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[Assistant] But the lonely moon never seemed to gaze comfortably down at her. One day, Min Li and the dragon came upon a body of water. In the distance, they saw the woods continue. As the compass pointed across the water, the dragon swam the inlet with Min Li riding his back. How far do we go before we get to Neverending Mountain? The dragon asked. Well, Min Li said slowly.


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[Assistant] Even though no fish has seen the Dragon Gate, we all know about it. Perhaps the story was told to us through the waves of water while we were eggs, or whispered to us by the roots of the lotus flowers.


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[Assistant] We all know that somewhere in one of the rivers of the land there is a great and powerful waterfall. It is so high and so vast.


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[Assistant] That it is as if water was gushing from a cut in the heavens. At the top of that waterfall, beyond anyone's view, is the Dragon Gate. The Dragon Gate is an entryway to the sky. It is old.


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[Assistant] 999 small dragon ornaments perched on the ridges of those tiled roofs.


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[Assistant] For if ever a fish is able to swim up the waterfall and pass through the gate, the dragons will shake with power. As the fish goes through, its spirit enters the gate and bursts out of one of the ornaments, changing the fish into the form of a flying dragon.


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[Assistant] It doesn't seem likely that a fish that small could swim up a waterfall, Dragon said. Even if she does find the right river, she might not be able to get to the gate. If there is a gate, Aunt Jen will find a way through it, the fish said. She's very wise. If you knew her, you'd understand. Maybe I do know her, Min Li said softly, thinking hard about the goldfish she set free.


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[Assistant] Min Li answered for the dragon when she saw his discomfort.


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[Assistant] People of bright moonlight might be shocked to see a real dragon. The last dragon sighted was about a hundred years ago.


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[Assistant] Called out their wares while people rushed past. Some pushing wheelbarrows or balancing baskets on their shoulders.


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[Assistant] How do I get to the palace? Min Li asked. Just follow the black stones, the boy said, pointing at the road paved with polished bricks. They'll lead you to the city. Wait, Min Li said. Isn't this the city? The palace is in another city? You must not be from around here, the boy laughed. The city of bright moonlight is divided into two. This is the outer city where anyone can live and travel.


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[Assistant] The inner city is where the palace is, where the king and officials live. You have to have permission to go into the inner city. If you don't, you're not going to be able to see the king or the palace. There are thousands of guards protecting the inner city. They won't let anyone through without permission. I'll find a way, Min Li said confidently. Thanks. And she let go of the boy's arm and headed toward the black road.


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[Assistant] However, as Min Lee got closer to the inner city, she realized the boy was right.


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[Assistant] Min Li turned and saw the buffalo boy standing next to her. Min Li gave him a wry look. Boys, she thought to herself, always thinking they know everything. Still, she had to admit he was right. She had no idea how she would see the king. They must let people into the inner city sometimes, Min Li said. They do, the boy said. Once a year at the Moon Festival,


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[Assistant] At the moon festival, one of the stable men wanted to order me around and thought he could trick me into thinking he was the king. But when I asked why he wasn't wearing a golden dragon, he knew his prank wasn't going to work. Do you think I was stupid?


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[Assistant] Everyone knows a golden dragon is always and only worn by kings and the emperor. The people in there think we're a bunch of dumb oxen. The buffalo beside the boy gave a snort at that. Sorry, the boy said, patting the buffalo on the nose. You know I didn't mean that. But by this time, the inner city guards had seen them lingering by the gate. View their kids. One of them barked, move along. Come on.


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[Assistant] Min Li followed the boy through the maze of streets and alleyways for what seemed like a long time. If it weren't for the big buffalo that was always in view, Min Li would have easily lost him many times. Not too far now, the boy said to her. Min Li realized that the boy lived very far from the inner city. The road was no longer stone, but dirt. Even from a distance,


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[Assistant] She could see that the outer city wall was cracked and broken. I live over here, the boy said, pointing. And Min Li looked down a muddy path that led to a shabby, rickety hut that looked as if the first strong wind would blow it away. The boy brought the buffalo right into the hut, and Min Li went in after. She looked around the small, meager home.


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[Assistant] And he shook his head when she told about the dragon, but he didn't interrupt once. I don't know how you're going to see the king, the boy told her when she finished. Even if you do see him, I doubt you'll be able to ask for a bar of wine, especially when you don't even know what it is. But I have to, Minly said. There must be a way. Well, I always think better after I've eaten, the boy said, and he stood up and opened one of the crates.


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[Assistant] Sometimes during the hot summer days, there's not enough water for my buffalo.


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[Assistant] Apart, I don't think anyone from the city has ever seen before. The trees seemed to reach the clouds, the green grass felt like a silk blanket, and there was a lake of clear water, so pure and clean, it looked as if it were a piece of the sky. But the most beautiful things there were the seven girls swimming in it. But when the girls saw me and the buffalo come through the trees, they screamed. They jumped out of the water, grabbed their robes, and ran away.


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[Assistant] And she kept her promise. Like she said, it was hard for her to get away. But every night on the full moon, when she visits her grandfather, she stops here. Sometimes you can only stay for a little while. Sometimes you can stay for hours. Whenever I see her, we laugh enough to last for the month. She's my best friend. And someday when we're old enough, I'm going to talk her into staying here forever.


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[Assistant] It was funny how the Buffalo Boys whole manner changed when he talked about her. His vaguely mocking attitude and tough expression washed away and he lit up like a lantern.


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[Assistant] That's what she brings to her grandfather when she visits. Glad that she spins. Hey, I know. I'll ask her how you can see the king. She'll know. How will a weaving girl know about the king? Min Li asked. Does she live in the inner city? No, she lives far away, the boy said vaguely. But she knows a lot of things. Min Li shrugged


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[Assistant] It didn't seem likely to her that a friend of the buffalo boy would know how she could see the king. But if she didn't have any ideas of her own, she would hope.


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[Assistant] The moonlight streamed in from the window, lighting the bear hut. The boy had given her his pile of grass to sleep on, and joined the buffalo, using some of its grass as a pillow. But as the buffalo snored loudly, Min Li could see the bowl-shaped hollow in the hay was empty. I wonder where he went? Min Li said, and she found herself thinking of Ma and Ba, and Dragon all waiting for her. Suddenly, the silence of the room seemed to ache with loneliness.


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[Assistant] Everything about her seemed finer and more delicate than the average person.


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[Assistant] Don't you think it's mysterious that you only see her once in a while? And you never visit her, she only visits you?


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[Assistant] After two years, I remember the rest of that day and that night and the next day only as an endless drill of police and photographers and newspaper men in and out of Gatsby's front door.


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[Assistant] A rope stretched across the main gate, and a policeman by it kept out the curious. But little boys soon discovered that they could enter through my yard, and there were always a few of them clustered open-mouthed about the pool.


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[Assistant] Someone with a positive manner, perhaps a detective, used the expression madman as he bent over Wilson's body that afternoon, and the adventitious authority of his voice set the key for the newspaper reports next morning.


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[Assistant] Most of these reports were a nightmare, grotesque, circumstantial, eager, and untrue.


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[Assistant] When Michaelis' testimony at the inquest brought to light Wilson's suspicions of his wife, I thought the whole tale would shortly be served up in racy pasquenade. But Catherine, who might have said anything, didn't say a word.


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[Assistant] She showed a surprising amount of character about it too, looked at the coroner with determined eyes under that corrected brow of hers, and swore that her sister had never seen Gatsby, that her sister was completely happy with her husband, that her sister had been into no mischief whatever.


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[Assistant] She convinced herself of it and cried into her handkerchief as if the very suggestion was more than she could endure.


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[Assistant] So Wilson was reduced to a man deranged by grief in order that the case might remain in its simplest form, and it rested there.


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[Assistant] But all this part of it seemed remote and unessential.


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[Assistant] I found myself on Gatsby's side and alone.


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[Assistant] From the moment I telephoned news of the catastrophe to West Egg, every surmise about him and every practical question was referred to me. At first I was surprised and confused.


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[Assistant] Then, as he lay in his house and didn't move or breathe or speak hour upon hour,


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[Assistant] It grew upon me that I was responsible because no one else was interested.


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[Assistant] Interested I mean with that intense personal interest to which everyone has some vague right at the end.


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[Assistant] I called up Daisy, half an hour after we found him, called her instinctively and without hesitation.


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[Assistant] I wanted to get somebody for him, I wanted to go into the room where he lay and reassure him, I'll get somebody for you Gatsby, don't worry, just trust me and I'll get somebody for you. Maya Wolfsheim's name wasn't in the phone book.


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[Assistant] The butler gave me his office address on Broadway and I called information, but by the time I had the number it was long after five and no one answered the phone. Will you ring again? I've rung them three times. It's very important. Sorry, I'm afraid no one's there.


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[Assistant] I went back to the drawing room and thought for an instant that they were chance visitors, all these official people who suddenly filled it. But as they drew back the sheet and looked at Gatsby with unmoved eyes, his protest continued in my brain. Look here, old sport, you've got to get somebody for me. You've got to try hard. I can't go through this alone.


