Natural Hearing (Aristotle's Physics)
29. Three Is Enough: The Number Three in Logic, Rhetoric, Music, Physics and Theology
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[0:00] It is clear then that the element or the beginnings is neither one nor more than two or three, but which of these, as we have said, has great difficulty? See, when you were reading ten, it seemed quite probable that there is just two things, right? The two contraries, right? And now it seems that there is reason to think there is a third thing, right? You know, and it reminds me, you know, a little bit of my rule of two or three.

[0:27] See, but we're kind of expanding on that, huh? I know sometimes things can be divided into two or into three, and you can make it sensible in both ways, huh? Just take a simple example from logic, right? Huh? When you talk about one name, set of many things, huh? Well, you could divide that into two, and say either you have one name set of many things with the same meaning in mind in all cases, right?

[1:04] Or with what other meanings in mind? Either there's one meaning, or there's many, meaning more than one meaning, right? Okay, that's only two possibilities, right? Unless you have no meaning in mind, just a sound, right? Okay. And then you could subdivide one name set of many things with many meanings, right? Subdivide that. You could call that equivocal, and the other one univocal. And then you say, well, sometimes there's a reason why the same name is said with many meanings because there's some connection among the meanings.

[1:40] Sometimes there's no connection, right? Okay. And so you call one equivocal by what Reason. reason, and the other equivocal by what chance, right? Okay. But now sometimes Thomas will divide it into three right away, and say either they have wholly the same meaning, or wholly different meanings, right? Or partly the same and partly different, right? Yet the same three, but you divide immediately into what three? Huh?

[2:21] You want to divide all the goods of man. Well, the Greeks usually divide all the goods of man, like Socrates does there in the Apology, into the goods of the soul, goods of the body, and exterior or outside goods, huh? Okay. Aristotle gives the same division in the seventh book of the Politics, huh? Exhausts all the goods of man. Early to bed, early to rise makes a man healthy, wealthy, and wise, huh?

[2:50] I touched upon that division into three: because health is a very important good of the body, wealth is an excellence of outside goods, and wisdom is one of the greatest goods, if not the greatest, of the goods of the soul, right? But sometimes I divide them into just two, right? The goods of man inside of man, whether it be inside his soul or inside his body, and the goods of man outside of man, like his car and his house and his clothes and so on, right?

[3:20] Okay. That makes sense, doesn't it? And so it's exhaustive, inside or outside, right? So, but sometimes you have have an even more difference between the two divisions, like when Aristotle divides plot in the Poetics, he divides plot into beginning, mid, and end. And he praises Homer, you know, for seeing that the unity of a plot. Is not in its being about one man, but in its being about a course of action as a beginning, a middle, and an end.

[4:01] Then later on in the in the poetics, he talks about a plot has two parts: tying the knot and then untying the knot. So,

[4:18] you see that, right? So sometimes, I mean, there's reason to divide something into two, sometimes into three, but sometimes there's reason to divide it into both, huh? And they they they bring out something, right?

[4:37] I mean, sometimes we divide the family into the parents and the children, but sometimes we think it makes sense to say father, mother, and children. Especially nowadays, very important to that division. We need that division nowadays. What's

[5:01] interesting, Aristotle? You know, a little hesitation here, but you know, good to keep that in mind. Would it? It starts from showing there's two, and then there has to be an underlying.

[5:23] Could you have started from saying it seems that they all posit some underlying thing, and then saying they need the contraries for change. Yeah, but in a sense, the the opposition of the contraries kind of stand out in the idea of change, right? Because if you ask, "What is change?" Right? Is it staying the same or becoming different? Basically, what's becoming different than you were? So you're thinking of the opposition, you know, between the way it was and the way it has become, right?

[5:57] So you tend to think of the contraries, opposites, alongside each other, kind of stand out, huh? And the third thing, the subject, is obscure in some way because its inability, huh? Inability is less known than what? Act, huh? It's kind of a strange thing because the butter is it hard or soft? Well, no, it's able to be hard, but it's also able to be soft, right? It has an ability for both.

[6:28] In a way, it's the same ability for both, but it can't be actualized. You know, it's it's an obscure thing when you come down to it, huh? Is it because it's really one of those things that's just really obvious, so we really don't think of it? Which? The fact that that there's something that undergoes the change. Well, in some ways, it was more obscure, huh? Because we'll see as we go on in the course here.

[6:54] The difficulty people have in understanding ability. We'll talk about why it's so difficult to understand, but you first be kind of introduced to the idea of ability there.

[7:09] You get to the ninth book of wisdom there. Aristotle mentioned the Megarians who deny that there is any such thing as ability. Very strange position, but there are people who, you know, if you read Heisenberg's what, Gifford lectures there, right? Talks about how people want to transfer the actuality of things in the world around us down to the fundamental particles as if they were as actual as the things here.

[7:35] That's an illusion, he says. You're dealing with a world of what things exist only in potency, huh? Okay. Heisenberg says we know matter only through the forms of matter. Aristotle said something like that, you know, long time before. Okay. Now, but let's stop in the thing here, and stop comes to the idea that three is enough, huh? Three is all, and it's such a common thing in the arts and sciences and in life that one should stop and think about that, huh?

