CHAPTER XXII WOMEN TO WOMEN They came to the town and left Gerald at the railway station. Gudrun and Winifred were to come to tea with Birkin, who expected Ursula also. In the afternoon, however, the first person to turn up was Hermione. Birkin was out, so she went into the drawing-room looking at his books and papers and playing on the piano. Then Ursula arrived.  "'It is a surprise to see you,' she said. "'Yes,' said Hermione. "'I've been away at Aix.' "'Oh, for your health?' "'Yes.'" The two women looked at each other. Ursula resented Hermione's long grave downward looking face. There was something of the stupidity and the unenlightened self-esteem of a horse in it. "'She's got a horse-face,' Ursula said to herself. "'She runs between blinkers.' It did seem as if Hermione, like the moon, had only one side to her penny. There was no obverse. She stared out all the time, on the narrow but to her complete world of the extant consciousness. In the darkness she did not exist. Like the moon, one half of her was lost to life. Herself was all in her head. She did not know what it was spontaneously to run or move like a fish in the water or a weasel on the grass. She must always know. But Ursula only suffered from Hermione's one-sidedness. She only felt Hermione's cool evidence which seemed to put her down as nothing. Hermione, who brooded and brooded till she was exhausted with the ache of her effort at consciousness, spent and ashen in her body, who gained so slowly and with such effort, her final and barren conclusions of knowledge, was apt in the presence of other women whom she thought simply female, to wear the conclusions of her bitter assurance like jewels, which conferred on her an unquestionable distinction, established her in a higher order of life. She was apt, mentally, to condescend to women such as Ursula, whom she regarded as purely emotional. Poor Hermione, it was her one possession, this aching certainty of hers. It was her only justification. She must be confident here, for God knows she felt rejected and deficient enough elsewhere. In the life of thought, of the spirit, she was one of the elect, and she wanted to be universal. But there was a devastating cynicism at the bottom of her. She did not believe in her own universals, they were sham. She did not believe in the inner life, it was a trick, not a reality. She did not believe in the spiritual world, it was an affectation. In the last resort, she believed in Mammon, the flesh and the devil, these at least were not sham. She was a priestess without belief, without conviction, suckled in a creed outworn, and condemned to the reiteration of mysteries that were not divine to her. Yet there was no escape. She was a leaf upon a dying tree. What help was there then, but to fight still for the old withered truths, to die for the old outworn belief, to be a sacred and inviolate priestess of desecrated mysteries. The old great truths had been true, and she was a leaf of the old great tree of knowledge that was withering now. To the old and last truth then, she must be faithful, even though cynicism and mockery took place at the bottom of her soul. I am so glad to see you, she said to Ursula in her slow voice that was like an incantation. You and Rupert have become quite friends. Oh yes, said Ursula, he is always somewhere in the background. Hermione paused before she answered. She saw perfectly well the other woman's vaunt. It seemed truly vulgar. Is he, she said slowly, and with perfect equanimity. And do you think you'll marry? The question was so calm and mild, so simple and bare and dispassionate, that Ursula was somewhat taken aback, rather attracted. It pleased her almost like a wickedness. There was some delightful naked irony in Hermione. Well, replied Ursula, he wants too awfully, but I'm not so sure. Hermione watched her with slow, calm eyes. She noted this new expression of vaunting. How she envied Ursula a certain unconscious positivity, even her vulgarity. Why aren't you sure? she asked in her easy sing-song. She was perfectly at her ease, perhaps even rather happy in this conversation. You don't really love him? Ursula flushed a little at the mild impertinence of this question. And yet she could not definitely take offence. Hermione seemed so calmly and sanely candid. After all, it was rather great to be able to be so sane. He says it isn't love he wants, she replied. What is it, then? Hermione was slow and level. He wants me really to accept him in marriage. Hermione was silent for some time, watching Ursula with slow, pensive eyes. Does he? she said at length without expression, then rousing. And what is it you don't want? You don't want marriage? No, I don't, not really. I don't want to give the sort of submission he insists on. He wants me to give myself up and I simply don't feel that I can do it. Again there was a long pause before Hermione replied, not if you don't want to. Then again there was silence. Hermione shuddered with a strange desire. Ah, if only he had asked her to subserve him, to be his slave. She shuddered with desire. You see, I can't, but exactly in what does— They had both begun at once. They both stopped. Then Hermione, assuming priority of speech, resumed as if wearily. To what does he want you to submit? He says he wants me to accept him non-emotionally and finally. I really don't know what he means. He says he wants the demon part of himself to be mated physically, not the human being. You see, he says one thing one day and another the next, and he always contradicts himself. And always thinks about himself and his own dissatisfaction. Said Hermione slowly. Yes! cried Ursula, as if there were no one but himself concerned. That makes it so impossible. But immediately she began to retract. He insists on my accepting God knows what in him, she resumed. He wants me to accept him as an absolute, but it seems to me he doesn't want to give anything. He doesn't want real, warm intimacy. He won't have it. He rejects it. He won't let me think, really. And he won't let me feel. He hates feelings. There was a long pause, bitter for Hermione. Oh, if only he would have made this demand of her. Her. He drove into thought, drove inexorably into knowledge, and then execrated her for it. He wants me to sink myself, Ursula resumed, not to have any being of my own. Then why doesn't he marry an odourless? said Hermione in her mild sing-song. If it is that he wants. Her long face looked sardonic and amused. Yes! said Ursula vaguely. After all, the tiresome thing was he did not want an odourlisk. He did not want a slave. Hermione would have been his slave. There was in her a horrible desire to prostrate herself before a man. A man who worshipped her, however, and admitted her as the supreme thing. He did not want an odourlisk. He wanted a woman to take something from him, to give herself up so much that she could take the last realities of him. The last facts. The last physical facts. Physical and unbearable. And if she did, would he acknowledge her? Would he be able to acknowledge her through everything, or would he use her just as his instrument, use her for his own private satisfaction, not admitting her? That was what the other men had done. They had wanted their own show, and they would not admit her. They turned all she was into nothingness. Just as Hermione now betrayed herself as a woman, Hermione was like a man she believed only in men's things. She betrayed the woman in herself. And Birkin, would he acknowledge, or would he deny her? Yes, said Hermione, as each woman came out of her own separate reverie. It would be a mistake. I think it would be a mistake. To marry him, asked Ursula. Yes, said Hermione slowly. I think you need a man, soldierly, strong-willed. Hermione held out her hand and clenched it with rhapsodic intensity. You should have a man like the old heroes. You need to stand behind him as he goes into battle. You need to see his strength and to hear his shout. You need a man physically strong and virile in his will, not a sensitive man. There was a break, as if the pythoness had uttered the oracle, and now the woman went on in a rhapsody-weird voice. And you see, Rupert isn't this. He isn't. He is frail in health and body. He needs great, great care. Then he is so changeable and unsure of himself. It requires the greatest patience and understanding to help him. And I don't think you are patient. You would have to be prepared to suffer dreadfully. I can't tell you how much suffering it would take to make him happy. He lives an intensely spiritual life at times. Too, too wonderful. And then come the reactions. I can't speak of what I have been through with him. We have been together so long. I really do know him. I do know what he is. And I feel I must say it. I feel it would be perfectly disastrous for you to marry him. For you, even more than for him. Hermione lapsed into bitter reverie. He is so uncertain, so unstable. He worries and then reacts. I couldn't tell you what his reactions are. I couldn't tell you the agony of them. That which he affirms and loves one day. A little later he turns on it, a fury of destruction. He is never constant, always this awful, dreadful reaction. Always the quick change from good to bad, bad to good. And nothing is so devastating. Nothing. Yes, said Ursula humbly, you must have suffered. An unearthly light came on Hermione's face. She clenched her hand like one inspired. And one must be willing to suffer, willing to suffer for him hourly, daily, if you are going to help him, if he is to keep true to anything at all. And I don't want to suffer hourly and daily, said Ursula. I don't. I should be ashamed. I think it is degrading not to be