Prima Pars
Lecture 63: Divine Knowledge and the Absence of Discourse in God

Transcript
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Do I say, three-sided plain figure known by Perkwist? Because then none of us would be ever knowing the same thing, would we? And I could never have learned about the triangle from Euclid, because his knowledge would have been what? His definition of triangle would include known by Euclid. And my definition of triangle would include known by Perkwist, so we don't have the same definition. But yet it's always true of what is known by me that it's known by me. But in that case, it's accidental to what I know that it's known by me, even though it's necessarily known by me, if I know it. What does Aristotle say? The falcy of the accident deceives even the wise. But I think it especially deceives the wise when it's necessarily, what, there. You know, Hegel kind of universalizes the mistake of the accident when he speaks of the portentous power of the negative. Everything arises from negative. Can I teach you something you already know? I only teach you if you're ignorant of something, right? So the only reason why you're able to learn is because you're ignorant. Right? Is that true? Is your ignorance your ability to learn, your ability to know? Well, see, you come to know what you don't know to something you know already, right? Now you're ignorant of it before you come to know it, necessarily. But is it through your ignorance that you come to know it? And Richard II there, Norfolk, speaks of dull, barren, unfeeling ignorance, right? And why is it called ignorance-bearing? It's through itself. Yeah, yeah. So before I multiply the length by the width, I don't know the, what, area. And it's necessarily true, right? But do I come to know the area through my ignorance of the area? Through your knowledge of the width. Yeah, yeah. So even though my ignorance of the area necessarily comes before my learning the area, it's not really the cause of my coming to know it. It's something that happens to the real cause. But it's something accidental to my coming to know. And, you know, we've talked before, I think, about the mistake there of Sartre, you know, where he takes our freedom to be a kind of non-being. Well, you know, if I go to the restaurant and they give me a menu there, and if I'm really, what, free to choose between steak and chicken or something else, then before I choose, my will is, what, determined to choose steak rather than chicken? But then my will is not free, right? Right. So he says, before I choose, then, there must be this non-being in my will, this lack of determination, right? And that's my freedom, he said. Is that true? He's identifying my ability to choose between steak and chicken, right, with my lack of choice between the two. Are they the same thing? That's like confusing my ability to know with my ignorance or something, huh? But because it necessarily is found there before I choose, you can think that that is the real, what, cause. Cause, yeah. But the modern mind is that your knowledge is like an empty stomach or something. That's a good thing there, you know, about do opposites attract, right? You know? Such, you know. Now, the second objection was saying, well, the divine nature is as far away from the nature of the creature as the reverse, right? But he says, the nature of the creature is compared to the nature of God, the essence of the creature, to the essence of God, as an imperfect act to a, what, universally perfect one. And therefore, the nature of the creature does not sufficiently lead us to a knowledge of the divine essence, but the, what, reverse, huh? In other words, the nature of the creature is contained already in God in a superior way, a more excellent way, than it's found in the creature. But that's not true, that the nature of God is found in a more excellent way in the creature than in itself, but in, what, an imperfect partaking of it. So you can't really know that, right? Now, the third one is the one we're talking about here, you know, what they call the universal representation, right? For the third, it should be said, that the same is not able to be taken as the reason of diverse things by way of a kind of, what, equality, right? But the divine essence is something exceeding all creatures, huh? Whence it can be taken as the proper reason of each thing, according as it is in diverse ways, able to be partaken of or to be imitated by diverse creatures, huh? So if God knows himself perfectly, then he knows every way in which he's able to be, what? Partaken of, yeah. Or every way in which he can be imitated, right? Some ways more perfectly, and some ways less perfectly, right? So he wouldn't know himself perfectly if he didn't know how he could be imitated. But the creature in knowing himself couldn't know God, right, huh? Because he's only, in a perfect way, like God, huh? I guess we've got to kind of stop right now, 4.50, huh? Mm-hmm. Mm-hmm. Okay, in the name of the Father, and the Son, and the Holy Spirit, Amen. God, our enlightenment, guardian angels, strengthen the lights of our minds, order to illumine our images, and arouse us to consider more correctly. St. Thomas Aquinas, Angelic Doctor, help us to understand all that you've written. In the name of the Father, and the Son, and the Holy Spirit, Amen. I'm going to give you a little cider now from the Epistle of St. Jude. I was reading a golden chain there on the Gospel of Matthew, and of course, I'm up in the 10th chapter there, where the 12 apostles are enumerated, right? So the church has all kinds of things to say, right? And I didn't realize that the mark has a little