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[Assistant] Someone started to ask me questions, but I broke away and going upstairs looked hastily through the unlocked parts of his desk. He'd never told me definitely that his parents were dead. But there was nothing, only the picture of Dan Cody, a token of forgotten violence staring down from the wall.


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[Assistant] Next morning I sent the butler to New York with a letter to Wolfsheim, which asked for information and urged him to come out on the next train.


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[Assistant] That request seemed superfluous when I wrote it. I was sure he'd start when he saw the newspapers, just as I was sure there'd be a wire from Daisy before noon. But neither a wire nor Mr. Wolfsheim arrived.


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[Assistant] No one arrived, except more police and photographers and newspaper men.


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[Assistant] When the butler brought back Wolfsheim's answer, I began to have a feeling of defiance, of scornful solidarity between Gatsby and me against them all.


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[Assistant] Dear Mr. Carraway, this has been one of the most terrible shocks of my life. To me, I can hardly believe that it is true at all. Such a mad act as that man did should make us all think.


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[Assistant] I cannot come down now as I am tied up some very important business and cannot get mixed up in this thing now.


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[Assistant] If there is anything I can do a little later, let me know in a letter by Edgar. I hardly know where I am when I hear about a thing like this, and I'm completely knocked down and out. Yours truly, Meyer Wolfschein.


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[Assistant] And then haste the addenda beneath. Let me know about the funeral, etc. I do not know his family at all.


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[Assistant] When the phone rang that afternoon and long distance said Chicago was calling, I thought this would be Daisy at last.


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[Assistant] But the connection came through as a man's voice, very thin and far away. This is Slagle speaking.


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[Assistant] Yes, the name was unfamiliar. Hell of a note, isn't it? Get my wire? There haven't been any wires.


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[Assistant] Young Park's in trouble, he said rapidly. They picked him up when he handed the bonds over the counter. They got a circular from New York giving him the numbers just five minutes before.


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[Assistant] What do you know about that, hey? You can never tell in these hick towns. Hello? I interrupted breathlessly. Look here. This isn't Mr. Gatsby. Mr. Gatsby's dead.


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[Assistant] There was a long silence on the other end of the wire, followed by an exclamation, then a quick squawk as the connection was broken.


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[Assistant] I think it was on the third day that a telegram signed Henry C. Gatz arrived from a town in Minnesota. It said only that the sender was leaving immediately and to postpone the funeral until he came. It was Gatsby's father, a solemn old man, very helpless and dismayed.


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[Assistant] Bundled up in a long cheap ulster against the warm September day, his eyes leaked continuously with excitement.


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[Assistant] And when I took the bag and umbrella from his hands, he began to pull so incessantly at his sparse gray beard that I had difficulty in getting off his coat.


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[Assistant] He was on the point of collapse, so I took him into the music room and made him sit down while I sent for something to eat. But he wouldn't eat, and the glass of milk spilled from his trembling hand. I saw it in the Chicago newspaper, he said.


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[Assistant] It was all in the Chicago newspaper I started right away. I didn't know how to reach you.


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[Assistant] His eyes, seeing nothing, moved ceaselessly about the room. It was a madman, he said. He must have been mad. Wouldn't you like some coffee? I urged him. I don't want anything. I'm all right now, Mr. Carraway. Well, I'm all right now. Where have they got Jimmy?


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[Assistant] I took him into the drawing room where his son lay and left him there. Some little boys had come up on the steps and were looking into the hall


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[Assistant] When I told them who had arrived, they went reluctantly away.


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[Assistant] After a little while, Mr. Gatz opened the door and came out, his mouth ajar, his face flushed slightly, his eyes leaking, isolated and unpunctual tears.


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[Assistant] He had reached an age where death no longer has the quality of ghastly surprise.


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[Assistant] And when he looked around him now for the first time, and saw the height and splendor of the hall, and the great rooms opening out from it into other rooms,


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[Assistant] His grief began to be mixed with an odd pride.


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[Assistant] I helped him to a bedroom upstairs. While he took off his coat and vest, I told him that all arrangements had been deferred until he came. I didn't know what you'd want, Mr. Gatsby. Gats is my name.


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[Assistant] Uh, Mr. Gatz, I thought you might want to take the body west. He shook his head.


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[Assistant] Jimmy always liked it better down east. He rose up to his position in the east.


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[Assistant] Were you a friend of my boys, mister? We were close friends.


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[Assistant] He had a big future before him, you know. He was only a young man, but he had a lot of brain power here. He touched his head impressively and I nodded. If he'd have lived, he'd have been a great man. A man like James J. Hill. He'd have helped build up the country. That's true, I said uncomfortably.


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[Assistant] He fumbled that the embroidered coverlet, trying to take it from the bed and lay down stiffly, was instantly asleep.


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[Assistant] That night an obviously frightened person called up and demanded to know who I was before he would give his name. This is Mr. Carraway, I said.


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[Assistant] Oh, he sounded relieved. This is Clipspringer.


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[Assistant] I was relieved too, for that seemed to promise another friend at Gatsby's grave. I didn't want it to be in the papers and draw a sightseeing crowd, so I'd been calling up a few people myself. They were hard to find.


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[Assistant] The funeral's tomorrow, I said. Three o'clock here at the house. I wish you'd tell anybody who'd be interested. Oh, I will. He broke out hastily.


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[Assistant] Of course, I'm not likely to see anybody, but if I do, his tone made me suspicious. Of course you'll be there yourself.


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[Assistant] Well I'll certainly try. What I called up about is, wait a minute, how about saying you'll come. Well the fact is,


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[Assistant] The truth of the matter is that I'm staying with some people up here in Greenwich and they-


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[Assistant] My address is careofbf. I didn't hear the rest of the name because I hung up the receiver.


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[Assistant] After that, I felt a certain shame for Gatsby.


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[Assistant] One gentleman to whom I telephoned implied that he had got what he deserved.


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[Assistant] However, that was my fault, for he was one of those who used to sneer most bitterly at Gatsby on the courage of Gatsby's liquor, and I should have known better than to call him.


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[Assistant] The morning of the funeral, I went up to New York to see Meyer Wolfsheim. I couldn't seem to reach him any other way.


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[Assistant] The door that I pushed open on the advice of an elevator boy was marked the Swastika Holding Company, and at first there didn't seem to be anyone inside.


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[Assistant] But when I shouted hello several times in vain, an argument broke out behind a partition, and presently a lovely Jewess appeared at an interior door and scrutinized me with black hostile eyes.


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[Assistant] Nobody's in, she said. Mr. Wolfsheim's gone to Chicago.


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[Assistant] The first part of this was obviously untrue for someone had begun to whistle the rosary tunelessly inside. Please say that Mr. Carraway wants to see him. I can't get him back from Chicago, can I?


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[Assistant] At this moment, a voice, unmistakably Wolfshime's, called Stella from the other side of the door.


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[Assistant] Leave your name on the desk, she said quickly. I'll give it to him when he gets back. But I know he's there.


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[Assistant] She took a step toward me and began to slide her hands indignantly up and down her hips.


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[Assistant] You young men think you can force your way in here any time, she scolded. We're getting sick and tired of it. When I say he's in Chicago, he's in Chicago. I mentioned Gatsby. Oh, she looked at me over again. Were you just, what was your name? She vanished.


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[Assistant] In a moment, Meyer Wolfsheim stood solemnly in the doorway, holding out both hands. He drew me into his office, remarking in a reverent voice that it was a sad time for us all, and offered me a cigar.


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[Assistant] My memory goes back to when I first met him, he said. A young major just out of the army and covered over with medals he got in the war. He was so hard up he had to keep on wearing his uniform because he couldn't buy some regular clothes. First time I saw him was when he come into Weinbrenner's pool room at 43rd Street and asked for a job.


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[Assistant] He hadn't eaten anything for a couple of days. Come on, have some lunch with me, I said. He ate more than four dollars worth of food in half an hour.


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[Assistant] The Jews start him in business, I inquired. Start him, I made him. Oh. I raised him up out of nothing, right out of the gutter.


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[Assistant] I saw right away he was a fine-appearing, gentlemanly young man, and when he told me he was in Oxford, I knew I could use him good.


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[Assistant] I got him to join up in the American Legion and he used to stand high there. Right off he did some work for a client of mine up to Albany. We were so sick like that and everything. He held up two bulbous fingers, always together.


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[Assistant] I wondered if this partnership had included the World Series transaction in 1919. Now he's dead, I said after a moment. You were his closest friend, so I know you'll want to come to his funeral this afternoon. I'd like to come. Well, come then. The hair in his nostrils quivered slightly, and as he shook his head his eyes filled with tears.


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[Assistant] I can't do it. I can't get mixed up in it, he said. There's nothing to get mixed up in. It's all over now.


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[Assistant] When a man gets killed, I never like to get mixed up in it in any way I keep out.


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[Assistant] When I was a young man it was different. If a friend of mine died, no matter how, I stuck with them to the end.


