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[Assistant] So unworldly was he, or so capricious, that he frequently refused his help to the powerful and wealthy where the problem made no appeal to his sympathies.


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[Assistant] While he would devote weeks of most intense application to the affairs of some humble client whose case presented those strange and dramatic qualities which appealed to his imagination and challenged his ingenuity.


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[Assistant] In this memorable year 95 a curious and incongruous succession of cases had engaged his attention, ranging from his famous investigation of the sudden death of Cardinal Tosca, an inquiry which was carried out by him at the express desire of His Holiness the Pope,


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[Assistant] Down to his arrest of Wilson, the notorious canary trainer, which removed a plague spot from the east end of London.


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[Assistant] Close on the heels of these two famous cases came the tragedy of Woodman's Lee and the very obscure circumstances which surrounded the death of Captain Peter Carey.


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[Assistant] No record of the doings of Mr. Sherlock Holmes would be complete which did not include some account of this very unusual affair.


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[Assistant] During the first week of July my friend had been absent so often and so long from our lodgings that I knew he had something on hand.


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[Assistant] The fact that several rough-looking men called during that time and inquired for Captain Basil made me understand that Holmes was working somewhere under one of the numerous disguises and names with which he concealed his own formidable identity.


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[Assistant] He had at least five small refuges in different parts of London, in which he was able to change his personality.


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[Assistant] He said nothing of his business to me, and it was not my habit to force confidence.


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[Assistant] The first positive sign which he gave me of the direction which his investigation was taking was an extraordinary one.


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[Assistant] He had gone out before breakfast, and I had sat down to mine when he strode into the room, his hat upon his head, and a huge barbed-headed spear tucked like an umbrella under his arm.


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[Assistant] Good gracious, Holmes," I cried. You don't mean to say that you've been walking about London with that thing. I drove to the butcher's and back. The butcher's? And I return with an excellent appetite.


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[Assistant] There can be no question, my dear Watson, of the value of exercise before breakfast.


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[Assistant] But I am prepared to bet that you will not guess the form that my exercise has taken. I will not attempt it." He chuckled as he poured out the coffee.


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[Assistant] If you could have looked into Allardyce's back shop, you would have seen a dead pig swung from a hook in the ceiling, and a gentleman in his shirt sleeves furiously stabbing at it with this weapon.


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[Assistant] I was that energetic person, and I have satisfied myself that by no exertion of my strength can I transfix the pig with a single blow. Perhaps you would care to try. Not for worlds, but why were you doing this?


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[Assistant] Because it seemed to me to have an indirect bearing upon the mystery of Woodman's Lee.


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[Assistant] Ah, Hopkins, I got your wire last night and I have been expecting you. Come and join us.


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[Assistant] Our visitor was an exceedingly alert man, thirty years of age, dressed in a quiet tweed suit, but retaining the erect bearing of one who was accustomed to official uniform.


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[Assistant] I recognised him at once as Stanley Hopkins, a young police inspector for whose future Holmes had high hopes, while he in turn professed the admiration and respect of a pupil for the scientific methods of the famous amateur.


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[Assistant] Hopkins's brow was clouded, and he sat down with an air of deep dejection.


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[Assistant] No, thank you, sir. I breakfasted before I came round. I spent the night in town, for I came up yesterday to report. And what have you to report? Failure, sir. Absolute failure. You have made no progress? None. Dear me! I must have a look at the matter.


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[Assistant] I wish to heavens that you would, Mr Holmes. It's my first big chance, and I'm at my wits' end. For goodness sake, come down and lend me a hand.


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[Assistant] Well, well, it just happens that I have already read all the available evidence, including the report of the inquest, with some care. By the way, what do you make of that tobacco pouch found on the scene of the crime? Is there no clue there?" Hopkins looked surprised.


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[Assistant] It was the man's own pouch, sir. His initials were inside it, and it was of seal-skin, and he was an old sealer. But he had no pipe.


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[Assistant] No sir, we could find no pipe. Indeed, he smoked very little, and yet he might have kept some tobacco for his friends.


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[Assistant] No doubt. I only mention it because if I had been handling the case I should have been inclined to make that the starting point of my investigation.


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[Assistant] However, my friend Dr. Watson knows nothing of this matter, and I should be none the worse for hearing this sequence of events once more. Just give us some short sketches of the essentials.


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[Assistant] Stanley Hopkins drew a slip of paper from his pocket.


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[Assistant] I'll have a few dates here which will give you the career of the dead man. Captain Peter Carey. He was born in 45, fifty years of age. He was the most daring and successful seal and whale-fisher.


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[Assistant] In 1883 he commanded the steam-sealer Sea Unicorn of Dundee.