[8:23] Three is enough, and sometimes three is all. Aristotle is is in the book on universe. There, he's talking about there being only three dimensions, right? And of course, in geometry and mathematics, we can show there's only three dimensions because we can show that

[8:49] you can't draw more than three lines, each of which is at right angles to the other. what? Two, right? I've drawn these two angles, lines at straight at right angles to each other, right? Now, if you have a third line here, right, perpendicular to the page here, which would be at right angles to both of those, you know, And extending two, you know, the opposite side to the board, right?

[9:12] But can you draw a fourth line? It's going to be at right angles to these three. No, no. But in the book on the universe, when he talks about this, he assumes the reason from geometry, and all he gives is a sign that three is all there is, right? And the sign is drawn from language, right? The fact that if you have just two, we say both, and three is the first number about which we say all.

[9:45] So if you and I are going to the movies, we'd say we're both going, right? Wouldn't say we're all going. We're both going. But if you and I and the third person were going, we'd say what? We're all going, huh? And that's kind of a sign that very often three is all there is.

[10:09] Okay. And this is a good example of it, right? Aristotle says two is not enough, but three is all you what need, huh? Now,

[10:23] that isn't always the case, and we'll see even Aristotle, right? You know, he doesn't think this is always the case, right? But it is common enough that it's worth what stopping and and noting, huh? Okay. Now let me just kind of you know run through life a bit and run through all the arts and sciences to kind of illustrate this a bit, huh? Okay.

[10:50] How many meals do you need? Yeah, most people think you need three, right? And they seem to. And sometimes, you know, you know, I'd skip lunch at school to to lose weight or something, and I'm getting too much weight. And then you tend to stuff yourself for the night or something. And of course, the secretaries are always trying to lose weight. Y'all, secretaries are a big woman, and and that's not the way to go.

[11:21] You know, they all know that. So you can't just, you know, you seem to need three meals, huh? But now, also with a meal, right? And like in the main course, don't you seem to need three things? You seem to need a a meat or a fish, something like that, right? And you need something like potato or rice or something that sort, and some kind of a vegetable, right?

[11:47] You know. And if you just have two of these, there seems to be something kind of missing, right? Okay. Remember my brother Mark saying that when he was a bachelor, right, and just cooking for himself, well, it's kind of you know too much to be cooking three things, right? So maybe you cook some meat and you have a salad or you you know Yes. But you always felt there was something missing without that third thing, right?

[12:14] And one way he got around it was when he cooked the meat and the vegetable, and then get some of that good San Francisco sourdough bread or something, right? But that sense of incompleteness without the what third thing, huh? Say. Um. When I was in Quebec, you know, and you'd be looking, you know, eating the restaurants a lot as a student, and you'd see the sign says, you know, prices on repas complet.

[12:45] What does that mean? Three quarters. Yeah, yeah. You get some kind of an appetizer, you know. Nothing necessarily great, right? Then the main course and some kind of dessert, maybe jelly or something, but I mean, you know, as if it's not complete without those what three things, right? You see. Those are some very simple examples, just from daily life of how two doesn't seem to be enough.

[13:12] You seem to need three meals a day, right? You seem to need, you know, for complete meal, repas complet. I said they're not philosophers; they're just, you know, that's the way we speak in daily life, right? You eat, but everybody understands what repas complet has those three parts. And the main course seems to have those three, huh? Okay. When you're a student, you know the the Quebecers tend to cook their meat less than we do, see.

[13:39] So if we're really hungry, your plate comes out. You eat all the French fries up or the vegetables, and then you call the waitress and say the meat isn't done enough, and she takes it back to the thing, and they don't just bring the piece of meat out there. It's a walkie pit. Yeah, It's a little trick, you know. We learned, but it seems you know incomplete just to have the meat on there, Right, and so okay.

[14:04] But now let's go to the to the the fundamental arts or sciences, you know, the the trivium and the quadrivium, right? Okay. Now, did three have anything to do with logic? When you studied logic, three acts of the mind. Yeah, yeah, that's all there is, right? Understanding what a thing is, understanding the true or the false, and then reasoning, right? That's all there is. Three is enough.

[14:32] But in the syllogism, right, you have that three and two, don't you? The syllogism has two premises but three terms, right? Two and three. Okay. Um.

[14:47] You tend to, in a definition, have at least three parts, huh? And that's because you know, as Porphyry defines, even the difference it's said of more than one species, so you need at least two differences. It's like in the definition of a square is an equilateral and right-angled quadrilateral, right?

[15:08] Um. Let's go to rhetoric now, which is in the trivium too, huh? Okay. Now rhetoric is the art of what? Persuasion. Persuasion, right? Okay. And how many means of persuasion are there? Three. Three. Was Aristotle who discovered that there are three means of persuasion, right? And the three means of persuasion are the image you project of yourself,

[15:40] and the way you move the emotions and the prejudices of your what audience, and then the arguments or apparent arguments you give. And you know, when the the art of rhetoric started in in Sicily, huh? In the Greek cities of Sicily, when they cast out the tyrants and they got a more democratic form of government, then it became important to be able to persuade the the jury or persuade the assembly, right?