happy. Hermione stopped and looked at her a long time. Do you? she said at last. And this utterance seemed to her a mark of Ursula's far distance from herself. For to Hermione suffering was the greatest reality, come what might. Yet she too had a creed of happiness. Yes, she said. One should be happy. But it was a matter of will. Yes, said Hermione listlessly now. I can only feel that it would be disastrous. Disastrous. At least to marry in a hurry. Can't you be together without marriage? Can't you go where and live somewhere without marriage? I do feel that marriage would be fatal for both of you. I think for you even more than for him, and I think of his health. Of course, said Ursula, I don't care about marriage. It isn't really important to me. It's he who wants it. It is his idea for the moment, said Hermione, with that weary finality and a sort of caesionnesse savet infallibility. There was a pause. Then Ursula broke into faltering challenge. You think I'm merely a physical woman, don't you? No indeed, said Hermione. No indeed, but I think you're vital and young. It isn't a question of years or even of experience. It is almost a question of race. Rupert is race old. He comes of an old race. And you seem to me so young. You come of a young inexperienced race. Do I? said Ursula. But I think he is awfully young on one side. Yes, perhaps childish in many respects. Nevertheless, they both lapsed into silence. Ursula was filled with deep resentment and a touch of hopelessness. It isn't true, she said to herself, silently addressing her adversary. It isn't true, and it is you who want a physically strong, bullying man, not I. It is you who want an unsensitive man, not I. You don't know anything about Rupert, not really, in spite of the years you've had with him. You don't give him a woman's love, you give him an ideal love, and that is why he reacts away from you. You don't know.  Any kitchen maid would know something about him, you don't know. What do you think your knowledge is, but dead understanding, that doesn't mean a thing? You are so false and untrue, how could you know anything? What is the good of your talking about love, you untrue specter of a woman? How can you know anything when you don't believe? You don't believe in yourself and your own womanhood, so what good is your conceited, shallow cleverness? The two women sat on in antagonistic silence. Hermione felt injured that all her good intention, all her offering, only left the other woman in vulgar antagonism. But then Ursula could not understand, never would understand, could never be more than the usual jealous and unreasonable female, with a good deal of powerful female emotion, female attraction, and a fair amount of female understanding, but no mind. Hermione had decided long ago that where there was no mind it was useless to appeal for reason, one had merely to ignore the ignorant. And Rupert, he had now reacted towards the strongly female, healthy, selfish woman, it was his reaction for the time being, there was no helping it at all.  This violent and directionless reaction between animalism and spiritual truth would go on in him till he tore himself in two between the opposite directions and disappeared meaninglessly out of life. It was no good, he too was without unity, without mind in the ultimate stages of living.  They sat on till Birkin came in and found them together. He felt at once the antagonism in the atmosphere, something radical and insuperable, and he bit his lip, but he affected a bluff manner. Hello Hermione, are you back again? How do you feel? Oh, better. And how are you? You don't look well. Oh, I believe Gudrun and Winnie cry are coming into tea, at least they said they were. We shall be a tea party. What train did you come by, Ursula? It was rather annoying to see him trying to placate both women at once. Both women watched him, Hermione with deep resentment and pity for him. Ursula very impatient. He was nervous and apparently in quite good spirits, chattering the conventional common places. Ursula was amazed and indignant at the way he made small talk. He was adept as any far in Christendom. She became quite stiff, she would not answer. It all seemed to her so false and so belittling. And still Gudrun did not appear. I think I shall go to Florence for the winter, said Hermione at length. Will you, he answered, but it is so cold there. Yes, but I shall stay with palestrides as quite comfortable. What takes you to Florence? I don't know, said Hermione slowly. Then she looked at him with her slow, heavy gaze. Barnes is starting his school of aesthetics, and Olandese is going to give a set of discourses on the Italian national policy. Both rubbish, he said. No, I don't think so, said Hermione. Which do you admire then? I admire both. Barnes is a pioneer, and then I am interested in Italy, in her coming to national consciousness. I wish she'd come to something different from national consciousness then, said Birkin, especially as it only means a sort of commercial industrial consciousness. I hate Italy and her national rant, and I think Barnes is an amateur. Hermione was silent for some moments in a state of hostility, but yet she had got Birkin back again into her world, how subtle her influence was. She seemed to start his irritable attention into her direction exclusively in one minute. He was her creature. No, she said. You're wrong. Then a sort of tension came over her. She raised her face like the pitherness inspired with oracles, and went on in rhapsodic manner. She went on in Italian, as if in thinking of the Italians, she thought in their language. He listened with a shade of distaste to her rhapsody, then he said, for all that I don't like it. Their nationalism is just industrialism, that and a shallow jealousy I detest so much. I think you're wrong. I think you're wrong, said Hermione. It seems to me purely spontaneous and beautiful, the modern Italian's passion, for it is a passion for Italy. L'Italia, do you know Italy well? Ursula asked of Hermione. Hermione hated to be broken in upon in this manner, yet she answered mildly. Yes, pretty well.  My mother died in Florence. Oh! there was a pause, painful to Ursula and to Birkin. Hermione, however, seemed abstracted and calm. Birkin was white, his eyes glowed as if he were in a fever, he was far too overwrought. How Ursula suffered in this tense atmosphere of strained wills, her head seemed bound round by iron bands. Birkin rang the bell for tea, they could not wait for Gudrun any longer. When the door was opened, the cat walked in. Micho, Micho, called Hermione in her slow deliberate sing-song. The young cat turned to look at her, then with his slow and stately walk he advanced to her side. Vieni, vieni qua, Hermione was saying, in her strange, caressive, protective voice, as if she were always the elder, the mother superior. Viene dire buongiorno alla zia, mi ricorde, mi ricorde bene, non è vero piccolo, è vero che mi ricordi, è vero.  Does he understand Italian? said Ursula, who knew nothing of the language. Yes, said Hermione at length, his mother was Italian. She was born in my waste-paper basket in Florence, on the morning of Rupert's birthday. She was his birthday present. Tea was brought in. Birkin poured out for them. It was strange how inviolable was the intimacy which existed between him and Hermione. Ursula felt that she was an outsider. The very teacups and the old silver was a bond between Hermione and Birkin. It seemed to belong to an old past world which they inhabited together, and in which Ursula was a foreigner. She was almost a parvenu in their old cultured milieu. Her convention was not their convention. Their standards were not her standards, but theirs were established. They had the sanction and the grace of age. He and she together, Hermione and Birkin, were people of the same old tradition, the same withered, deadening culture. And she, Ursula, was an intruder. So they always made her feel. Hermione poured a little cream into a saucer. The simple way she assumed her rights in Birkin's room maddened and discouraged, Ursula. There was a fatality about it as if it were bound to be. Hermione lifted the cat and put the cream before him. He planted his two paws on the edge of the table and bent his gracious young head to drink.  It was always the same, this joy in power she manifested, peculiarly in power over any male being.  Hermione laughed in her short grunting fashion. She made a vivid picture so calm and strange with the cat. She had a true static impressiveness. She was a social artist in some ways.  