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[Assistant] You may think that's sentimental, but I mean it. To the bitter end.


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[Assistant] I saw that for some reason of his own he was determined not to come, so I stood up.


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[Assistant] Are you a college man? He inquired suddenly.


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[Assistant] For a moment I thought he was going to suggest a connection, but he only nodded and shook my hand.


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[Assistant] Let us learn to show our friendship for a man when he is alive and not after he is dead, he suggested. After that, my own rule is to let everything alone.


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[Assistant] When I left his office, the sky had turned dark, and I got back to West Egg in a drizzle.


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[Assistant] After changing my clothes, I went next door and found Mr. Gatz walking up and down excitedly in the hall.


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[Assistant] His pride in his son and in his son's possessions was continually increasing. And now he had something to show me.


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[Assistant] Look there! And then sought admiration from my eyes.


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[Assistant] He had shown it so often that I think it was more real to him now than the house itself. Jimmy sent it to me. I think it's a very pretty picture. It shows up well. Very well. Had you seen him lately?


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[Assistant] He come out to see me two years ago and bought me the house I live in now.


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[Assistant] Of course we was broke up when he run off from home, but I see now there was a reason for it.


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[Assistant] He knew he had a big future in front of him, and ever since he made a success he was very generous with me.


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[Assistant] He seemed reluctant to put away the picture, held it for another minute, lingeringly before my eyes.


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[Assistant] Then he returned the wallet and pulled from his pocket a ragged old copy of a book called Hop Along Cassidy.


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[Assistant] Look here, this is a book he had when he was a boy. It just shows you.


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[Assistant] He opened it at the back cover and turned it around for me to see.


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[Assistant] On the last fly leaf was printed the word SCHEDULE, and the date September 12, 1906, and underneath RISE FROM BED, 6 o'clock a.m.


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[Assistant] Baseball and sports, 4.30 pm to 5 o'clock. Practice elocution, poise and how to attain it, 5 o'clock to 6 o'clock. Study needed inventions, 7 o'clock to 9 o'clock.


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[Assistant] General resolves. No wasting time at shafters, or a name indecipherable. No more smoking or chewing.


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[Assistant] Bath every other day. Read one improving book or magazine per week. Save five dollars crossed out three dollars per week. Be better to parents.


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[Assistant] I come across this book by accident, said the old man. It just shows you, don't it? It just shows you.


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[Assistant] Jimmy was bound to get ahead. He always had some resolves like this or something. Do you notice what he's got about improving his mind? He was always great for that. He told me I ate like a hog once and I beat him for it.


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[Assistant] He was reluctant to close the book, reading each item aloud and then looking eagerly at me. I think he rather expected me to copy down the list for my own use.


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[Assistant] A little before three, the Lutheran minister arrived from Flushing.


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[Assistant] And I began to look involuntarily out the windows for other cars. So did Gatsby's father.


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[Assistant] And as the time passed and the servants came in and stood waiting in the hall, his eyes began to blink anxiously, and he spoke of the rain in a worried, uncertain way. The minister glanced several times at his watch, so I took him aside and asked him to wait for half an hour. But it wasn't any use. Nobody came.


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[Assistant] About five o'clock our procession of three cars reached the cemetery and stopped in a thick drizzle beside the gate.


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[Assistant] First a motor-hearse, horribly black and wet.


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[Assistant] Then Mr. Gatz and the minister and I in the limousine.


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[Assistant] And a little later four or five servants and the postman from West Egg in Gatsby's station wagon all wet to the skin.


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[Assistant] As we started through the gate into the cemetery I heard a car stop and then the sound of someone splashing after us over the soggy ground. I looked around.


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[Assistant] It was the man with owl-eyed glasses whom I had found marveling over Gatsby's books in the library one night three months before. I'd never seen him since then.


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[Assistant] I don't know how he knew about the funeral or even his name.


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[Assistant] The rain poured down his thick glasses and he took them off and wiped them to see the protecting canvas unrolled from Gatsby's grave.


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[Assistant] I tried to think about Gatsby then for a moment, but he was already too far away.


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[Assistant] And I can only remember without resentment that Daisy hadn't sent a message or a flower.


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[Assistant] And then the owl-eyed man said, Amen to that in a brave voice.


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[Assistant] He took off his glasses and wiped them again, outside and in.


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[Assistant] One of my most vivid memories is of coming back west from prep school and later from college at Christmas time.


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[Assistant] Those who went farther than Chicago would gather in the old dim Union Station at six o'clock of a December evening with a few Chicago friends, already caught up into their own holiday gaieties to bid them a hasty goodbye.


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[Assistant] I remember the fur coats of the girls returning from Miss This or That's, and the chatter of frozen breath, and the hands waving overhead as we caught sight of old acquaintances, and the matchings of invitations, are you going to the Ordways, the Herses, the Schulzes, and the long green tickets


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[Assistant] When we pulled out into the winter night and the real snow, our snow, began to stretch out beside us and twinkle against the windows and the dim lights of small Wisconsin stations moved by, a sharp wild brace came suddenly into the air.


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[Assistant] We drew in deep breaths of it as we walked back from dinner through the cold vestibules, unutterably aware of our identity with this country for one strange hour before we melted indistinguishably into it again. That's my Middle West.


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[Assistant] Not the wheats, or the prairies, or the lost swede towns, but the thrilling returning trains of my youth.


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[Assistant] And the street lamps and sleigh bells in the frosty dark. And the shadows of holly wreaths thrown by lighted windows on the snow. I am part of that.


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[Assistant] A little solemn with the feel of those long winters.


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[Assistant] I see now that this has been a story of the West after all.


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[Assistant] Tom and Gatsby, Daisy and Jordan and I were all Westerners.


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[Assistant] And perhaps we possessed some deficiency in common.


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[Assistant] Which made us subtly unadaptable to Eastern life.


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[Assistant] Even when the East excited me most, even when I was most keenly aware of its superiority to the bored, sprawling, swollen towns beyond the Ohio, with their interminable inquisitions which spared only the children and the very old, even then


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[Assistant] It had always for me a quality of distortion.


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[Assistant] West Egg especially still figures in my more fantastic dreams.


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[Assistant] I see it as a night scene by El Greco, a hundred houses at once conventional and grotesque, crouching under a sullen overhanging sky and a lustreless moon.


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[Assistant] In the foreground, four solemn men in dress suits are walking along the sidewalk with a stretcher on which lies a drunken woman in a white evening dress. Her hand, which dangles over the side, sparkles cold with jewels.


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[Assistant] Gravely the men turn in at a house, the wrong house, but no one knows the woman's name and no one cares.


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[Assistant] After Gatsby's death, the East was haunted for me like that. Distorted beyond my eyes power of correction.


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[Assistant] So when the blue smoke of brittle leaves was in the air and the wind blew the wet laundry stiff on the line, I decided to come back home. There was one thing to be done before I left, an awkward, unpleasant thing, that perhaps had better have been let alone.


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[Assistant] But I wanted to leave things in order and not just trust that obliging an indifferent sea to sweep my refuse away.


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[Assistant] I saw Jordan Baker and talked over and around what had happened to us together and what had happened afterward to me.


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[Assistant] And she lay perfectly still listening in a big chair. She was dressed to play golf, and I remember thinking she looked like a good illustration.


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[Assistant] Her chin raised a little jauntily, her hair the color of an autumn leaf, her face the same brown tint as the fingerless glove on her knee.


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[Assistant] When I had finished she told me without comment that she was engaged to another man. I doubted that. Though there were several she could have married in a nod of her head. But I pretended to be surprised. For just a minute I wondered if I wasn't making a mistake.


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[Assistant] Nevertheless, you did throw me over, said Jordan suddenly. You threw me over on the telephone.


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[Assistant] I don't give a damn about you now, but it was a new experience for me and I felt a little dizzy for a while. We shook hands.


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[Assistant] Oh, and do you remember, she added, a conversation we had once about driving a car.


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[Assistant] Why, not exactly. You said a bad driver was only safe until she met another bad driver. Well, I met another bad driver, didn't I? I mean, it was careless of me to make such a wrong guess. I thought you were rather an honest, straightforward person. I thought it was your secret pride.


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[Assistant] He was walking ahead of me along Fifth Avenue in his alert, aggressive way.


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[Assistant] His hands out a little from his body as if to fight off interference. His head moving sharply here and there, adapting itself to his restless eyes. Just as I slowed up to avoid overtaking him, he stopped and began frowning into the windows of a jewelry store. Suddenly he saw me and walked back, holding out his hand. What's the matter, Nick? Do you object to shaking hands with me? Yes. You know what I think of you.


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[Assistant] You're crazy, Nick, he said quickly. Crazy as hell. I don't know what's the matter with you. Tom, I inquired. What did you say to Wilson that afternoon? He stared at me without a word.


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[Assistant] And I knew I had guessed right about those missing hours.


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[Assistant] I started to turn away but he took a step after me and grabbed my arm. I told him the truth, he said.