[16:10] And but at first, what they're emphasizing was the way to move the emotions, right? But you have to give something of a reason for the things you're advocating, too, you see. But then Aristotle said they don't realize that the image that the speaker projects of himself is very important. That's why our politicians are always worrying about their image or redoing their image, and so on, right? Okay.

[16:36] But if you want a good example of the three means of persuasion there and how they're ordered, read Shakespeare's play Othello, right? Where Iago, the villain there, is trying to persuade Othello that his wife is unfaithful, when she's completely innocent, a very good woman, in fact, Desdemona, right? But he first, you know. Projects the image that makes him credible. He he pretends to be what Othello's friend, right?

[17:11] But he also gives the appearance of a man who is very perceptive and sees into people, right? A close observer and so on, right? But he also gives the impression of a man that doesn't like to state his suspicions, you know? Kind of got to force them out of him, right? The man is very careful, sneaky, right? So the sort of man that you would implicitly what trust, right?

[17:34] See, that's the first means of persuasion, right? And and you'll see how Shakespeare reflects that. You know, this man undoubtedly knows more than he he's willing to say, right? You see, you know, you know, at one time, you know, Othello and Iago are coming along, and and Cassius is talking to Othello's wife, and Yago. like almost I like that you know I like that you know something like that what oh nothing nothing nothing my Lord.

[18:04] you know and does he perceive something between my wife and Cassio that I don't perceive right I guess he was bothered by it but didn't want to say it because you know of course he's always worrying him against being jealous you know or you know but then he starts to arouse the jealousy of what of Othello. Well, that's going to make him more easily persuaded right and as Iago himself says even a flimsy proof now flimsy argument right will seem like holy writ scripture to a man who's this what jealous right huh of course we know that that somebody you know who's emotionally disposed in certain ways you know easily convinced by even a you know weak argument huh and then he just presents that

[18:59] very weak argument about the the handkerchief right see but so there but there there are three means of persuasion and to be a full possessor of the art of persuasion you have to what

[19:16] have all three things that's all you need how many species of rhetoric are there three yeah yeah the two main ones are what what they call political rhetoric from its highest use right but in general you know when you're trying to persuade somebody to do something right about the future right and then there's what the courtroom rhetoric right then there's what they call sometimes a ceremonial rhetoric that you use on Memorial Day or something of this sort when you're praising those who acted nobly right that's all there is three

[19:58] when Aristotle talks about the enthymeme being an argument from signs he distinguishes three kinds of signs he compares them to the three what figures of syllogism

[20:15] he talks about example there's three kinds of examples there's the historical example right and then there's the invented example the proportional example and the fable so there's three kinds huh when I used to teach the rhetoric a little bit I would you know give the students sometimes three the three kinds of examples for the what same conclusion right

[20:49] so I'd say you know you're going to college and you get married Well, let me tell you about this guy that got married. He never finished his college degree, you know. He had to get out and get a job, and you know, he's you know, the backwaters the rest of his life and so on. That would be an historical example, right? Okay. Now, proportional one. You know, they say that nations never appreciate their liberty, right, until they lose it to some tyrant.

[21:17] We don't really appreciate your liberty now, right? See, that's proportion, right? Okay. Now the fable is the weakest, right? But you know, they say. Do

[21:34] you hear about the goose that laid the golden egg? Each day it laid a golden egg, and said, "My, this is wonderful. Well, let's kill the goose and get it all." Hey Chris, that was the end of it, right? Well, each each date you have with Judy, wherever it is, right? Oh, it's wonderful, you know. I don't regret Judy and having her all the time, right?

[21:58] Well, they say climax spoils romance, huh? And so on, see. But when you know you can give all three arguments, right? The three kinds of examples, huh? So rhetoric, in a way, is you can say very much dominated by three there. huh? Now take the third liberal art there in the trivium, which is grammar, right? Okay. That's three important there. Well, a learned grammarian was one time explaining to me, and he says there is something in this idea that three is is all is all you need.

[22:35] He said, and I said, well, how's that? Well, he says the fundamental part of speech is the noun, like like a substance in way it stands under everything else.

[22:47] Now he says you could add a word to the noun, right? You can add to it an adjective, or you can add to it a what verb, right? Okay. So an adjective, in a way, is a word that presupposes a word, right? Okay. Let's see, he's a man, and he's what a wise man, right, or a foolish man, right? Okay. We can add a verb. The man walks, right?

[23:22] To the man runs, right? Okay. But he says you seem to require a third word, a word that presupposes a word that presupposes a word. And what is that third word? Yeah. And of course, he has the same name for the adverb added here and there, right?

