Natural Hearing (Aristotle's Physics)
50. Motion, the Continuous, and the Discrete: Why the Continuous Dominates Our Naming
https://berquistcourse.com/course/philosophy/3-natural-hearing/050-motion-the-continuous-and-the-discrete-why-the-continuous/

[0:00] what we look at the text of Aristotle I just kind of helps you to see it, you know, the way that, uh struggling with those people who later on denied the possibility of it, you know.

[0:34] Get enough copies yourself. We say a little prayer. The name of the Father and the Son, the Holy Spirit. Amen. God our enlightenment. Guardian angels strengthen the lights of our minds, order and illuminate images, and arouse us to consider more correctly. Saint Thomas Aquinas.

[0:58] Help us to understand all that you've written. Name of the Father, the Son, the Holy Spirit. amen. Did I mention last time the passage in Shakespeare that's caught my fancy, and I've been meditating on it for weeks. The words of

[1:23] Romeo before he takes the poison he bought from the apothecary. It says, "Come, bitter conduct, come, unsavory guide, thou desperate pilot, now at once, run on the dashing rocks; thy seasick, weary bark." And he drinks the poison.

[1:56] Now, notice how he's got the image that Shakespeare is very fond of, and you find other poets too, that life is like a voyage in a ship. So in other plays, Shakespeare speaks of life's uncertain voyage. Of course, voyages in those days were very uncertain. They say Elizabethan times that they had a kind of insurance policy. Before I go on my boat trip, I put up some money, and you people would match me, something like that.

[2:29] And if I come back alive, I gather it off. If I don't, you get the the money, right? So it's kind of like fifty-fifty, right?

[2:40] So he's comparing in a way his reason, right, to a pilot, who instead of steering his ship safely into the harbor of happiness, right? Suffers what? Shipwreck, huh? And in fact, the Greek word—I mean, not the Greek word—the English word for the opposite of happiness, misery, is wretchedness, huh? And etymologically, I guess it's related to the word for shipwreck, huh? Shipwreck, wrecked, wretched, wretched, huh? So this is a famous, you know, somewhat common metaphor, simile that you have in Shakespeare, huh?

[3:21] And you see it in many plays, like in in King in Julius Caesar, where he, you know, he says the tide in affairs of men, right? Remember that particular line, you know, where if you take it at the tide, you're going to go on to fortune, but if not, you're going to be in shallow water all your life and so on. So there's a lot of beautiful imagery associated with that, huh?

[3:49] But what I was thinking about in particular was the the first words he says, huh? Which he's addressing as a word of pilot. I'm going to crash the rock here. And he says, "Come bitter conduct, but conduct there means conductor. Come bitter conduct, come unsavory guide. " When Thomas explains what wisdom is, he'll sometimes stop on the Latin word for wisdom, which is sapientia, and he'll explain it to mean sapida scientia, savory knowledge, right?

[4:28] And that fits very good what wisdom is—is something that you want to savor, you know, like a kid with a all-day sucker or something, you know. So you got good flavor, right? Or the way you savor a wine, say, by, you know, I don't savor my water or savor my soda pop or something, but wine you got to kind of let it roll around in your mouth and so on.

[4:54] And you have to do something like that with the mind, huh? A little bit like what Boethius says too, you know, that the philosopher is a ruminating animal. And there's supposed to be some symbolism there in the Old Testament, I guess, that they could eat ruminating animals, but not other ones. But the ruminating animal, he can, well, he has spare stomachs and he can bring up his food and chew it over again, huh?

[5:18] And or save it, you know, and then chew it again when he has a need to do so and so on. That's what the philosopher has to do—chew these things over again. I'm always trying to get my students to chew on these things, and and they don't, you know, it's in one ear and out the other ear. Never stops in there to be chewed up. And so when he says "come unsavory guide," he means what?