It's bad for him teaching him to eat at table, said Birkin. Yes, said Hermione, easily assenting. Then, looking down at the cat, she resumed her old mocking, humorous sing-song. Ti imparano fare brutte cose, brutte cose. She lifted the Mino's white chin on her forefinger, slowly. The young cat looked round with a supremely forebearing air, avoided seeing anything, withdrew his chin, and began to wash its face with his paw. Hermione grunted her laughter, pleased, bel giovannotto, she said. The cat reached forward again and put his fine white paw on the edge of the saucer. Hermione lifted it down with delicate slowness. This deliberate, delicate carefulness of movement reminded Ursula of Gudrun. Non viace al barbo, un signor gato cosi selvatico. And she kept her finger on the softly planted paw of the cat, and her voice had the same whimsical, humorous note of bullying. Ursula had her nose out of joint. She wanted to go away now. It all seemed no good. Hermione was established forever. She herself was ephemeral, and had not yet even arrived. I will go now, she said suddenly. Birkin looked at her almost in fear. He so dreaded her anger. But there is no need for such hurry, he said. Yes, she answered, I will go. And turning to Hermione, before there was time to say any more, she held out her hand and said, Goodbye. Goodbye, sang Hermione, detaining the hand. Must you really go now? Yes, I think I'll go, said Ursula, her face set and averted from Hermione's eyes. You think you will. But Ursula had got her hand free. She turned to Birkin with a quick, almost jeering, Goodbye. And she was opening the door before he had time to do it for her. When she got outside the house, she ran down the road in fury and agitation. It was strange the unreasoning rage and violence Hermione roused in her by her very presence. Ursula knew she gave herself away to the other woman. She knew she looked ill-bred, uncouth, exaggerated. But she did not care. She only ran up the road lest she should go back and jeer in the faces of the two she had left behind. For they outraged her. End of Chapter 22 Recording by Ruth Golding Chapter 23 of Women in Love This is a LibriVox recording. All LibriVox recordings are in the public domain. For more information or to volunteer, please visit LibriVox.org Recording by Ruth Golding Women in Love by D. H. Lawrence Chapter 23 Excurs Next day Birkin sought Ursula out. It happened to be the half-day at the grammar school. He appeared towards the end of the morning and asked her would she drive with him in the afternoon. She consented, but her face was closed and unresponding, and his heart sank. The afternoon was fine and dim. He was driving the motor-car and she sat beside him. But still her face was closed against him, unresponding. When she became like this, like a wall against him, his heart contracted. His life now seemed so reduced that he hardly cared any more. At moments it seemed to him he did not care a straw whether Ursula or Hermione or anybody else existed or did not exist. Why bother? Why strive for a coherent, satisfied life? Why not drift on in a series of accidents, like a Picker-esque novel? Why not? Why bother about human relationships? Why take them seriously, male or female? Why form any serious connections at all? Why not be casual, drifting along, taking all for what it was worth? And yet still he was damned and doomed to the old effort at serious living. Look, he said, what I bought. The car was running along a broad white road between autumn trees.  She took it and opened it. How lovely! she cried. She examined the gift. How perfectly lovely! she cried again. But why do you give them me? She put the question offensively. His face flickered with bored irritation. He shrugged his shoulder slightly. I wanted to, he said, coolly. But why? Why should you? Am I called on to find reasons? he asked. There was a silence whilst she examined the rings that had been screwed up in the paper. I think they are beautiful, she said. Especially this. This is wonderful. It was a round opal, red and fiery, set in a circle of tiny rubies. You like that best? he said. I think I do. I like the sapphire, he said. This. It was a rose-shaped, beautiful sapphire with small brilliance. Yes, she said. It is lovely. She held it in the light. She held it in the light. Yes, perhaps it is the best. The blue, he said. Yes, wonderful. He suddenly swung the car out of the way of a farm cart. It tilted on the bank. He was a careless driver, yet very quick. But Ursula was frightened. There was always that something regardless in him which terrified her. She suddenly felt he might kill her by making some dreadful accident with the motor car. For a moment she was stony with fear. Isn't it rather dangerous the way you drive? she asked him. No, it isn't dangerous, he said. And then, after a pause, don't you like the yellow ring at all? It was a squareish topaz, set in a frame of steel or some other similar mineral, finally wrought. Yes, she said. I do like it. But why did you buy these rings? I wanted them, their second hand. You bought them for yourself? No, rings look wrong on my hands. Why did you buy them, then? I bought them to give to you. But why? Surely you ought to give them to her mayony. You belong to her. He did not answer.  She wanted to try them on her fingers, but something in her would not let her. And, moreover, she was afraid her hands were too large. She shrank from the mortification of a failure to put them on any but her little finger. They travelled in silence through the empty lanes. Driving in a motor-car excited her. She forgot his presents even. Where are we? she asked suddenly. Not far from work-shop. And where are we going? Anywhere. It was the answer she liked. She opened her hand to look at the rings.  She would have to try them on. She did so secretly, unwilling to let him see, so that he should not know her finger was too large for them. But he saw nevertheless. He always saw if she wanted him not to. It was another of his hateful, watchful characteristics. Only the opal with its thin wire loop would go on her ring finger. And she was superstitious. No, there was ill-portant enough. She would not accept this ring from him in pledge. Look! she said, putting forward her hand, that was half-clothed and shrinking. The others don't fit me. He looked at the red, glinting, soft stone on her oversensitive skin. Yes, he said. But opals are unlucky, aren't they? she said wistfully. No, I prefer unlucky things. Luck is vulgar. Who wants what luck would bring? I don't. But why? she laughed. And consumed with a desire to see how the other rings would look on her hand, she put them on her little finger. They can be made a little bigger, he said. Yes, she replied doubtfully. And she sighed. She knew that in accepting the rings she was accepting a pledge. Yet fate seemed more than herself. She looked again at the jewels. They were very beautiful to her eyes, not as ornament or wealth, but as tiny fragments of loveliness. I'm glad you bought them, she said, putting her hand half unwillingly gently on his arm. He smiled slightly. He wanted her to come to him. But he was angry at the bottom of his soul and indifferent. He knew she had a passion for him really, but it was not finally interesting. There were depths of passion when one became impersonal and indifferent, unemotional. Whereas Ursula was still at the emotional personal level, always so abominably personal. He had taken her as he had never been taken himself. He had taken her at the roots of her darkness and shame, like a demon, laughing over the fountain of mystic corruption, which was one of the sources of her being, laughing, shrugging, accepting, accepting, finally. As for her, when would she so much go beyond herself? As to accept him at the quick of death. She now became quite happy. The motor car ran on. The afternoon was soft and dim. She talked with lively interest, analysing people and their motives. Gudrun, Gerald. He answered vaguely. He was not very much interested any more in personalities and in people. People were all different, but they were all enclosed nowadays in a definite limitation, he said. There were only about two great ideas, two great streams of activity remaining, with various forms of reaction therefrom. The reactions were all varied in various people, but they followed a few great laws and intrinsically there was no difference. They acted and reacted involuntarily, according to a few great laws, and once the laws, the great principles, were known, people were no longer mystically interesting. They were all essentially alike. The differences were only variations on a theme. None of them transcended the given terms. Ursula did not agree. People were still an adventure to her. But perhaps not as much as she tried to persuade herself. Perhaps there was something mechanical now in her interest. Perhaps also her interest was destructive, her analysing was a real tearing to pieces.  She seemed to touch for a moment this under-silence in herself. She became still, and she turned for a moment purely to Birkin. Won't it be lovely to go home in the dark? she said. We might have tea rather late, shall we, and have high tea? Wouldn't that be rather nice? I promised to be at Shortland's for dinner, he said. But it doesn't matter, you can go to-morrow. Hermione is there, he said, in rather an uneasy voice. She's going away in two days. I suppose I ought to say goodbye to her. I shall never see her again. Ursula drew away, closed in a violent silence. He knitted his brows, and his eyes began to sparkle again in anger. You don't mind, do you? he asked irritably. No, I don't care. Why should I? Why should I mind? Her tone was jeering and offensive. That's what I asked myself, he said. Why should you mind? But you seem to. His brows were tense with violent irritation. I assure you I don't. I don't mind, if at least go where you belong. It's what I want you to do.  It's finished between Hermione and me. She means much more to you if it comes to that than she does to me. For you can only revolt in pure reaction from her, and to be her opposite is to be her counterpart. Ah, opposite! cried Ursula. I know your dodges. I'm not taken in by your word twisting. You belong to Hermione in her dead show. Well, if you do, you do. I don't blame you, but then you've nothing to do with me. In his inflamed, overraught exasperation he stopped the car, and they sat there in the middle of the country lane to have it out. It was a crisis of war between them, so they did not see the ridiculousness of their situation.  