose the vulgar distinction between numbering number and number number, but what is that distinction? Okay? We say, since number is twofold, for we call number both the numbered and the numerable, and that by which we number. Time is the numbered, that's what they called numbered number, and not that by which we number. But arithmetic, the arithmetical philosophy is about the number by which we number, right? The abstract number, right? For that by which we number and the numbered are others, right? So it's like the distinction there, you know, you could apply to other things besides time, huh? The difference between seven and seven dogs, right, huh? Okay? Seven dogs is the numbered number, right? And seven, what? Is the number of which we number, okay? So time is not the number of which we number, but it's a numbered number. It's the number of the before and after in time, right? That's interesting because what you have here is the number of something, what? Continuous, huh? Okay? Just like if I say three yards, right? Three feet, that's the number of a what? Continuous thing, right? Okay? So we speak sometimes of time is, you know, more time or less time, and we speak sometimes of a long time or a what? Short time, right, huh? Now, if you look at these, huh? Long and short and more and less, they seem to refer to quantity, right? But more and less refer to discrete quantity, going back to categories, right? Number. So we wouldn't say, for example, that seven is longer than five, would we? Well, we say seven is more than five, right? And five is less than seven, right? Okay? But we speak of two lines, one's being longer or shorter than the other, right? Okay? But in the case of time, don't we use both words? That was a short time, time you get. It took me more time to see the question and the answer once I asked it. It took me more time, as Heisenberg said, right? It took more time to ask the right question, more time before we asked the right question, than after we get the answer once we asked it. But why both of these, right? Well, because it's the number of something what? Continuous, right? So because it's a number, we use more or less, right? But because it's a number of something continuous, you can speak of it as being long or what? Short, right? Now, in the 18th reading here, he's going to go to the right to the right to the right to the right to the right to the right to the right to the right to the right to the right to the right to the right to the right to the right to the right to the right to the right to the right to the right to the right to the right to the right to the right to the right to the right to the right to the right to the right to the right to the right to the right to the right to the right to the right to the right to the right to the right to the right to the right to the right to the right to the right to the right to the right to the right to the right to the right to the right to the right to the right to the right to the right to the right to the right to the right to the right to the right to the right to the right to the right to the right to the right to the right to the right to the right to the right to the right to the right to the right to the right to the right to the right to the right to Try to take up this problem we had about the now, right? Okay. Remember the problem there about the now. Is it the same now throughout all time or not? Well, if it's the same now throughout all time, then it's a really past and future. All events would be the same now, right? So the American Revolution would be taking place now at the same time as the war with the terrorists there in Afghanistan. What a mess that is over there. You view it on the newspaper and that stuff here. It's actually crazy what's going on in the world today. It's just absolutely bad. Just a crazy newspaper. Another crazy thing going on. It's absolutely incredible. So, are all these things now? But now if you say, it's always a different now, right? When does a now cease to be? Well, it doesn't cease to be in the now when it is, right? So, does it cease to be in some later now? Well, there is no next now, right? So, when does it cease to be? Whatever later now you put it in, it's never the next now. So, it's going to be simultaneous with all the nows in between it and any later now, right? About some of the problems there, right? And that's the way Aristotle's going to go about solving this. And it involves, you know, the ability to see a, what? Proportion, right? And his motion, he says, is always other and other, right? So, too is time. What existed once in the whole time is the same. For the now is the same as regards what it is. But being for the same is other. What does that mean? The now determines times insofar as it is before and after. So, what does that mean, right? Now he's going to start to explain that. The now is in one way the same, but in another way not the same, huh? For insofar as it is in other and other, it is different. For this was being for the now itself. But as something, the now is the same. But what does that mean? But now you've got to understand this by seeing the proportion, right? We talked about the importance of seeing proportions, didn't we? And incidentally, you know, if you studied Euclid, I don't think I've gotten as far as book five, right? But, you know, if you can do book one of you, because you can do books two, three, and four, right? But then you get to book five, it's something kind of new in a way. And this, you have this theory of proportions, if you want to call it, right? And apparently what happened was that they made a scandalous discovery, right? And what was the scandalous discovery that came before the discovery of the things taught in book five of Euclid? What was the scandalous