Natural Hearing (Aristotle's Physics)
57. Time as the Number of Motion, and the Problem of the Now
https://berquistcourse.com/course/philosophy/3-natural-hearing/057-time-as-the-number-of-motion-and-the-problem-of-the-now/

[0:00] the second paragraph of the seventeenth 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.

[0:26] And now he's saying something similar to that about before and after. The before and after is first in place and there 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. I know what he's saying there. Proportion to those, right? So,

[0:59] you know, I always follow Euclid's way of using the word proportion, as opposed to Thomas Aquinas's way of using the word proportion, right? And

[1:15] Thomas, 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 he's a Greek word, right? For a likeness of ratios. Okay.

[1:46] So two to three would be an example of a ratio, right? Three to four would be another example of a ratio. Four to six would be another example of ratio. Got three separate ratios there, right? And then you come back upon these ratios and you see, well,

[2:12] two is to three, not as three is to four, right? As 8 is to 12, like 9 is to twelve, is it? But two is to three as what? Four is to six. 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 the alternating proportion, right? And say the first is to the third as the Second to the fourth.

[2:45] Anyway, that's basically what you mean by proportion. So, if you have a 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, if AB is to BC, so the motion over AB is to the motion over what BC, right?

[3:31] And then further on, take the time it takes, right? That's the same, right? Okay. Now, if you get complicated, you go faster and slower. But I mean, basically, that's what you're doing. Okay. Um. So

[3:50] that's why in that first sense of before, in first sense of before, Aristotle gives you reduce the other senses, huh? First sense he gives of before is before in time, right? But to that you 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, huh?

[4:23] And as Shakespeare says, or this he says in his play, "Troilus and Cressida, things in motion sooner catch the eye than what not stirs," right? So motion is what you know. You know my my little childy has a little thing just screw it up and what? It goes makes 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 that kind of you know distracts them, right?

[4:55] Things in motion sooner catch the eye than what not stirs, huh? You know Aristotle talks about the rattle there, you know, and the baby needs the rattle, you know, they can't be quiet because their arms and legs are always kind of moving, in fact, when they're awake, I suppose their muscles are developing, right? Eventually be able to stand up, you know, and run around. And he turned around.

[5:18] The other one's running. You know, the one that I saw sawed Omaha's running around now, or standing up anyway. And this little baby next to me said, "You're probably chilly." Um. Uh. So 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 which one is before two is much more abstract, right?

[5:41] And and not as concrete to the senses, huh? Okay. So he's saying now in the third paragraph that before and after is first in place there in position, huh? And this kind of firm position there because one place is places not moving, right? Okay. 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?

[6:18] Other is that clear enough? Yeah. Um. You might you might ask, you know, why did Aristotle make the first sense of before that in time, right? 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 till we see the definition of time, right? Okay. 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?

[6:52] And why the definition of motion we didn't use before and after, did we? So there is 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? 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?

[7:22] Yeah. But soon it's more clear to us, right? The sense in which things are in in place than they're in time, right? Sense in which things are in time is a first little bit obscure, right? You know.

[7:42] But I'm in this room. That's kind of stands out, right? But in the case of before and after, you know, it's much more explicit in the definition in the understanding of time than is that of magnitude. It's coming in the very definition of it. And you can see that in daily life when we use the word before and after, we we tend to think first of all of time.

[8:12] If I say I'm going to do this before I do that, right? I think in time, don't you? Right? Not thinking of the place, but of time right away.

[8:29] You know, we speak of afternoon. That's very common word, afternoon, right? But you know, you also speak of forenoon sometimes. It comes up more immediately, right?

[8:46] Okay. When you take the before and after in magnitude, yeah. You might think that you're kind of presupposing the other before and after because why is A B before B C? unless you're thinking of a motion. That's true too. Yeah. Yeah. Yeah. I mean, it's just a little more arbitrary, you know. See, is this the beginning and that's the end, or or vice versa, right? You know.

[9:17] Why, in the case of time, time seems to be what? Even the physicists wonder about that, right? Time seems to be one directional, right? You'll say, by a way of distance, I can go here and come back again, right? But I can't do that in time. at least I haven't been able to manage it myself, even going the wrong, direction. I can't go back and. Get younger, right?

[9:43] Except I can do it in the movies, right? By the ejuated. 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?

[10:17] What the heck does he mean there? Make the distinction that it's the thing is the same. There's not a different thing, motion and the motions before and after. No, right, but it's it's not the same

[10:50] 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, 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?