[5:41] Foolish guide, huh? If wisdom is savory knowledge, then folly is unsavory. Right to use another word, insipid. Reading the modern philosophers, right? This is insipid. I mean, how can a man even read this fool? Now I

[6:03] was thinking of the other word. He says, "Come, bitter conduct. Come, unsavory guide." So in the manudductio there by opposites, right? The opposite of bitter, of course, is what? Sweet. Yeah. So elsewhere Shakespeare speaks of sweet philosophy, right? Okay. And that reminds me what Thomas, you know, was often quoting some of the lines in the Book of Wisdom, say in chapter eight, in the Summa Contra Gentiles, and other places he quotes the first verse I get is in chapter eight, where it says, "Wisdom reaches strongly or mightily from end to end, ordering all things."

[6:50] And the Latin text translates the Greek word there sweetly, right? Could be translated gracefully, but sweetly, huh? So it kind of strikes me, right, that Shakespeare thinks of folly as being what bitter, right, and unsavory, because wisdom is just the what? Yeah, yeah.

[7:11] And later on in that same chapter eight, there is another thing that Thomas quotes sometimes when he's in the beginning of the Summa Contra Gentiles, when he's talking about how no knowledge is more sublime, more perfect, you know, more useful and so on than wisdom. And he quotes another line in that same chapter where it says that there is no bitterness in wisdom.

[7:45] And every other knowledge might have a little bit of the bitter in it, right? Because you are tasting something besides the Lord, who you know, taste and see how sweet is the Lord, right? You know the famous thing. And

[8:02] coming back again, you know, to Shakespeare, it reminds me too of that prayer of Thomas, where the Church has singled out after Vatican II as being of special importance in the tradition of the Church. This prayer, the Adorote Devote. Well, in the one of the quatrains there, huh? He's talking about the Eucharist and receiving it, right? O memoriale mortis Domini, O memorial of the death of the Lord.

[8:29] Panus vivus, right? Living bread. Vitam praestat homini praesta meae menti de te vivere. And in the last line, et te ili, what? Semper dulce sapere. Sweetly, what? Savor, right? The two are right together, right? Dulce sapere. He wants to sweetly savor Christ, whose wisdom itself, truth itself, right? In the what reception of the Eucharist, huh? You know. Well, as we say, you know, manuductio proposita, right? Shakespeare is speaking of the foolish pilot, right?

[9:07] The desperate pilot who's running his ship on the rocks, huh? Come, bitter conduct, come, unsavory guide, huh? Just the opposite of dulce sapere, huh? So, it's amazing that precision of Shakespeare. I don't know where it comes from, but it's incredible the things that you, you know. In fact, you know, I was first struck by the word unsavory. I got thinking about the word bitter, you know, and a couple of those too.

[9:34] You just his mind goes just like that, you know. You know that that metaphor you don't need to be, you know. Yeah. You get just the right word to use. It's amazing. It just. Well,

[9:54] so let's look now again at the first reading here, and we'll come and look at the text of Aristotle here. And that's just to recall now, since you've been all knocked for a loop here by

[10:11] the flu, huh? Yeah. Okay. The sick do want to be better. Yes, yes. You know Aristotle says in the Nicomachean Ethics, you know, people, you know, have these different opinions about what the best thing in life is. The sick think it's health, you know, and the poor think it's money, you know, and and the same person changes the opinion now when he's, you know, when he's healthy but poor, he thinks it's wealth, you know.

[10:37] That's what make him happy, and then he has the money, but he's sick, you know. if he doesn't have health. Okay so Aristotle begins this third book, huh? He says, since nature is the beginning of motion and change,

[10:57] that wasn't the very definition, right, of nature. The full definition was it's a beginning and a cause, right, of motion, but motion in the broad sense to include change and rest, right? And the road we are following is about nature. Aristotle often calls philosophy in the Greek a what? Methodos, right? It's over a road, or it follows a road, huh?