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[Assistant] He came to the door while we were getting ready to leave, and when I sent down word that we weren't in, he tried to force his way upstairs.


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[Assistant] He was crazy enough to kill me if I hadn't told him who owned the car.


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[Assistant] His hand was on a revolver in his pocket every minute he was in the house he broke off defiantly.


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[Assistant] What if I did tell him? That fellow had it coming to him. He threw dust into your eyes just like he did in Daisy's, but he was a tough one. He ran over Myrtle like you'd run over a dog and never even stopped his car. There was nothing I could say.


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[Assistant] Except the one unutterable fact that it wasn't true. And if you think I didn't have my share of suffering,


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[Assistant] Look here, when I went to give up that flat and saw that damn box of dog biscuits sitting there on the sideboard, I sat down and cried like a baby. By God, it was awful. I couldn't forgive him or like him.


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[Assistant] But I saw that what he had done was to him entirely justified.


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[Assistant] It was all very careless and confused.


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[Assistant] They were careless people, Tom and Daisy. They smashed up things and creatures and then retreated back into their money or their vast carelessness or whatever it was that kept them together and let other people clean up the mess they had made.


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[Assistant] It seemed silly not to, for I felt suddenly as though I were talking to a child.


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[Assistant] Then he went into the jewelry store to buy a pearl necklace or perhaps only a pair of cuff buttons, rid of my provincial squeamishness forever.


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[Assistant] Gatsby's house was still empty when I left. The grass on his lawn had grown as long as mine.


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[Assistant] One of the taxi drivers in the village never took a fare past the entrance gate without stopping for a minute and pointing inside. Perhaps it was he who drove Daisy and Gatsby over to East Egg the night of the accident. And perhaps he had made a story about it all his own.


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[Assistant] Because those gleaming dazzling parties of his were with me so vividly.


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[Assistant] That I could still hear the music and the laughter faint and incessant from his garden and the cars going up and down his drive.


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[Assistant] One night I did hear a material car there and saw its lights stop at his front steps, but I didn't investigate.


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[Assistant] Probably it was some final guest who had been away at the ends of the earth and didn't know that the party was over.


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[Assistant] On the last night, with my trunk packed and my car sold to the grocer,


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[Assistant] I went over and looked at that huge, incoherent failure of a house once more.


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[Assistant] On the white steps an obscene word scrawled by some boy with a piece of brick stood out clearly in the moonlight.


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[Assistant] And I erased it, drawing my shoe raspingly along the stone.


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[Assistant] Then I wandered down to the beach and sprawled out on the sand.


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[Assistant] And there were hardly any lights except the shadowy moving glow of a ferryboat across the sound.


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[Assistant] And as the moon rose higher, the inessential houses began to melt away.


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[Assistant] Until gradually I became aware of the old island here that flowered once for Dutch sailors eyes. A fresh green breast of the new world.


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[Assistant] It's vanished trees. The trees that had made way for Gatsby's house had once pandered in whispers to the last and greatest of all human dreams.


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[Assistant] For a transitory, enchanted moment, man must have held his breath in the presence of this continent, compelled into an aesthetic contemplation he neither understood nor desired.


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[Assistant] Face to face for the last time in history with something commensurate to his capacity for wonder.


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[Assistant] And as I sat there brooding on the old unknown world,


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[Assistant] I thought of Gatsby's wonder when he first picked out the green light at the end of Daisy's dock. He had come a long way to this blue lawn.


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[Assistant] And his dream must have seemed so close that he could hardly fail to grasp it.


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[Assistant] He did not know that it was already behind him.


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[Assistant] Somewhere back in that vast obscurity beyond the city, where the dark fields of the Republic rolled on under the night.


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[Assistant] Boats against the current, born back ceaselessly into the past.


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[Assistant] It's been a long day without you my friend.


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[Assistant] Come on everybody, you can do it too. Get your skinny jeans on, move on through.


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[Assistant] We're gonna shake, shake, shake, that's it, you're doing just fine. It makes no difference if it's day or night. With your skinny jeans on, you'll be alright.


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[Assistant] Alex, I've never met your family. Do you have a big family?


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[Assistant] That's very nice. How about your dad? Do you look like him?


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[Assistant] Wow, good for them. Sounds like they've worked hard to be successful in life.


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[Assistant] It seems your family is full of gamers. It's not just you.


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[Assistant] So you are the youngest of your siblings and Lindsay is the oldest.


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[Assistant] I bet. I guess that's what happens when your mom is a kindergarten teacher.


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[Assistant] You are so lucky to have such a wonderful family, Alex. Thanks for telling me all these interesting details about them.


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[Assistant] So uhm, these drugs aren't exactly, they're not exactly in mainstream cancer treatments right now. For anyone out here who has cancer, what would you recommend? Do you recommend pursuing these treatments now for most cancer patients?


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[Assistant] Okay, let me start again. Thanks for helping, uh,


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[Assistant] With Professor Rao and working on the labs, uh, the last two times, uhm,


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[Assistant] I was saying the labs were really for his class, which is...


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[Assistant] 90 minutes so that we were kind of running out of time just answering those questions.


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[Assistant] Uh, you know, getting the system to say, okay, keep going. Anyway, uh, he's gonna develop those, uh, and I think they'll be a good thing. So, actually, the second lab,


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[Assistant] Uh, I was, as I was watching it, I, I was thinking of a math question. And may I report to you on that math question? So, you remember the lab was completing a matrix.


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[Assistant] You've got some entries, and you can put in any other entries in the other positions. And the question was, can you complete it to a rank 1 matrix?


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[Assistant] And, uh, so what, here's my question. What positions...


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[Assistant] Are okay and what positions could you maybe not be able to?


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[Assistant] Complete to a rank one matrix. Examples are the best. Okay. So, so I'm looking at this question here. Okay. So, suppose I, suppose,


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[Assistant] I'm looking for a rank one matrix of the form x column y transpose. Or uv transpose, I guess.


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[Assistant] Those are the letters we're used to. U-V transpose.


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[Assistant] And that means, of course, that aij, each aij is ui times vj.


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[Assistant] Right. So we've got, we're able to choose, uh, we have M used. Let me ask a question. Could I complete, so let me take M equal N equals 3. So 3 by 3 matrix.


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[Assistant] I'm going to give you m plus n minus 1, which is 3 plus 3 minus 1, 5.


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[Assistant] And suppose I, and for, and give, uh, some non-zeros.


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[Assistant] Five positions. So why is


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[Assistant] Where is that number m plus n minus 1 coming from? Well, because I have mu's and I have nv's for a rank 1 matrix. i goes from 1 to m, j goes from 1 to n. So I have m plus n.


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[Assistant] But obviously there, I could, I could make, I could require the first u to be a 1. In other words, when I'm multiplying those, there's one degree of freedom that, that, uh, is sort of repeated here because, uhm, uh, if I'm just given


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[Assistant] If I'm just, if, just in the one, oh, anyway, you see it, that, that, uh, uh,


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[Assistant] I can rescale the u so that the first u is a 1.


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[Assistant] And that leaves me m plus n minus 1. So could I give you these five numbers and could you complete that to a rank 1 matrix? So those are non-zeros. Why do I say non-zeros? Because


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[Assistant] If that number happened to be a zero, I'd have bad news there. If I prescribed that one and I prescribed it to be zero, then, uh,


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[Assistant] If every column has to be a multiple of that column, these would all have to be zero. So I don't want that. I want, uh, to be able to prescribe five numbers and therefore they better, better not be zero. Okay. Could you complete the job with that choice of five positions? I think you could. Because how would you decide on that number?


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[Assistant] Uh, well, at least one way to look at it is, what would that number be there?


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[Assistant] That number would be chosen. There would be one and only one choice for that, uh, that would give rank 1.


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[Assistant] In fact, that little 2 by 2 determinant would have to be 0, right?


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[Assistant] All the rows, all the columns are supposed to be multiples of one column.


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[Assistant] All the rows are supposed to be multiples of one row, all the two by twos.


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[Assistant] Because I have to get a, every two by two determinant has to be zero here. If I want rank one, I can't stand any two by twos that are, that are invertible matrices. So all determinants have to be zero. Okay, and of course then,


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[Assistant] Those three numbers would allow me to fill that. Those three numbers would allow me to fill that. It'd be easy. Easy. So that I can see that those are five positions that work. Now give me five positions that won't work. So this is good. This is check. Now I want one where I can't make it work. So let me give that number, that number,


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[Assistant] Okay, well, so I'm looking for something that fails, a set of positions that fails, and then I want to be able to test. Does the set of positions work for any non-zeros, or does it not work?


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[Assistant] Okay, so I want to get one another, what am I looking for here, another, a different one that works? Okay, so what else would work apart from that? Let's see, I suppose I take that one. Now what about that position there? I must not


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[Assistant] Choose that one, right? I must not choose that one because that would complete a two by two and if


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[Assistant] If I gave the wrong numbers, the determinant wouldn't be zero and I would be failed. So I must not give that position. Maybe I could give that position. Maybe I could give this one. How's that? If I had those five, would I be able to complete? It looks good anyway.