[11:20] What he's trying to point out here is that he, or why he's leading up, what 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 before and after in time, which is not in the definition of motion.

[11:55] 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. That's true, even if you talk about the now, right? Unless you realize that this now is not the now in which I fell asleep, right?

[12:22] 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.

[12:38] 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, is something in between there, huh? For when we understand the extremities of the middle to be other,

[13:00] 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? So just as if you say, you know, that that this point is not that point, right?

[13:30] Then you have some distance in between them, right? So if this now is not that now, that 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. number, right?

[13:57] 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.

[14:27] 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, make a little more concrete here, in a sense.

[14:52] Would you say I was gone for some time? In Massachusetts. Yes. Yeah. I was gone. I don't know. I left on Friday. I came back on Monday. The night of Monday. So, how many days was I gone? You know, gone not ten days. Okay. Yeah. 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?

[15:29] Like ten days I was gone. Movement of the sun. Yeah. Time around. See, goes around, okay. Now, you know, if I if I was 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?

[16:02] 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? Okay. And after one set 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? The apparent motion of the sun around the earth, right?

[16:35] Okay. Now we're going to see how fast you can run this distance, right? Okay. So I have my my watch, right? And it goes around once. I said one minute has gone by. Two minutes, right? Not back yet. Three minutes. You know, I'll be back in five minutes. You sure about that? Four minutes. Five minutes, right? Okay. What I'm doing? I'm this, in the sense, is imitating the what movement of the sun around the earth.

[17:07] It's circular, but I'm counting the what the circulations, right? One of which is before, and the other is after, right? So time is ten days. I could take ten hours, right? But again, if I take hours, the way I'm dividing one circulation of the sun around the earth, kind of arbitrarily into twenty-four parts, right? But the motion from here to here is before the motion from here to here, and so on, right?

[17:44] 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.

[18:21] He asks what time is it. So we're asking the question, not what time is it. It's what three thirty-three, but we're asking what is time, right? And time is always a what

[18:44] a number, right? But a number of a before and after in some motion. We take and as often take the motion of the sun around the earth, and we'll see why he takes that particular motion, right? But that's what what it is. Okay.

[19:08] A sign is, he says, that we judge more and less by number, but motion more and less by time, right? Therefore, time is some number, huh?

[19:24] Now this is what John St. Thomas calls the the vulgar distinction, right? Between numbering number and numbered number, right? Okay. My teacher of history, he wrote his doctoral thesis 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.

[20:05] 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 it other things besides time. The difference between seven and seven dogs, right?

[20:31] 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 so what you have here is the number of something what continuous.

[21:05] Okay. It's like if I say three yards, right? Three feet. That's a number of a what continuous thing, right? Okay. So we 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?

[21:42] Now, if you look at these, long and short and more and less, they seem to refer to quantity, right? But more and less refer to discrete quantity. Went back to categories, right? Number. So we wouldn't say, for example, that seven is 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 what shorter than the other, right?

[22:16] Okay. But in the case of time, don't we use both words? That was a long time. That was a short time. I can run that less time. You can.

[22:47] Took me more time to see the question and answer once I asked it. Took me more time, as Heisenberg said, right? Took more time to ask the right question, or more time before we asked the right question, than after we get the answer once we asked it. But 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?

[23:20] But because it's a number of something continuous, we speak of it as being long or what short, right? Okay. Now in the eighteenth reading here, he's going to. Try to take up this problem we had about the

[23:51] the now, right? Okay. I 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. Presently, all events would be in the same now, right? So the American Revolution would be taking place now, the same time as the war with the terrorists there in Afghanistan. Huh?

[24:32] I messed that up over there. You view it on the reader newspaper and that stuff here. It's actually crazy what's going on in the world today. You know, it's just absolutely bad Just a crazy I mean, you know, just turning pages of each page newspaper. Another crazy thing going on. Yeah. It's absolutely incredible.

[24:56] So, are all these things now? Okay. But now, if you say it's always different now, right? When does a now cease to be? Well, it doesn't cease to be in the now when it is, right? Okay. So, does it cease to be in some later now?

[25:30] Well, there is no next now, right? So, when does it cease to be? Whatever later now you put it in is 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 involves you know the ability to see a what proportion, right?

[26:10] 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?

[26:37] The now determines times insofar as it is before and after. What does that mean? Now he's going to start to explain that. The now is in one way the same, but in another way not the same.