different order there for the first four. You see, what Matthew says, Peter and his brother Andrew, James, the son of the 70s, and his brother John. That's the way it goes. Well, Mark has Peter first, and then James, and then John, and then Andrew fourth. And they say, what? It's the order of dignity. Because those three were the ones who were taken up and long, you know, for the Transfiguration, and in the Garden of Gethsemane, and in the, you know, when he raised the daughter of Jairus, was it? And so on. So they have a certain thing. But anyway, they were saying, you know, that in one text, I guess, in Matthew, he's called Thaddeus, and in other cases, Jude, I guess. And he's supposed to be the brother of what? James, the lesser, James Alphaeus. And so I was reading that, and he said, he says this one is Epistle, right? And so I said, okay, I'll go look at Epistle. It's very short. Epistle, you know, it's the last one here. And he says he's the brother of James, you know. Doesn't say which James, but go over there. But I was struck by this verses 20, 21. I don't know if you're familiar with those. But if you perhaps know, sacred doctrine is presented in at least three different orders. And one order sacred doctrine is presented in is, of course, sacred scripture. The order in the books of the Bible and so on. And then another order is the one that you have in the Summas. It's God in himself, and God is the maker, and God is the end, basically. But certain variations on that. But then there's another order which Augustine follows in the Enchiridion on faith, hope, and charity, and which Thomas Aquinas follows in the Catechetical Instructions, and which he also follows in his Compendium of Theology, which he didn't complete. And there you divide sacred doctrine according to faith, hope, and charity. And what Augustine does, and Thomas does too, following Augustine, when you talk about faith, you talk about the Creed and explain the articles of faith. And then for hope, you talk about the Our Father. Sometimes the Hail Mary too, but primarily the Our Father. So that prayer corresponds to hope. And then for charity, you talk about the Two Commandments of Love and the Ten Commandments. And the Enchiridion of Augustine is written for kind of like an educated man, but a layman, you might say, right? And he wanted kind of a summary of these things, and so Augustine gave it in that order, which is different than the order here, and different than the order you have in the Scripture. But although these orders are all touched upon in Scripture, and Thomas, when his catechetical instructions are called, the Naples sermons that he knows life, follows that same order. And when his brother, you know, asked him, you know, to give him kind of a thing he could carry around and, you know, kind of a certain version, he gave the same order, faith, hope, and charity. It's much longer than the catechetical instructions, but that same order here. Well, you could also say that by faith, hope, and charity we're ordered to, what, God is our end. We're ordered to, what, eternal life, huh? Beauty and Vision. And, uh, because these are the three virtues that have God himself as their object, huh? As you know, I'm very fond of the premium to Dei Verbum in Vatican II, and it's very well ordered that little premium. But it begins by talking about eternal life and how we're invited to this and so on. And then it ends up by talking about faith, hope, and what, charity. Quoting Augustine, you know, by believing we come to hope and by hope we come to love. So you see that order of faith, hope, and charity to eternal life, huh? In the, uh, premium to Dei Verbum. Well, you have something like that in this little passage here from, uh, there's no chapter of Vision that she was just, she versus, but it's verses 20 and 21, huh? And so he says, if you can listen, stand my Greek here, humeis ad agapete, but you, beloved, right, huh? Look, he's addressing us now, huh? And then he says, ep oikodomuntes. Now, that comes from the Greek word for what? Building a house and generalizing to building or to building upon something, right? And so he says, ep oikodomuntes, building up is the way they translate it here, yourselves, huh? Hiotos, te hajiotate humon piste, in the most holy or by the most holy, what? Faith of you, right? Of course, it struck me that Greek word I was looking up in the dictionary at home, ep oikodomuntes, because I know it's related to the word for house, right? And it gives the first meaning of this, of the verb form, building a house, right? And then it's kind of generalized. It reminds me of the explanation you get in some of the church fathers when they're talking about the 126th Psalm. It says, unless the Lord build the house, they labor in vain who build it. And one meaning of that, of course, can be the house which is the church itself, right? But another meaning even for the individual soul is that the foundation of the house is faith and the walls are hope and then the roof is charity, right? So that word he chose is there, ep oikodomuntes. So you get to write economics from oikos, a household science, huh? We had two economists at school there who are husband and wife, right? And so when they both got hired, not at the same time, but eventually there, and I see them walking down the hall together and they say, well, now I know that economics is a household science. But it's kind of fun. So he says, building up themselves in the most holy faith, right, huh? And then the next words is all one sentence. In penumiti, hagio, in the Holy Spirit, pros uku menoi, huh? So praying in the Holy Spirit, huh? It doesn't mention the word