Alice's Adventures in Wonderland, by Lewis Carroll, CHAPTER IX. You can't think how glad I am to see you again, you dear old thing," said the Duchess, as she tucked her arm affectionately into Alice's, and they walked off together. Alice was very glad to find her in such a pleasant temper, and thought to herself that perhaps it was only the pepper that had made her so savage when they met in the kitchen. When I'm a Duchess," she said to herself, not in a very hopeful tone, though, I won't have any pepper in my kitchen at all. Soup does very well without. Maybe it's always pepper that makes people hot-tempered. She went on, very much pleased at having found out a new kind of rule, and vinegar that makes them sour, and chamomile that makes them bitter, and—and barley-sugar and such things that make children sweet-tempered. I only wish people knew that. Then they wouldn't be so stingy about it, you know. She had quite forgotten the Duchess by this time, and was a little startled when she heard her voice close to her ear.  I can't tell you just now what the moral of that is, but I shall remember it in a bit. Perhaps it hasn't one, Alice ventured to remark. Child, said the Duchess, everything's got a moral, if only you can find it. And she squeezed herself up closer to Alice's side as she spoke. Alice did not much like keeping so close to her, first because the Duchess was very ugly, and secondly because she was exactly the right height to rest her chin upon Alice's shoulder, and it was an uncomfortably sharp chin. However, she did not like to be rude, so she bore it as well as she could. The game's going on rather better now, she said, by way of keeping up the conversation a little. "'Tis so,' said the Duchess, and the moral of that is, "'Tis love, tis love, that makes the world go round.' Somebody said, Alice whispered, that it's done by everybody minding their own business. "'Ah, well, it means much the same thing,' said the Duchess, digging her sharp little chin into Alice's shoulder, as she added. And the moral of that is, take care of the sense, and the sounds will take care of themselves.' "'How fond she is of finding morals in things,' Alice thought to herself. "'I dare say you're wondering why I don't put my arm round your waist,' the Duchess said after a pause. "'The reason is that I'm doubtful about the temper of your flamingo. Shall I try the experiment?' "'He might bite,' Alice cautiously replied, not feeling at all anxious to have the experiment tried. "'Very true,' said the Duchess. Flamingos and Mustard both bite, and the moral of that is, birds of a feather flock together. "'Only Mustard isn't a bird,' Alice remarked. "'Right as usual,' said the Duchess. "'What a clear way you have of putting things.' "'It's a mineral, I think,' said Alice. "'Of course it is,' said the Duchess, who seemed ready to agree to everything that Alice said. "'There's a large Mustard mine near here, and the moral of that is, the more there is of mine, the less there is of yours.' "'Oh, I know,' exclaimed Alice, who had not attended to this last remark. "'It's a vegetable. It doesn't look like one, but it is.' "'I quite agree with you,' said the Duchess, and the moral of that is, be what you would seem to be, or if you'd like to put it more simply, never imagine yourself not to be otherwise, and what it might appear to others, that what you were or might have been was not otherwise, and what you had been would have appeared to them to be otherwise.' "'I think I should understand that better,' Alice said very politely. "'If I had it written down, but I can't quite follow it as you say it. "'That's nothing to what I could say if I chose,' the Duchess replied in a pleased tone. "'Pray, don't trouble yourself to say it any longer than that,' said Alice. "'Oh, don't bother about trouble,' said the Duchess. "'I make you a present of everything I've said as yet.' "'A cheap sort of present,' thought Alice. "'I'm glad they don't give birthday presents like that, but she did not venture to say it out loud.' "'Thinking again?' the Duchess asked, with another dig of her sharp little chin. "'I've a right to think,' said Alice sharply, for she was beginning to feel a little worried. "'Just about as much right,' said the Duchess, as pigs have to fly, and the mm-mm-mm.' But here, to Alice's great surprise, the Duchess's voice died away, even in the middle of her favourite word, moral, and the arm that was linked into hers began to tremble. Alice looked up, and there stood the Queen in front of them, with her arms folded, frowning like a thunderstorm. "'A fine day, Your Majesty,' the Duchess began in a low, weak voice. "'Now, I give you fair warning,' shouted the Queen, stamping on the ground as she spoke.  Take your choice.' The Duchess took her choice, and was gone in a moment. "'Let's go on with the game,' the Queen said to Alice, and Alice was too much frightened to say a word, but slowly followed her back to the croquet ground. The other guests had taken advantage of the Queen's absence, and were resting in the shade. However, the moment they saw her, they hurried back to the game, the Queen merely remarking that a moment's delay would cost them their lives. All the time they were playing, the Queen never left off quarrelling with the other players, and shouting, "'Off with his head!' or, "'Off with her head!' Those whom she sentenced were taken into custody by the soldiers, who, of course, had to leave off being arches to do this, so that by the end of half an hour or so there were no arches left, and all the players, except the King, the Queen, and Alice, were in custody, and under sentence of execution. Then the Queen left off, quite out of breath, and said to Alice, "'Have you seen the mock-turtle yet?' "'No,' said Alice.  "'I never saw one, or heard of one,' said Alice. "'Come on, then,' said the Queen, "'and he shall tell you his history.' As they walked off together, Alice heard the King say in a low voice to the company generally, "'You are all pardoned. Come, that's a good thing,' she said to herself, for she had felt quite unhappy at the number of executions the Queen had ordered.  I must go back and see after some executions I have ordered.' And she walked off, leaving Alice alone with the Gryphon. Alice did not quite like the look of the creature, but on the whole she thought it would be quite as safe to stay with it, as to go after that savage Queen, so she waited. The Gryphon sat up and rubbed its eyes. Then it watched the Queen till she was out of sight. Then it chuckled. "'What fun,' said the Gryphon, half to itself, half to Alice. "'What is the fun?' said Alice. "'Why, she,' said the Gryphon, "'it's all a fancy that. They never execute, nobody you know. Come on.' "'Everybody says, come on here,' thought Alice, as she went slowly after it. I never was so ordered about in all my life, never.' They had not gone far before they saw the mock-turtle in the distance, sitting sad and lonely on a little ledge of rock. And as they came nearer, Alice could hear him sighing as if his heart would break. She pitted him deeply. "'What is his sorrow?' she asked the Gryphon, and the Gryphon answered very nearly in the same words as before. "'It's all his fancy that. He hasn't got no sorrow, you know. Come on.'  "'This ear-young lady,' said the Gryphon, "'she wants for to know your history, she do.' "'I'll tell it to her,' said the mock-turtle in a deep hollow tone. "'Sit down, both of you, and don't speak a word till I've finished.' So they sat down, and nobody spoke for some minutes. Alice thought to herself, "'I don't see how he can even finish if he doesn't begin,' but she waited patiently. "'Once,' said the mock-turtle at last, with a deep sigh, "'I was a real turtle.' These words were followed by a very long silence, broken only by an occasional exclamation of from the Gryphon, and the occasional heavy sobbing of the mock-turtle. Alice was very nearly getting up and saying, "'Thank you, sir, for your interesting story,' but she could not help thinking there must be more to come, so she sat still and said nothing. "'When we were little,' the mock-turtle went on at last, more calmly, though still sobbing a little now and then, we went to school in the sea. The master was an old turtle. We used to call him tortoise. "'Why did you call him tortoise if he wasn't one?' Alice asked. "'We called him tortoise because he tortoise,' said the mock-turtle angrily. "'Really, you are very dull.  At last the Gryphon said to the mock-turtle, "'Drive on, old fellow, don't be all day about it.' And he went on in these words. "'Yes, we went to school in the sea, though you may not believe it.' "'I never said I didn't,' interrupted Alice. "'You did,' said the mock-turtle. "'Hold your tongue,' added the Gryphon, before Alice could speak again. The mock-turtle went on. We had the best of educations. In fact, we went to school every day. "'I've been to a day-school, too,' said Alice. "'You needn't be so proud as all that.' "'With extras,' asked the mock-turtle, a little anxiously. "'Yes,' said Alice. "'We learnt French and music.' "'And washing,' said the mock-turtle. "'Certainly not,' said Alice indignantly. "'Ah, then yours wasn't a really good school,' said the mock-turtle, in a tone of great relief. Now, at hours, they had, at the end of the bill, French music and washing extra.' "'You couldn't have wanted it much,' said Alice, living at the bottom of the sea. "'I couldn't afford to learn it,' said the mock-turtle with a sigh. I only took the regular course.' "'What was that?' inquired Alice, reeling and rising, of course, to begin with.' The mock-turtle replied. "'And then the different branches of arithmetic. Ambition, distraction, aglification, and derision.' "'I never heard of aglification,' Alice ventured to say. "'What is it?' the Gryphon lifted up both its paws in surprise. "'What?' "'Never heard of ugly-fying,' it exclaimed. "'You know what to beautify is, I suppose?' "'Yes,' said Alice doubtfully. "'It means to make anything prettier.' "'Well, then,' the Gryphon went on.  