[11:28] What motion is then ought not to be hidden, huh, from us, huh, for studying nature? For this being unknown, necessarily nature is unknown. Motion is in the very definition of nature,

[11:43] and in a way, the the remaining six books of the of natural hearing are in some sense all about motion. In books three and four, we'll be talking about things that are very closely related to motion, like time, which is a measure of motion. But then in book five, he divides motion or change into the various kinds: change of place, and change of quality, and growth, and so on.

[12:17] And then in book six, he talks about the quantitative division of motion, and then in book seven, eight, he compares motion to movers, and that's where he works out the famous argument for the unmoved mover, right? But everything, in a way, revolves around motion. But why in natural philosophy? Because nature is defined by by motion. And sometimes, you know, like in the proemium to Nicomachean Ethics, when he refers to natural philosophy, there he says the subject, you know, is Natural things or motion, right?

[12:55] And kind of up front, it's motion, because nature loves to hide, as Heraclitus said. And the natures of things are revealed to us through what they they do or undergo, right? Through their changes and so on. So that's kind of up front, motion or change. So it's very much the subject here of of natural philosophy.

[13:22] Now, that's only actually the first thing, though he talks about in the first half of Book Three is motion. And what does he do in these other parts?

[13:34] Well, he says those determining about motion ought to try to go through in the same way the things which follow upon motion that are connected with motion. And the first thing he talks about is what's connected with motion intrinsically, huh? That motion is something what continuous, right? Okay. And maybe later on we'll look at the philosophy of the continuous, which is in Book Six, huh? And it's very important to understand the continuous, huh?

[14:10] Um, in in logic, right? When they talk about quantity, Aristotle divides quantity into two kinds, huh? And one kind we translate English as discrete quantity. C R there, and the other kind of quantity as the continuous. Okay.

[14:45] C R E. Um. And the main kind of discrete quantity is number, huh? And the main kinds of continuous quantity are the line, which is continuous in one dimension, and the surface in what two, and the body in what three, right? Okay.

[15:16] Now time and place are also in some way continuous, but basic ones are those. And this distinction is important in mathematical philosophy. If you look at Euclid's elements, for example, the first six books are mainly about what continuous quantity, huh? Lines and angles and figures, right? Later on, the last books, he'll be talking about solid figures, spheres and cubes and so on, right? But Books Seven, Eight, and Nine are about what number, right?

[15:56] Arithmetical philosophy. So this distinction here is important, first of all, for understanding the difference between geometry and what the Greeks called arithmetica, right? Not arithmetic in the sense of simply the art of calculating, but the science of numbers and their properties. So that's one reason why this distinction is important.

[16:32] Now, it's another place that's going to be very important is when we look at the three books about the soul. Even the first book, when he's critiquing Plato, there he says that thoughts are like what numbers? Thoughts are like the discrete. Thoughts are not really what continuous, right?

[17:03] That's going to be very important for understanding the immateriality, the non-bodily nature of reason. You see that reason's thoughts are not continuous, and that reason understands continuous things in a non-continuous way. And this is obviously not due to the thing being understood if it's a continuous thing understanding, right? So the fact that we eventually discover that reason knows even continuous things in a non-continuous way is a sign that the reason is not something continuous, but a body is something continuous.

[17:55] Therefore, reason is not a what body, right? Okay. So this is going to be very important for understanding the soul, and as Thomas says, I study the body in order to study the soul. I study the soul and I study the angels, and I study the angels and I study God, and that's it. That's the end of my thinking.

[18:21] So what is this distinction between the discrete and the continuous? And it's important to know here because he's saying that motion inwardly is something continuous rather than discrete, and he's going to say the same thing about time in Book Six, you know, the magnitude or the line of the rotor which you might go forward or roll forward. So this distinction between the discrete and continuous is very important for many many reasons.

[18:58] I just gave you some of the main reasons. Now, in logic, there's one way of distinguishing them, which will be recalled here later on in Book Six in Natural Philosophy. But in Natural Philosophy, he works out a second definition of the continuous.