hope, but they mention Augustine and Thomas connect prayer with hope, huh? This is beautifully said, right? Praying in the Holy Spirit, like he groans in us, like St. Paul says and so on. And then the next part, which is still in the same sentence, keep yourselves in the love of God, huh? He autos, in agape theu, te resete, Keep yourselves in the love of God. So you've got the three in that same order, right? But then it goes on to eternal life, huh? It's still in the same sentence. Pros dekomenoi, huh? Awaiting, right? It's beautifully said here. To Ilias, the mercy, right? To curio hemon, of the Lord of us, right? Iesu Christu, Jesus Christ, eis zoen Ionian, in eternal life, huh? So it's beautiful. That same idea that you find in the Ukrainian to de verbo, but different texts, right? But here it's all in one little, what? To Ilias, verses 20 and 21, huh? Can you read the whole thing again? What? Could you just read the whole, the complete thing? In Greek or Latin or in English? Just your English one. English one, okay. Actually, this is a fun translation. But ye, beloved, building up yourselves on your most holy faith, praying in the Holy Ghost, huh? Keeping yourselves in the love of God, looking for the mercy of our Lord Jesus Christ unto eternal life. It's a beautiful way it ties together eternal life with those three theological virtues like it does in the premium, but I appreciate that. Again, it also touches upon that way of dividing sacred doctrine that's most appropriate for a beginner. Okay, let's go back now to Thomas, huh? And you're in your brother. The goal in life is to, what, understand and love God, right? They're not the same thing, right? But perhaps understanding God, right, helps you to some extent to love God, right? So he gives you reasons for loving God, right? You don't get too tied up in the thoughts. You know, where St. Francis, they wanted to study theology rigorously in the Franciscan order of all places. He finally gave permission, provided they don't extinguish the spirit of, what, devotion, okay? But vice versa, you could say loving God. If you really love God, that should make you want to understand him too, right? So these two things should work together, right? Understanding God should help you to love God more, right? Although you can love God more in this life than you can understand him, right? But vice versa, loving God should incline you to want to understand God so far as you, what, can, right, huh? You've got to be careful. You don't want to throw maybe the people of the parish right into this. But sometimes one of the relatives all start off and say, Oh, stop that, stop that. Now, Article 7 is following upon these articles which show that God knows other things, right? And you might say, in a way it could be misunderstood, God knows other things than himself and knows them properly, but he knows other things than himself, through knowing himself, right, huh? Okay? Now, you can understand that, right? Because I know the conclusion of a syllogism through knowing the premises, huh? And I know the premises before my mind moves, by what we call discourse, to the conclusion, right? Well, is that the way God knows? You know, he's thinking about himself, and all of a sudden he draws a conclusion about you or me, see? Well, no, it might be better to say God knows other things in knowing himself, right, huh? It's not from knowing himself, because that can imply that there's a movement in God, right? And God is, as one of the other canonic epistles says, there's no shadow of change in him, right? Not even the shadow of change, it's a bit of change, okay? To the seventh, one proceeds thus, it seems that the knowledge of God must be discursive. Now, we talked about the word discourse when we were explaining Shakespeare's definition of reason as reason, right? Its ability for a large discourse, looking before and after, right? So he defined reason by what? Discourse, huh? And in the Middle Ages, sometimes, in the medieval Egyptians, discursus is sometimes used as almost a synonym for reasoning. But it comes in the Latin words to what? Discurari, to run from one thing to another, right? It has the same root as race course does, huh? Okay? Or win in the course of human events, huh? But this is a movement inside of reason itself. Okay? But it could be used for any movement from one thing to another reason. But it's especially used for knowing one thing to another, right? But coming to know what you don't know to what you do know, right? But there's a real movement of the mind from one thing to another. Okay. First objection. For the knowledge of God is not according to knowing and habit, but knowing and act. But according to the philosopher in the second book about the places, it's a book on dialectical reasoning, one can know habitually at the same time many things, right? Like I know all 48 theorems in book one of Euclid. In habit, huh? Okay? But I can understand only one of those at a time in act. Since, therefore, God knows many things, because he knows both himself and other things, as we've shown in the previous articles, it seems that he does not at once know all things, but he runs from one thing to another, right? This is really drawing God down to the level of our, what? Mind. I was looking at Thomas' thing on the Trinity here one time, and he's talking about how we try to understand generation and God, right? You have to understand it in the way St. John explains it in the beginning of his gospel, right? It's an intelligible generation. And it's like what you find, therefore, in the higher creatures, right? So he says you can't, you know, take your likeness from the lower