Alice did not feel encouraged to ask any more questions about it, so she turned to the mock-turtle and said, "'What else had you to learn?' "'Well, there was mystery,' the mock-turtle replied, counting off the subjects on his flappers. Mystery, ancient and modern, with seeography, and drawing. The drawing-master was an old conger eel that used to come once a week. He taught us drawing, stretching, and faintinging coils.' "'What was that like?' said Alice. "'Well, I can't show it to you myself,' the mock-turtle said. "'I'm too stiff,' and the Gryphon never learned it. "'Hadn't time,' said the Gryphon. I went to the classics-master, though. He was an old crab, he was. I never went to him,' the mock-turtle said with a sigh. He taught laughing and grief, they used to say. "'So he did, so he did,' said the Gryphon, sighing in his turn, and both creatures hid their faces in their paws. "'And how many hours a day did you do lessons?' said Alice, in a hurry to change the subject. "'Ten hours the first day, nine the next, and so on,' said the mock-turtle. "'What a curious plan,' exclaimed Alice. "'That's the reason they're called lessons,' the Gryphon remarked, because they lessen from day to day. This was quite a new idea to Alice, and she thought it over a little before she made her next remark. Then the eleventh day must have been a holiday.' "'Of course it was,' said the mock-turtle. "'And how did you manage on the twelfth?' Alice went on eagerly. "'That's enough about lessons,' the Gryphon interrupted in a very decided tone. "'Tell her something about the games now.' The end of Chapter 9 of Alice's Adventures in Wonderland by Lewis Carroll. Chapter 10 of Alice's Adventures in Wonderland by Lewis Carroll. This is a LibriVox recording. All LibriVox recordings are in the public domain. For more information or to find out how to volunteer, please contact LibriVox.org. Recording by Peter Yersley. Chapter 10 The Lobster Quadril The mock-turtle sighed deeply, and drew the back of one flapper across his eyes. He looked at Alice and tried to speak, but for a minute or two Sobs choked his voice. Same as if he had a bone in his throat, said the Gryphon, and it sets to work shaking him and punching him in the back. At last the mock-turtle recovered his voice, and with tears running down his cheeks he went on again. "'You may not have lived much under the sea.' "'I haven't,' said Alice, and perhaps you were never even introduced to a lobster. Alice began to say, "'I once tasted, but checked herself hastily, and said, "'No, never.' "'So you can have no idea what a delightful thing a lobster quadril is.' "'No, indeed,' said Alice. "'What sort of a dance is it?' "'Why?' said the Gryphon. "'You first form into line along the seashore.' "'Two lines,' cried the mock-turtle. "'Seals, turtles, salmon, and so on. Then, when you've cleared all the jellyfish out of the way, that generally takes some time,' interrupted the Gryphon. "'You advance twice?' "'Each with a lobster as a partner,' cried the Gryphon. "'Of course,' the mock-turtle said. "'Advanced twice, set to partners. "'Changed lobsters, and retire in same order,' continued the Gryphon. "'Then, you know,' the mock-turtle went on. "'You throw the—' "'The lobsters!' shouted the Gryphon, with a bound into the air. "'As far out to see as you can, swim after them,' screamed the Gryphon. "'Turn a somersault in the sea,' cried the mock-turtle, capering wildly about. "'Changed lobsters again,' yelled the Gryphon at the top of its voice. "'Back to land again, and—' "'That's all the first figure,' said the mock-turtle, suddenly dropping his voice. And the two creatures, who had been jumping about like mad things all this time, sat down again very sadly and quietly, and looked at Alice. "'It must be a very pretty dance,' said Alice timidly. "'Would you like to see a little of it?' said the mock-turtle. "'Very much indeed,' said Alice. "'Come, let's try the first figure,' said the mock-turtle to the Gryphon. "'We can do without lobsters, you know. Which shall sing?' "'Oh, you sing. I've forgotten the words,' said the Gryphon. So they began solemnly dancing round and round Alice, every now and then treading on her toes when they passed too close, and waving their forepaws to mark the time, while the mock-turtle sang this very slowly and sadly. "'Will you walk a little faster?' said a whiting to a snail. "'There's a porpoise close behind us, and he's treading on my tail. See how eagerly the lobsters and the turtles all advance. They are waiting on the shingle. Will you come and join the dance? Will you want you? Will you want you? Will you join the dance? Will you want you? Will you want you? Won't you join the dance? You can really have no notion how delightful it will be when they take us up and throw us with the lobsters out to sea. But the snail replied, too far, too far, and gave a look at sconce. Said he thanked the whiting kindly, but he would not join the dance. He would not, could not, would not, could not, would not join the dance. Would not, could not, would not, could not, could not join the dance. What matters it how far we go, his scaly friend replied, There is another shore, you know, upon the other side. The further off from England, the nearer is de France. Then turn not pale, beloved snail, but come and join the dance. Will you want you? Will you want you? Will you join the dance? Thank you. It's a very interesting dance to watch. Said Alice, feeling very glad that it was over at last. And I do so like that curious song about the whiting. Oh, as to the whiting, said the mock turtle. Say, you've seen them, of course. Yes, said Alice. I've often seen them, but I didn't. She checked herself hastily. I don't know where Din may be, said the mock turtle. But if you've seen them so often, of course, you know what they're like. I believe so, Alice replied thoughtfully. They have their tails in their mouths, and they're all over crumbs. You're wrong about the crumbs, said the mock turtle. Crumbs would all wash off in the sea. But they have their tails in their mouths.  Tell her about the reason and all that, he said to the Gryphon. The reason is, said the Gryphon, that they would go with the lobsters to the dance, so they got thrown out to sea, so they had to fall a long way. So they got their tails fast in their mouths, so they couldn't get them out again. That's all. Thank you, said Alice. It's very interesting. I never knew so much about a whiting before. I can tell you more than that, if you like, said the Gryphon. Do you know why it's called a whiting? I never thought about it, said Alice. Why? It does the boots and shoes. The Gryphon replied very solemnly. Alice was thoroughly puzzled. Does the boots and shoes? She repeated in a wondering tone. Why, what are your shoes done with? said the Gryphon.  Alice looked down at them, and considered a little before she gave her answer. They're done with blacking, I believe. Boots and shoes under the sea, the Gryphon went on in a deep voice. Are done with a whiting? No, you know. And what are they made of? Alice asked in a tone of great curiosity. Souls and eels, of course, the Gryphon replied rather impatiently. Any shrimp could have told you that. If I'd been the whiting, said Alice, whose thoughts were still running on the song, I'd have said to the porpoise, keep back, please, we don't want you with us. They were obliged to have him with them. The mock-turtle said, no wise fish would go anywhere without a porpoise. Wouldn't it really? said Alice in a tone of great surprise. Of course not, said the mock-turtle. Why, if a fish came to me, and told me he was going a journey, I should say, with what porpoise? Don't you mean purpose? said Alice. I mean what I say. The mock-turtle replied in an offended tone, and the Gryphon added, Come, let's hear some of your adventures. I could tell you my adventures, beginning from this morning, said Alice a little timidly. But it's no use going back to yesterday, because I was a different person then. Explain all that, said the mock-turtle. No, no, the adventures first, said the Gryphon in an impatient tone. Explanations take such a dreadful time. So Alice began telling them her adventures, from the time when she first saw the white rabbit. She was a little nervous about it, just at first. The two creatures got so close to her, one on each side, and opened their eyes and mouths so very wide. But she gained courage as she went on. Her listeners were perfectly quiet, till she got to the part about her repeating, You are old, Father William, to the caterpillar, and the words all coming different. And then the mock-turtle drew a long breath and said, That's very curious. It's all about as curious as it can be, said the Gryphon. It all came different. The mock-turtle repeated thoughtfully. I should like to hear her try and repeat something now. Tell her to begin. He looked at the Gryphon, as if he thought it had some kind of authority over Alice. Stand up and repeat, Tis the voice of the sluggard, said the Gryphon. How the creatures order one about, and make one repeat lessons, thought Alice. I might as well be at school at once. However, she got up and began to repeat it.  And the words came very queer indeed. Tis the voice of the lobster. I heard him declare, You have baked me too brown, I must sugar my hair. As a duck with its eyelids, So he with his nose, Trims his belt and his buttons, And turns out his toes.  But when the tide rises and sharks are around, His voice has a timid and tremulous sound. That's different from what I used to say when I was a child, said the Gryphon. Well, I never heard it before, said the Mock Turtle. But it sounds uncommon nonsense. Alice said nothing. She had sat down with her face in her hands, wondering if anything would ever happen in a natural way again. I should like to have it explained, said the Mock Turtle. She can't explain it, said the Gryphon hastily. Go on with the next verse. But about his toes, the Mock Turtle persisted. How could he turn them out with his nose, you know? It's the first position in dancing, Alice said, but was dreadfully puzzled by the whole thing, and longed to change the subject. Go on with the next verse, the Gryphon repeated impatiently. It begins by passed by his garden. Alice did not dare to disobey, though she felt sure it would all come wrong, and she went on in a trembling voice. I passed by his garden, and marked with one eye how the owl and the panther were sharing a pie. The panther took pie crust and gravy and meat, while the owl had the dish as its share of the treat. When the pie was all finished, the owl as a boon was kindly permitted to pocket the spoon. While the panther received knife and fork with a growl, and concluded the banquet, what is the use of repeating all that stuff? The Mock Turtle interrupted. If you don't explain it as you go on, it's by far the most confusing thing I ever heard. Yes, I think you'd better leave off, said the Gryphon, and Alice was only too glad to do so. Shall we try another figure of the lobster quadrill, the Gryphon went on? Or would you like the Mock Turtle to