[19:22] And what is the difference between those two definitions of the continuous? And why is one definition appropriate to logic, and the other to what? Natural Philosophy.

[19:38] Well, let me just recall here the distinction in logic between the discrete and the continuous. What's common to any kind of Quantity is that you have a multiplication of parts, huh? Okay.

[19:57] And so the way Aristotle distinguishes them in the logic is from the fact that in a continuous quantity, the parts meet at a common boundary, huh, or a common limit, huh. So if I take for example something continuous in one dimension, you could say this part and this part meet at a what point, huh? Okay. They're continuous at that point, huh? If I had a surface, right?

[20:32] You could say this part and this part meet at a what line, right? You had a circle and you had the diameter, right? The diameter there in a way is the end of this part, but the beginning of that part, right? So they're continuous at a what limit, right? The two parts of the chalk here you could say are continuous at a what surface, right? Like a circle there, imagine in the middle.

[21:05] So a continuous quantity is a quantity whose parts meet at a common boundary, right? Understand the genus? Whose parts meet at a common boundary.

[21:28] Let's say they're continuous at that common boundary, huh? And the discrete we can define by the negation of that, right? Okay. Whose parts do not meet at any boundary. So if you had the number seven and you thought of the parts of seven, you could take three and four, you could take two and five, whatever you want to do. But the three and the four, the two and five, they don't meet in anything, do they?

[22:07] No. Okay. And as I mentioned in the first book of about the soul, Aristotle will point out that thoughts are like numbers. Thoughts don't have a common boundary.

[22:33] Okay. But we're not going to try to manifest that fully now. But that's going to be the starting point for seeing that the mind of the reason is not something continuous and therefore not a body. It's very important to see that.

[22:53] Now, in the text there, and more explicitly unfolded in the sixth book, although he recalls this definition, he works out another definition of the continuous, and that is a definition that is the one of the natural philosopher, as opposed to the logician. And the second definition is it's that which is divisible

[23:31] forever. Okay, that which is divisible forever. By the discrete quantity is not divisible forever. So I could divide seven to three and four, and I could divide four into what two and two, and I can divide two into one and one. Can you divide further?

[24:08] Now, sometimes a modern mathematician with his fractions and so on gets you all mixed up on this, right? Because he's thinking really of what numbers on a continuum, right? Okay, so one line, yeah, is divisible, right? Okay, it is the the one in the pure science of number divisible. Yeah. No, the one in the pure science of number is simpler than the point in geometry. Hmm. The point in geometry has no parts, right?

[24:46] It's indivisible, but it does have position. Why the arithmetical one? It's indivisible, but doesn't have any position. It's neither here nor there. So that's why, in the second book, or the end of the first book, rather, the Posterior Analytics, Aristotle says that arithmetic is more certain and sure than geometry. And the reason he's giving there is that there's more things to be considered in geometry. And he points to the point and to the one.

[25:26] They're both indivisible, but the point has in addition position as here or there, right? And in practice, if you do geometry, huh? Like we have Heath's edition, let's say of Euclid, huh? Um, you find in some of the geometrical theorems there is a number of cases to be distinguished. Right. Yeah. And what Euclid does is to Give you the most difficult case usually, and leaves the less difficult cases for us, Nitsch, to figure out on our own, right?

[26:04] But he will maybe refer to Proclus or some other commentator on him who distinguishes the other cases, huh? And sometimes they distinguish more cases than you need to distinguish. But I know myself in learning about those cases. You kind of, you know, I got all the essential cases now, right? I covered all the the angles, right?

[26:32] And so there's a less certitude there, right? Than in arithmetic we have to consider where the point might be. I'll take a simple example to use the points, huh? If you take three as opposed to three points, the three points could all be on a straight line, right? Or you could draw a straight line through them, or they could be such you couldn't draw a straight line through all three of them, right?