You'd see that one could be decent, even when one has been wrong. I was wrong to go on all those years with Hermione. It was a deathly process. But after all, one can have a little human decency. But no, you would tear my soul out with your jealousy at the very mention of Hermione's name. I jealous. I jealous. You are mistaken if you think that. I'm not jealous in the least of Hermione. She has nothing to me. Not that. And Ursula snapped her fingers.   It is what Hermione stands for that I hate. I hate it. It is lies. It is false. It is death. But you want it. You can't help it. You can't help yourself. You belong to that old deathly way of living. Then go back to it. But don't come to me, for I've nothing to do with it. And in the stress of her violent emotion she got down from the car and went to the hedge-row, picking unconsciously some flesh-pink spindle-buries, some of which were burst, showing their orange seeds.  He cried bitterly with some contempt. Yes, I am.  And thank God for it.  God be praised.  Go to them. They're your sort. You've always had a string of them trailing after you, and you always will. Go to your spiritual brides, but don't come to me as well, because I'm not having any thank you. You're not satisfied, are you? Your spiritual brides can't give you what you want. They aren't common and fleshy enough for you, aren't they? So you come to me and keep them in the background. You'll marry me for daily use, but you'll keep yourself well provided with spiritual brides in the background.  Suddenly a flame ran over her, and she stamped her foot madly on the ground, and he winced, afraid that she would strike him. And I, I'm not spiritual enough. I'm not as spiritual as that Hermione.  Then go to her. That's all I say.  She's spiritual. Spiritual. She. A dirty materialist as she is. She's spiritual. What does she care for? What is her spirituality? What is it?  He shrank a little. I tell you it's dirt. Dirt and nothing but dirt. And it's dirt you want. You crave for it. Spiritual. Is that spiritual? Her bullying? Her conceit? Her sordid materialism? She's a fishwife. A fishwife. She's such a materialist. And all so sordid. What does she work out to in the end with all her social passion, as you call it? Social passion. What social passion has she? Show it me. Where is it? She wants petty immediate power. She wants the illusion that she is a great woman. That is all. In her soul she's a devilish unbeliever common as dirt. That's what she is at the bottom. And all the rest is pretense. But you love it. You love the sham spirituality. It's your food. And why? Because of the dirt underneath.  I do. And it's that foulness you want.  Then have it. Have it.  She turned away, spas modically tearing the twigs of spindleberry from the hedge, and fastening them with vibrating fingers in the bosom of her coat. He stood watching in silence. A wonderful tenderness burned in him at the sight of her quivering, so sensitive fingers, and at the same time he was full of rage and callousness. This is a degrading exhibition, he said coolly. Yes, degrading indeed, she said. But more to me than to you. Since you choose to degrade yourself, he said. Again the flash came over her face. The yellow lights concentrated in her eyes.  It stinks your truth and your purity.  You are foul, foul, and you must know it.  Yes, thank you, we've had some. What you are is a foul, deathly thing, obscene. That's what you are, obscene and perverse. You love. You may well say you don't want love. No, you want yourself, and dirt and death. That's what you want. You are so perverse, so death-eating. And then there's a bicycle coming, he said, rising under her loud denunciation. She glanced down the road. I don't care, she cried. Nevertheless she was silent. The cyclist, having heard the voices raised in altercation, glanced curiously at the man and the woman, and at the standing motor-car as he passed. Afternoon, he said cheerfully. Good afternoon, replied Birkin coldly. They were silent as the man passed into the distance. A clearer look had come over Birkin's face. He knew she was in the main right. He knew he was perverse, so spiritual on the one hand and in some strange way degraded on the other. But was she herself any better? Was anybody any better? It may all be true, lies and stink and all, he said. But Hermione's spiritual intimacy is no rottner than your emotional jealous intimacy. One can preserve the decencies even to one's enemies for one's own sake. Hermione is my enemy to her last breath. That's why I must bow her off the field.  A pretty picture you make of yourself. But it takes nobody in but yourself. I, jealous, I. What I say, her voice sprang into flame. I say because it is true. Do you see?  That's why I say it, and you hear it. And be grateful, he added with a satirical grimace. Yes, she cried, and if you have a spark of decency in you, be grateful. Not having a spark of decency, however, he retorted. No, she cried, you haven't a spark. And so you can go your way and I'll go mine. It's no good, not the slightest. So you can leave me now. I don't want to go any further with you. Leave me. You don't even know where you are, he said. Oh, don't bother. I assure you I shall be all right. I've got ten shillings in my purse, and that will take me back from anywhere you have brought me to. She hesitated. The rings were still on her fingers. Two on her little finger, one on her ring finger. Still she hesitated. Very good, he said.  You are quite right, she said. Still she hesitated.  She pulled the rings from her fingers and tossed them at him. One touched his face, the others hit his coat, and they scattered into the mud. And take your rings, she said, and go and buy yourself a female elsewhere. There are plenty to be had who will be quite glad to share your spiritual mess, or to have your physical mess and leave your spiritual mess to her mayony. With which she walked away desulterally up the road.  She was sullenly picking and pulling at the twigs of the hedge as she passed. She grew smaller. She seemed to pass out of his sight. A darkness came over his mind. Only a small mechanical speck of consciousness hovered near him. He felt tired and weak. Yet also he was relieved. He gave up his old position. He went and sat on the bank. No doubt Ursula was right. It was true, really, what she said. He knew that his spirituality was concomitant of a process of depravity. A sort of pleasure in self-destruction. There really was a certain stimulant in self-destruction for him, especially when it was translated spiritually. But then he knew it, he knew it, and had done. And was not Ursula's way of emotional intimacy, emotional and physical, was it not just as dangerous as Hermione's abstract spiritual intimacy? Fusion, fusion, this horrible fusion of two beings which every woman and most men insisted on, was it not nauseous and horrible anyhow, whether it was a fusion of the spirit or of the emotional body? Hermione saw herself as the perfect idea to which all men must come. And Ursula was the perfect womb, the bath of birth to which all men must come. And both were horrible. Why could they not remain individuals, limited by their own limits? Why this dreadful all-comprehensiveness, this hateful tyranny? Why not leave the other being free? Why try to absorb or melt or merge? One might abandon oneself utterly to the moment, but not to any other being. He could not bear to see the rings lying in the pale mud of the road. He picked them up and wiped them unconsciously on his hands. They were the little tokens of the reality of beauty, the reality of happiness in warm creation.  There was a darkness over his mind, the terrible knot of consciousness that had persisted there like an obsession was broken, gone. His life was dissolved in darkness over his limbs and his body. But there was a point of anxiety in his heart now. He wanted her to come back. He breathed lightly and regularly like an infant that breathes innocently, beyond the touch of responsibility. She was coming back. He saw her drifting desultrally under the high hedge, advancing towards him slowly. He did not move. He did not look again. He was, as if asleep, at peace, slumbering and utterly relaxed. She came up and stood before him, hanging her head.  He saw the clump of coloured bells and the tree-like tiny branch, also her hands with the over-fine, oversensitive skin. Pretty! he said, looking up at her with a smile, taking the flower. Everything had become simple again, quite simple, the complexity gone into nowhere. But he badly wanted to cry, except that he was weary and bored by emotion. Then a hot passion of tenderness for her filled his heart. He stood up and looked into her face. It was new and oh so delicate in its luminous wonder and fear. He put his arms round her, and she hid her face on his shoulder. It was peace, just simple peace, as he stood folding her quietly there on the open lane. It was peace at last. The old, detestable world of tension had passed away at last. His soul was strong and at ease. She looked up at him. The wonderful yellow light in her eyes now was soft and yielded. They were at peace with each other. He kissed her, and she said to her, yielded. They were at peace with each other. He kissed her softly, many, many times.  Did I abuse you? she asked. He smiled too and took her hand that was so soft and given. Never mind, she said. It is all for the good. He kissed her again, softly, many times. Isn't it? she said. Certainly, he replied. Wait, I shall have my own back. She laughed suddenly with a wild catch in her voice and flung her arms around him.  