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[Assistant] It looks good. Uh, let's see, how would I go about completing that?


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[Assistant] Uh, let's see. I could, I would know what that number had to be from this 2 by 2. From this 2 by 2 I would know that number.


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[Assistant] From this, where now? This and this and this. Now that's not any good. What do I do now? To get, how would I get this number?


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[Assistant] Oh, okay, I guess I have to use, so this would complete that.


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[Assistant] Or this 2 by 2, oh yeaah, okay, no problem. That would complete that one, right? But this one, I don't think I can get immediately.


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[Assistant] But I can get it, once I know these, then obviously I can get that, I can get that, right? So I have to, it's a sort of nice combinatorial problem, which


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[Assistant] Which, uh, five positions will work? Which five, which five will not work? How do I tell?


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[Assistant] So, or, of course, that's for a three by three. Uh, yeaah. So let me, I had a, uh,


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[Assistant] Like a bigger example. Let me, let me move up to four by four. So, so now, here's, here comes the idea that I learned last night from a math professor who does combinatorics. So these people who do combinatorics, they know stuff that the rest of us don't. Okay. So here's the, his, his view is to take, uh, have, these would be rows.


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[Assistant] One, two, three, I may, I may add another row. Let me do a four by four. And these would be columns.


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[Assistant] One, two, three, four, okay. Now I'm looking for seven.


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[Assistant] So, so if I prescribe an entry, I'll put in a edge between them.


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[Assistant] Yeah, yeah, here's a good one. Actually, I'll just draw this picture. So suppose I prescribe the 1-1, oh yeah, and over here I'll show you what I've done. So that I'm putting in the 1-1 position. I'm looking for 7, right? 4 plus 4 minus 1, 7 numbers. Okay, then I'll put in, uh, this is row 2, column 1. Row 2, column 1, that would be there.


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[Assistant] Then I'll put in a 2 to 4. So that would be row 2, column 4. Then I'll put in a 3 to 4.


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[Assistant] So that would be row three, column four.


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[Assistant] So how many have I done? One, two, three, four. And I've got to get up to seven? Prescribed seven? Well, let me, let me, I'll put, I'll put more in. Okay. So, so on row four, I gave two, three, and four.


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[Assistant] And did I put in this one? Yes, I did. Okay.


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[Assistant] Well, so I've now prescribed seven, seven numbers. Could I complete the matrix to rank one matrix?


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[Assistant] How, that, you see the math question. If I'm given seven positions there,


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[Assistant] I can, this is another way to look at the same picture. This is, I put in an edge for every x.


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[Assistant] So if I have seven x's, I've got seven edges.


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[Assistant] And this is called a bipartite graph. So it's a graph. I've got four nodes here, four nodes here, so I have eight nodes. It's a bipartite graph because the nodes, I have one part of nodes over there.


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[Assistant] One part of nodes here, bipartite means two parts.


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[Assistant] So the rows give me one part of the edges, the columns give me the other part of the edges, and all the connections go between the parts. I'm not, I don't have any lines from


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[Assistant] From a row to a row because all the, the whole code is that, uh,


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[Assistant] This tells me where those seven positions are. Okay, now I'm just going to ask you, can I complete the graph? Can I complete the matrix? Can I complete rank one matrix there? Okay. What do you think? So the real question is, what's the rule?


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[Assistant] What's the, uh, how can I see when I can't complete the matrix, something gets in the way.


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[Assistant] Here what got in the way was this two by two.


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[Assistant] And actually, I asked the question on email, is it, can I always complete it? Yeah, so let me, that would be the question I could ask you. Can I always complete the graph, complete the matrix to have rank 1?


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[Assistant] When there, when I don't run into this, is that all I have to avoid? A 2 by 2 where I've given 3.


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[Assistant] Where I'm given all four entries. Oh yeah, here, this I was able to complete. Yeah, so, so, sorry to, let's do one. If I, if I'm given those entries, and maybe some others,


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[Assistant] I guess seven all together. That's a failure, right?


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[Assistant] If I can't prescribe any non-zeros in those seven positions, because if I prescribe any non-zeros, I probably won't have a zero determinant here. I won't have rank one.


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[Assistant] That, that column will be, will not be a multiple of that column. Whatever I do here, I've screwed up already. So that's a fail.


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[Assistant] And how do I, let me take that picture and turn it into this picture. So rows, columns. So if I take these seven, that's row one, row one, two, three, four. So row one goes to one and two.


[User] Please transcribe this text

[Assistant] Row two goes to one and two, row three goes to four, and row four goes to three and four.


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[Assistant] That's a failure. And how do I know it's a failure? I want to now come up with the answer.


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[Assistant] Come up with the answer. So if I give any seven positions or any m plus n minus one positions like that, I can create a graph like that.


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[Assistant] Just following the rule that you saw. Those seven.


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[Assistant] Uh, positions gave me seven edges in my graph, and it's a bipartite graph because every edge goes from this part over to this part.


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[Assistant] And that's a failure. And the reason it's a failure is, the reason it's a failure is that I have here a cycle. If I go,


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[Assistant] Across, down, across, down, I come back where I started. That would be a cycle.


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[Assistant] Everybody sees, I can't give these four numbers generally. I would have to, once I've given you three, I don't have any freedom left with that fourth one.


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[Assistant] And the way to see that in this picture is...


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[Assistant] That that's, that there's a cycle. So here's the combinatorics thing that, that Professor, uh, uh, Postnikov told me about last night.


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[Assistant] You can complete to a rank one matrix if and only if no cycles. So that was a.


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[Assistant] That was a, that's a, just answered my question perfectly. This one is one where I can complete and it's got a cycle. Cycle meaning, uh, you come back to where you started. But, so I, I thought maybe, so my question to him, which was, was,


[User] Please transcribe this text

[Assistant] Can you always complete it if there are no two by twos in the way?


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[Assistant] That maybe the 2 by 2s could be okay, but there could be a bigger cycle, a longer cycle that would screw you up. So let me close with an example of that sort. Okay. So this is going to be fail again, but no 2 by 2 is responsible. In other words,


[User] Please transcribe this text

[Assistant] It's gonna fail, I won't be able to complete this matrix, even though there aren't any


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[Assistant] Completed two by twos. The two by two I knew immediately was failure. So let me see if I can do that. Okay. Okay, so here is a failure.


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[Assistant] Row one to, this is rows one, two, three, four.


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[Assistant] And this is columns 1, 2, 3, 4. And I think I'm going to have a...


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[Assistant] One given there, and yeaah, I sort of started this before. And 2 goes to 1 and 4. And 3 goes to 4.


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[Assistant] Okay, now I've only put in 2, 4, 5, and I'm allowed 7. But I think I'm already in trouble here.


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[Assistant] So let me, let me draw this picture for the, so this is rows 1, 2, 3, 4. And this is columns 1, 2, 3, 4. And now what have I, I've prescribed that one.


[User] Please transcribe this text

[Assistant] I've, oh no, that goes from, oh, I've forgotten the right way to do the picture.


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[Assistant] One, two, three, four. Okay, now I'm going to do the


[User] Please transcribe this text

[Assistant] The bipartite graph picture that goes with this picture. So one to one, one, two to one.


[User] Please transcribe this text

[Assistant] 2 to 4. What I'm gonna do, let me just say what I'm gonna do. I'm gonna create a cycle over here of length 6.


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[Assistant] A cycle of length four is what I got from a two by two. From a two by two that took me


[User] Please transcribe this text

[Assistant] One, one way, back another, back another, back another. I completed a cycle. I came back to where I started with just four edges. Now I want to complete one, complete a cycle with six edges. So let me, let me draw it in the picture here. Then, now I'm going to put an edge from four back to one. So, so one, one to one, one to four.


[User] Please transcribe this text

[Assistant] Two to one, two to four. Have I got any, yeaah, I think. One, two, ah, damn.


[User] Please transcribe this text

[Assistant] I didn't want a short cycle. I want a bigger, longer cycle. Let me, let me get the darn thing here. So 2 to 4 is not what I want. So I start a cycle. Okay. Go somewhere. Go back. Go somewhere. Go back. Go somewhere. Go back. Now there I got it. Length 6.


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[Assistant] Length 6, so let me put the x's in where they belong now. So 1 is connected to 1 and 4, that's right. 2 is connected to 2 and 4.


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[Assistant] Three is not connected to anybody. Let's put that one in. And four is connected to one and two. Four is connected to one and two. Okay, I believe this.


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[Assistant] I believe that picture goes with that picture. Now, my claim is that there are no, there are no two by two in here that shows me immediately failure. But I will fail. I can't live with that, with those. That looks like eight. Sorry, I've got, I only want seven.


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[Assistant] Three, four, and it shouldn't be there, right? Okay, thanks. Alright.


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[Assistant] You see, I'm not a combinatorics person, but it's so beautiful to have the inspiration to convert that picture to this picture and then realize that a problem in this picture


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[Assistant] It's a cycle in this picture. That's the whole message. That's the whole message.