sing you a song? Or a song, please, if the Mock Turtle would be so kind, Alice replied, so eagerly that the Gryphon said in a rather offended tone, No accounting for tastes. Sing her Turtle Soup, will you old fellow? The Mock Turtle sighed deeply, and began in a voice sometimes choked with sobs to sing this. Beautiful soup, so rich and green, Waiting in a hot terrain, Who for such daint is wood not stoop? Soup of the evening, beautiful soup, Soup of the evening, beautiful soup, Beautiful soup, beautiful soup, Soup of the evening, beautiful, beautiful soup, Beautiful soup, who cares for fish, Game or any other dish, Who would not give all else for two? Penny worth only of beautiful soup, Penny worth only of beautiful soup, Beautiful soup, beautiful soup, Soup of the evening, beautiful, beautiful soup. Chorus again, cried the Gryphon, and the Mock Turtle had just begun to repeat it when a cry of The trial's beginning was heard in the distance. Come on, cried the Gryphon, and, taking Alice by the hand, it hurried off, without waiting for the end of the song. What trial is it? Alice panted as she ran, but the Gryphon only answered, Come on, and ran the faster, while more and more faintly came carried on the breeze that followed them. The melancholy words, soup of the evening, beautiful, beautiful soup. The end of Chapter 10 of Alice's Adventures in Wonderland by Lewis Carroll. Chapter 11 of Alice's Adventures in Wonderland by Lewis Carroll. This is a LibriVox recording. All the LibriVox recordings are in the public domain. For more information or to find out how to volunteer, please contact LibriVox.org. Recording by Peter Yersley. Chapter 11 Who Stole the Tarts? The King and Queen of Hearts were seated on their throne when they arrived. With a great crowd assembled about them, all sorts of little birds and beasts, as well as the whole pack of cards. The nave was standing before them in chains, with a soldier on each side to guard him, and near the King was the white rabbit, with a trumpet in one hand and a scroll of parchment in the other. In the very middle of the court was a table, with a large dish of tarts upon it. They looked so good that it made Alice quite hungry to look at them. I wish they'd get the trial done, she thought, and hand round the refreshments. But there seemed to be no chance of this. So she began looking at everything about her, to pass away the time. Alice had never been in a court of justice before, but she had read about them in books, and she was quite pleased to find that she knew the name of nearly everything there. That's the judge, she said to herself, because of his great wig. The judge, by the way, was the King, and as he wore his crown over the wig, look at the frontispiece if you want to see how he did it. He did not look at all comfortable, and it was certainly not becoming. And that's a jury-box, thought Alice, and those twelve creatures. She was obliged to say creatures, you see, because some of them were animals, and some were birds. I suppose they are the jurors. She said this last word two or three times over to herself, being rather proud of it, for she thought, and rightly so, that very few little girls of her age knew the meaning of it at all. However, jurymen would have done just as well. The twelve jurors were all writing very busily on slates. What are they doing? Alice whispered to the Gryphon. They can't have anything to put down yet before the trials began. They put in down their names, the Gryphon whispered in reply, for fear they should forget them before the end of the trial.  But she stopped hastily, for the white rabbit cried out, Silence in the court! And the king put on his spectacles, and looked anxiously round to make out who was talking.  And she could even make out that one of them didn't know how to spell stupid, and that he had to ask his neighbour to tell him. A nice muddled their slates will be in before the trials over, thought Alice. One of the jurors had a pencil that squeaked. This, of course, Alice could not stand, and she went round the court and got behind him, and very soon found an opportunity of taking it away. She did it so quickly that the poor little juror, it was Bill, the lizard, could not make out at all what had become of it. So, after hunting all about for it, he was obliged to write with one finger for the rest of the day. And this was of very little use, as it left no mark on the slate. Herald, read the accusation, said the king. On this the white rabbit blew three blasts on the trumpet, and then unrolled the parchment scroll, and read as follows. The Queen of Hearts! She made some tarts, all on a summer day. The nave of hearts, he stole those tarts, and took them quite away. Consider your verdict, the king said to the jury. Not yet, not yet. The rabbit hastily interrupted. There's a great deal to come before that. Call the first witness, said the king, and the white rabbit blew three blasts on the trumpet, and called out. First witness! The first witness was the Hatter. He came in with a teacup in one hand, and a piece of bread and butter in the other. I beg pardon, your Majesty! He began, for bringing these in, but I hadn't quite finished my tea when I was sent for. You ought to have finished, said the king. When did you begin? The Hatter looked at the March Hare, who had followed him into the court, arm in arm with the door-mouse. Fourteenth of March, I think it was, he said. Fifteenth, said the March Hare. Sixteenth, added the door-mouse. Write that down, the king said to the jury. And the jury eagerly wrote down all three dates on their slates, and then added them up and reduced the answer to shillings and pence.  It isn't mine, said the Hatter. Stolen! the king exclaimed, turning to the jury, who instantly made a memorandum of the fact. I keep them to sell, the Hatter added, as an explanation. I've none of my own. I'm a Hatter. Here the queen put on her spectacles and began staring at the Hatter, who turned pale and fidgeted. Give your evidence, said the king, and don't be nervous, or I'll have you executed on the spot. This did not seem to encourage the witness at all. He kept shifting from one foot to the other, looking uneasily at the queen, and in his confusion he bit a large piece out of his teacup, instead of the bread and butter. Just at this moment Alice felt a very curious sensation, which puzzled her a good deal, until she made out what it was. She was beginning to grow larger again, and she thought at first she would get up and leave the court. But on second thoughts she decided to remain where she was, as long as there was room for her. I wish you wouldn't squeeze so, said the door-mouse, who was sitting next to her. I can hardly breathe. I can't help it, said Alice very meekly. I'm growing. You've no right to grow here, said the door-mouse. Don't talk nonsense, said Alice more boldly. You know you're growing too? Yes, but I grow at a reasonable pace, said the door-mouse. Not in that ridiculous fashion. And he got up very sulkily and crossed over to the other side of the court. All this time the queen had never left off staring at the Hatter, and just as the door-mouse crossed the court, she said to one of the officers of the court, Bring me the list of the singers in the last concert, on which the wretched Hatter trembled so that he shook both his shoes off. Give your evidence, the king repeated angrily, or I'll have you executed whether you're nervous or not. I'm a poor man, your Majesty, the Hatter began, in a trembling voice. And I hadn't begun my tea, not above a week or so. And what with the bread and butter getting so thin, and the twinkling of the tea? The twinkling of the what? said the king. It began with the tea, the Hatter replied. Of course twinkling begins with a tea, said the king sharply. Do take me for a dunce? Go on. I'm a poor man, the Hatter went on. And most things twinkled after that. Only the March Hare said, I didn't, the March Hare interrupted in a great hurry. You did, said the Hatter. I deny it, said the March Hare. He denies it, said the king. Leave out that part. Well, at any rate, the Dormouse said. The Hatter went on, looking anxiously round, to see if he would deny it too. But the Dormouse denied nothing, being fast asleep. After that, continued the Hatter. I cut some more bread and butter. But what did the Dormouse say? One of the jury asked. That I can't remember, said the Hatter. You must remember, remarked the king. Or I'll have you executed. The miserable Hatter dropped his tea-cup and bread and butter, and went down on one knee. I'm a poor man, your Majesty! He began.  Here one of the guinea pigs cheered, and was immediately suppressed by the officers of the court. As that is rather a hard word, I will just explain to you how it was done. They had a large canvas bag, which tied up at the mouth with strings.  I'm glad I've seen that done, thought Alice. I've so often read in the newspapers at the end of trials there was some attempt at applause, which was immediately suppressed by the officers of the court. And I never understood what it meant till now. If that's all you know about it, you may stand down, continued the king. I can't go no lower, said the Hatter. I'm on the floor as it is. Then you may sit down, the king replied. Here the other guinea pig cheered, and was suppressed. Come, let's finish the guinea pigs, thought Alice. Now we shall get on better. I'd rather finish my tea, said the Hatter, with an anxious look at the queen. Who was reading the list of singers? You may go, said the king, and the Hatter hurriedly left the court, without even waiting to put his shoes on. And just to take his head off outside, the queen added to one of the officers. But the Hatter was out of sight, before the officer could get to the door. Call the next witness, said the king. The next witness was the Duchess's cook. She carried the pepper box in her hand, and Alice guessed who it was, even before she got into the court. By the way, the people near the door began sneezing all at once. Give your evidence, said the king. Shant, said the cook. The king looked anxiously at the white rabbit, who said in a low voice, Your Majesty must cross-examine this witness. Well, if I must, I must. The king said with a melancholy air. And after folding his arms and frowning at the cook, till his eyes were nearly out of sight, he said in a deep voice, What are tarts made of? Pepper mostly, said the cook. Tray call, said a sleepy voice behind her. Call of that door-mouse, the queens shrieked out. Behead that door-mouse! Turn that door-mouse out of