Yes, he said, softly. His voice was so soft and final, she went very still, as if under a fate which had taken her. Yes, she acquiesced, but it was accomplished without her acquiescence. He was kissing her quietly, repeatedly, with a soft, still happiness that almost made her heart stop beating. My love, she cried, lifting her face and looking with frightened, gentle wonder of bliss. Was it all real? But his eyes were beautiful and soft and immune from stress or excitement, beautiful and smiling lightly to her, smiling with her. She hid her face on his shoulder, hiding before him, because he could see her so completely. She knew he loved her. And she was afraid, she was in a strange element, a new heaven round about her. She wished he were passionate, because in passion she was at home, but this was so still and frail, as space is more frightening than the world. Again quickly she lifted her head. Do you love me? She said quickly, impulsively. Yes, he replied, not heeding her motion, only her stillness. She knew it was true. She broke away. So you ought, she said, turning round to look at the road. Did you find the rings? Yes. Where are they? In my pocket. She put her hand into his pocket and took them out. She was restless. Shall we go? she said. Yes, he answered. And they mounted to the car once more, and left behind them this memorable battlefield. They drifted through the wild late afternoon in a beautiful motion that was smiling and transcendent. His mind was sweetly at ease. The life flowed through him as from some new fountain. He was as if born out of the cramp of a womb. Are you happy? she asked him in her strange, delighted way. Yes, he said. So am I! she cried in sudden ecstasy, putting her arm round him, and clutching him violently against her as he steered the motor-car. Don't drive much more, she said. I don't want you to be always doing something. No, he said. We'll finish this little trip, and then we'll be free. We will, my love. We will! she cried in delight, kissing him as he turned to her. He drove on in a strange new wakefulness, the tension of his consciousness broken. He seemed to be conscious all over, all his body awake with a simple, glimmering awareness, as if he had just come awake, like a thing that is born, like a bird when it comes out of an egg, into a new universe. They dropped down a long hill in the dusk, and suddenly Ursula recognised on her right hand, below in the hollow, the form of subtle minster. Are we here? she cried with pleasure. The rigid, somber, ugly cathedral was settling under the gloom of the coming night, as they entered the narrow town. The golden lights showed like slabs of revelation in the shop windows. Father came here with mother, she said. When they first knew each other, he loves it, he loves the minster. Do you? Yes. It looks like quartz crystals sticking up out of the dark hollow. We'll have our high tea at the Saracen's head. As they descended, they heard the minster bells playing a hymn when the hour had struck six. When the hour had struck six. Glory to thee, my God, this night, for all the blessings of the light. So to Ursula's ear the tune fell out, drop by drop, from the unseen sky onto the dusky town. It was like dim bygone centuries sounding. It was all so far off. She stood in the old yard of the inn, smelling of straw and stables and petrol. Above she could see the first stars. What was it all? This was no actual world. It was the dream world of one's childhood, a great circumscribed reminiscence. The world had become unreal. She herself was a strange, transcendent reality. They sat together in a little parlor by the fire. Is it true? she said, wondering. What? Everything. Is everything true? The best is true, he said, grimacing at her. Is it? she replied, laughing, but unassured. She looked at him. He seemed still so separate. New eyes were opened in her soul. She saw a strange creature from another world in him. It was as if she were enchanted, and everything were metamorphosed. She recalled again the old magic of the Book of Genesis, where the sons of God saw the daughters of men, that they were fair. And he was one of these, one of these strange creatures from the beyond, looking down at her and seeing she was fair. He stood on the hearth-rug looking at her, at her face that was upturned exactly like a flower, a fresh, luminous flower, glinting, faintly golden with the dew of the first light. And he was smiling faintly, as if there were no speech in the world save the silent delight of flowers in each other. Smilingly they delighted in each other's presence, pure presence, not to be thought of, even known. But his eyes had a faintly ironical contraction. And she was drawn to him strangely, as in a spell. Kneeling on the hearth-rug before him, she put her arms round his loins, and put her face against his thigh. Riches, riches, she was overwhelmed with a sense of a heavenful of riches. We love each other, she said in delight.  Unconsciously with her sensitive fingertips, she was tracing the back of his thighs, following some mysterious life-flow there. She had discovered something, something more than wonderful, more wonderful than life itself. It was the strange mystery of his life-motion, there at the back of the thighs, down the flanks. It was a strange reality of his being, the very stuff of being, there in the straight down-flow of the thighs. It was here she discovered him one of the sons of God, such as were in the beginning of the world, not a man, something other, something more. This was release at last. She had had lovers, she had known passion, but this was neither love nor passion. It was the daughters of men coming back to the sons of God, the strange, inhuman sons of God, who are in the beginning. Her face was now one dazzle of released golden light, as she looked up at him and laid her hands full on his thighs, behind as he stood before her. He looked down at her with a rich bright brow, like a diadem above his eyes. She was beautiful as a new marvellous flower opened at his knees, a paradisal flower she was, beyond womanhood, such a flower of luminousness. Yet something was tight and unfree in him. He did not like this crouching, this radiance, not altogether. It was all achieved for her. She had found one of the sons of God from the beginning, and he had found one of the first, most luminous daughters of men. She traced with her hands the line of his loins and thighs at the back, and a living fire ran through her from him darkly. It was a dark flood of electric passion she released from him, drew into herself. She had established a rich new circuit, a new current of passion electric energy between the two of them, released from the darkest poles of the body, and established in perfect circuit. It was a dark fire of electricity that rushed from him to her, and flooded them both with rich peace. Satisfaction.  My love! he answered, bending and kissing her, always kissing her. She closed her hands over the full rounded body of his loins as he stooped over her. She seemed to touch the quick of the mystery of darkness that was bodily him. She seemed to faint beneath, and he seemed to faint stooping over her. It was a perfect passing away for both of them, and at the same time the most intolerable accession into being, the marvellous fullness of immediate gratification, overwhelming, out-flooding, from the source of the deepest life-force, the darkest, deepest, strangest life-source of the human body, at the back and base of the loins. After a lapse of stillness, after the rivers of strange dark fluid richness had passed over her, flooding, carrying away her mind, and flooding down her spine and down her knees, past her feet. A strange flood, sweeping away everything, and leaving her an essential new being. She was left quite free.  So she rose, stillly and blithe, smiling at him. He stood before her, glimmering so awfully real that her heart almost stopped beating. He stood there in his strange whole body that had its marvellous fountains, like the bodies of the sons of God who were in the beginning. There were strange fountains of his body, more mysterious and potent than any she had imagined or known, more satisfying, ah, finally, mystically, physically satisfying. She had thought there was no source deeper than the phallic source. And now, behold, from the smitten rock of the man's body, from the strange marvellous flanks and thighs, deeper, further in mystery than the phallic source, came the floods of ineffable darkness and ineffable riches. They were glad, and they could forget perfectly. They laughed, and went to the meal provided. There was a venison pasty of all things, a large broad-faced cut ham, eggs and creses and red beetroot, and meddlers and apple tart, and tea. What good things! she cried with pleasure. How noble it looks! Shall I pour out the tea? She was usually nervous and uncertain at performing these public duties, such as giving tea, but today she forgot. She was at her ease, entirely forgetting to have misgivings. The teapot poured beautifully from a proud slender spout. Her eyes were warm with smiles as she gave him his tea. She had learned at last to be still and perfect. Everything is ours, she said to him. Everything, he answered.  