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[Assistant] He had then had several successful voyages in succession and in the following year, 1884, he retired.


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[Assistant] After that he travelled for some years, and finally he bought a small place called Woodmansley near Forest Row in Sussex. There he has lived for six years, and there he died just a week ago to-day. There were some most singular points about the man. In ordinary life he was a strict Puritan,


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[Assistant] A silent gloomy fellow. His household consisted of his wife, his daughter, aged twenty, and two female servants. These last were continually changing, but it was never a very cheery situation, and sometimes it became past all bearing.


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[Assistant] The man was an intermittent drunkard, and when he had to fit on him he was a perfect fiend.


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[Assistant] He has been known to drive his wife and daughter out of doors in the middle of the night, and flogged them through the park until the whole village outside the gates was aroused by their screams.


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[Assistant] He was summoned once for a savage assault upon the old vicar, who had called upon him to remonstrate with him upon his conduct.


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[Assistant] In short, Mr Holmes, you would go far before you found a more dangerous man than Peter Carey, and I have heard that he bore the same character when he commanded his ship.


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[Assistant] He was known in his trade as Black Peter.


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[Assistant] And the name was given him not only on account of his swarthy features and the colour of his huge beard, but for the humours which were the terror of all around him.


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[Assistant] I need not say that he was loathed and avoided by every one of his neighbours.


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[Assistant] And that I have not heard one single word of sorrow about his terrible end.


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[Assistant] You must have read in the account of the inquest about the man's cabin, Mr. Holmes, but perhaps your friend here has not heard of it.


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[Assistant] He had built himself a wooden outhouse. He always called it the cabin, a few hundred yards from his house, and it was here that he slept every night. It was a little, single-roomed hut, sixteen feet by ten.


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[Assistant] He kept the key in his pocket, made his own bed, cleaned it himself and allowed no other foot to cross the threshold.


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[Assistant] There are small windows on each side which were covered by curtains and never open.


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[Assistant] One of these windows was turned towards the high road, and when the light burned in it at night the folk used to point it out to each other and wonder what Black Peter was doing in there.


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[Assistant] That's the window, Mr Holmes, which gave us one of the few bits of positive evidence that came out at the inquest.


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[Assistant] You remember that a stonemason named Slater, walking from Forest Row about one o'clock in the morning, two days before the murder, stopped as he passed the grounds and looked at the square of light still shining among the trees.


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[Assistant] He swears that the shadow of a man's head turned sideways was clearly visible on the blind, and that this shadow was certainly not that of Peter Carey, whom he knew well.


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[Assistant] It was that of a bearded man, but the beard was short and bristled forward in a way very different from that of the captain.


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[Assistant] So he says, but he had been two hours in the public house, and it is some distance from the road to the window.


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[Assistant] Besides, this refers to the Monday, and the crime was done upon the Wednesday.


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[Assistant] On a Tuesday Peter Carey was in one of his blackest moods, flushed with drink and as savage as a dangerous wild beast.


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[Assistant] He rammed about the house, and the women ran for it when they heard him coming. Late in the evening he went down to his own hut.


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[Assistant] About two o'clock the following morning his daughter, who slept with her window open, heard a most fearful yell from that direction,


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[Assistant] But it was no unusual thing for him to bawl and shout when he was in drink, so no notice was taken.


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[Assistant] On rising at seven one of the maids noticed that the door of the hut was open.


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[Assistant] But so great was the terror which the man caused that it was midday before anyone would venture down to see what had become of him.


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[Assistant] Peeping into the open door, they saw a sight which sent them flying with white faces into the village.


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[Assistant] Within an hour, I was on the spot and had taken over the case.


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[Assistant] Well, I have fairly steady nerves, as you know, Mr. Holmes, but I give you my word that I got a shake when I put my head into that little house. It was droning like a harmonium with flies and blue bottles, and the floor and the walls were like a slaughterhouse.


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[Assistant] He had called it a cabin, and a cabin it was, sure enough, for you to thought that you were in a ship.


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[Assistant] There was a bunk at one end, a sea-chest, maps and charts, a picture of the sea unicorn, a line of log books on a shelf.


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[Assistant] All exactly as one would expect to find it in a captain's room.


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[Assistant] And there, in the middle of it, was the man himself, his face twisted like a lost soul in torment.


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[Assistant] And his great brindled beard stuck upward in his agony.


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[Assistant] Right through his broad breast a steel harpoon had been driven, and it had sunk deep into the wood of the wall behind him. He was pinned like a beetle on a card


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[Assistant] Of course, he was quite dead, and had been so from the instant that he had uttered that last yell of agony. I know your methods, sir, and I applied them.