[23:47] See, it seems at times I want to see not only that. Let's say Aristotle is wise, but he's what? He's very wise, right? Okay, okay. Or the girl is beautiful. I seem to need the third thing sometimes, right? She's very beautiful, right? Or the man runs. I want to say he runs fast or slow, right? Right. I seem to need that third one, right? But I don't need a fourth.

[24:16] Can I do it? That's it. Three is enough, huh? Interesting, huh? You can have articles and things like that, sorry, but I mean, basically, in order to express your thoughts, you need what? A word and a word that presupposes the word, right? And a word that presupposes the word that presupposes the word. That's it. Three is enough, isn't it? To express your thoughts. Okay.

[24:57] Now let's go to the to the poet, right? Okay. Of course, when the plot has a beginning, mid, on end, that's obviously a three. Okay, that's very important. That beginning, mid, on end. Later on, we'll talk about it a bit with the the Trinity, right? Okay, but beginning, mid, on end, that's very important, huh? And Aristotle in the Poetics, when he's giving a little bit of the history there of the development of the drama, he speaks of how it reaches perfection when Sophocles introduced the third actor.

[25:36] Striking, right? The greatest plays of all came about when Sophocles introduced the third actor. I remember in one time seeing performance of Jean-Paul Sartre. You know, I think it's called No Exit, right? You have just three actors on the stage, right? And you get kind of interesting story. You know, they end up down in hell, right? And of course, it seems like checking into hotel doesn't seem particularly, you know, disagreeable at all.

[26:06] But the three persons who have checked in cannot just get along, right? In many subtle ways, right? So it's kind of funny, but you seem to need three people to make something what? Interesting, right? Just like you know the common expression, you know what they call love triangle, right? A love triangle makes things interesting, right? You see, you need that third thing, okay?

[26:34] Apart from beginning, mid, on end, too, sometimes. Notice how common it is in fiction that you have trilogies, like C. S. Lewis's trilogies and other authors' trilogies, huh? Of course, some works obviously fall into three parts. You look at the Divine Comedy; it's obviously, you know, Inferno, Purgatorio, and Paradiso, right? Okay. Now you look at, say, Milton's Paradise Lost, and that's divided into twelve books. How many is it three?

[27:04] Right. But if you read it, the first four books, the action moves forward, right? The devil is approaching, right? Adam and Eve there, who are tranquilly living there in the Garden of Eden, right? And the temptation is about to take place, right? And then all of a sudden he interrupts that, right? And down comes an angel, a good angel, right, to warn Adam, right? And he recounts then the origin of the world from God, right, and the fall of the angels and so on, and that goes on for four more books.

[27:41] And then what? The action resumes, right, the temptation and the fall, the last four books, right. So it naturally falls into what three parts, even though at first it has twelve books, right? You look at at uh Fielding's novel, Tom Jones, which is in the Great Books, so called, and that's got what eighteen books, right? You know, if you look a little more closely, the first six books take place what in the countryside, right?

[28:14] The second six books take place in the inns and taverns on the way to London, and the last six books in London, right? They tend to fall into threes, huh? Okay.

[28:32] If you look at Shakespeare's images, they often fall into threes, huh? In a very formal way, in the what sonnets, right? I take the sonnet there about old age, huh? Well, you know, a sonnet has three quatrains, huh? And then a couplet kind of concludes it. Well, this sonnet here has got three images for old age, huh? And the first one is that time of year thou mayst in me behold, when the yellow leaves are none or few to hang upon those boughs, which check against the cold, bare ruin'd choirs where late the sweet birds sang.

[29:13] So he's comparing old age to that time of year, right? Late fall, right? Winter almost upon us, right? Then the second quatrain compares it to the last part of day. In me thou see'st the twilight of such day as after sunset fades in the west, which, by and by, black night doth take away. death's second self which seals up all rest, that kind of a little bit of glow after the sun's gone down, but it's right, big darkness, right?

[29:40] That's in the light, right? See? Then the third quatrain says, In me thou see'st the glowing of such fire as on the ashes of his youth doth lie, as the deathbed whereon it must expire, consumed with that which it was nourished by. Okay, so you have three images of old age, right? But they're properly arranged, right? Because the last part of the year is longer than the last part of the day.

[30:08] The last part of the day is longer than that little, you know, for the little bit of glow before it goes out completely, right? And then he says, This thou perceivest, and makes thy love more strong to love that well which thou must leave ere long. Beautiful, right? But you have three images, and then you have the what?

[30:31] Summing up, right? See? Okay. I was talking to to a colleague one time, and he says, "Well, when I was you know taking speech course, professors said never give more than three examples, huh? Because the audience can't take in more than three, huh? And you just you know lose it, huh? Even Aristotle in that first reading, he had three kinds of examples to show that the confused is.

[30:52] Before the what distinct, huh? But you see, Shakespeare in the plays, like when when things are going pretty bad for Macbeth, right, and his wife has died and so on, and he says, "Out, out, brief candle." See? okay, he's you know life has become pretty meaningless for him, right? But then he says, "Life's but a walking shadow, a poor player that struts and frets his hour upon the stage, and then is heard no more.