I'm so glad! she cried with unspeakable relief. So am I, he said. But I'm thinking we'd better get out of our responsibilities as quick as we can. What responsibilities! she asked, wondering. We must drop our jobs like a shot. A new understanding dawned into her face. Of course, she said, there's that! We must get out, he said. There's nothing for it, but to get out quick. She looked at him doubtfully across the table. But where, she said? I don't know, he said. We'll just wander about for a bit. Again she looked at him quizzically. I should be perfectly happy at the mill, she said. It's very near the old thing, he said. Let us wander a bit. His voice could be so soft and happy-go-lucky it went through her veins like an exhilaration. Nevertheless, she dreamed of a valley and wild gardens and peace. She had a desire too for splendour, an aristocratic extravagant splendour. Wandering seemed to her like restlessness, dissatisfaction. Where will you wander, too? she asked. I don't know. I feel as if I would just meet you and we'd set off just towards the distance. But where can one go? she asked anxiously. After all, there is only the world and none of it is very distant. Still, he said, I should like to go with you nowhere. It would be rather wandering just to nowhere. That's the place to get to, nowhere. One wants to wander away from the world's somewheres into our own nowhere. Still, she meditated. You see, my love, she said. I'm so afraid that while we're only people, we've got to take the world that's given because there isn't any other. Yes, there is, he said. There's somewhere where we can be free, somewhere where one needn't wear much clothes, none even, where one meets a few people who have gone through enough and can take things for granted, where you be yourself without bothering. There is somewhere, there are one or two people. But where, she sighed. Somewhere, anywhere. Let's wander off. That's the thing to do. Let's wander off. Yes, she said, thrilled at the thought of travel, but to her it was only travel. To be free, he said, to be free in a free place with a few other people. Yes, she said wistfully. Those few other people depressed her. It isn't really a locality, though, he said. It's a perfected relation between you and me and others, the perfect relation, so that we are free together. It is, my love, isn't it? she said. It's you and me. It's you and me, isn't it? She stretched out her arms to him.  Her arms closed round him again.  The sense of the awfulness of riches that could never be impaired flooded her mind, like a swoon, a death in most marvellous possession, mystic sure. She possessed him so utterly and intolerably that she herself lapsed out. And yet she was only sitting still in the chair, with her hands pressed upon him, and lost. Again he softly kissed her. We shall never go apart again, he murmured quietly. And she did not speak, but only pressed her hands firmer down upon the source of darkness in him. They decided, when they woke again from the pure swoon, to write their resignations from the world of work there and then. She wanted this. He rang the bell and ordered note paper without a printed address. The waiter cleared the table.  Now then, I don't know how one really stands. I suppose one could get out of it in less than a month. Anyhow, sir, I beg to resign my post as class mistress in the Willy Green grammar school. I should be very grateful if you would liberate me as soon as possible, without waiting for the expiration of the month's notice. That'll do. Have you got it? Let me look. Ursula Brangwen. Good, now I'll write mine. I ought to give them three months, but I can plead health. I can arrange it all right. He sat and wrote out his formal resignation. Now, he said, when the envelopes were sealed and addressed, shall we post them here both together? I know Jackie will say, here's a coincidence when he receives them in all their identity. Shall we let him say it or not? I don't care, she said. No, he said pondering. It doesn't matter, does it? she said. Yes, he replied, their imagination shall not work on us. I'll post yours here, mine after. I cannot be implicated in their imaginings. He looked at her with his strange, non-human singleness. Yes, you are right, she said. She lifted her face to him all shining and open. It was as if he might enter straight into the source of her radiance. Its face became a little distracted. Shall we go? he said. As you like, she replied. They were soon out of the little town, and running through the uneven lanes of the country. Ursula nestled near him into his constant warmth, and watched the pale, lit revelation racing ahead the visible night. Sometimes it was a wide old road, with grass spaces on either side, flying magic and elfin in the greenish illumination. Sometimes it was trees looming overhead. Sometimes it was bramble bushes, sometimes the walls of a crew-yard, and the butt of a barn. Are you going to Shortland to dinner? Ursula asked him suddenly. He started. Good God, he said, Shortland's never again, not that. Besides, we should be too late. Where are we going then? To the mill. If you like. Pity to go anywhere on this good dark night. Pity to come out of it, really. Pity, we can't stop in this good darkness. It is better than anything ever would be, this good immediate darkness. She sat, wondering. The car lurched and swayed. She knew there was no leaving him. The darkness held them both, and contained them. It was not to be surpassed. Besides, she had a full, mystic knowledge of his suave loins of darkness, dark clad and suave. And in this knowledge there was some of the inevitability and the beauty of fate. Fate which one asks for, which one accepts in full. He sat still, like an Egyptian pharaoh, driving the car. He felt as if he were seated in immemorial potency, like the great carven statutes of real Egypt, as real and as fulfilled with subtle strength, as these are, with a vague, inscrutable smile on the lips. He knew what it was to have the strange and magical current of force in his back and loins, and down his legs. Force so perfect that it stayed him immobile, and left his face subtly, mindlessly smiling. He knew what it was to be awake and potent in that other basic mind, the deepest physical mind. And from this source he had a pure and magic control. Magical, mystical. A force in darkness like electricity. It was very difficult to speak. It was so perfect to sit in this pure living silence, subtle, full of unthinkable knowledge and unthinkable force, upheld immemorial in timeless force, like the immobile supremely potent Egyptians seated forever in their living subtle silence. We need not go home, he said. This car has seats that let down and make a bed, and we can lift the hood. She was glad and frightened. She cowered near to him. But what about them at home? she said. Send a telegram. Nothing more was said. They ran on in silence. But with a sort of second consciousness, he steered the car towards a destination. For he had the free intelligence to direct his own ends. His arms and his breasts and his head were rounded and living like those of the Greek. He had not the unawakened straight arms of the Egyptian, nor the sealed slumbering head. A lampent intelligence played secondarily above his pure Egyptian concentration in darkness. They came to a village that lined along the road. The car crept slowly along until he saw the post office. Then he pulled up. I will send a telegram to your father, he said. I will merely say spending the night in town, shall I? Yes, she answered. She did not want to be disturbed into taking thought. She watched him move into the post office. It was also a shop, she saw. Strange he was. Even as he went into the lighted public place, he remained dark and magic. The living silence seemed the body of reality in him, subtle, potent, indiscoverable. There he was. In a strange uplift of elation she saw him, the being never to be revealed, all full in its potency, mystic, and real. This dark, subtle reality of him, never to be translated, liberated her into perfection, her own perfected being. She too was dark and fulfilled in silence. He came out throwing some packages into the car. There is some bread and cheese and raisins and apples and hard chocolate, he said, in his voice that was as if laughing because of the unblemished stillness and force which was the reality in him. She would have to touch him, to speak, to see was nothing. It was a travesty to look and to comprehend the man there. Darkness and silence must fall perfectly on her. Then she could know mystically in unrevealed touch. She must lightly, mindlessly connect with him, have the knowledge which is death of knowledge, the reality of surety in not knowing. Soon they had run on again into the darkness. She did not ask where they were going, she did not care. She sat in a fullness and a pure potency that was like apathy, mindless, and immobile. She was next to him and hung in a pure rest as a star is hung, balanced unthinkably. Still there remained a dark lambency of anticipation. She would touch him. With perfect, fine fingertips of reality, she would touch the reality in him. The suave, pure, untranslatable reality of his loins of darkness. To touch mindlessly in darkness, to come in pure touching upon the living reality of him. His suave perfect loins and thighs of darkness. This was her sustaining anticipation. And he too waited in the magical steadfastness of suspense for her to take this knowledge of him as he had taken it of her. He knew her darkly with the fullness of dark knowledge. Now she would know him and he too would be liberated. He would be night-free, like an Egyptian, steadfast in perfectly suspended equilibrium, pure mystic nodality of physical being. They would give each other this star equilibrium which alone is freedom. She saw that they were running among trees, great old trees with dying bracken undergrowth. The pale-ish gnarled trunks showed ghostly. And like old priests in the hovering distance, the fern rose magical and mysterious. It was a night all darkness with low cloud. The motor-car advanced slowly. Where are we? she whispered. In Sherwood Forest. It was evident he knew the place. He drove softly, watching. Then they came to a green road between the trees. They turned cautiously round and were advancing between the oaks of the forest down a green lane. The