creatures, right? You've got to take it from the higher ones to get something like God. But even that, he says, oh, sure. And this is a good example I've done. Furthermore, to know the effect through the cause is to know in a way that the one discoursing knows. The one running from one thing to another does. And Thomas sometimes, you know, he talks about the discourse of our reason from one thing to another. He'll distinguish four main kinds of discourse from one thing to another thing, right? Sometimes our reason runs from the cause to the effect. More often, though, it runs in the opposite direction, from the effect to the cause. And sometimes it runs from one thing to another that is like it. And then it runs from one opposite to the other opposite, huh? So when I was trying to define comedy, I was running all the time from tragedy to comedy. And I said, well, if tragedy moves us to pity and fear, then comedy ought to move us to the contrary emotions. So I was running from opposite to opposite, huh? But reason often runs from like to like whenever you make a like this, this this to that, this that is to that, huh? You're running from like to like. And then sometimes you run from cause to effect and effect to cause. Well, it seems that God is one of these, right? Because he knows the effects of himself through himself, the cause, huh? So he's knowing the effect to cause. He's just like us, right? So he must fund from one to the other. Moreover, God knows more perfectly each creature than we know each creature. But we, in created causes, know their effects. And thus we run from causes to the cause, huh? Therefore it seems that likewise it must be in God. Well, it seems to quote Plato there in the, uh, the, uh, sophist, right? That likeness is a dangerous thing. It's a slippery thing, you know, if Plato has a way of saying it easily upsets you, huh? But against all this is what the great Augustine says in the 15th book about the Trinity, huh? Now, I'm of the opinion that that's Augustine's greatest work. It's certainly not his most popular work. I suppose the Confessions is the one that we put him on everybody's shelf. But, uh, I think the Trinity is his greatest. The subject is the greatest. Okay? Okay? So God does not, in a particular way or bit by bit, right, see all things, huh? As he looks first here and then there and so on. But he sees all things at once. Okay? Together. He's seen those the opposite of what? Before and after, which is in the definition of discourse, right? So Thomas says, I answer, it should be said that in the divine knowledge there is no discourse, huh? I might mention that, you know, if you ever get around to studying the angels, right? Remember when I said to my old teacher, you know, I want to study the angels. Anytime he says, you know, he'd like to talk about the angels. But the angels don't have discourse either, right? And therefore, you know, Thomas is always quoting some philosopher, a philosopher called Isaac, you know, who says that we live in the shadow of understanding. We have to think about things a lot to understand until we do, right? But the angels are everything you understand right away. That's why they, but right away they either chose God or they, you know, went back to God with what they had. Or else they said, ah, this is it. Yeah, me, I'm the most wonderful thing. And, uh. Yeah, me, I'm the most wonderful thing. They're beautiful creatures, huh? I answered, it should be said that in the divine science there's no discourse, which in this way becomes clear. Now this is a distinction I often use when I talk about Shakespeare's definition, right? In our knowledge, there is a two-fold, what, discourse. One by succession only, right? As when, after we understand something and act, we turn to understanding something else, right? And the other discourse is by causality, you know? And what does he mean by that? He means that not only do you go from one thing to another, but the first thing is the cause, and you're going to the second thing. So if you know the premises, then you, what, go to the conclusion, but the conclusion is what? Yeah, yeah. So what's the definition? Let's recall the definition there of syllogism, huh? This is the most effective one. But if you see a speech in which some statements, and it's usually just two, right? Speech in which some statements laid down. Okay? That means firmly in the mind, right? Another, meaning another statement, right? Follows necessarily because, that's in the definition, of those laid down. Now notice, I went from Jude to, what, this article, right? Which kind of discourse is that? But was I drawing conclusions about whether God is discursive or not? From what we said about faith, hope, and charity, and eternal life? No. Just success. Yeah. No, I just think about that thing, now I was thinking about this thing, right? No, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no It's false necessarily and because of those laid down, right, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, no, night follows day necessarily, but is it because of day that night follows? Is day the cause of night? No, it's some third thing, right? Maybe the sun going around the earth, maybe the earth turning on its axis, depending upon it, you see? But if the earth necessarily turns on its axis, then day and night necessarily follow each other, right? But night is not following day because of day, right? Night is following day because of the rotation of the earth, right? But in the syllogism, not only do you have one thing following anything necessarily, but the thing that follows necessarily is because of what came before, right, huh? Okay? Now, it's