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[Assistant] That when I'm looking here, a cycle means that I've built in a requirement which


[User] Please transcribe this text

[Assistant] Random non-zeros won't satisfy. So you see that anyway. You see the cycle.


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[Assistant] One, two, three, four, five, six. Yeah. Yeah. So there's a cycle there. So somehow those six x's


[User] Please transcribe this text

[Assistant] Whichever they are, I guess all but the 3 by 3. So I could take, I could take away this part of the graph and just have 3 and 3.


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[Assistant] And, uh, there would be six numbers in there, and that's too many. Yeah. Okay. Okay, I'm going to stop there.


[User] Please transcribe this text

[Assistant] Exactly halfway through the class. Uh, but, well I'm going to stop there with a question, which I don't know, I don't know if I dare


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[Assistant] Send another question to Professor Posnikoff, who answered this one perfectly. But my question would be, when could you complete a rank 2 matrix? What positions could you fill in?


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[Assistant] And be able to reach rank 2. That would be trouble, right? I don't know where we would go with that. But anyway, that's, but that's, for us, for 18.065, that's the natural question. When could I, rank 1 is super special for us, and rank 2 or rank R would be the general case. Yeah. So, so they're good math questions.


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[Assistant] Lab in the course, just happened to have a...


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[Assistant] Convolution and use that word and so on, but we did not


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[Assistant] Connect that with the lectures. So now I'd like to talk about convolutions, which are extremely important. And they're important in machine learning, uh, because


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[Assistant] They give you a set of, uh, weights, uhm, connecting, uhm, they're an efficient way to, to, let me show you. Let me show you. Okay. So, a convolution matrix.


[User] Please transcribe this text

[Assistant] And this will be a cyclic convolution maker. Okay, and the word


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[Assistant] Sickly convolution matrix is circulant. So what is a circulant? I'll call it C. A circulant has some, it has constant diagonals. That's what convolution means matrix-wise. Convolution means constant down each diagonal.


[User] Please transcribe this text

[Assistant] And cyclic means complete. Circle around again. The diagonals


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[Assistant] So it has some entry to, there is one diagonal. Here is another diagonal.


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[Assistant] But if it's going to be a circulant matrix, and this is the best family of matrices in the world, the algebra is just


[User] Please transcribe this text

[Assistant] Terrific for these matrices and that's why they're the heart of signal processing.


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[Assistant] So this is a constant diagonal matrix, but it's not yet a circulant. That diagonal circles around to put


[User] Please transcribe this text

[Assistant] To be completed, every diagonal has four entries here. So let me take another one, uh, say one, one, then that would circle around to one, one, and this guy could be zero.


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[Assistant] You understand then what, uh, the, the, the, you only need four numbers.


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[Assistant] Say the first column, if you, if you prescribe the first column of a circular matrix.


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[Assistant] Then you've told MATLAB, for example, all it needs to know. If you tell it one column,


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[Assistant] It can get all the other columns just by cyclic shift.


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[Assistant] There's the first column, 2, 0, 1, 5. The second column is 2, 0, 1, 5, shifted down by 1. The next column is again shifted down by 1, 2, 0, 1, 5. And the last column is 2, 0, 1, 5. So they're all the same columns after a cyclic shift. So the key matrix in this is really


[User] Please transcribe this text

[Assistant] A cyclic shift matrix, say 0, uh, 1, 0, 0, 0, 0. So it just has one non-zero diagonal, and then it's cyclic.


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[Assistant] Do you see that in fact this matrix C is


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[Assistant] I can produce this matrix C from P and P squared, yeaah. Can I just put in? What would P squared be?


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[Assistant] So if I square that matrix, what matrix would I get? So this is a shift by one.


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[Assistant] If I shift by 1 again, that's multiplying again by p, so that would give me p squared.


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[Assistant] So this will be zero zero one zero.


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[Assistant] This will be 0, 0, 0, 1. Then I'm, it's cyclic still. So I'm, I'll put in the ones there and then just fill in the zeros.


[User] Please transcribe this text

[Assistant] You start out with this one, uh, yeaah.


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[Assistant] Yeah, let's just, let's just make it multiply a vector. x0, x1, x2, x3.


[User] Please transcribe this text

[Assistant] And, and cyclically, so the x2, x3 that got shifted off the bottom come back to the top. Okay.


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[Assistant] What I want to, so the first property is of circulance.


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[Assistant] So, so suppose I have matrices C and D, circular.


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[Assistant] So if I multiply circulant matrices, I get more circulant matrices.


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[Assistant] And the identity is a circular matrix. I have a little group of matrices. The best little group of matrices there is. I can multiply two guys in the group.


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[Assistant] And I get another one in the group. Why is CD also a circular?


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[Assistant] Is c naught times the identity circulant plus c1 times the single shift.


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[Assistant] Plus c2 times the double shift plus c3 times the triple shift. That's what it takes to put


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[Assistant] C0, C1, C2, and C3 on those diagonals.


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[Assistant] C0 i is obviously on the main diagonal. C1 p, remember what p is.


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[Assistant] Put C1 on the next diagonal. Then C2P squared. When I square this, I've shifted by one more. So it will put C2 on that diagonal. And finally, C3 would go in those positions.


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[Assistant] Circulant matrix is a polynomial in P, in a single shift. This is any combination of shift


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[Assistant] This is a single shift, that's a double shift, that's a triple shift, that's a zero shift, and if I take combinations, I get, I get a circulant matrix. So, so now I can see why CD is also a circulant, because this is a polynomial in P, and this is a polynomial


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[Assistant] In p, and when I multiply those together, I get a polynomial in p.


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[Assistant] Usually, if I multiply a third degree polynomial by another third degree polynomial,


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[Assistant] So say I'm looking at 4 by 4 circular matrices.


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[Assistant] So this would be a polynomial of p in p of third, third, degree three.


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[Assistant] So that would give me a polynomial of degree 6. But I don't want that. That's somehow I have to define multiplication so that I want this to be degree. These are all supposed to be 4 by 4 matrices. No, just like that one.


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[Assistant] That's twice the identity plus 5p plus 1p squared plus 0p cubed. And suppose I square that.


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[Assistant] Then again, I'm going to get up a circulant matrix, and I don't want it to go up to degree seven. I want, you know, I just want four terms in my polynomial. I just want


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[Assistant] The main diagonal and the next three diagonals and then cycling around completes the matrix. So why, what's, how do I get, how to get degree three?


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[Assistant] That's the question, and can you just tell me the answer?


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[Assistant] Yeah, let's just do an example. So I have c0, c1p, c2p squared, c3p cubed.


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[Assistant] And I'm writing the 4 by 4 matrix that way. This is, this should be the identity, of course. You knew that.


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[Assistant] Okay, so when I multiply those guys, why do I not get degree 6? Why am I, why is that product like p cubed times p cubed


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[Assistant] C3 P cubed times C3 P cubed, that gives me C3 D3 P to the sixth power. So what's up? What do I do? Yeah? Yes, that's the key. That's the periodic part. P to the fourth equal the identity. Thank you. Yeah.


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[Assistant] So the P to the sixth term is really a P squared term. The P to the fifth term is really a P term.


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[Assistant] The p to the fourth term is really a p to the zero term.


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[Assistant] Yeah, so I'm, I'm just doing, I'm doing what you, I'm doing cyclic convolution, actually. Let me just say, when I'm multiplying, yeah.


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[Assistant] So now I'm telling you what's, I can first tell you what convolution is, and then what cyclic convolution is. And this is, listen up to this, because it's a good thing to know. Uh, yeaah. So first of all, convolution.


[User] Please transcribe this text

[Assistant] So suppose I want to take the convolution of 3, 1, 2.


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[Assistant] That's often the symbol for convolution with four, six, uh, one. Okay.


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[Assistant] So how do I, how, what does that mean? I've got a vector. So what's hiding, for me what's hiding there is, uh, is, is polynomials 3 plus x plus 2x squared.


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[Assistant] Times 4 plus 6x plus 1x squared. And I just multiply them out, and I get 5.


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[Assistant] 3 times 6x is 18x, but I've also got 4x from here, so I've got 22x.


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[Assistant] I just do that multiplication of polynomials, and what I'm doing is convolution with the vectors.


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[Assistant] And here, here's the way you wrote it in, in, uh, first grade. Okay, so here's first grade. Okay, 2, 12, 8. This is, you haven't learned to carry yet. So 12 goes in there as 12. Then 1 is 4, 6, 1. And 3 is 12, 18, 3. And then you add up. So you have 2.


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[Assistant] 13, 17, 22, and 12. So let me just, so, so that, that's the answer there. That the convolution, I guess I have to take it from, yeaah, 12. 3 times 4 gave 12.


[User] Please transcribe this text

[Assistant] Now 3 times 6 plus 1 times 4, that's the 22. Oh yeah, we already started here. But now,


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[Assistant] What's after that? Seventeen? Why did I say seventeen?