court! Suppress him! Pinch him! Off with his whiskers! For some minutes the whole court was in confusion, getting the door-mouse turned out. And by the time they had settled down again, the cook had disappeared. Never mind, said the king with an air of great relief. Call the next witness. And he added in an undertone to the queen. Really, my dear, you must cross-examine the next witness. It quite makes my forehead ache. Alice watched the white rabbit as he fumbled over the list, feeling very curious to see what the next witness would be like. For they haven't got much evidence yet, she said to herself. Imagine her surprise when the white rabbit read out at the top of his shrill little voice the name Alice! The end of Chapter 11 of Alice's Adventures in Wonderland by Lewis Carroll Chapter 12 of Alice's Adventures in Wonderland by Lewis Carroll This is a LibriVox recording. All LibriVox recordings are in the public domain. For more information or to find out how to volunteer, please contact LibriVox.org, recording by Peter Yersley. Chapter 12 Alice's Evidence Here cried Alice, quite forgetting in the flurry of the moment how large she had grown in the last few minutes, and she jumped up in such a hurry that she tipped over the jury-box with the edge of her skirt, upsetting all the jury-men onto the heads of the crowd below. And there they lay, sprawling about, reminding her very much of a globe of goldfish she had accidentally upset the week before. Oh, I beg your pardon! she exclaimed in a tone of great dismay, and began picking them up again as quickly as she could, for the accident of the goldfish kept running in her head, and she had a vague sort of idea that they must be collected at once and put back into the jury-box or they would die. The trial cannot proceed, said the king in a very grave voice, until all the jury-men are back in their proper places. All, he repeated, with great emphasis, looking hard at Alice as he said so. Alice looked at the jury-box and saw that in her haste she had put the lizard in, head downwards, and the poor little thing was waving its tail about in a melancholy way, being quite unable to move. She soon got it out again and put it right. Not that it signifies much, she said to herself, I should think it would be quite as much use in the trial one way up as the other. As soon as the jury had a little recovered from the shock of being upset, and their slates and pencils had been found and handed back to them, they set to work very diligently to write out a history of the accident, all except the lizard, who seemed too much overcome to do anything but sit with its mouth open, gazing up into the roof of the court. What do you know about this business, the king said to Alice? Nothing, said Alice. Nothing whatever persisted the king. Nothing whatever, said Alice. That's very important, the king said, turning to the jury. They were just beginning to write this down on their slates, when the white rabbit interrupted. Unimportant your majesty means, of course, he said in a very respectful tone, but frowning and making faces at him as he spoke. Unimportant, of course, I meant, the king hastily said, and went on to himself in an undertone. Important, unimportant, unimportant, important, as if he were trying which word sounded best. Some of the jury wrote it down, important, and some unimportant. Alice could see this as she was near enough to look over their slates. But it doesn't matter a bit, she thought to herself. At this moment the king, who had been for some time busily writing in his notebook, called out, Silence! and read out from his book, Rule 42, all persons more than a mile high, to leave the court. Everybody looked at Alice. I'm not a mile high, said Alice. You are, said the king. Nearly two miles high, added the queen. Well, I shan't go at any rate, said Alice. Besides, that's not a regular rule, you invented it just now. It's the oldest rule in the book, said the king. Then it ought to be number one, said Alice.  Consider your verdict, he said to the jury in a low, trembling voice. There's more evidence to come yet, please, your majesty. said the white rabbit, jumping up in a great hurry. This paper has just been picked up. What's in it? said the queen. I haven't opened it yet, said the white rabbit. But it seems to be a letter written by the prisoner, too, to somebody. It must have been that, said the king, unless it was written to nobody, which isn't usual, you know. Who was it directed to? said one of the jurymen.  In fact, there's nothing written on the outside. He unfolded the paper as he spoke, and added, It isn't a letter after all. It's a set of verses. Are they in the prisoner's handwriting? asked another of the jurymen. No, they're not, said the white rabbit. And that's the queerest thing about it. The jury all looked puzzled. He must have imitated somebody else's hand, said the king. The jury all brightened up again. Please, your majesty, said the naive. I didn't write it, and I can't prove I did. There's no name signed at the end. If you didn't sign it, said the king, that only makes the matter worse. You must have meant some mischief, or else you'd have signed your name like an honest man. There was a general clapping of hands at this. It was the first really clever thing the king had said that day. That proves his guilt, said the queen. It proves nothing of the sort, said Alice. Why, you don't even know what they're about. Read them, said the king. The white rabbit put on his spectacles. Where shall I begin, please, your majesty? he asked. Begin at the beginning, the king said gravely, and go on till you come to the end. Then stop. These were the verses the white rabbit read. They told me you had been to her, and mentioned me to him. She gave me a good character, but said I could not swim. He sent them word I had not gone. We know it to be true. If she should push the matter on, what would become of you?  They all returned from him to you, though they were mine before. If I or she should chance to be involved in this affair, he trusts to you to set them free exactly as we were. My notion was that you had been, before she had this fit, an obstacle that came between him and ourselves and it. Don't let him know she liked them best, for this must ever be a secret kept from all the rest, between yourself and me. That's the most important piece of evidence we've heard yet. Said the king, rubbing his hands. So now let the jury, if any one of them can explain it, said Alice. She had grown so large in the last few minutes, that she wasn't a bit afraid of interrupting him. I'll give him sixpence. I don't believe there's an atom of meaning in it. The jury all wrote down on their slates. She doesn't believe there's an atom of meaning in it. But none of them attempted to explain the paper. If there's no meaning in it, said the king. That saves a world of trouble, you know, as we needn't try to find any. And yet I don't know. He went on, spreading out the verses on his knee, and looking at them with one eye. I seemed to see some meaning in them, after all. Said I could not swim. You can't swim, can you? He added, turning to the nave. The nave shook his head sadly. Do I look like it? He said, which he certainly did not, being made entirely of cardboard. All right, so far? Said the king. And he went on muttering over the verses to himself. We know it to be true. That's the jury, of course. I gave her one. They gave him two. Why, that must be what he did with the tarts, you know. But it goes on. They all returned from him to you. Said Alice. Why, there they are. Said the king triumphantly, pointing to the tarts on the table. Nothing can be clearer than that. Then again, before she had this fit. You never had fits, my dear, I think? He said to the queen. Never! Said the queen furiously, throwing an ink stand at the lizard as she spoke. The unfortunate little bill had left off writing on his slate with one finger, as he found it made no mark. But he now hastily began again, using the ink that was trickling down his face. As long as it lasted. Then the words don't fit you. Said the king, looking round the court with a smile. There was a dead silence. It's a pun! The king added in an offended tone, and everybody laughed. Let the jury consider their verdict. The king said for about the twentieth time that day. No, no! said the queen. Sentence first! Verdict afterwards! Stuffened nonsense! said Alice loudly. The idea of having the sentence first. Hold your tongue! said the queen, turning purple. I won't! said Alice. Off with her head! The queen shouted at the top of her voice. Nobody moved. Who cares for you? said Alice. She had grown to her full size by this time.  At this the whole pack rose up into the air, and came flying down upon her.  Wake up, Alice, dear! said her sister. Why, what a long sleep you've had! Oh, I've had such a curious dream! said Alice. And she told her sister, as well as she could remember them, all these strange adventures of hers, that you have just been reading about. And when she had finished, her sister kissed her, and said, It was a curious dream, dear, certainly. But now run into your tea. It's getting late. So Alice got up and ran off, thinking while she ran, as well as she might, what a wonderful dream it had been. But her sister sat still, just as she left her. Leaning her head on her hand, watching the setting sun, and thinking of little Alice, and all her wonderful adventures, till she too began dreaming after a fashion, and this was her dream. First, she dreamed of little Alice herself, and once again the tiny hands were clasped upon her knee, and the bright, eager eyes were looking up into hers. She could hear the very tones of her voice, and see that queer little toss of her head to keep back the wandering hair that would always get into her eyes. And still, as she listened, or seemed to listen, the whole place around her became alive with the strange creatures of her little sister's dream. The long grass rustled at her feet, as the white rabbit hurried by. The frightened mouse splashed his way through the neighbouring pool. She could hear the rattle of the tea-cups, as the March Hare and his friends shared their never-ending meal. And the shrill voice of the Queen, ordering off her unfortunate guests to execution. Once more, the pig-baby was sneezing on the duchess's knee, while plates and dishes crashed around it. Once more, the shriek of the Gryphon, the squeaking of the lizard's slate-pencil, and the choking of the suppressed guinea pigs, filled the air, mixed up with the distant sobs of the miserable mock turtle. So she sat on, with closed eyes, and half-believed herself in wonderland. Though she knew she had buts to open them again, and all would change to dull reality, the grass would be only rustling in the wind, and the pool rippling to the waving of the reeds. The rattling tea-cups would change to tinkling sheep-bells, and the Queen's shrill cries to the voice of the shepherd-boy. And the sneeze of the baby, the shriek of the Gryphon, and all the other queer noises, would change, she knew, to the confused clamour of the busy farmyard, while the lowing of the cattle in the distance would take the place of the mock turtle's heavy sobs. Lastly, she pictured to herself how this same little sister of hers would in the after-time be herself a grown woman, and how she would keep through all her riper years the simple and loving heart of her childhood, and how she would gather about her other little children, and make their eyes bright and eager with many a strange tale, perhaps even with the dream of Wonderland of long ago, and how she would feel with all their simple sorrows, and find a pleasure in all their simple joys, remembering her own child life and the happy summer days. The End of Alice's Adventures in Wonderland by Lewis Carroll