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[Assistant] Before I permitted anything to be moved, I examined most carefully the ground outside, and also the floor of the room. There were no foot-marks. Meaning you saw none. I assure you, sir, that there were none. My good Hopkins,


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[Assistant] I have investigated many crimes, but I have never yet seen one which was committed by a flying creature.


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[Assistant] As long as the criminal remains upon two legs, so long must there be some indentation, some abrasion, some trifling displacement, which can be detected by the scientific searcher. It is incredible that this blood-bisfettered room contained no trace which could have aided us.


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[Assistant] I understand, however, from the inquest that there were some objects which you failed to


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[Assistant] The young inspector winced at my companion's ironical comments.


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[Assistant] I was a fool not to call you in at the time, Mr. Holmes. However, that's past praying for now. Yes, there were several objects in the room which called for special attention.


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[Assistant] One was the harpoon with which the deed was committed. It had been snatched down from a rack on the wall.


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[Assistant] Two others remained there, and there was a vacant place for the third.


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[Assistant] It seemed to establish that the crime had been done in a moment of fury, and that the murderer had seized the first weapon which came his way.


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[Assistant] The fact that the crime was committed at two in the morning, and yet Peter Carey was fully dressed, suggested that he had an appointment with the murderer, which is borne out by the fact that a bottle of rum and two dirty glasses stood upon the table.


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[Assistant] Yes," said Holmes, I think that both inferences are permissible.


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[Assistant] Was there any other spirit but Rum in the room?


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[Assistant] Yes, and there was a tantalus containing brandy and whisky on the sea-chest. It is of no importance to us, however, since the decanters were full, and it had therefore not been used.


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[Assistant] For all that, its presence has some significance, said Holmes.


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[Assistant] However, let us hear some more about the objects which do seem to you to bear upon the case. There was this tobacco pouch upon the table. What part of the table?


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[Assistant] It lay in the middle, and it was of course seal-skin, the straight-haired skin with a leather thong to bind it. Inside was P.C. on the flap. There was half an ounce of Strong Ships tobacco in it. Excellent! What more?


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[Assistant] Stanley Hopkins drew from his pocket drab-covered notebook. The outside was rough and worn, the leaves discoloured. On the first page were written the initials J. H. N. and the date 1883.


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[Assistant] Holmes laid it on the table and examined it in his minute way, while Hopkins and I gazed over each shoulder.


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[Assistant] On the second page were the printed letters CPR, and then came several sheets of numbers.


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[Assistant] They appear to be lists of stock exchange securities. I thought that JHN were the initials of a broker, and that CPR may have been his client.


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[Assistant] Try Canadian Pacific Railway, said Holmes.


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[Assistant] Stanley Hopkins swore between his teeth and struck his thigh with his clenched hand.


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[Assistant] I have already examined the old stock exchange lists, and I can find no one in 1883, either in the house or among the outside brokers, whose initials correspond with these.


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[Assistant] Yet I feel that the clue is the most important one that I hold.


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[Assistant] You will admit, Mr Holmes, that there is a possibility that these initials are those of the second person who was present—in other words, of the murderer.


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[Assistant] I would also urge that the introduction into the case of a document relating to large masses of valuable securities gives us from the first time some indication of a motive for the crime.


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[Assistant] I confess that this notebook, which did not appear at the inquest, modifies any views which I may have formed. I had come to a theory of the crime in which I can find no place for this. Have you endeavoured to trace any of the securities here mentioned? Inquiries are now being made at the offices.


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[Assistant] But I fear that the complete register of the stockholders of these South American concerns is in South America.


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[Assistant] And that some weeks must elapse before we can trace the shares.


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[Assistant] Holmes had been examining the cover of the notebook with his magnifying lens.


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[Assistant] Surely there is some discoloration here, said he.


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[Assistant] Yes sir, it is a blood-stain. I told you that I picked the book off the floor. Was the blood-stain above or below? On the side next to boards.


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[Assistant] Which proves of course that the book was dropped after the crime was committed.


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[Assistant] Exactly, Mr Holmes. I appreciated that point, and I conjectured that it was dropped by the murderer in his hurried flight. It lay near the door.


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[Assistant] I suppose that none of these securities have been found among the property of the dead man. No, sir. Have you any reason to suspect robbery? No, sir. Nothing seemed to have been touched.


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[Assistant] Dear me, it is certainly a very interesting case. Then there was a knife, was there not? A sheath-knife, still in its sheath. It lay at the feet of the dead man.


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[Assistant] I suppose I shall have to come out and have a look at it. Stanley Hopkins gave a cry of joy.