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[Assistant] Oh, 8 plus 6 plus 3, thanks. 17, uh, and then 12 plus 1, 13, and then 2. That's non-cyclic.


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[Assistant] If I, if I want it to be non-cyclic I don't put a circle in.


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[Assistant] So that's a symbol for ordinary convolution. If you do the MATLAB command CONV for convolution, if you gave it those vectors, it would give you


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[Assistant] Five, uh, uh, vector with five components as a result. But if you now let me make it cyclic. Okay, so what's going to happen now when I make it cyclic?


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[Assistant] So this represents 12, 22p, 17p squared, 13p cubed. And what happens with 13p cubed? If I'm doing, if n is 3, and I'm doing 3 by 3 matrices, then 13p cubed is the same as 13, right? p cubed is i. So the 13 will go back there, and the 2 will be p fourth.


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[Assistant] So I'm getting back a vector of length 3.


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[Assistant] Just as I want to do if I have a 3 by 3 matrix.


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[Assistant] Convolution, cyclic, circulant matrix with those three diagonals.


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[Assistant] And these three diagonals, and I want the answer to be a three by three matrix, were these diagonals.


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[Assistant] So again, matrix multiplication of circulant matrices corresponds exactly to


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[Assistant] Multiplying polynomials cyclically, and that's cyclic convolution.


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[Assistant] And then there's just one little trick to see if you got the numbers right. I believe that


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[Assistant] It should be true that if 3 plus 1 plus 2 is 6, 4 plus 6 plus 1 is 11, and I believe that those should add to, add to what?


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[Assistant] What do I hope that they add to? 66.


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[Assistant] I'm a little nervous about doing it, but I think we can, yeaah. So 49, 59, 66, check, yeaah. So the digits, the sum of the digits of one factor,


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[Assistant] Multiply the sum of the digits of the other factor to give the sum of the digits in the convolution. And that would be true whether we're doing cyclic, which is bringing the 13 and the 2 back in, or not cyclic, where we have 5 numbers.


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[Assistant] Yeah, so that's, that's actually a check that...


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[Assistant] Little, I don't know if you ever thought about that in second grade. Uh, multiplying these numbers, multiplying that number by that number, and getting some answer.


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[Assistant] Which probably half the class did not get, right? Then fifth grade, they're kind of getting it.


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[Assistant] But if they knew a check, so they could have just added these numbers to get 11, added these numbers to get 6, multiplied those to get 66, and checked that those added to 66.


[User] Please transcribe this text

[Assistant] That never occurred to me, I admit, in second grade either. But, uh, it's a good thing. Now you know. Now you can pass second grade. Okay. So, so this is, uh, the picture for cyclic convolutions.


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[Assistant] And I just have a few minutes left to tell you about the eigenvalues and eigenvectors of these matrices.


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[Assistant] So what can you tell me about the eigenvalues and, or say the eigenvectors? I have a matrix P, happens to be a permutation matrix. But it's a matrix. Then I take this polynomial in the matrix.


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[Assistant] What can you tell me about the eigenvectors of this matrix C? So I have, right, my C looks like


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[Assistant] Looks like that, and I'm asking you for the eigenvectors of that. And I'm saying that that is, uh,


[User] Please transcribe this text

[Assistant] Is a sum of, is a polynomial sum of powers of p, like so. In fact, the numbers here just come off the diagonals. Uh, so what about the eigenvectors?


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[Assistant] Well, that is an eigenvector. That's true. The vector of all ones will be an eigenvector. With what eigenvalue, actually?


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[Assistant] The eigenvectors of C are the same as the eigenvectors of P.


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[Assistant] If I have an eigenvector of P, that's also an eigenvector of P squared and P cubed in a combination. So eigenvectors.


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[Assistant] So then the question is, what are the eigenvectors of P?


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[Assistant] Looking for eigenvectors, what those numbers were.


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[Assistant] The point is that those numbers were constant on diagonals and that they, therefore they, I had, it's built out of one matrix P.


[User] Please transcribe this text

[Assistant] Built out of one matrix P, so if all I have to do is the eigenvectors of P. Yeah. So that's the final step here.


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[Assistant] What are the eigenvectors and eigenvalues of P?


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[Assistant] So somebody mentioned that the vector of 1, 1, 1, 1, that is an eigenvector.


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[Assistant] Because if I do that multiplication, it shifts this vector down and cyclically around, but that just brings back the same vector. So lambda is 1, and that's an eigenvector.


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[Assistant] Well alright, tell me an eigenvector for a minus 1.


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[Assistant] Uh, do you want to just alternate signs there? So let me, let me do that multiplication.


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[Assistant] Of course I don't have to do this multiplication. I'm just going to shift this. So I'm going to shift that down, 1 minus 1, 1, and cyclically around. And now what's the eigenvalue? It is an eigenvector. And what's the eigenvalue that makes


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[Assistant] What multiple of that vector gives the, gives that vector? Minus one.


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[Assistant] But the rest of what you said was a bad idea.


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[Assistant] Uh, because uhm, we've got to look, the next eigenvectors are going to be somewhere else.


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[Assistant] The other two. So what are the other two eigenvalues of this permutation matrix?


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[Assistant] One, that's right. We're in a circulant world. Draw a circle.


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[Assistant] So the eigenvectors are the four roots of 1. Complex. So 1 and minus 1 you got. These are the lambdas. But the other ones are i and minus i.


[User] Please transcribe this text

[Assistant] Yeah, yeah. Why don't I leave until, since time's up?


[User] Please transcribe this text

[Assistant] Let me leave until Friday the eigenvalues and eigenvectors, uh, for in general, uhm, for arbitrary size, but that's a picture of the eigen, we're close to the eigenvectors and eigenvalues of every


[User] Please transcribe this text

[Assistant] All circulants have the same eigenvectors. All circulants have that eigenvector. Also, four by four.


[User] Please transcribe this text

[Assistant] All circulants have that eigenvector, four by four, and we'll find the other two.


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[Assistant] Okay, so I'll see you Friday for those and the...


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[Assistant] Convolution rule, which is the most important rule in signal processing. Okay, thanks.


[User] Please transcribe this text

[Assistant] Hello. Can I see your tickets and passports, please?


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[Assistant] How many carry-on bags are you taking with you? Two bags.


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[Assistant] Okay, here are your boarding passes and your passports.


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[Assistant] You will be boarding at Gate B2 at 1210. Okay, thank you very much.


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[Assistant] Welcome aboard. I hope you enjoy your flight with us today. Here are your seats.


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[Assistant] You can put your bags into the overhead compartment.


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[Assistant] Please fasten your seatbelt, because the plane is going to take off soon.


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[Assistant] What would you like for your in-flight meal? We have chicken and rice, or pasta.


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[Assistant] Would you like anything to drink with that?


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[Assistant] Everything I do and everything I do professionally, my life has been shaped.


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[Assistant] I worked in Zambia, Kenya, Ivory Coast, Algeria, Somalia, in projects of technical cooperation with African countries. I worked for an Italian NGO.


[User] Please transcribe this text

[Assistant] I'm not going to tell you the damage that the money has done. Just go and read her book.


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[Assistant] We western people are imperialist, colonialist missionaries. And there are only two ways we deal with people. We either patronize them or we are paternalistic.


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[Assistant] The two words come from the Latin root pater, which means father, but they mean two different things.


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[Assistant] Paternalistic. I treat anybody from a different culture as if they were my children. I love you so much.


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[Assistant] Patronizing, I treat everybody from another culture as if they were my servants. That's why the white people in Africa are called buana, boss.


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[Assistant] Above all in economic development, if people do not wish to be helped, leave them alone.


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[Assistant] And say, can we, can you imagine a city that is not neocolonial?


[User] Please transcribe this text

[Assistant] I decided, when I was 27 years old, to only respond to people.


[User] Please transcribe this text

[Assistant] And I invented a system called enterprise facilitation, where you never initiate anything, you never motivate anybody.


[User] Please transcribe this text

[Assistant] But you become a servant of the local passion.


[User] Please transcribe this text

[Assistant] The servant of local people who have a dream to become a better person. So what you do, you shut up.


[User] Please transcribe this text

[Assistant] You never arrive in a community with any ideas. And you sit with the local people. We don't work from offices. We meet at the cafe. We meet at the pub. We have zero infrastructure. And what we do, we become friends. And we find out what that person wants to do. The most important thing is passion.


[User] Please transcribe this text

[Assistant] You can give somebody an idea. If that person doesn't want to do it, what are you going to do?


[User] Please transcribe this text

[Assistant] The passion that the person has for her own growth is the most important thing. The passion that the man has for his own personal growth is the most important thing. And then we help them to go and find the knowledge because nobody in the world can succeed alone.


[User] Please transcribe this text

[Assistant] I had this idea. Why don't we fall once?


[User] Please transcribe this text

[Assistant] There is a problem with community meetings. Entrepreneurs never come.


[User] Please transcribe this text

[Assistant] And they never tell you in a public meeting what they want to do with their own money.


[User] Please transcribe this text

[Assistant] Has this blind spot. The smartest people in your community you don't even know. Because they don't come to your public meetings.