Our operation is comprised of owned land and leased land, and then we also run on two allotments on the Grand River National Grasslands. Our permits on the Grand River National Grassland are summer permits. They're from the first part of May till the end of October is the outside dates of the permit. On one allotment, we run a compressed season. So instead of five and three-quarter months, we only run on there for two months with more numbers. During this part of the summer, all of our cows are on national grasslands. Starting back in the 30s, the government launched the land utilization program to respond to some economic and agricultural impacts the country was facing. And that was the result of the Great Depression and the Dust Bowl era. That program was rolled out to start reacquiring some of those sub-marginal lands at that time. The people that went broke in the Depression could get out of here or to get at least something for their land and to move on. And so the government started a program where they would buy up these small places and make bigger pasture units. I think over the course of history, I think around nine or ten million acres was reacquired in that time. And shortly after in the 1930s, the Solar Conservation Service initially took the role of managing those lands up until 1954. And at that time, the Forest Service took over managing a large share of those land utilization project lands. In 1960 is when 3.8 million acres of those lands were then designated as the national grasslands. And so at that time there was, I believe, 18 national grasslands and present day there are 20 national grasslands. And so under USDA Forest Service, we managed numerous national forests but only 20 national grasslands. My dad moved into this area in the late 30s and he took advantage of this government permit while you had to be in the grazing district to be able to use that permit. So it wasn't just for everybody. The idea was to have everybody around close to it that maybe would have had a chance to buy the land to have a chance at using the government permit. And so my dad, even though he didn't have the number of cattle to utilize the whole permit, he did pay a non-use for a number of years until he got his herd built up to run on the government land. The place that I grew up on in Southeast Aleman, South Dakota, I came back to the ranch after I graduated college and just could never quite leave. It was just, it was just the place that I needed to be. So thankfully Drew showed up in town and he decided to stay around and we're still here. We have three little girls, Sadie, Emmy and Henley. I married my wife in 2010. We started ranching full time here in South Dakota in 2011. A lot of this place that we're on has had been farmed in the past. A lot of it had been ceded back to perennial forage. We have pretty well ceded the rest of it back to perennials. There's only 30 acres of ground that is being farmed right now. We've done a variety of different things with that. Some of it we hay. Some of the crop line that's been ceded back has only been grazed since it's been ceded back. We do a lot of bale grazing. We kind of started out as a trial. We just left the bales in the field after we hayed and then we strung a polywire and moved the cows every four days to a week at a time through the winter. Through adding, not just taking off the land but adding something back is just amazing to see the production and the amount of diversification that happens and then the bright greenness that happens around the hay piles where we bale graze. You're seeing a lot more native western wheatgrass is something that usually likes to crop up first when you're trying to heal the land. One of my goals is to be able to have a cow on every acre to be able to graze every acre that we have. We're not quite there but that's kind of one of our goals is every acre is grazeable. These grasslands need grazing and that's how we maintain its health and improve its health. I'm proud of the fact that we can live on the same place as my parents and get along because that's not always the case. Dad's been very gracious in how we handle our operations where he knows that he needs to operate his own cattle his way and we need to make our decisions but yet we're still there to help each other and it's worked really well that way. You just kind of follow where life takes you. I mean I had ambitions of a career off the ranch. The opportunity just kept coming back to be on the ranch so that's the way it turned out. And of course I'm glad that our family is willing to take the reins and move on into the future with it.


Hey beauties I'm Bianca Renee and you're watching Bianca Renee Today and today we're gonna be talking about the under eye area making everything lifted tight wrinkle free. You might be thinking I'm too young for this video I don't have any wrinkles then you're exactly who needs to be paying attention because you actually want to prevent wrinkles from coming versus getting them and then trying to get rid of them. So whether you don't have them or you do I have something for you. Bars. Clarence Total Eye Lift made to keep everything lifted and smooth. Today's video is sponsored by Clarence so thank you for sponsoring this video and supporting my channel but before I even agreed to make this video I did do some research and I started looking at the reviews for this product because you know the internet comment section is always going to tell you how they feel whether they want to hurt your feelings or not but I saw comments like I got a free sample tried it for a couple days fell in love instantly went out and bought the full bottle. I also read finally an eye cream that actually does what it says it's going to do so I was like okay I'm getting a lot of positive feedback here let's check it out. Now I've been trying this for maybe one or two weeks now and my favorite thing about it is that it claims to give you results in 60 seconds. Most skin care you have to wait like a month to truly see any type of results and I'm pretty impatient so the fact that I can try this on camera and show you an instant before and after I was okay let's do this. So that's what I'm going to show you today because it's a very specific way to apply this to your face you can't just you know rub it all on all willy nilly like your other basic eye creams. No this one you got to be very strategic so I'm going to show you exactly how to apply it. Before I apply it let's talk about this beautiful packaging. Red is my favorite color so one time for the packaging and is made with airless technology to help preserve the efficiency of the formula. This eye cream was made with 94% natural ingredients according to the box that includes two potent plant extracts to help you to promote an instant lift effective on the eyelids and will visibly smooth fine lines and wrinkles around the eye contours. It has organic harangana or is that right extract which helps replenish and visibly tighten the skin. It has Cassie wax that is known for its visibility for smoothing and supportive properties and the eyes will look more open and lifted. It has plant caffeine, horse chestnut and albezia extract to help promote a less fatigued look by reducing the look of dark circles, shadowy eyes and puffiness. Eyes will appear fresher, rested and more radiant. I need all of that because you guys follow me on instagram you know that I'm notorious for staying up late. I'm always up till around 2-3 a.m editing or just on my phone scrolling aimlessly hanging out friends who knows and I also have a child on top of that so sleep is something that I definitely don't get enough of that's why I need an eye cream in my life to help make me look more awake even when I'm not but now let me show you how to properly apply the total eyelid so what you're gonna want to do is open up the beautiful red packaging put a couple like one maybe two pumps and then you're going to rub it together on your fingers to warm up the product once you warm it all up you're gonna press it onto your skin so you're gonna go one two three four and then on your brow bone one two three four truly pressing the lightweight formula into your skin the final step is to drain this gentle pressing motion in between your eyebrows will help stimulate lymphatic drainage which helps remove toxins from your skin to depuff this is also good for your lashes helping them grow and look fuller so we're gonna do one little pass on the eyelids as well this is how we do it after 60 seconds these are my results so as you can see from these before and after photos I look a little bit more awake and the photo on the top versus the photo on the bottom it's very subtle but I do see a difference I also feel a difference after I use it like my skin feels just a little bit tighter and I just feel like it keeps me looking more awake so those are the type of results I see in 60 seconds imagine how well it's going to be for your skin if you use it every morning and every night over and over and over again eventually it's going to keep everything really nice and tight and actually help prevent those wrinkles if you had to choose between morning or night I would suggest using in the morning so you could just look more awake while you're actually out and about doing things and it works well under your makeup but I have been using it every morning and night to really get the most benefits and it's also super important to be applying it correctly because you don't want to splurge on a really effective product and then not apply it correctly and not get the full benefits and this eye cream is suitable for all ages all skin types even if you wear contacts and even if you have sensitive eyes so if you are looking for an eye cream that's going to help with anti-aging wrinkles dark circles puffiness crows feet and also help your lashes this is going to be the one you're going to want to grab because people are seeing real results in as fast as 60 seconds so if you want to add this to your daily routine I'll put a link in the description box you guys can get one today if you enjoyed this video make sure to give me a thumbs up and subscribe I post new videos every week you also go follow me on instagram tick tock and twitter at miss beyond grenade i'll see you guys next time thanks for watching beyond grenade today