this kind of discourse, the second kind of discourse, that I think you should understand when you talk about the definition of reason, right? Because to some extent, with our senses and even our imagination, I can go from what? When I read the book with papers, I go from imagining one scene to imagining another scene, right? And so on. When I go to look up there at those cards, I can go from looking at one card and the next one, next one, right? See? But I don't see the second card through seeing the first card, do I? I don't see. But when I reason, I know the second thing through knowing the first one, right? Okay? So that's what he means, he says, the other discourse is by causality, as when through principles, huh? Or premises, we arrive at a knowledge of, what? Conclusions. He says, the first kind of discourse cannot belong to God, right, huh? For the many things which, what? We understand excessively, if each one of them is considered in itself, right? All of them we understand at the same time, if we understand them in something one, right? If, for example, we understand the parts in the whole, or if we see diverse things in the, what? What? Mirror, right, huh? Okay? It's like if, if I think about what a man is, right? That's one thinking of mine. And then I think about what a stone is, that's another thinking, right? But if I think that man is not a stone, then I'm knowing man and stone at the same time. Because they're in that one, what? Statement, right? And then I'm not thinking, you know, at one time of man, at the other time of stone. I could never know that man is not a stone unless I could think of man and stone together, right? Yeah. But when I think of what man is, I don't at all at all think of what a stone is, right? When I think of what a stone is, I don't at all think of what man is, right? But when I think that man is not a stone, I know both of them together in the one, what? Statement, yeah. Well, God knows all things in himself, right? And so he knows all things, what? At once, together. Simo can be, you know, translated at the same time or together, right? But God, however, sees all things in one thing, namely himself, right? Whence at once or together, and not successively, he sees, what? All things, huh? Likewise, also, the second discourse cannot belong to God, right? And he gives a number of reasons for this. First, because the second discourse presupposes the first. For in proceeding from the principles or premises to the conclusions, one does not consider both, what? Together, right? First you consider the premises, right? And then you proceed from them. So that's one reason, huh? Okay? So that first kind of discourse is involved in that, right? Then, because such a discourse is that of one proceeding from the known to the unknown. Once it is manifest that when the first is known, the second is still ignored, huh? Or unknown. And thus, the second is not known at first, you could say, in the first, right? But from the first, right? But the end of the discourse is when the second is seen in the first, huh? When you resolve the effects into the causes, huh? Then the discourse, what? Ceases, right? So it's like, there's kind of a circuit analogy. You go from the premises to the conclusion, and then you break the conclusion back down into the, what, premises. And that's why those two books of Aristotle about the perfection of reasoning are called the prior and the posterior analytics, huh? Because, at the end, you take apart the conclusion, and then it's back to the, what, premises, huh? We have to go through that discourse. Whence, since God sees the effects in himself as in a cause, his knowledge is not, what, discursive, huh? But you could say, if God was also going from, what, the known to the unknown, he would be some change in him, right? He'd be coming to know. And would he be knowledge itself? God's altogether simple. Is there any distinction between God and his knowledge? He'd be knowledge. He'd be knowledge. He'd be knowledge. So can knowledge itself be ignorant? That'd be like whiteness itself being black, right? And heat itself being cold. Now to the first objection he says, that although there is only one understanding in God, right? Nevertheless, it can happen that many understood in something one. And he understands whatever else he understands in himself, right? Okay, so notice that the language of Thomas, going back to the body of the article again, and I said this before, but look at it again there. He's talking about reasoning. He says, and thus the second is not known in primo said ex primo, right? Okay, so it says better to say, don't misunderstand the thing, that God knows other things in knowing himself, right? He doesn't know other things from knowing himself, right? Although he could say it if he understood it properly, perhaps, but it could be misunderstood, right? Okay? And likewise, he said he knows other things through knowing himself. Well, you can say that, but you've got to be kind of careful, right? Because if I'd imply that there's a discourse in God, right, that through knowing himself he comes to know other things, that isn't so. But he knows other things in knowing himself, right? Okay? And at the same time, right, just like I, knowing that man is not a stone, know both man and stone together at the same time in that one what statement? And the same way, you know, it's kind of a marvelous thing in the syllogism, right? But in the syllogism, you've got to have in mind at the same time both premises to draw the what? Yeah. If I thought the major premise and then forgot about it or stopped knowing it, and then I thought about the minor