[26:57] For in so far as it is an other and other, it is different. For this was being for the now itself, but as some thing, the now is the same. But what does that mean? Well, now you got to understand this by seeing the proportion, right? We talked about the importance of seeing proportions, didn't we? Okay. And incidentally, you know, if you study Euclid and if you got as far as Book Five, right?

[27:26] 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?

[27:54] What's the scandalous discovery? Incommensurable magnitudes. Yeah, yeah. They discovered that sometimes two lines don't have the ratio of a what number to a number, and therefore they realize that you can't simply what assimilate ratio among lines to what ratios among numbers. Okay, and that seems something irrational, right?

[28:26] 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.

[28:43] But then they had to rethink this whole thing, right? And that the Book Five is really kind of 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 in sense geometry, but in the light of that, and all of a sudden you realize how powerful this has become.

[29:10] And and the kind of the stock example there is that what you saw in the Pythagorean theorem, right, the marvelous thing that's the completion of Book One there. This is shown to be true for every what? Incommensurable figure. Yeah, yeah. So if you put a pentagon, right, on the sides of the right angle, right, and likewise a pentagon, equilateral, equiangular pentagon, right, the two would equal the right, and you put a what?

[29:46] Hexagon, right? Why is that? so? Amazing, right? You know, I mean the the power that that you suddenly have, you know, it's it's actually astounding, right? Isn't it? And

[30:02] the ability to see a proportion is is is so important in the whole philosophy. But you first see it there, you know, when you first use the word proportion.

[30:12] Now, what is proportion? He's going to bring out there. For as has been said, motion follows upon magnitude in time to this, we say. And the thing carried along is similar to the what? Point by which we know motion and before and after in it.

[30:34] Now, what does he mean, huh? Well, you know, the ball gets hit in the infield there, right? Huh? Okay. And is it the same ball that was hit in the infield and is caught in the outfield, or what? Better be.

[30:56] Or something's very fishy about this 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? Somewhere. Somewhere 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 doesn't become a football or a basketball or something else, right?

[31:29] 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 regards what it is, but in its position you might say it's always other, another, right? Okay.

[31:49] And so he's saying that as time in a way is to motion, so the now is to what? Mobile. Yeah, the thing in motion, right? Okay.

[32:06] 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 another way, always what? Other, and therefore it makes time in so far as it's always what? Other, right? Okay. Just as you could say that the ball the ball in motion, right, makes motion in so far as it's always what?

[32:37] Other in place, right? Okay. But always remains the same as to what it is, huh? I thought you could repeat that time is to motion as. As as the now is to the thing in motion, right? Then the portion.

[33:14] Something like time is to 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?

[33:52] Before and after, huh? Okay. So, way it isn't corrupted, is it? Any more than the ball, right? Is being corrupted, right? It's the same ball. Remains always. This regards what it is, huh?

[34:11] This, as we'll go back to begin the paragraph. For 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.

[34:29] And the before and after in it, huh? Just like in arithmetic, we sometimes assimilate to that, right? You know, they say that a point by its motion makes a line, right? Okay. So we can replace thing and motion with point. No, no, no, no. Well, I mean, you're making a comparison there, but it reminds me of what you know the Platonists would say, huh? That a point by its motion makes, say, what?

[34:59] 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 to explain to them the importance of definition, right? Okay. And 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 the circle into two what?

[35:46] Equal parts, right? Okay. Now, I say to the students, huh? How do you know that the diagonal divides the circle into two parts that are in fact equal, right? How do you know that?

[36:09] Well, my students want to say, "Well, that's the definition of a diagonal." I say, just posit that, so to speak, right? Just posit things, no need whatsoever. And I say, "Well, but that's not the definition of diagonal, is it? What's the definition of diagonal?" The line that goes through the center from one circumference to yeah. It's a line drawn from any point of the circumference of a circle, right?

[36:42] To the what? Center. Through the center to the opposite side. That's all. It's not in the definition of diagonal that it's a line drawn from one point in a circle to the opposite one, dividing the circle into 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, how do you know the triangle has three sides?

[37:09] 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 two sides? Huh? Would you? Well that's what a triangle is is. Okay, but that's not what a diagonal is by definition. Okay, so how do you know it divides the circle into equal parts? How do you know that? That's a really simple thing.

[37:38] You know, it's no big metaphysical proof 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 what what the first philosopher did, Thales, he said, now if you imagine this part, right, laid on this part, right, as we're flipped over, right, and you have the same base, so of course they coincide, right?