[31:18] Tis a tale told by an idiot, full of sound and fury, signifying nothing." That's it. Three images, right? And he stops. Now it seems to be in most in so many cases, huh? Enough. You don't want any more than what three, huh?

[31:40] Now you see that in music too. I just give a little passage here by John Dallman Tang. Do you know Handel's trio sonatas, the Opus Five? Anyway,

[32:00] this is the notes here. I don't know what it is. The combination of two treble instruments or voices, accompanied by a continuo bass, was much favored by composers of the Baroque period, as the simplest and most economical ensemble, which could display most aspects of musical craft. All you needed was three instruments to display most. The three lines could move independently in ingenious counterpoint, or come together to define full harmonies.

[32:33] Alternately, either the upper parts could be treated as a solo line, giving opportunity for imitative exchanges or competitive virtuosity between the players. It seemed to be enough to do all these things in the field of instrumental music. The idea of particular forms for complete works in trio texture, that is, trio sonatas, huh, was established by the great what Italian violinist and composer, Arcangelo Corelli. He's a very great composer who published four sets of twelve trio sonatas between 1683 and 1694, which I have on CDs.

[33:19] Okay. Now, just a little quote here from Paul Henry Lang. He's got this famous biography of Handel. Right, of course, Handel was quite dependent upon Corelli. Right, great influence upon him. But talking about this another, from Opus Five onward, that one we mentioned, Handel combines the sonata with the suite, the gathered gravity and resonance of the one fraction with the lighter dance of the other. But he says.

[33:53] I think this is a good judgment from what I know. The exquisitely turned trios of Opus Five of Handel stand with Bach's trio sonatas, right, at the head of the Baroque chamber music literature. That's great, huh? But the trios seem to be enough. Kind of interesting, okay?

[34:18] A couple examples here from Mozart there in the piano concertos. Taken from my kind of the classic work by Girdlestone right, on Mozart piano concertos. He says the period which precedes that of Mozart shows a great diversity in the concerto form. The three-movement plan is not yet predominant. Neither is the tradition of the rondo finale, and the structure of each movement varies from composer to composer. With all their variety of form and content, Mozart's piano concertos keep throughout certain features which never change.

[34:54] They all have three movements. The first always begins with an orchestral prelude. The second is nearly always an andante. The third generally a rondo. Now notice in the major forms, you seem to always need what three movements, huh? Okay. Now it became traditional in Vienna to say they have four movements for the quartet or the quintet, huh? And and the symphonies, right? Okay. But say Mozart's early quartets, like say the Milano quartets, and the first one he wrote in Lodi in Italy, they have just three movements, right?

[35:33] But they're considered complete works, huh? Okay. Um, and if you look at Mozart's symphonies, they usually have four movements, the later ones. Um, but so like, say the 38th and the 34th, which are very mature works, they have just three movements, but they're considered complete what symphonies? So though you could have four movements, three is what enough. The only really famous and great symphony I know that has just two is known to posterity as Schubert's unfinished symphony.

[36:12] Is it? It seems to need that third thing, huh? That's interesting, huh? If you compare Mozart's piano concertos say with his symphonies, huh, which have four movements usually, the piano concerto is closer to a drama. It has more of a plot with a beginning, middle, and end. While the symphonies are more an imitation of a virtue huh So Mozart's say Mozart's Jupiter Symphony and his Linz Symphony, which are both written in C major, that's not by accident either.

[36:51] They're both representations of what magnanimity, huh? And especially the Jupiter Symphony. I remember saying to De Koninck one time, you know, I think that the Jupiter Symphony's representation magnanimity. says you're probably right there. But the Thirty-six Symphony anticipates that too, huh? I always remember the first time I heard the Thirty-six Symphony is at the Saint Paul Public Library. They had a room where you could reserve and just go hear something, you know.

[37:17] And I first heard the Thirty-six Symphony in there. And of course, it was one of these days, you know, where you had these big windows go up in like two stories, and had the windows open like that. It was one of these days with the blue sky, these majestic clouds. And I first heard the Linz Symphony. But it's got an orchestral introduction, you know. And one critic said, you know, if all that had survived of Mozart was this introduction, right?

[37:37] The Linz Symphony would have been sufficient to establish his greatness, you know. But it's really, you know, you see that, huh? But but they can share those. Really have a plot, huh? And the first movement, and the second movement, and the third movement, you can kind of almost put words sometimes how they form a beginning, middle and end, huh? When I was in high school, I first noticed this, and I started to, you know, to write the plot of the the twentieth and the twenty-third concerto, and so on, so to Father Baumgartner there at the seminary, and so on.

[38:09] And the first, time I met De Koninck. In fact, you know, he came down on his lecture tours. I wanted to meet him, so my professor Kasurik you know, had arranged some of these lectures and so on. So he was staying at Kasurik's house. So I had questions that Kasurik couldn't answer. and Kasurik said when De Koninck comes down, you ask him those questions." Okay. So he invited me over to the house, and De Koninck came down, and so I put all these questions that Kasurik couldn't answer.