discovery? Inconventional magnitudes. Yeah, yeah. They discovered that sometimes two lines don't have the ratio of a, what, number to a number. And therefore they realized that you can't simply, what, assimilate ratio among lines to, what, ratios among numbers. And that seems something irrational, right? And they say the guy who revealed this, you know, drowned in the ocean or in the lake, right? You know, being punished for this, right? All kinds of stories about this horrible discovery, right? Leaking out, right? Irrational. But then, they had to rethink this whole thing, right? And then the book five, you kind of read a whole different thing, really, from what you've seen before. But then, after the theory of proportions there for the continuous has been established, then in book six, he goes back, right? And does it, in a sense, geometry by the light of that. And all of a sudden, you realize how powerful this has become. And the, kind of the stock example there is that what you saw in the Patagorean theorem, right? The marvelous thing that's the completion of book one there. This is shown to be true for every, what? Yeah, yeah. So, if you put a pentagon, right? On the side of the right angle, right? And likewise, a pentagon, equilateral, equiangular pentagon, right? The two would equal the right. And you put a, what? Hexagon, right? Why is that so amazing, right? You know, I mean, the power that you suddenly have, you know, it's actually astounding, right? You see? And the ability to see a proportion is so important in the whole philosophy. But you first see it there, you know, when you first use the word proportion. Now, what is the proportion he's going to bring out there? For as has been said, motion follows upon magnitude in time to this, as we say. And the thing carried along is similar to the, what? Point by which we know motion and before and after in it. Now, what does he mean, huh? Well, you know, the ball gets hit in the infield there, right? Okay. And is it the same ball that was hit in the infield and is caught in the outfield or what better be? Or something's very fishy about this game, right? Okay. But you can still say that the ball, although it's the same ball that was hit in the infield and caught in the outfield, in some way the ball is always other because it's always what? Some are other. Some are other, right? Okay. So in one way the ball is always the same as to what it is, right? It's always a baseball and it doesn't become a football or a basketball or something else, right? But now it's what? Here and then it's there and so on, right? Yeah. So, you see the distinction there, right? In one way it's the same as to what it is, but in its position you might say it's always other and other, right? Okay. And so he's saying that as time in a way is to motion, so the now is to what? Mobile. Wow. Yeah. The thing in motion, right? Okay. Okay. And this is going to help you to understand how it is that the now is in some way always the same and therefore incorruptible, right? But in another way, always what? Other. And therefore it makes time insofar as it's always what? Other, right? Mm-hmm. Okay? Just as you could say that the ball in motion, right, makes motion insofar as it's always what? Other in place, right? Mm-hmm. Okay? But always remain the same as to what it is, huh? I've got to get you repeat that time is to motion as... as the now is to the thing in motion, right? Okay? It's in the form of motion. And so just as the thing in motion is always the same as regards what it is, but it's always other as regards where it is, right, as far as its position is concerned, so the now, right, in some way is always the same, right? It never ceases to be what it is, right? But it's always, what, other, you might say, in position, right? Before and after, huh? So in a way it isn't corrupted, is it? Any more than the ball, right? It's being corrupted, right? It's the same ball. It remains always, as we guarantee what it is, huh? This is, we'll go back to begin the paragraph. For it has been said, motion follows upon magnitude and time to this, meaning to motion, as we say. And the thing carried along is similar to the point by which we know motion. And the before and after in it, huh? Just like in arithmetic we sometimes assimilate to that, right? They say that a point by its motion makes a line, right? Okay? So we could replace thing in motion with point? No, no, no, no. Well, I mean, you're making a certain comparison there, but as you remind me of what, you know, the Platonists would say, huh? That a point by its motion makes a, what? A line, right? Remember that thing that we talked about in geometry a bit, I think? But when I talk to students, right? And I try and explain to them the importance of definition, right? Okay? And the example I give sometimes is the one from geometry, where Euclid defines circle, right? And then he defines diagonal, right? And then he makes the statement without any proof that the diagonal of a circle divides a circle into two, what? Equal parts, right? Okay? Now, I say to the students, huh? How do you know that the diagonal divides a circle into two parts that are, in fact, equal, right? How do you know that? Well, my students want to say, well, that's the definition of a diagonal. And I say, well, but that's not the definition of a diagonal, is it? What's the definition of a diagonal? The line that goes through the center from one circumference to another. It's a line drawn from any point of circumference of a circle, right, to the, what, center, through the center, to the opposite side. That's all. It's not in the definition of a diagonal that it's a line drawn from one point, a circle, to the opposite one, dividing the circle into two equal parts. That's not in the definition at all, is