A warm welcome to the 41st session in the first module of the course signals and systems. In this module, we shall first discuss the typical kind of linear shift invariant system that we encounter in many different situations as far as the input-output description goes. Let us now come to it. The typical linear shift invariant input-output description. Now, let us recall the example that we began with, the RC circuit. We had xt, the input voltage and yt, the output voltage here. And we said that yt plus the current multiplied by the resistance. The current is c times dy t dt multiplied by the resistance, gives you the voltage across the resistance and the capacitor voltage plus the resistor voltage is equal to the input voltage. This was what we called the system description for the RC sub. Of course, we could always abbreviate, we could say RC is equal to tau and therefore, we could replace this by yt plus tau times dy t dt is xt. Now, what is the typical form that we see here? The typical form is the following.  So, you could have, let us say, b0 times xt plus the first derivative multiplied by a suitable constant. All this is equal to yt, so yt equals all of this. This is a typical form. In fact, this form occurs very frequently in realistic systems, whether they be electrical systems or mechanical systems or hydraulic systems or abstract systems. So, of course, we call these differential equations, but these are differential equations of a special kind. Let us identify what that kind is. So, the first thing we see is the coefficients are constant, all these and further the equation is linear, linear in all term. So, this is what is typically called a linear constant coefficient differential equation and this is a typical form and we can abbreviate it by L C C D E or L double C D E where D stands for differential. Now, let us look at a typical discrete system. In fact, in a typical discrete system, we have the same abbreviation, but a different interpretation. So, let us see. Typical discrete LSI system or system description to be more precise. Here the output yn is equal to some a1 times y of n minus.  We do not want to go into that right now when we have causal system, typical causal system description would look like this. So, here again, these coefficients are constant and the equation is linear in all terms. So, here again we have an L double C D E. The only change is that we are talking about a linear constant coefficient difference equation, difference not. There it was differential, here it is difference. So, the output at a particular n is a linear combination of the past outputs at n minus 1, n minus 2 up to n minus capital N and the present input xn and the past inputs xn minus 1 up to xn minus capital N. So, you are involving capital N past outputs and capital N past inputs, including the current input to calculate the current output and all these are involved linearly. Now, I am mentioning this, we are not going further right now to analyze these systems. So, we have done little segments of it here and there in our discussion. I am mentioning this at this time because we are going to see these systems in greater detail in the second course later. But at the moment, we must know in the first module, what is the typical system description that we often encounter and these are the two systems, you know it is very easy to remember L double C D E, linear constant coefficient differential equation for continuous independent variable and linear constant coefficient difference equation for discrete independent variable. Now, with this, we have come to a good point in our whole discussion of signals and systems. We began with the meaning of abstraction going from many systems which have similar input output behavior to one abstraction that describes all of them. We saw that in the earlier part of the course and then we realized that from the abstraction one needed to ask certain questions in the context of the abstraction which leads to properties of systems. So, we identified additivity, homogeneity, shift invariance, of course then we also had the notion of memory or lack of memory, causality and finally stability. So, main properties were additivity, homogeneity or scaling, scaling of the dependent variable I mean, shift invariance, causality and stability and an auxiliary property was memory. We said that additivity, homogeneity and shift invariance often come together in many of the system models that we wish to analyze and make the system what is called linear and shift invariant and since then we have been talking just linear shift invariant. We have been doing all kinds of things with linear shift invariance system and there is a reason for it. I also explained the philosophical reason. Let us just quickly recapitulate because we are now going to move on to a slightly different trail of discussion. You see, additivity essentially says that if I have two different things happening to the system, I can analyze the effect of the system on the two different things separately and then put those effects together to see the effect of the things happening together. Homogeneity says that if I step up or step down, the output of the effect is also stepped up or stepped down, so it tells us you know whether the system behaves the same way at all scales. If I increase the input, but keep the nature of the input the same, does it retain the nature of the effect even though the quantum of the effect might increase and shift invariance is essentially a statement of whether the system behaves like that forever. If the system behaves like that for some time and then loses certain behavior, then it is not shift invariant, so does the system retain its properties forever, so does the system retains input-output relationship forever, that is what is essentially being tested when we talk about shift invariance. In a simple model, we would like both of these things to happen. We would like the combined effect due to two individual causes to be the same as the two individual effects put together and we would like the effect to increase as the cause increases in the same proportion. And we would like this to continue, the system to continue behaving as it does for as long as we wish to, that is what linearity and shift invariance means. And once you make an assumption of linearity and shift invariance, then you have the very simple one experiment description of the system, namely give an impulse, now in fact you know that impulse was itself an interesting idea. We brought in the idea of an impulse in continuous time which required us to go to generalized functions and we also had the notion of an impulse which is very easy to understand in discrete time. It was just a sequence because one at one point and zero everywhere else. So the impulse response told us everything about linear shift invariant system, whether it was continuous or discrete independent variable. And we also saw you know that when we proved this, the proof was constructive meaning I could tell you how I could obtain the output from the input if I were given the impulse response. The how came through an operation called convolution. We looked at various properties of convolution, we have been discussing that for quite some time in this module. We looked at several important properties being commutativity and associativity and we worked out a few examples of convolution, both for continuous and for discrete time. In fact we brought in what we call the trained platform analogy to explain convolution. Now if we said the impulse response told us everything about the linear shift invariant system, we should also be able to talk about the causality and the stability of the linear shift invariant system by looking at the impulse response and yes indeed both for continuous and discrete time, if and only if the impulse response was zero all the way from minus infinity to time or variable equal to zero could we say the system is causal. So causality was equivalent to the impulse response being absent up to zero from minus infinity and present if at all afterwards. And stability corresponded to absolute summability or absolute integrability of the impulse response depending on whether you are talking about discrete systems or continuous variable systems. For discrete independent variable systems LSI system being stable is equivalent to the impulse response being absolutely summable and for continuous independent variable systems LSI system being stable is equivalent to the impulse response being absolutely integrable. We proved this. We have come to a good point where we can now conclude the discussions in this module. In this module we were looking at signals and systems in their natural domain in the domain in which they occur naturally which we call the independent variable. What we now need to do is to evolve the whole idea of looking at signals and systems in a domain different from their natural domain because we could probably try putting on glasses or taking an instrument and looking at the system. An instrument which gives us certain insights which brings us some knowledge of the system that we did not have when we were looking at the system in the natural domain. And we will take the first step in that direction in the next module of this course. So it is with pleasure that I conclude this first module and we shall soon proceed to the second module where we will look at one of the steps in going to what we call a transform domain namely the Fourier transform. Thank you.