[38:35] and De Koninck gave a very clear and reasonable answer to all of them, right? You know. And then Kasurik said, "now Duane it's something to tell you. He wanted me to explain my ideas at Mozart, you know. " And De Koninck says, "He liked them. He says, write them up. He says, we'll publish them, you know. " I never got around to writing them because I started, you know, rewriting the ideas, you know, and trying to perfect them, and just never got the thing done.

[38:58] But you can see, you know, in a symphony, like you say, in a concerto, like the twenty-third, which is many people's in A major, their favorite. I remember Brother Mark's favorite concerto, and Jay Hubbard teaches philosophy at the College of Saint Thomas. There, it's his favorite. It's my my wife's favorite. It's lots of people's favorite. We know the concertos. But you know, the first movement, it's in the major key and it's joyful, but there's some kind of sadness underlying it.

[39:23] There's little hints at that, right? In the development, there's a little bit, huh? So you expect something, you know. The second movement is written in F sharp minor, which you hardly ever use, right? And you have this whole sadness coming out now that was underlying this, huh? But it's eventually purged away at the end, right? Okay. And then the third movement begins with a series of bright melodies, right?

[39:48] Huh? You know, like a they say it's like what? You know, letting bright sunlight into a dark and musty room suddenly, right? Why the first movement they compare it to, you know, March day when the sun is shining but not very convincingly, right? But then Mozart, you know, to show that that's not just escapism from that sadness, right? These we overcome it. You have a little bit of that sadness brought back, but you have this confidence that you can face it and overcome it.

[40:16] And you have to hear the music; it's really doing that, right? And then at the end, when he brings back that string of melodies, he he has a device where he kind of interrupts it and makes it seem absolutely inevitable, you know. It's perfectly constructed.

[40:34] What? What was that again? The twenty-third piano concerto in A major, yeah, one of the greatest ones, and it's one of the simplest ones too, you know, harmonically and so on. But you see, the concertos being always in three movements, right? And that's partly the fact that they're closer to a drama. See, they're more an imitation of an action as a beginning, a middle, and end. Okay.

[41:01] Um. Listen to what Girdlestone says here he's talking about the first movement of the concertos, huh? Because they tend to, well, he basically says here first, huh? In the classical concertos, in the symphony, the first allegro is the chief movement, the one which sets its mark upon the work, and on it one is tempted to found one's judgment of the concertos as a whole. It begins with a fairly long tutti at the end of which the solo enters.

[41:30] This prelude, which serves as a first exposition and contains the movement's main subjects, finishes in the tonic. The solo's entry starts a new exposition, usually longer, which ends as in a symphony in the key of the dominant or the relative major. Apart from this double exposition, a concerto first movement follows an out of form. The development comes next, right? Then the recapitulation. Okay, that's four, right? The second exposition is in its structure much more like the exposition of a symphony than the first, but the effect it produces on the listener is quite different from that of a true exposition.

[42:15] It gives one more the impression of a development. Some of the chief ideas are already known; they have been heard in the tutti, and the second exposition seldom reproduces them without change. The true development itself is so short compared with the rest of the movement, especially in Mozart, that one hardly thinks of isolating it from what precedes. The result is that for him who listens without worrying about forms or formulae, the real development begins with the solo entry, and instead of dividing a concerto first movement into four parts as do the textbooks, it would be more sensible to keep a threefold division.

[42:54] As for the sonata and the symphony, right? The two the exposition, the development, including the solo exposition, the development, and the textbook ends in the recapitulation, right? But the sonata form lends itself to division into what three, right? Incidentally, Mozart's operas are done in that form too, right? They begin in the written key, at least the Italian operas, and they work their way to the dominant, the middle point, and back to the tonic.

[43:23] So you have a beginning, middle, and end, and then each part has a beginning, middle, and end. I once one time saw a book there, Le Nozze di Figaro, was on the Le Nozze di Figaro, right? The head of the Graduate School of Music there at Chicago, but he's showing how Mozart's opera had a beginning, middle, and end as a whole harmonically, and then each part had a beginning, middle, and end.

[43:44] But again, it naturally is falling into what three, huh? So we looked at grammar, rhetoric, logic, and. Fiction, music, three plays a very important role, huh? But now come back to to natural science here, right? And go from the philosophy of nature where we saw the importance of three, huh? But this comes later on in physics too. I mean, Aristotle would distinguish basically three kinds of motion, right?

[44:15] Which give rise to the three parts of of natural science in particular: change of place, change of quality, and growth, right? We of our physics, chemistry, and biology that division arose into three. Um. But let's take a little example here from Heisenberg from the experimental sciences, huh? And I have two passages here. One is from the the Gifford Lectures, of physics and philosophy, and the other is from another collection of Heisenberg's papers, which they call "Across the Frontiers," because he often, you know, takes a larger perspective.

[44:56] But give you the one here from physics and philosophy. The theory of relativity is connected with a universal constant in nature, the velocity of light, right? That's one constant, right? Quantum theory is connected with another universal constant of nature, Planck's quantum of action. It's two, right? There must exist a third universal constant in nature.