[User] Please transcribe this text

[Assistant] And to work one on one, you have to create a social infrastructure that doesn't exist. You have to create a new profession.


[User] Please transcribe this text

[Assistant] The profession is the family doctor of enterprise, the family doctor of business who sits with you in your house, at your kitchen table, at the cafe, and helps you find the resources to transform your passion into a way to make a living. I started this as a tryout.


[User] Please transcribe this text

[Assistant] In, uh, in Esperance, in Western Australia, I was doing a PhD at the time, trying to go away from this patronizing bullshit that we arrive and tell you what to do. And so,


[User] Please transcribe this text

[Assistant] And I helped him to sail to the restaurant in Perth to get organized. And then the fisherman came to me to say, you the guy who helped Maury.


[User] Please transcribe this text

[Assistant] Can you help us? And I help these five fishermen to work together and get this beautiful tuna. Not to the cannery in Albany for 60 cents a kilo, but we find a way.


[User] Please transcribe this text

[Assistant] To take the fish for sushi to Japan. For 15 dollars a kilo. And the farmers came to talk to me, say, hey, you help them, can you help us?


[User] Please transcribe this text

[Assistant] In a year I had 27 projects going on and the government came to see me to say, how can you do that?


[User] Please transcribe this text

[Assistant] We've done it in 300 communities around the world. We have helped to start 40,000 businesses.


[User] Please transcribe this text

[Assistant] There is a new generation of entrepreneurs who are dying of solitude. Peter Draka, one of the greatest management consultants in history, died aged 96 a few years ago.


[User] Please transcribe this text

[Assistant] Peter Draga was a professor of philosophy before becoming involved in business. And this is what Peter Draga says. Planning is actually incompatible with an entrepreneurial society and economy. Planning is the kiss of death of entrepreneurship.


[User] Please transcribe this text

[Assistant] So now you're rebuilding Christchurch without knowing what the smartest people in Christchurch want to do with their own money and their own energy. You have to learn.


[User] Please transcribe this text

[Assistant] We are at the end of the first industrial revolution, non-renewable fossil fuels manufacturing, and all of the sudden,


[User] Please transcribe this text

[Assistant] We have systems which are not sustainable. The internal combustion engine is not sustainable. Freon whale maintaining things is not sustainable. What we have to look at is at how we feed, cure,


[User] Please transcribe this text

[Assistant] Educate, transport, you know, communicate for 7 billion people in a sustainable way.


[User] Please transcribe this text

[Assistant] The technologies do not exist to do that.


[User] Please transcribe this text

[Assistant] There's a lovely story that I read in a futurist magazine many, many years ago.


[User] Please transcribe this text

[Assistant] There was a group of experts who were invited to discuss the future of the city of New York in 1860.


[User] Please transcribe this text

[Assistant] So what happens in 40 years time, in year 1900, in the United States of America, there were 1001 car manufacturing companies. 1001.


[User] Please transcribe this text

[Assistant] The, the idea of a funny different technology had absolutely taken over.


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[Assistant] And there were tiny, tiny little factories in backwaters. Dearborn, Michigan. Henry Ford.


[User] Please transcribe this text

[Assistant] However, there is a secret to work with entrepreneurs. First you have to offer them


[User] Please transcribe this text

[Assistant] Confidentiality, otherwise they don't come and talk to you. Then you have to talk, uh, offer them.


[User] Please transcribe this text

[Assistant] Absolute dedicated, impassionate service to them. And then you have to tell them the truth about entrepreneurship.


[User] Please transcribe this text

[Assistant] The smallest company, the biggest company has to be capable of doing three things beautifully. The product that you want to sell has to be fantastic. You have to have fantastic marketing. And you have tremendous financial management. Guess what?


[User] Please transcribe this text

[Assistant] Carnegie, Westinghouse, Edison, Ford, all the new companies, Google, Yahoo.


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[Assistant] There's only one thing that all the successful companies in the world have in common. Only one. None was started by one person. Now we teach entrepreneurship to 16 years old in Northumberland.


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[Assistant] And we start the class by giving them the first two pages of Richard Branson autobiography and the task of the 16 years old is to underline in the first two pages of Richard Branson autobiography how many times Richard uses the word I and how many times he uses the word we.


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[Assistant] Never the word I, and the word we, 32 times. He wasn't alone when he started.


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[Assistant] Nobody started the company alone. No one. So we can create a community.


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[Assistant] Where we have facilitators who come from a small business background sitting in cafes, in bars, and uh, your dedicated buddies.


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[Assistant] Who will go to you what somebody did for this gentleman who talk about, you know, this epic.


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[Assistant] Somebody who will say to you, what do you need? What can you do? Can you make it? Okay, can you sell it? Can you look after the money? Oh no, I cannot do this. Would you like me to find you somebody? We activate communities.


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[Assistant] We have groups of volunteers supporting the enterprise facilitator to help you to find resources and people.


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[Assistant] I heard about a high school in Chicago where students had to pass a certain number of courses to graduate, and if they didn't pass a course, they got the grade, not yet.


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[Assistant] And I thought that was fantastic. Because if you get a failing grade, you think, I'm nothing, I'm nowhere. But if you get the grade not yet, you understand that you're on a learning curve. It gives you a path into the future.


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[Assistant] Not yet also gave me insight into a critical event early in my career, a real turning point.


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[Assistant] Some of them reacted in a shockingly positive way. They said things like, I love a challenge.


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[Assistant] And in study after study, they have run from difficulty.


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[Assistant] Engage deeply. Their brain is on fire with yet. They engage deeply. They process the error.


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[Assistant] Are we raising them for now instead of yet?


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[Assistant] Are we raising kids who are obsessed with getting A's? Are we raising kids who don't know how to dream big dreams?


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[Assistant] And are they carrying this need for constant validation with them into their future lives?


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[Assistant] Maybe because employers are coming to me and saying, we have already raised a generation of young workers who can't get through the day without an award. So.


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[Assistant] Their effort, their strategies, their focus, their perseverance, their improvement.


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[Assistant] This process praise creates kids who are hearty and resilient. There are other ways to reward yet.


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[Assistant] From the University of Washington to create a new online math game that rewarded yet. In this game, students were rewarded for effort, strategy, and progress. The usual math game rewards you for getting answers right, right now. But this game rewarded process. And we got more effort, more strategies,


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[Assistant] More engagement over longer periods of time and more perseverance when they hit really, really hard problems.


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[Assistant] Just the words yet or not yet we're finding give kids greater confidence.


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[Assistant] That creates greater persistence and


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[Assistant] But those who were taught this lesson showed a sharp rebound in their grades. We have


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[Assistant] Showing this now, this kind of improvement with thousands and thousands of kids, especially struggling students.


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[Assistant] There are groups of students who chronically underperform. For example, children in inner cities or children on Native American reservations. And they've done so poorly for so long.


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[Assistant] When educators create growth mindset classrooms, steeped in yet.


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[Assistant] In a year to a year and a half.


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[Assistant] Native American students in a school on a reservation went from the bottom of their district to the top.


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[Assistant] Because the meaning of effort and difficulty were transformed. Before, effort and difficulty made them feel dumb, made them feel like giving up, but now effort and difficulty


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[Assistant] That's when their neurons are making new connections, stronger connections. That's when they're getting smarter.


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[Assistant] I received a letter recently from a 13 year old boy. He said, Dear Professor Dweck,


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[Assistant] And that's why I decided to put it into practice.


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[Assistant] Into my relationship with my family and into my relationship with kids at school. And I experienced great improvement in all of those areas.


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[Assistant] My name is Anna and I'll be taking care of you both today. Can I start you off with some drinks?


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[Assistant] We have herbal tea, coffee, and a variety of soft drinks.


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[Assistant] I love the Cobb salad and the grilled chicken sandwich. They're two of our most popular items. What exactly is Cobb salad? Romaine lettuce topped with fresh avocado.


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[Assistant] Actually I think I wanna change. I want to have a trendy look. I'm considering a short bob style. I don't want long wavy hair anymore. I want short straight hair.


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[Assistant] The hunchback of Notre Dame. Once upon a time in Paris, Minister Frollo was out on the streets making sure everything was in order in the great city, when a sound cut through the silence of the night.


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[Assistant] Never allowed to step out of the Bell Tower of Notre Dame.


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[Assistant] Quasimodo, Esmeralda, and Captain Phoebus rode long until they were outside the city of Paris. But Frollo and his guards did not stop chasing them. They took a different road and finally managed to ambush them.


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[Assistant] I was born on December 14, 2007. It was a Friday at 6 o'clock in the morning. I guess I'm an early riser.


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[Assistant] Yeaah, it's my favorite day of the week too. What about you? When were you born?


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[Assistant] Wow, that's nice. So, do you go back there very often?


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[Assistant] That's awesome. So do you like living here?


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[Assistant] My favorite subject is math because I like solving problems. The most difficult subject for me is history.


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[Assistant] I'm very bad at memorizing dates and names.