green lane widened into a little circle of grass, where there was a small trickle of water at the bottom of a sloping bank. The car stopped. We will stay here, he said, and put out the lights. He extinguished the lamps at once, and it was pure night, with shadows of trees like realities of other nightly being. He threw a rug onto the bracken, and they sat in stillness and mindless silence. There were faint sounds from the wood, but no disturbance, no possible disturbance. The world was under a strange ban, a new mystery had supervened. They threw off their clothes, and he gathered her to him, and found her. Found the pure, lambant reality of her forever invisible flesh. Quenched, inhuman, his fingers upon her unrevealed nudity, were the fingers of silence upon silence. The body of mysterious night upon the body of mysterious night, the night masculine and feminine, never to be seen with the eye, never to be seen with the eye, or known with the mind, only known as a palpable revelation of living otherness. She had her desire of him. She touched. She received the maximum of unspeakable communication in touch, dark, subtle, positively silent. A magnificent gift and give again, a perfect acceptance and yielding, a mystery. The reality of that which can never be known, vital, sensual reality, that can never be transmuted into mind content, but remains outside living body of darkness and silence and subtlety. And subtlety, the mystic body of reality. She had her desire fulfilled. He had his desire fulfilled, for she was to him what he was to her the immemorial magnificence of mystic, palpable, real otherness. They slept the chilly night through under the hood of the car, a night of unbroken sleep. It was already high day when he awoke. They looked at each other and laughed, then looked away, filled with darkness and secrecy. Then they kissed and remembered the magnificence of the night. It was so magnificent, such an inheritance of a universe of dark reality, that they were afraid to seem to remember. They hid away the remembrance and the knowledge. End of chapter 23, recording by Ruth Golding


Hi everybody and welcome to Analyzing Software Using Deep Learning. This is a course at the University of Stuttgart in summer 2020. In the second module of the course we will look at recurrent neural networks or short RNNs and how to use them for analyzing software. So this module will have three parts where the first focuses on recurrent neural networks and what they actually are. This first part is not really specific to analyzing software but basically gives a background on the machine learning side that we need to understand the rest of it. And then the second and the third part will show concrete applications of these recurrent neural networks. One of them is going to be about code completion. So how to complete code that is missing some parts. And then the third part of this module will be about repairing a specific kind of error, namely syntax errors and how to use recurrent neural networks for that. In the previous module we introduced some of the basics of neural networks and basically reasoned about them at the level of individual neurons. The first thing we will do today and also in the rest of this course is to abstract away from individual neurons and to instead look at layers of neurons. So what we'll do here is to go from neurons to layers. So to see how this works let's first have a look one more time at a neural network by looking at individual neurons. For example let's take a network that looks like this. So we have an input layer with three neurons then a hidden layer with two neurons and then an output layer with three neurons and everything is connected to everything like this. Now what the computation that is done at every individual neuron is the following. So the output of every neuron is some function and this could be any of these activation functions for example that we have seen and then for every neuron we take the weight of the incoming connection times the input that comes in plus some bias. And in this case these x and f and b values are all scalars. For example they could just be real numbers and the w here is this vector of weights. So this is a vector. For example this could be a vector of n real numbers if there are n input neurons or inputs that come into a neuron. Now instead of this look at individual neurons we will now abstract them into layers of neurons that I will represent using these little rectangles. And then the same network that we just looked at will look like this where we basically have these three layers an input layer a hidden layer and an output layer. And now we can express our computation also in terms of layers where we say that for each layer the following is computed as the output. So the output is again some function f which may be an activation function for example but now we have capital W times x plus b and to reflect the fact that we do not talk about individual neurons anymore but about layers these values x and f and b are now all vectors. For example vectors in r to the power of n and capital letter w is now a matrix which is our matrix of weights and this could for example be in r to the power of m times n where n is the dimension of input connections that come into a layer and n is the number of neurons that we have in the layer. Based on this notion of layers we can now have a look at recurrent neural networks which will be the focus of this module. So what we have seen so far are feedforward networks and feedforward networks are not recurrent networks. And what we want to look at mostly in this module today are recurrent networks. So what's the main difference between them a feedforward network basically looks like this we have some input layer we have some hidden layer maybe some more hidden layers in between and then eventually some output layer. Let's call this input layer x the hidden layer h and the output layer y and let's also give these matrices some names that control how the inputs or how the outputs of one layer are transformed to give us the outputs of the next layer and let's call these matrices u and and v so x and h and y here correspond to the input layer a hidden layer and an output layer and u and w u and v and w which we'll introduce in a second correspond to these weight matrices that control how the layers actually work. Now the feedforward network on the left just processes one input at a time and in contrast to this a recurrent network looks as follows so it also has an input layer it also has a hidden layer maybe more of them and then eventually has an output layer and again we call them x h and y and also the matrices that control what happens between these layers is basically the same again u and v but what's new now is that we also have a connection from the hidden layer to the next time step of this same hidden layer and I'll use this little rectangle here as a symbol to denote that this is a connection that goes over time and we'll see in a second what this over time really means and this connection over time is controlled by yet another weight matrix w which tells us how the value of h at some time step t depends on the values of this value of this layer h at a previous time step t minus one so just to give my arrows a little bit more meaning here so if we if I use this normal error then this is just a normal function and if I use this arrow that has this little black rectangle on top then this is a function that also has a delay of a single time step why do we care about this delay here well it's important for two reasons one of them is that it is very useful for representing sequences of inputs and also sequences of outputs and the basic idea here is that every element of such a sequence is represented as one time step and then by going through time we can basically process the entire sequence and the second reason why this is useful is that this hidden layer that takes some information from the past in a sense is able to store some information about previous inputs so if you are given a sequence of elements then what this hidden layer essentially does is to store some information about the past elements that we have already seen so that we can use all of this information to make want to determine the output of the hidden layer let's make all of this a little bit more concrete by looking at the concrete example and this example will be to predict the next word in a sentence so as a concrete sentence let's say we have a sentence that starts with A S D L the name of this course is the best and then the missing word comes and as you may be able to guess the word that we would like to see here is course and now let's have a look at how we could get this prediction from a feedforward network and from a recurrent network so for a feedforward network what we could do is the following we could basically feed one word at a time into the network and then it's supposed to predict the next word for us so for example we would start with A S D L and hope that the network is able to predict is for us and then we do this for all following words and at the end we hopefully query it for best and it hopefully gives us the answer course now this is really hard for the model because it basically sees only one word at a time so given the word best it is supposed to answer course but it doesn't really know the rest of the sentence so it's it's it's very hard to to be right here in contrast a recurrent network will see all the words that have already happened in the past so basically the beginning of the sentence and we'll use this to predict the rest of the sentence so at time step one we will provide the