[45:32] So clearly, Heisenberg, huh? He says this is obvious for purely dimensional reasons. Makes you think of the three dimensions again, huh? He says the universal constants determine the scale of nature, the characteristic quantities that cannot be reduced to other quantities. One needs at least three fundamental units for a complete set of units. This is most easily seen from such conventions as the use of the CGS system, that means centimeter, gram, second, huh?

[46:13] Of time, by physicists, right? A unit of length, one of time, and one of mass is sufficient to form a complete set. But one must have at least three units. One could replace them by units of length, velocity, and mass, or by units of length, velocity, and energy, etc. But at least three fundamental units are necessary. So clear, Heisenberg. Now going back to the universal constants. Now the velocity of light and Planck's constant of action provide only two of these units.

[46:51] There must be a third one. I see. There's another Nobel physicist like him out, there like Gamow, right? And only a theory which contains this third unit can possibly determine the masses and other properties of the elementary particles. Judging from our present knowledge of these particles, the most appropriate way of introducing the third universal constant would be by the assumption of a universal length, the value of which would be roughly ten to the minus 13 centimeters.

[47:20] That is somewhat smaller than the radius of the light atomic. nuclei It's interesting, right? He was convinced there had to be a third universal constant, and I see at least in Gamow who got to know about Planck too, right? But you know, he compares it to the fact that you have basically what three units like in the CGS system. Did that happen? I don't think it's established now, but okay.

[47:49] Now here's a statement of again in a essay entitled "Planck's Discovery," right? In the philosophical problems. of. Atomic theory, and this is from the volume Across the Frontiers, which is also published by Harper and Row. I think it's on paperback. I don't think, but anyway. Following recognition of the basic significance of the two universal constants of nature, Planck's quantum of action, right, and the velocity of light, right, it was natural to ask how many such independent constants of nature there can actually be.

[48:26] It's like the question at the beginning of this reading, right? How many? The answer is there must be at least three such universal constants, but that probably all other constants of nature can be traced back to these three by way of mathematical relations that are still in part unknown.

[48:51] That three such independent natural units of measure must exist is something most simply made clear to the physicist or technician by considering how the customary physical or technical systems of measurement all contain three such units of measure: the centimeter for length, right, the second for time, and the gram for mass. If we wish to replace these three conventionally established units by natural ones, Planck's quantum of action and the velocity of light must be supplemented by yet another constant.

[49:32] The atomic structure of matter makes it natural to choose as our third unit a length of an atomic order of magnitude, for example, a length of the order of the diameter of simple atomic nuclei. But a precise formulation of this unit of length can be given only if we are able to express mathematically the natural laws in which it figures as an essential quantity. Quantum theory and relativity theory obviously cannot be combined without difficulties.

[50:02] After what has emerged in recent years, we have every reason to suppose that success in combining the two theories can be achieved only if we also take into account the field of into the field of consideration, the third basic structure, which is bound up with the existence of a universal length of the order of ten to the minus 13 centimeters. So I mean, that's interesting, right? You know, the role that he sees for three there in in what physics, right?

[50:30] Okay. Now, if you go to theology, of course, you can see how theology is dominated by three, right? Starting with the what Trinity, of course, the most famous example of this, right.

[51:01] But second mystery after Trinity is the Incarnation, right? And there the three are that Christ as man is what, King, Priest, and what, Prophet or Teacher, right?

[51:22] And if you study the Second Vatican Council, there are documents, you know, pastoral documents directing bishops and so on, are about the bishop. There are pastoral document about the priest, right? There pastoral document about the laity, right? But you'll notice in talking about the bishop or in talking about the priest or in talking about the layman, Vatican II will try to bring out how each of them in a different way, right,

[51:57] shares in the three offices of Christ. And so to talk about the bishop and what way he shares in the, you know, prophetic or teaching role of Christ, right? What way is King, is ruler, and so on, and is Priest, right? Okay, and then take up the same thing for the for the priest, right? And then they'll talk even about the priesthood of the laity, which is a different thing, but you know, it's a shared, right, in in those three.

[52:25] So that's another very important three, right? And the third three that always comes to mind in theology is is the three faith, hope, and what, charity, which is the way that

[52:44] Saint Augustine and Thomas divide what the catechetical instructions are, going to faith, hope, and what, charity, right? So three is a very dominant thing there.

[53:01] But in in the theological works, Thomas will sometimes take up this objection. You know, Thomas will say that the Trinity is known only by faith, not by natural reason.

[53:21] One of these objections is taken from Aristotle's book on the universe, which they call in Latin De Caelo et Mundo, where Aristotle says, "And by this number, namely three, we praise God, right, and so on, right? " He said, "Well, God, Aristotle knows something about this, right? " And Thomas, in reply to this objection, he says, "According to the exposition of the commentator that Zabara was, right?

[53:50] Aristotle did not intend to place a Trinity of persons in God, right? Even though he saw three as a number to praise God with, right? " But in account of this, that in all creatures there appears perfection in three, as in a beginning, middle, and what, end, right? And therefore the ancients honored God in threefold sacrifices and prayers. Okay, sort of interesting, huh? Okay.