[26:58] So that because their position, but you don't have that variety there with the three ones and three. They're neither in a straight line nor the triangular arrangement, right?

[27:19] So sometimes the students think you can divide one into two halves or three into, or five into two and a half or something, right? So I always tell, well, you got five points now, huh? If you could always divide five into two and a half, then you could divide by the point, right? Because there's five points there.

[27:47] If you got four, I don't care whether it's four legs of a chair or four legs of a dog, you take away two, you got two left, right? Okay. So you could take away two and a half from five, then you could have two and a half points. But my mathematician kind of you know mixes up the mind there.

[28:10] Now that again, when you're trying to understand how thoughts are like numbers, they're also like numbers in the sense that they're not divisible forever.

[28:27] For example, in a definition, right? Sometimes part of a definition is what in need of being defined, right? So Euclid defines, let's say, a square as an equilateral and right-angled quadrilateral. But you can divide that into the definition of quadrilateral, rectilinear plane figure contained by four straight lines, right? You can divide that into the definition of rectilinear plane figure, and that into the definition of plane figure, and that into the definition of figure.

[29:02] But does that go on forever? Well, if it did, there'd be an infinity of definitions before what? Any definition, right? And there'd be an infinity of things you have to understand before you can understand anything. And we never understand anything by definition in that case. So there must eventually be something which is known, not by definition, right? At the beginning of all definitions. So definitions are not divisible forever.

[29:36] In the same way of reasoning, right? We can break down a statement back into the statements from which you reasoned it out, and sometimes they have to be reasoned out, right? But does that go on forever? Well then there'd be an infinity of what proofs before the proof of any statement. So eventually you come to a statements that are known without having to be proven.

[30:05] But the statement, the statements exist, right? You can't really avoid that, can you? When I say statements exist, it's a statement, right? And if you want to say statements do not exist, you're making a statement too. There's no way to get around that. The ball game's over, right? There are statements that are known that are known without what having to be proven.

[30:35] And so when you divide thoughts, you get back eventually to those statements, or when you divide definitions, eventually get back to something that is known without definition. Descartes thought it was motion. Aristotle gives us a true answer in Book Nine of the Wisdom. It's act that is known without definition. But he points out in the ninth book. But

[31:05] you know, you see that little comparison I make two two words. You look up a word in the dictionary. They explain it by other words, right? And sometimes one of those words is not known. so. You look that up, right? Does that go on forever?

[31:24] Do you know all words by other words? No. Eventually, you have to know a word by associating it with something you can sense. So the first words are not known to other words.

[31:42] The first. That's going to be very important, as they say, in understanding that reason is not a body. Every body is continuous, right? Now, if you look at these two definitions

[32:07] of the continuous, you see they're both, in a way, in terms of the parts, right? Because quantity seems to consist as soon, you know, multiplicity of parts and so on. But in the one definition, the one in logic, you seem to be looking at how the parts come together to form the whole, right? They meet at a common what? Boundary, right? Well, here you're looking at the parts as simply what?

[32:44] In the direction from the whole down to the parts. Well, the parts of a thing are like matter. Whole is like form. Well, logic is an immaterial science, so it defines it in terms of its wholeness, its form, you might say. And the natural philosopher defines it in terms of its what? Matter. Okay, we talked about the four kinds of causes? Remember that? Aristotle pointed out how, in a way, all parts are like matter, while the wholeness is like the what?

[33:23] Form, right? So the whole is to the parts something like form is to matter. Okay. Matter is that of which something is made, and the whole would seem to be made out of its parts, right? So in the second definition, you're thinking of the parts

[33:50] going the direction of division, right? When you divide, you're going from the whole towards the parts. So it's more like what? Defining by matter, which is appropriate to natural philosophy. Here you're thinking of the parts coming together to form the whole. They come together and meet, right? Okay. Just like a triangle, right? The three lines meet at their endpoints, right? That's like

[34:19] the wholeness there. So to define by form and define by matter, the difference between logic, right, and natural philosophy. Natural philosophy, as we saw in the distinction there between natural philosophy and mathematics, right? That natural philosophy defines with matter or motion, and mathematics you don't have that. Well, logic is even more formal one than mathematics. Doesn't even have that imaginative extension that you have in math, which sometimes we call kind of intellectual.