first word to this model so this looks very similar to what we do for the feedforward network and now the difference is that at later time steps we still have the information from the words that we have seen at the beginning because of this recurrent layer that is the important feature of a recurrent network and that means when we later at time step 4 see the query that starts the query given the word best it now sees the information from from the past and is hopefully able to predict course simply because in this hidden layer here we're storing information about the beginning of the sentence so this recurrent connection remembers the beginning of the sentence so now what does it really mean to remember something let's have a deeper look at what this really means by unfolding the computational graph which means by basically looking at what happens in the model during these different time steps so by unfolding the computational graph I essentially mean that we'll look at individual time steps instead of just having this recurrent little arrow that doesn't really show us what's going on under the hood so the not yet unfolded version of this model and I'm just writing it yeah slightly differently looks like this we have this input layer the hidden layer and the output layer and they're connected just as before with the only difference now that I've basically turned it on the side and we have these matrices here that control how these different layers are connected with each other and now the unfolding happens where we look at individual time steps so we have this notion of the past which I just abbreviate with dot dot dot the past gives us something we'll see what this is in a second and then for every time step we have some input some hidden layer and some output so here this is time step t minus one so this is the input x of t minus one which is given to the hidden layer at t minus one which will then produce the output y at t minus one and then at the next time step this output of h of t minus one is taken as the next input to the hidden layer so the hidden layer at time step t and in addition of course it gets the next input so this will be the input at time step t and then produces an output at time step t and this goes on and on and on for different time steps basically until the end of our input sequence so until this reaches the end of the sequence now let's get back to our concrete example so for example at t minus one the input might be is and the model may be able to predict that the output should be there then we take this output that was predicted by the model and feed it into the next time step and now what the model knows is that the is the next input but it also knows something about the past because of this connection from h of t minus one and combining these two pieces of information it may be able to predict best and then we basically do the same we take this predicted output best and feed it into the model again which also takes all the information from the past through the connection from h of t and then hopefully is able to predict course as the as the missing word so let's also have a look at how this works mathematically so basically the output of h at some time t is a function of the state of h at t minus one and of the input x at time step t and then the output of the whole model at a time step t so y of t is a function of h of t which is defined just above to make this more concrete let's have a look at how this could be typically implemented so for example this could be implemented as follows that h of t is the hyperbolic tangent 10h of the state of h of t minus one multiplied by this weight matrix w that we also see on the folded image on the left plus the input that we get from x at time step t multiplied with the other weight matrix that we also see on the left namely u plus some bias the hyperbolic tangent is just yet another activation function so let me just give you an idea of how this looks like so it basically looks similar to the sigmoid function that we've seen earlier just that this is now shifted a little towards the negative numbers and looks something like this so it comes in from here then goes through zero zero and then goes up here so it again has this s like shape but can have a negative value as well as a positive value to give you a concrete example of how this function of y of t could look like so one option that people might use if they want to predict words out of a given vocabulary for example to predict the next word in a sentence would look as follows so we would say y of t is the result of the softmax function and we'll see in a minute what this really means of the value of h of t multiplied with the weight matrix v plus some other bias which we here call c just to disambiguate it from the bias that we use for the hidden layer so let's now have a look at what this softmax function is and why we want to use it here to compute the output of y of t so what softmax does is to essentially give us a vector that we can interpret as a probability distribution so it takes a vector of k numbers that are all real real valued numbers and then squashes them such that they sum up to one and such that each of these values is in the range between zero and one so essentially this looks like a probability distribution and if we interpret this interpret the output of a softmax function as a probability distribution we can for example predict how likely each of the different words that might come next are according to the model so let's have a look at how this is defined so in order to compute the softmax function this formula here is computed so we take all the elements in our vector y and then for each of them compute e to the power of y divided by the sum of all these e to the power of y values so for example if we have this value given which does not look like a probability distribution at all then what softmax will do for us is to turn it into this vector which basically has the same gives the same importance to each of these values so the value four here in the middle corresponds to this one and it still is the largest value but this vector that we get from softmax now looks like a probability distribution so the sum of all the values is one and each of the values is between zero and one so to double check if this idea was clear let's have a little quiz where you're basically given a few vectors and the question is which of these vectors could be the output of the softmax function so I invite you here to pause the video in order to think independently about these four vectors and once you think you know which of those could be the outcome of the softmax function then resume the video so let me show you the solution so the first one is clearly not a possible output of the softmax function because it's all zeros so it does not look like a probability distribution simply because its values do not sum up to one the second one looks fine all the values are in the zero to one range and the sum of all these values is one the same for the third one which is a kind of strange probability distribution because it basically gives all the probability to the second element but it is one so that's fine and the third one again looks sorry the fourth one looks fine at first because all the values are between zero and one but the sum is not equal to one and therefore this is not a legal probability distribution and hence not a possible outcome of the softmax function so you now have an idea of what these are and ends these return neural networks are before we look into applications for analyzing software let's have a look at some applications and other domains where are and ends are useful so essentially you can use them for any task where the input and maybe also the output is a sequence of something so just to give you a few examples so one concrete application where this could be useful is for unsegmented connected handwriting recognition where you basically have handwriting that is not yet split into individual characters and the model simply gets a sequence of these pixels that represent the different chunks of your handwriting and then is supposed to predict the actual characters or maybe digits another example is machine translation of natural languages where we have sequences of words in one language given as the input and then would like the model to predict a sequence of words in some other language for example to translate from English to German yet another example is video classification by frames where the sequence is a sequence of frames that built up the video and then we want to classify this video for example to say whether this is about cats and dogs or about something else yet another example is speech recognition because speech naturally is a sequence it's just a sequence of of audio that comes in and this sequence can also be fed into an RNN in order to recognize what a person is actually saying and as a final example what you can also do with RNNs is to do a sentiment analysis of Twitter messages where you want to find out whether the person writing a message is angry or happy or or whatever and here the sequence would be a sequence of words or maybe a sequence of characters that make up this Twitter message so and this already brings us to the end of this first part of this module on using recurrent networks for analyzing software so you now hopefully know or at least have an idea of what a recurrent neural network is and in the second and third part we can now see how to use these recurrent neural networks for two applications in software namely code completion and automated program repair thanks for listening and see you next time