[54:24] Now that's taken from the sentences here. Now another passage in the sentences where he's explaining the what they call the vestige of the Trinity. You know, the distinction between the image of the Trinity and the vestige of the Trinity. But in the image of the Trinity, you always have three of course, because here. But now, this particular article is entitled: Whether the parts of the vestige, the footprint of Trinity, are three only or two, right?

[54:57] Okay. And he says, vestigium, which is like footprint, huh, is found in the creature in so far as it imitates the divine perfection. The perfection, however, of the creature is not had at once in its principles in its beginnings, right? Which are imperfect, as is clear in matter and form, of which neither has by itself for perfect being. But in the joining of the creature to its end.

[55:28] But nature does not join things at a distance without something in the middle. And therefore, in creatures, there is found a beginning, a middle, and an end, according to which three things Pythagoras laid down the perfection of each creature.

[55:46] And according to this reason of these three things, there is represented in creatures the distinction of the divine what persons, in which the Son is the middle person, right? And the Holy Spirit is the one in which the procession of persons is terminated, right? Okay.

[56:08] Okay. And now he's applying for objection. You know, the same part that that's where you find is three, right? In that bond article, but this is objection. A footprint is said in the creature according as it represents the Creator, but there are presented in creatures many attributes of God, huh, which are partaken of by the creatures. It is clear through Dionysius in the Divine Names, chapter nine.

[56:33] Once it seems that there are more parts than just what three, right? To the third, Thomas says it should be said that the properties of the creature, from which we are led to the divine attributes, although they are many, they have nevertheless the order to each other of beginning, middle, and end, under which. Notions they lead us to the three persons, no matter how they are diversified.

[57:03] Okay, and then another little passage here, another distinction there in the senses. He's talking about something kind of funnier about the the sins there, and because perfection of every quantity is comprehended by three on account of the beginning, middle, and end, therefore a threefold difference is laid down. Okay, but you also do that when you talk about the what the three stages of charity, you know, the beginners and, the middle, and the perfect, right?

[57:41] That corresponds to the three parts of the Psalms when Augustine and Thomas divided the Psalms into three fifties, and the first fifty, you know, according to the correct numbering now, not this more contemporary numbering, the first fifty into the Psalm of what? Asking for forgiveness, right? The second fifty end with a psalm dealing with what? Good action, right? And the third fifty end with a psalm of praise, right?

[58:09] That's characteristic of each group, huh? Because the first stage is where you're mainly what fighting against your vices and sins and repenting. Second one, you're trying to go forward in the virtues from virtue to virtue. The third, you're resting in God, you know.

[58:27] So, some people see, you know, three as being so prevalent in preachers, right, and things we study, because you know, the Trinity in some way, right?

[58:49] Now, if you read, you know, fairy tales, like you know, if you get the famous fairy tales, you can get them still in Dover books. You know, the blue book of fairy tales and the green book, and you know, all different colors. But all these stories, they always got what? Three people in them. Oh.

[59:07] But just to end on a lighter note here of three, here. This is taken from Henry Shelley's book, which is The Inns and Taverns of Old London.

[59:22] He says, no one can glance even casually over a list of tavern signs without observing how frequently the numeral three is used. Various explanations have been offered for the propensity of mankind to use that number.

[59:43] One deriving the habit from the fact that primitive man divided the universe into three regions: heaven, earth, and water. Pythagoras, it will be remembered, called three the perfect number. Jove is depicted with three forked lightning. Neptune bears a trident. Pluto has his three-headed dog. Again, there are three fates, three furies, three graces, and three muses. Of course, you might mention that there are what? Three hierarchies of angels, right?

[1:00:15] And each hierarchy has what? Three orders, right? Like the highest hierarchy has the what? The seraphim, the cherubim, and the thrones, right? And in the middle one has the what? The lords and the virtues and the powers. The lowest one, the princes, the archangels, and angels, right? And Dionysius tells us within each one of those orders is a beginning, middle, and end, too. So you have three hierarchies, and each hierarchy three orders, right?

[1:00:40] And each order you have beginning, middle, and two. So it's just dominated by three, huh? The angels, huh? It is natural then to find the numeral so often employed in the signs of inns and taverns. Thus we have the three angels, the three crowns. The three compasses, the three cups, the three horseshoes, the three tons, the three nuns, and many more.

[1:01:13] And he says, in the city of London proper, the three cups was a favorite sign, and the three tons was hardly less popular. There were also several three nuns. The most famous of which was situated Aldergate High Street, where its modern representative still stands. In the bygone years, it was a noted coaching inn and enjoyed an enviable reputation for the rare quality of its punch.

[1:01:45] I just hit a little light layer note there, and three, you know. This is not complete, you know. I don't know if you just a few interesting, you know, ones you can have if you want.

[1:01:57] Getting my three cans. To get to wisdom, you find out the wisdom is about three things. Well, let's get there to get to wisdom. Okay. Now,