[38:13] Now, when you flip 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

[38:31] 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 a circle that it's a plane figure contained by one line, every point on which is equally distant from a point in the interior called the center, right? So I say 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 that the diagonal bisects the circle into equal parts.

[39:14] Okay. Now, it might seem though sometimes to a student, well, then how do you know that all the radii are equal? How do you know that all the the lines drawn from the center to the circumference, right? And it seems a little bit maybe arbitrary in the way that I was claiming they were being arbitrary when they said that the what diameter, in fact, bisects a circle, right?

[39:47] Into equal parts. Just 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? Almost, huh, okay. Say well, but if you go back to the generation of a circle, how is it generated? Say, well, you take a straight line, right, and you rotate it around one end, right? That's like a circle in a way a little bit like the way Euclid defines a sphere, right?

[40:20] He says take a a circle and the diameter of a circle, and rotate the circle around the diameter, that's a sphere, okay? He doesn't define the circle that way in the first book, right? But you could define it like that, right? Say, so if the circle is imagined to be the figure

[40:43] cut out, so to speak, right, drawn out by rotating a straight line around it, then it becomes not arbitrary but obvious why all the points in circumference are distant from a point in the interior called the center, right? Okay. Now you take that back one step further, right? And you say, now what's a straight line?

[41:11] What's a line? Period. Right. And you say, Now, how do you know it doesn't have any any any width, right? Right. Okay. It seems kind of what

[41:28] arbitrary, right? Well, that's just what we mean by a line, okay? But that that makes everything up for grabs in a sense, right? I remember I was I was in this kind of a freshman English or mathematics class at the College of Saint Thomas there, and 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.

[41:54] He apparently, had been a parachute, you know, man. Once I get his old bad leg, we kind of you know, a nice guy. who got to know him. I remember he and Marcus, my brother Marcus, in some discussions, you know, and he was saying his his position was I can define anything you know I want to define, right? You know, define it what you want to, and see where you go from there.

[42:18] I think it's kind of foreign to what Euclid's really doing, right? Always followed by brother Marcus saying, right? But that's just the way the modern mind thinks, right? You know, one of the crazy things going on now t here is a t here is a lawsuit. A bunch of homosexuals, you know, are suing for the rights to be admitted as a marriage, right? That they've been denied their rights and so on, right?

[42:42] Well, I mean, this is the thing, right? You can define marriage any way you want to, right? Purely arbitrary, right? You know, so it's okay. So. Again, if you want to avoid that what might seem arbitrary to somebody, you say, "Well, a line is what? A limit of a surface. 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?

[43:19] A line. See? Of course, the point has no width, right? Oh, so that's why it has no width. Is it? And then you get the line, and you can rotate that and get a circle, right? You're not always arbitrary, is right? But I think that's part of the reason why, 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 to in a way go all the way back to the point, and then you imagine the line as being formed by the motion of the point, the circle by the rotation of the line, and the sphere by the rotation of the circle around its diameter.

[44:01] 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. Yeah, thing is, yeah, and not really going back and resolving the imagination, right?

[44:32] You see. You read the books, you know, speaking of a straight line meaning itself, right? How can a straight line mean itself. 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.

[45:05] It's kind of amazing you read sometimes these mathematicians. I mean, it seems such an obvious what fallacy of equivocation, right? Say, well, sometimes a triangle can have more than two right angles, right? Or 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? Okay, we can see in a way how we might speak of a of one of the lines of longitude hitting the equator as hitting it at right angles, but it's not really right angles because it's not a straight line meeting a straight line.

[45:53] So you got two of these things coming down here meeting the equator at right angles. So you got two right angles down there. You got some angle left here. So sometimes a triangle has more than two right angles. And it's obviously you're equivocating on what you mean by triangle. Talking about a a flat figure on a flat plane, right? You see, talking about this thing here, right?

[46:26] 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.

[46:39] That a what? It does mean a right angle because there's some likeness there, right? But it's not really exactly the same meaning, is it? So this sort of stuff they're doing it all the time. And

[47:01] or some of them were going out in the mountains, was it, and shooting light beams between the mountains to see if they were really true the Pythagorean, I mean the theorem that the interior angles to two right angles.

[47:24] Yeah. But is it those you know determining? Is those 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?

[47:58] Okay. And so to imagine these things clearly and so on, you've got in a way resolved all the way back to the point, 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.

[48:25] But notice you could say that when the point by its motion is 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? So you can compare it a bit to that. But it's the motion.

[48:51] 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? 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?

[49:18] But it's always other as to where it is, huh? Okay.