Hello and welcome to daily debrief brought to you by People's Dispatch, I am Shriya. In today's episode, Taiwan's President leaves for a 10-day trip to Central America. We also talk about UN fact-finding missions report on human rights violations in Libya and finally a history is made in women's cricket as the inaugural edition of Women's Premier League comes to an end. On Wednesday, March 29, Taiwan's President leaves for an official visit to Central American countries of Guatemala and Belize with stopovers in the United States, where she is expected to deliver a speech in New York. Taiwan's President's visit comes at an interesting time and shortly after Honduras announced opening ties with China, ending the long diplomatic relationship between the two countries. Guatemala and Belize also happened to be the only Central American nations left, which formally recognized Taiwan's sovereignty. Anish joins us now with latest updates on the story. Welcome back to this episode Anish, glad to have you with us. So why is this visit happening? Well, at this point in time, Taiwan, you know, what it represents itself, which is the so-called the Republic of China, is fast-losing allies around the world. It has now with Honduras' exit and it's reverting its relationship back to the People's Republic of China, which is, you know, the bigger one. Taiwan is definitely just trying to, you know, keep its allies intact and Guatemala and Belize, the country that Tsai Ing-wen is going to visit, are the last of the 13 countries now left that still recognizes Taiwan as the Republic of China. Now, the issue is that if it was just, you know, Taiwan, Taiwan's President visiting one of these countries that still recognizes it diplomatically speaking, that would have been fine. It is something, but China's issue here is the fact that it is happening with a transit in New York on her way to these countries and a transit through Los Angeles on her way back to Taiwan. So in both cases, there's definitely a significant amount of time left for her to make visits and even meet with officials in the United States. And that is the red line that China does not want the Taiwanese President or the United States to cross. Now, there are already rumors about that Tsai Ing-wen is scheduled to meet with Kevin McCarthy, the House Speaker of the US Congress, House of Representatives. And it might happen in Los Angeles or her transit through Los Angeles, so-called transit. So this is definitely something that is going to raise alarm bells because for one, this is not just some, you know, belligerent, two belligerent nations, why for influence? This is a this is a matter of basically sovereignty over Taiwan and over the rest of China as well. As far as China sees, it is its territory is the same as true for Taiwan, which through its constitution claims a whole of China for itself. So in both the cases, if you abide by the one China policy, you're recognizing sovereignty of one over the other as well by default. But the United States is not ready to go through that and is making these provocatives moves that is going to only heighten tensions in the region. Right, Anish, and you mentioned also about the significance of the, you know, the US stopovers and what, how is it likely to change the relationship that Taiwan and US have shared so far? I mean, there is a lot changing in the region. Will this relationship also change? It is very difficult to say what the United States intends to do with Taiwan. Obviously, we have seen over the past few years, under the Trump administration, now continued under the Biden administration, the US state machinery, the foreign policy machinery has taken this sort of a stand whereby it is trying to pretend that Taiwan is some kind of an independent nation in and by itself and that it has. And obviously, we have also seen recent legislations being passed by the US Congress that will necessitate any kind of US intervention, even military intervention, in case there is an armed conflict, in case an armed conflict breaks out between US, sorry, China and Taiwan. So, obviously, they are trying to change this relationship. But to what end is quite unsure? Obviously, the US officials are not forthcoming about what they think about Taiwan. They're not very clear if they support any kind of an independent or independent Taiwan as certain reactionary groups in Taiwan would like to go for or it thinks that Taiwan, the so-called Republic of China is the true representative of the whole of China. So, these factors need to be spelled out, but the US is refusing to do so in the kind of especially important because at a time of such brinkmanship, if you're going to fight for a cause, it has to be a very clearly defined one, but in the case of Taiwan, there is nothing of that sort. So, the relations we have, whether it is going to change any kind of relations between US and Taiwan and by extension China, we have to wait and see if Kevin McCarthy is going to meet with Tsai Ing-wen to begin with. But if it doesn't happen, obviously, it's a different thing, but if it does happen, we are going to see a very spiraling case of tensions in the region and we do not know what is going to be at store in the coming days. Right, thank you so much for joining us for this episode, Anish. The UN appointed independent fact-finding mission in Libya released a report on Monday, March 27 on the human rights violations that have taken place in the country since 2016. According to investigators, the European Union and its member countries have provided monetary and material aid to Libyan authorities and armed militias that have been responsible for widespread human rights violations including war crimes and crimes against humanity. We now joined by Abdul from People's Dispatch who has more details on this story. Welcome to this episode, Abdul. First off, can you tell us what are the details of this UN report? The report basically is quite detailed in the fact that it claims that more than 100 victims and the witnesses have been interviewed and it also had talked with different officials on the ground and with that the report talks about various parts of human rights violations, various kinds of human rights violations in Libya. It says that the Libyan authorities have been involved in arbitrary detention, torture, murder, rape, even sexual slavery for women and most of these things are primarily related to the treatment of the migrants. As it is well known now that how Libya has become a kind of a transit point for people from different parts of the world coming there in order to kind of migrate further to European countries and this is primarily because of the chaos and anarchy which has been created because of the Nettolite invasion in 2011. So since then there is a systematic, you can say, there has been no system, report indicates that there has been no system in place in Libya which basically can implement rule of law. So because of the absence of rule of law, absence of authorities which have influenced all over Libya, there are regional forces and all the regional forces have basically used their military power to make basically oppress whatever descent is emerging in Libya and to make money out of the migration crisis. So this is the primary finding of the report and it basically talks about how the detention centers for migrants in particular are, have been the primary space where different kinds of human rights violations are happening. For example, in Tripoli, even in Tripoli, capital Tripoli, there were reports about how the conditions, migrations are kept in are really bad, there is no food, enough food available for them, there is no sanitation, overcrowded sales, sales are there in which most of, in some times, migrants are, there are reports of migrants dying because of suffocation, because of starvation, because of the health related issues. So the report basically clubs all these findings in last five or six years and says that the Libyan authorities have been responsible for war crimes and crimes against humanity. So it is basically, it talks about the severity of law and order situation in Libya and talks about how it can be improved as well. Right and Abdul there is also an element in the report about the European Union's simplicity, can you tell us what is that about? Well, that is the most important part of the report, as I said earlier that Libya has become a kind of hub for human trafficking where people from different parts of the world are brought in with the, with the, with promises that they will be, there will be a facilitation of their further migration into European Union, given the fact that most of the countries in Africa and in Asia are suffering from economic crisis, from wars of different kinds, most of these wars are the results of the imperialist interventions, particularly in Africa. So people are trying to find better ways of living. That particular condition is exploited by the human traffickers and a large number of people are brought in Libya. The report says that within one year from last March till this, last April till this March means April 2022 till March 2023, they found that around 400,000 such migrants were available, were present in Libya. So it says the scale, the wide scale at which this particular thing is happening. But Europeans have a very strict border control laws. They have invested heavily in their front-ex which basically controls the movement of migrants through the sea and they also provide a lot of money to Libyan authorities to prevent any attempt of sea crossing, which basically leads to a large number of deaths in sea because boats which carry the migrants across the Mediterranean Sea are stranded there. Sometimes they are overcrowded and therefore they sink in the sea and so on and so forth. So every year, thousands of migrants die in this because of the European border control policies and their funding to the Libyan authorities. The report also says that the detention centers in Libya, different parts of Libya, basically and the forces which basically maintain these detention centers are funded by European countries. They are also provided weapons and boats and other equipment to control the movement of people into the sea. It means in direct or indirect way, European Union and the European countries have been involved with the Libyan authorities knowing very well that these Libyan authorities are involved in heinous criminal activities and in violations of human rights of people. Despite knowing that, they have been basically continued. They have continued their financial support and support through the equipment to Libyan authorities. Thank you so much for joining us, Abdul. In our final story of this episode, a landmark development takes place in the world of women's cricket. The inaugural edition of Women's Premier League concluded on Sunday, March 26, heralding a new beginning for the game and its players. Senior journalist Sharda Ugra now joins us for the story. Glad to have you with us for this very special episode Sharda and my first question is that this is the biggest cricket league in terms of the audience, audience receptions and it's been taking place in other countries, for example, US, Australia. But it took a lot of time for a women's version of the Indian Premier League to launch here in India. What is the context and why did it take for such a long time? It's very difficult to give an official answer to why it took a long time. It just tended to be a little bit of sluggishness on the part of the administrators. They will say that look, there was a court case that was going on and therefore we couldn't get things into motion, but they did manage to hold the IPL regardless of court cases and so on. So there has always been, from the BCCI until about say 2013-2014, there had always been a little bit of lack of interest in the women's game. After 2013-2014, you see that the contracts have been introduced from the first time. You have women's academies that are functioning. You get to know about them. But this whole league happened. This is my theory. It is based on nothing but just a journalist's mind. At the moment, the Pakistan Cricket Board announced that they are going to start a Pakistan Super League for the women. I think there became a little bit of unease and almost urgency on the part of the BCCI to say listen, we need to get the IPL started. There had always been interest in it from franchises in the IPL that wanted to have women's teams. They held this women's challenge three, four matches for the last two, three seasons, just almost like cursory, a little bit of what shall we call it breadcrumbs, which even the women were very happy to take part in and just share the experience. So when this actually began, if you look at it, it literally took a couple of months for everything to happen very quickly one after the other. They said they are going to announce it. They released the franchises. They got the media rise. They announced the franchises that were there. They did the bidding. They got the sponsors and the tournament was done in three weeks. So look at the speed with which it's happened and you're thinking that if this could be done so quickly now, why not earlier? Right. And for a first tournament, can you also highlight for us what were some of the positives that can be positive takeaways from this first tournament and how are they likely to shape the game in the coming future? I think the first tournament, the biggest takeaway for the women's game is the fact that they had people come to watch and take interest in and follow on television. We are not sure what the exact numbers are. I mean, some numbers have been shared. They've said 50 million. You know, you don't know whether that's a combined viewership or what it is. But incredible numbers, incredible popularity in the sense of the fact that people are coming to the stadium. They'll say, oh, that's because the tickets are free. But ticket buying in India is such a complicated for a cricket match is such a complicated experience that when it was sort of streamlined, you look at the way people turned up to watch. The support from the Mumbai fans was incredible. That was the big, the quality of the cricket that we saw was also excellent. There were a lot of women involved in the game itself. You had umpires, the match referees that were there. So there was, it was almost a women's ecosystem was working alongside the BCCI's male sort of working system. And another thing it showed you, you know, look at the quality of the turnaround with which you're able to do this event. It's not easy to do it, even though they had restricted it to two cities and one city, two venues and three weeks.  So those are the big ones. Very interesting to watch on television, the kind of advertising that it generated. You had ads that were specifically targeted, they're featuring women that were there. Whether it was about sunscreen, whether they had cars, whether they had things about jewelry, gold, big ads from the gold council. So an interesting stream of ads which shows you that there is another parallel market for women's sport. You know, and it doesn't have to be something unlike what happens in, I mean, that's different. I mean, it could be different in terms of a material, what is in front of you, but it's not any less. What will always happen now will be the comparison. Oh, look at the men's IPL, it's crazy, it's crazy, but it's been going for 15 years. And why the women's IPL could have been started earlier, we have no idea. If the women would not have made the 2017 final of the 50 World Cup in England, I don't think any of this would have happened. But I think that that has been one catalyst that just sort of set things in motion. Really good, really good outcomes, some really good performances, some sort of not so great performances from particularly star Indians, but a really good feel good about this event all pretty much all around. Thank you so much for joining us, thank you so much for your time. And that's all we have for today, for more such stories, keep following peoplesdispatch.org. You can also follow us on Facebook, Twitter and Instagram.