premise, I wouldn't be able to draw any conclusion, right? See? You've got to put these things together firmly in your mind at the same time, right? And then there's a kind of unity, right, huh? That's kind of marvelous that our mind can do that, huh? Okay. The second objection is saying, yeah, God knows the effect through the cause in a way like we do, you know, but we do it by a discourse, right? Okay, we run from one to the other, huh? But God knows the effect in the cause, right? In himself, huh? Okay? And it shows the imperfection of our mind. That's why Isaac says we live in the shadow of understanding, right? That in knowing the cause, we don't right away see all the consequences of it, huh? Okay? And, you know, when you go through Euclid there, you know, and he draws up another conclusion out of something, you know, and you say, oh, why, marvelous, marvelous. But you didn't see the consequence of what you already knew, right? Yeah. You didn't in the beginning see the conclusion in the premises. And you had to go through this discourse, huh? You know? It's kind of used to say we practically did, you know, our mind did. You're a little bit of a bush, you know. So, Thomas says sometimes that our understanding is by way of motion. And now the third objection, huh? God more perfectly knows each creature than we know them, huh? But we, in created causes, know their effects. And thus we run from causes to cause, right? Well, he says the effects of created causes, God sees in the causes themselves, much better than we do, right? Not, however, such that the knowledge of effects is caused in him from the knowledge of what? The created causes as in us. But again, he sees them, right, huh? In the causes right away. Whence his knowledge is not, what? Discursive, huh? So, how can Shakespeare say that reason is God-like in the exhortation? When he defines reason as ability for a large discourse. What's only insofar as our reason is able to understand, to some extent, that it's what becomes like God, right? And the more you understand, the more you become, what? Like God, huh? Especially become like God when you understand God. Because you don't really, strictly speaking, you understand God in this life, but he has some kind of consolation understanding, as Thomas says, huh? This is to console our mind for, before we get to see God as he is, huh? Or as Augustine says, I'm just a sort of man who would want to understand what he believes. And, of course, that's natural, right? See, it's natural for our mind to guess or believe another, right? Before we know, right? And so that's observed even in the supernatural order, right? That we have to believe God before we will, what, see him as he is. So he's not demanding something imperfect, huh? You know, someone comes to me and says, Burkwist, I've heard about this Pythagorean theorem. You know, he showed it to me. You sure you want to know it? So the only proof I know is Proposition 47, in the book 1 of Euclid, and there are about 46 theorems. You've got to do it before you get there. And most of them, or if not all of them, are necessary to get there, huh? Are you sure you want to do this? Well, he doesn't know that going through those 46 is going to lead to that, does he? He's got to believe me. But if he doesn't believe me, he'll go through the 46, he'll probably never get there. Most of us will never get there, huh? And I'll tell you about this theorem I was looking just recently in Euclid there. How to draw from a point outside a circle a line to touch a circle. Did I mention that theorem? Is that? It's a very subtle thing here, huh? It's a subtle. Suppose you've got a circle and you've got a point outside here. You want to draw a line from the point to touch a circle, right, huh? I already know this theorem that, you know, that if it's a radius, right, it's drawn to a point and you draw a line that the right angle is going to touch it, right? Okay. But now, the problem here is I've got to find that point on the circumference of the circle to which I can draw this line, so it'll be touching, right? Mm-hmm. There's an infinity of possible points in that thing. Okay. So how do you find that point? Well, what Euclid does is to draw four lines in a certain order, right? And they have to be drawn in a certain order. And finally, you get that point. So he says, draw a straight line from the center circle to that point, right? See? You see what the problem here is, right? You know, in geometry, you can always draw a straight line between the two points. So if you do the point here, it would make the line touch. You could do it right away. You can find that point. So what you do is first draw a straight line from this to that point, right? Oh, sure. That's the first line you draw. Yeah. Then you use that to make it in a circle. Oh. It's really subtle. It's what Euclid does. Yeah, yeah, yeah. Okay? That's the second line you draw. Now what do you do? Then you draw at right angles to this line a straight line, right? And then you draw a straight line from this point here to the center, okay? Now, either or not, that's the point you want to draw it to. But isn't that amazing? How do you have to figure it out? You have to go through four lines, right? You have to first draw this line, right? Then you have to draw the circle. Then you have to draw this tangent, right? I mean, it's perpendicular. And then from where that hit the outer circle, you have to draw a straight line down there, okay? Now, the proof is kind of easy because these two triangles are equal. And then you have to draw a straight line down there, okay? And then you have to draw a straight line down there, okay?