it? No. See? So I said, how do you know that? It's not by definition. In fact, you know, how do you know that a triangle is three sides? Well, you say, well, that's what you mean by triangle, right? You know? Did you ever try to do a reason why the triangle has three sides? Would you? Well, that's why triangle is. Okay? But that's not what a diagonal is by definition. Right. Okay? So how do you know it divides the circumference to two equal parts? Do you know that? That's a very simple thing, actually. You know, there's no big metaphysical truth or something, right? But how do you know that? You know? You know? How do you know it? You could imagine if they coincided, if you put them over. Okay. But apparently, to put what the first philosopher did, Thales, he said, now if you imagine this part, right, laying on this part, right, as we're flipped over, right? And you have the same base, so of course that would coincide, right? Now, when you hook this over, if this line here coincided with this, well, then it would be obvious that they're equal, right? Okay? But if it didn't coincide, but fell either below or above the other, right, then all the radii of the circle would not be equal. This is the radius of the circle, and this whole line is the radius of the circle, right? And all radii are not equal. So it contradicts the definition of circle, that it's a plan figure contained by one line, every point at which is equi-distant from point in the interior called the center, right? So I said, if you didn't know the definition of circle, right, if you didn't know the circle by its definition, you wouldn't be able to see something as obvious in a way as if the diagonal bisects the circle to go parts. Okay? Now, it might seem, though, sometimes to a student, well, then, how do you know that all the radii are equal? Well, how do you know that all the lines drawn from the center to the circumference, right? And it seems a little bit, maybe, arbitrary in the way that I was playing their big arbitrary when they said that the, what, diameter, in fact, bisects the circle, right? Because in equal parts, that's part of the definition of it, right? If I say, well, that's just what we mean by a circle, right? It seems just, you know, gratuitous, right? Well, it's done. Okay? Say, well, but if you go back to the generation of the circle, how is it generated? Well, you take a straight line, right? And you rotate it around one end, right? And that's how you get a circle. In a way, it's a little bit like the way Euclid defines a sphere, right? It says, take a circle in the diameter of a circle and rotate the circle around the diameter. That's a sphere. Okay? And he doesn't define a circle that way in the first book, right? But you could define it like that, right? So if the circle is imagined to be the figure cut out, so to speak, right, drawn out by retaining a straight line around it, then it becomes not arbitrary but obvious why all the points of the circumference seem to be distant from pointing into your father's center, right? Okay? Now, you take that back one step further now, right? And you say, now, what's a straight line? What's a line? Period. Right. And you say, now, how do you know it doesn't have any width, right? Right? Okay. It seems kind of what? Well, that's just what we mean by line. Okay. And that makes everything up for grabs in a sense, right? I remember when I was in this kind of a freshman English, you know, mathematics class at the College of St. Thomas there, and it was my brother because he was taking it, too, at the same time, and kind of a tough mathematician used to smoke a cigar in class, you know. He apparently had been a parachute, you know, man, you know, so he had a little bit of a bad leg. We kind of, you know, a nice guy who got to know him. I remember he had Marcus, my brother Marcus, in some discussions, you know, and he was saying, his position was, I can define anything who I want to find, right? You know, define anything who you want to and see where you go from there. I think it's kind of foreign to what you could be doing, right? I'm always involved by Brother Marcus saying that, right? But that's just the way the modern mind thinks, right, you know? And one of the crazy things going on now, there's a lawsuit, a bunch of homosexuals, you know, are suing for their rights to be admitted as a marriage, right? That they're being denied their rights and so on, right? Well, I mean, this is the thing, right? You can define marriage any way you want to, right? It's purely arbitrary, right? You know? So, okay. So, again, if you want to avoid that, what might seem arbitrary to somebody, you'd say, well, a line is what? A limit. I'm assuming this one. Well, you could do that, yeah. It's only a proportion, yeah. But another way is to say that, in a way the paganist did, that a point, by its motion, makes a what? A line, see? And of course, a point has no width, right? Oh, wow. So that's why you had no width. You see? And the thing at the line, when you rotate that and get the circle, right? You're one of those arbitrary things, right? But I think that's part of the reason why in geometry you go all the way back to the, what? Point, right? Because to imagine these things as you should imagine them. You've got it in a way all the way back to the point. And then you imagine the lion as being formed by the motion of the point, the circle by the rotation of the lion, and the sphere by the rotation of the circle around its diameter. And now everything is clear, right? Your imagination is not followed up like the modern imagination is followed up very often in these things. So is it that when people say you could, well, why can't we define it the way we want to, it seems they're thinking of just giving a meaning to a word, whereas you're