[35:03] So it's remarkable the care with which Aristotle defines it in logic, as opposed to the way he eventually defines it in natural philosophy. How appropriate, right? It is for that science.

[35:19] That shows how artful Aristotle what is adapts himself perfectly to instrument. I would have, I guess, I would have thought it's also true that the divisible forever is less manifest, even maybe needs to be proved in a way. The definition from logic. That seems kind of evident, but if someone said, "Well, it's divisible forever," that could be true too. Yeah, yeah, yeah. He does, in fact, say recall the one from logic, right?

[36:10] Because logic in a way directs us in all the sciences, right? So he does recall that from logic. That's interesting observation. Yeah, you get to book six. There we'll see how he proves that, right? And his number ways of proving it.

[36:30] There's one way where he proves it by taking distance and time together. Did I mention that before when we talked about inexhaustibility huh? We all know that some bodies move faster than others. So the faster body moves the same distance as the slower body in less time. But in that lesser time, the slower body would move a lesser distance. But the faster body would cover that lesser distance in a lesser time.

[37:01] So just building on that, you can see that time and distance are divisible what forever, but we'll see many things about that when we go to book six.

[37:22] Now Aristotle mentions the word unlimited because he's thinking of the fact that motion is something continuous that's going to be shown more explicitly in book six. But there's something unlimited about the divisibility of the continuous, huh?

[37:43] So he says those determining about motion ought to try to go through in the same way the things which follow upon motion. For motion seems to be among the continuous things. He says seems to be because he hasn't yet what proven that right, and it's really proven in the what sixth book, huh? And the unlimited, he says, first appears in the what continuous, huh? It's divisible forever.

[38:15] Now another thing about the the continuous, huh? And all these things that we'll be talking about here, like motion and place itself and time, they're going to all be continuous. And he'll be showing that you know in the philosophy of the continuous in book six. But the continuous is also very important in all of our what knowledge, huh? In all of our naming, huh? When you study our reason there in the third book about the soul, you'll find out that our reason in this life it never thinks without at the same time, our imagining something, huh?

[39:05] And when we imagine something, we always involve the what continuous, huh? And when you examine the way we name things, we tend to name things as we know them, right?

[39:26] And our knowing starts with our senses and with our imagination and so on, and these things are all continuous. And so we tend to name the continuous before anything else. So like when you study the word beginning in in the fifth book of wisdom, the first meaning of beginning is is the beginning of the desk right here,

[39:52] and the first meaning of end that's the end of the desk down there. But it's the limit of the continuous that you're first calling a beginning, right? Now when God says I am the alpha and the omega, the beginning the end, that's a much later sense of the word beginning, right? But we start with this sense here, and then Aristotle gradually what moves forward to the less known senses, right?

[40:22] Eventually come to the sense in which God is the beginning of things. You may recall the chapter that we had from the categories there on before and after. And the first meaning of before was the before in what time, right? Okay, and to that sense of before you would lead back the before in the motion, right? As time is, as we'll see, is tied up with the before and after in motion, and the magnitude over which you go.

[40:53] So again, the first meaning of before is tied up with what something continuous, motion, time, right? Okay. In in the fourth book of Natural Hearing, Aristotle takes up place,

[41:13] and things are said to be in place. In one place, he distinguishes the central meanings of the word in, and he gives eight different meanings: whole and part, whole in the parts, the part in the whole, genus in the species, species in the genus. I got you in my power. I left my heart in San Francisco.