You surely know the Taylor expansion with which we can approximate function f at a point by a simpler Taylor series. The more terms we take in the Taylor series, the better the approximation becomes in the vicinity of the chosen point. As you can see, the Taylor series represented by this gray function is a good approximation of the function f in the vicinity of the expansion point. However, if we move further away from the point, we see that the Taylor series is not a good approximation there. So the Taylor expansion is a method with which we can approximate a function only locally. But if we care about approximating a function on a whole interval, then we need a Fourier series of the function. As we will see, the Fourier series is a linear combination of simple periodic basis functions, like cosine and sine, or complex exponentials, which in some can approximate the function f within an interval. In the following we assume an interval of the length L. We can represent a vector living in an n-dimensional vector space as a linear combination of basis vectors eK spanning the vector space. You should know this from linear algebra. By the way, this is a modern, much better notation for the old sum sign sigma. With the help of a basis, we can represent every possible vector in this vector space. Here vk are the components of the vector in the chosen basis. The components are not unique. By choosing a different basis, the vector will have different components. We can also apply this concept of linear combination to infinite-dimensional vectors. A function f of x can be interpreted as such an infinite-dimensional vector, which we can then represent as a linear combination. We interpret the function values f of x0, f of x1, f of x2, and so on up to f of x0 plus L as components of f. Here we cheated a bit because the argument x is a real number, and theoretically there are infinitely many values, for example between x0 and x1. Nevertheless, this is still a good way to think of a function as a vector with infinitely many components. In a linear combination for a function, the basis vectors are called basis functions. In optics, the basis functions are also called Fourier modes. The components vk of a finite vector become Fourier coefficients fk tilde if we represent a function and not a finite vector as a linear combination. If we represent a function as such a linear combination of basis functions, then we refer to this sum as a Fourier series of f. You can determine the Fourier coefficients in the same way as you determine the vector components in linear algebra. How does this work again in linear algebra? To get the k-th component of a finite-dimensional vector v, we have to form the scalar product between the k-th basis vector and the vector v. The scalar product of two finite-dimensional vectors is the first component of the k-th basis vector multiplied by the first component of v plus the product of the second components plus the product of the third components and so on. We can write down the sum more compactly with a summation sign. Here we sum over the index j. If we do not work with finite-dimensional vectors but with functions, then we have to form the scalar product between the k-th basis function and the function f to get the k-th Fourier coefficient of f. To indicate that we are working here with an infinite-dimensional vector space, we call this operation not a scalar product but inner product and write it in bracket notation as physicists. Let's first write out the inner product analogously to the finite-dimensional case. The only difference is that we interpret the components of the function as function values, f of x0, f of x1 and so on. We also interpret the components of the basis functions as function values. Here we sum up to the point x equals x0 plus l because Fourier series in general can only be constructed for functions in a finite interval. But don't take this summation mathematically too seriously because we only want to motivate the formula for the inner product for functions. We can compactly write the summation over the function argument with a sum sign. And here we have a problem. How should this summation work at all for a function? The summation index x is a continuous variable in the case of functions. Even between the points x0 and x1, there are theoretically infinitely many other function values which we have simply omitted here. But we can easily eliminate this problem. Because we are dealing with a continuous summation here, we simply have to replace the sum sign with an integral. In order to use this inner product for complex valued functions f, we have to complex conjugate the first argument in the integral. If we would not complex conjugate it, this integral would not be a proper inner product in the case of complex valued functions because it would not satisfy the mathematical properties of an inner product. Therefore, never forget the asterisk. So, hopefully now you understand how to determine the Fourier coefficients and how this formula is obtained. You simply have to form the inner product of the function f with the basis functions. In other words, you have to calculate this integral. Let's move on to the basis functions. Which basis functions can we use for the Fourier series? All those that satisfy the properties of a basis. To call a set of vectors, or as in our case a set of functions, a basis, they must satisfy two conditions. First, the basis functions must be orthonormal. That is orthogonal to each other and normalized. Second, the set of basis functions must be complete. In other words, they must span the space in which the functions f live. A typical basis used in physics are the complex exponential functions 1 over square root of l times eikx. The factor 1 over square root of l ensures that the basis functions are normalized. For each different wave number k, you get a different basis vector. Maybe you have seen another basis for the Fourier series, like cosine and sine. As I said, we are free to choose a basis. Here we just choose complex exponentials as a basis, because they can be written nice and compact, especially for explaining the Fourier series. The Fourier series in this basis of exponentials would then look like this. Let's look at the first property of basis functions, orthonormality. We can check the orthonormality by taking two basis functions with k and k prime and forming the inner product. For the two functions to be orthonormal, their inner product, that is this integral, must yield 1 if k equals k prime. In other words, it yields 1 if we take the inner product of a function with itself. And the inner product must yield 0 if k is not equal to k prime. So if we really take two different functions, we can combine the two cases into one equation if we use a chronicle delta. The second property that the set of function must fulfill in order to be a basis is the completeness relation. With this relation, we make sure that we can represent every function as a linear combination of the chosen basis functions. We can easily show that the set of exponential functions is orthonormal and complete. However, only under one condition. The exponential functions must be l-periodic if we want to represent a function in the interval of the length l as a Fourier series. l-periodic means that the value of the exponential function at the beginning of the interval is equal to the value of the exponential function at the end of the interval. This periodic boundary condition has the consequence that the wave number k cannot be arbitrary but can only take the values 2 pi times n divided by l, where n is an integer. The proof of orthonormality and completeness does not bring much insight, so I'll leave the proof out of the video and you'll find it in the related lesson, linked in the video description. Now you should have a solid intuitive understanding of a Fourier series and how to theoretically construct it for a function. Let's do an example. Let's look at a sawtooth function between 0 and 1, which is defined piecewise as minus x in the range between 0 and 1 half and is 1 minus x in the range between 1 half and 1. The total interval length is l equals 1. Thus, the normalization factor for the exponential basis functions is also 1. When determining Fourier series, we always have to do two things. First, choose a basis, we have already done that, and insert it into the Fourier series. Second, calculate the Fourier coefficients and insert them into the Fourier series as well. You determine the kth Fourier coefficient with the inner product between the kth basis function and the sawtooth function. In other words, we need to calculate this integral. Since the sawtooth function is defined piecewise, we split the integral. In the first integral, we insert minus x and integrate between 0 and 1 half. In the second integral, we put 1 minus x and integrate between 1 half and 1. With integration by parts or with an integral calculator, you can solve the two integrals. As a result, you get 1 divided by i k times e to the power of minus i k over 2. As we know, the wave number k takes only discrete values 2 pi n divided by l. In our case, l is equal to 1. If we insert concrete values for the integer n, we get the individual Fourier coefficients we are looking for. Thus, we have determined all Fourier coefficients for the chosen basis. Let's just insert the Fourier coefficients into the Fourier series and combine the two exponential functions. We are done. This is the Fourier series for the sawtooth function in the considered interval. With this Fourier series for the sawtooth function, we basically got two advantages. First, we can stop the summation in the Fourier series at a certain n value and get an arbitrarily good approximation for the sawtooth function. For example, here you see an approximation where we summed up to n equals 1. But the approximation becomes even better if we sum up to n equals 20. The second advantage is, since we have determined the Fourier coefficients, we know which building blocks the sawtooth function is composed of. This breaking down of the function into individual components is called Fourier analysis. But we will take a closer look at that in another video. With this in mind, may the physics be with you.


Yes, as we've seen, studies have shown over and over again that health food store employees on average didn't know what the heck they were talking about, but maybe nobody does when it comes to supplements. Two North American studies were recently published, one in Canada, one here in the States, comparing the advice gotten from health food stores compared to community pharmacies. In Canada, research went in and asked questions like, will ginseng give me more energy? Will beta carotene help me prevent cancer? Will shark cartilage help cure my cancer? What percentage of visits to 192 different health food stores were researchers given advice considered accurate or at least fairly accurate based on the balance of available scientific evidence? 100% of the time? Half the time? No. 7% of the time. Pharmacists did about 10 times better. In the U.S. study, they got actors to walk into pharmacies and health food stores feigning classic symptoms of type 1 diabetes, excessive thirst and fatigue, unexplained weight loss despite overeating, peeing like crazy all the time. They asked the health food and pharmacy staff what they thought they had, what they should take, and whether they thought they should go see a doctor. Given that type 1 diabetes can be fatal if untreated, the answer to that last question is yes, they should indeed go see a doctor. And all 8 out of the 8 pharmacists got that right. Good for them. But only half. 6 of the 12 health food store employees thought it necessary. And 2 of the 6 naysayers explicitly advised against going to a doctor, the rationale being that the physician would, quote, just give them riddle in or missed the true diagnosis, which they felt was something like mold infestation or adrenal exhaustion, which luckily they had just the right supplements for at a bargain for only up to $200 a month.