trying to say what something, a thing is. And not really going back and resolving the imagination, right? But you read the books and I'll speak of a straight line meaning itself, right? How can a straight line mean itself, right? I mean, obviously using the word straight line there in some other, who knows what sense, right? I don't think you can sort of say, you know, I read the book and it's talking of a straight line meaning itself. I put the book down, I said. It's kind of amazing, you read sometimes these mathematicians, I mean, it seems such an obvious, what, fallacy of equivocation, right? I say, well, sometimes a triangle can have more than two right angles, right? Well, they're imagining, you know, on a sphere, right? They're drawing, let's say, two lines on a sphere down to the equator of the sphere, right? We can see in a way how we might speak of one of the lines of longitude hitting the equator as meaning it at right angles, huh? But it's not really right angles, because it's not a straight line meaning a straight line, see? So you've got two of these things coming down here, meaning the equator at right angles. So you've got two right angles down there, you've got some angle left here. So sometimes a triangle has more than two right angles, see? And it's obviously, you're equivocating on what you mean by triangle, you're talking about a flat, a figure on a flat plane, right? You see? You're talking about this thing here, right? And I myself, you know, if I was talking about drawing a line from the North Pole down to the equator, right? I might call that a, what? There's a meaning at a right angle, because there's a sort of lightness there, right? But it's not really exactly the same meaning, is it? So this sort of stuff, we do it all the time, you see? And some of them are going out in the mountains, was it? And shooting light beams between the mountains to see if there were really true the theorem that the interior angles are going to right angles? Very close. Right. Yeah. But as if that was, you know, determining, as if that was a test of the geometrical idea, right? Right, right. You find that, you have the idea that, in a sense, you don't understand the difference, as we pointed out, between math and natural philosophy, right? Notice that they're thinking of Euclidean geometry is geometry. It's measuring the sensible world, right? Well, no, it's not really doing that. It's talking about quantity and separation from sensible matter, right? And so to imagine these things clearly and so on, you've got to, in a way, resolve all the way back to the point, huh? And then imagine, in a sense, the line made by the point and then the circle by the rotation of the line and the sphere by the rotation of the circle around its diameter. But, notice you could say that with a point by its motion making a line, the point has no length, right? So it's always the same point as it goes along, right? But it's here and now, what? There, right, huh? So you can compare it a bit to that. But it's the motion that you're saying and that. Well, no, what he's saying is that the now, it's a portion there, right? The now is to the thing in motion as time is to motion, right? So we have to try to understand how the now is in some way always the same, right? In another way, always other, but in a way proportional to the thing in motion which is, as regards what it is, always the same, right? But it's always other as to where it is, huh? Okay? This as some thing, he says, right? Is the same, the thing in motion, huh? For it is a point or a stone. And in a sense, there's a plenus especially spoken that way, so he's, you know, the point. But on the strict sense of motion, as we'll see in the sixth book, a point can't move. Okay? For it is a point or a stone or something other this kind. But in a count, it's other. In a position, it's other. And notice, he even compares to what the sophists say, right? Just as the sophists take cariscus in the lyceum and cariscus in the marketplace as what? Other, right? Okay? And notice that distinction a little bit, the way we do it. Or take maybe even the thing maybe simpler to see in a way. You know, the one, there's a knock on that door over there, I'd say, right? Behind us now, right? And I say, do you know who's knocking on the door? You open the door and it's, like, this floor or something. Or it's your mother or somebody, right? Okay. You see, you didn't know who's knocking at the door, right? Right? Well, you don't know your own mother. You don't know your own superior. So notice, you know your mother as such, right? As your mother, right? That's what she is. But you don't know her as the one knocking at the door, right? Okay. I knew my glass case, right? But not as in the playpen. Okay. So, is the ball that's hit in the infield the same as the ball that's caught in the outfield? Yes and no. Yeah. Yeah. As regards what it is, it's the same ball, right? Right? It doesn't become a football or a basketball as I said before, right? But as far as where it is, it's other, right? Right? Is it caught as it is in the infield? I said the ball was hit in the infield, you know, in the case of it back, right? And it hits the ball, right? Okay. And then it's caught in the outfield, right? Okay. Now, it's the same ball that was hit in the infield and caught in the outfield, right? But was it caught as it was in the infield? And was it hit as it was in the outfield? No. No. So, in some way, it was other, right? Okay. But not as regards what it is, but as regards what? Where it is, right? Okay. So, in some sense, it was other, right? Yeah. But this and being in one place and another is different. But the now follows the thing carried along as time the motion. So, you see the proportion there, right? For abide to carry the law.