[41:41] Form in matter, right? And I'm in this room. And he doesn't order the eight meanings, In that text, anyway. Okay. So Thomas, when he comes to commentate meanings, he says, "Now, Aristotle doesn't order these meanings. We're going to have to order them ourselves, huh? But following the way he taught us in the fifth book of wisdom. So Thomas says, "What does Aristotle do there? with the word beginning, right?

[42:16] He starts with the meaning that is most what obvious to our senses, huh? And then he goes forward, ordering the meanings from that. So the first meaning of in is what we're in this room. It's much more obvious than the way that a genus is in a species. or a species is in a genus, right? Even a part and a whole. And then he orders perfectly, Thomas.

[42:41] Huh? The other seven meanings, exactly where each one comes, all the way to the last meaning. And we could stay there some time. You want to? And it's a very important thing, huh? But notice the first meaning again is in place, is tied up with something continuous, huh? The first meaning of before is tied with time, something continuous, huh? First meaning of beginning, the limit here of right, something continuous like this desk.

[43:09] So you find that the continuous dominates, huh? All of our naming, huh? And you know, of course, you go back to the senses, but

[43:26] what you're using there is what you'll find is called the common sensible, huh? Because the continuous is something that more than one sense knows, as opposed to color or sound, which just one sense knows. And those proper sensibles like color and sound, they aren't that important as far as carrying the word over to mean other things. Sometimes we do, but it's not so important, huh? But the continuous, the names the continuous, they're all carried over, right?

[43:59] And all of our thinking expressed in words goes back to those. In fact, even when we talk about discrete things like numbers, right? Sometimes we borrow the word continuous, huh? And one important example of that is when you're talking about proportions in

[44:37] arithmetic and You know, they say two is to three as four is to six, and then you have something like this: four is to six as six is to what? Nine. And sometimes they call this a what? Continuous proportion, right? Okay, that's that's a different meaning of continuous, right? Those numbers are not continuous in the way we define them, but it's because you have the same number, right?

[45:12] The number that ends this ratio is the number that begins that one, right? Okay. And sometimes, you know, I borrow the same word and I apply it to logic, right? And I speak of continuous syllogisms. What does that mean? The conclusion of one is the premise of the next. Yeah, the conclusion of one syllogism is the premise in the next one, right? Or you can speak of continuous definitions.

[45:42] So the definition of motion is continuous to the definition of nature. Okay. So when you define nature, you put motion in the definition, and then you define that, right? So there's a link there. You can see that in Euclid, right? When he is defining, he defines I think figure, and then plane figure, and then rectilineal plane figure, and then quadrilateral, and then square. Right? They're all continuous those definitions, huh?

[46:14] But notice we're borrowing a word from the continuous, huh? And of course you all aware the fact that you know even today we still speak of square numbers, right? And cube numbers, right?

[46:35] Euclid speaks of the sides of a number, right? What we call factors. But he speaks the same way. Do when he speaks of a square number, right? So maybe instead of saying the factors of six are two and three, you'd say the sides of six are two and three. Interesting. What we name that, right? Okay.

[46:58] And we've talked here about how I started using the word road and all the Greek philosophers like Empedocles and Heraclitus and Parmenides and Plato himself. We speak of a road in our knowledge, right? But the road is originally something what? Continuous, right? Okay.

[47:22] And thoughts are not continuous, as we define the continuous, right? But what you'll see is how what one thing is linked with another thing in the science, right? We define nature, and then we see the connection between nature and what? Motion, right? Motion and the what, continuous and so on, huh? So, I've

[47:53] linked these sort of things. So you'll find that it's very common that most of these common words, in fact, an awful lot of them, seem to name first of all something continuous, so it's tied up with the continuous. Then later on, they're carried over and applied to other things. It's very clear that the word beginning, the word before, the word what, in right. How about the word under and above and below and those sort of words, right?

[48:32] I put Shakespeare above Chaucer, wouldn't you? I put Aristotle above Plato. That word originally is taken from what place, isn't it? On the continuous, huh? Understanding to stand under, right? Yeah.