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[Assistant] Thank you, sir. That will indeed be a weight off my mind. Home shook his finger at the inspector.


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[Assistant] It would have been an easier task a week ago," said he, but even now my visits may not be entirely fruitless. Watson, if you can spare the time, I should be very glad of your company. If you will call a four-wheeler, Hopkins, we shall be ready to start for Forest Row in a quarter of an hour.


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[Assistant] Alighting at the small wayside station, we drove for some miles through the remains of widespread woods, which were once part of that great forest which for so long held the Saxon invaders at bay, the impenetrable weald for sixty years the bulwark of Britain.


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[Assistant] Vast sections of it have been cleared, for this is at the seat of the first ironworks of the country, and the trees have been felled to smelt the ore.


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[Assistant] Now the richer fields of the north have absorbed the trade, and nothing save those ravaged groves and great scars in the earth show the work of the past.


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[Assistant] Here in a clearing upon the green slope of a hill stood a long low stone house, approached by a curving drive running through the fields.


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[Assistant] Nearer the road, and surrounded on three sides by bushes, was a small outhouse, one window and the door facing in our direction. It was the scene of the murder.


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[Assistant] Stanley Hopkins led us first to the house, where he introduced us to a haggard grey-haired woman.


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[Assistant] The widow of the murdered man, whose gaunt and deep-lined face, with the furtive look of terror in the depths of her red-rimmed eyes, told of the years of hardship and ill usage which she had endured.


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[Assistant] With her was her daughter, a pale fair-haired girl whose eyes blazed defiantly at us as she told us that she was glad that her father was dead, and that she blessed the hand which had struck him down.


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[Assistant] It was a terrible household that black Peter Carey had made for himself, and it was with a sense of relief that we found ourselves in the sunlight again, and making our way along a path which had been worn across the fields by the feet of the dead man.


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[Assistant] The outhouse was the simplest of dwellings—wooden-walled, shingle-roofed, one window beside the door and one on the far side. Stanley Hopkins drew the key from his pocket and had stooped to the lock when he paused with a look of attention and surprise upon his face. "'Someone has been tampering with it,' he said.


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[Assistant] There could be no doubt of the fact. The woodwork was cut, and the scratches showed white through the paint, as if they had been that instant done. Holmes had been examining the window.


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[Assistant] Someone has tried to force this also. Whoever it was has failed to make his way in. He must have been a very poor burglar.


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[Assistant] This is a most extraordinary thing," said the inspector. I could swear that these marks were not here yesterday evening.


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[Assistant] Some curious person from the village, perhaps? I suggested.


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[Assistant] Very unlikely. Few of them would dare to set foot in the grounds. Far less try to force their way into the cabin. What do you think of it, Mr Holmes? I think that fortune is very kind to us. You mean that the person will come again?


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[Assistant] It is very probable. He came expecting to find the door open. He tried to get in with the blade of a very small penknife. He could not manage it. What would he do? Come again next night with a more useful tool.


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[Assistant] So I should say. It will be our fault if we are not there to receive him. Meanwhile, let me see the inside of the cabin.


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[Assistant] The traces of the tragedy had been removed, but the furniture within the little room still stood as it had been on the night of the crime.


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[Assistant] For two hours, with most intense concentration, Holmes examined every object in turn. But his face showed that his quest was not a successful one. Only once he paused in his patient investigation.


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[Assistant] Have you taken anything off this shelf, Hopkins? No, I've moved nothing. Something has been taken.


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[Assistant] There is less dust in this corner of the shelf than elsewhere. It may have been a book lying


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[Assistant] Well, well, I can do nothing more. Let us walk in these beautiful woods, Watson, and give a few hours to the birds and the flowers. We shall meet you here later, Hopkins, and see if we can come closer quarters with the gentleman who has paid this visit in the night.


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[Assistant] It was past eleven o'clock when we formed our little ambuscade. Hopkins was for leaving the door of the hut open, but Holmes was of the opinion that this would rouse the suspicions of the stranger.


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[Assistant] The lock was a perfectly simple one, and only a strong blade was needed to push it back. Holmes also suggested that we should wait not inside the hut, but outside it, among the bushes which grew round the farther window.


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[Assistant] In this way we should be able to watch our man if he struck a light, and see what his object was in this stealthy nocturnal visit.


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[Assistant] It was a long and melancholy vigil, and yet brought with it something of the thrill which the hunter feels when he lies beside the water-pool and waits for the coming of the thirsty beast of prey. What savage creature was it which might steal upon us out of the dark?


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[Assistant] Was it a fierce tiger of crime, which could only be taken fighting hard with flashing fang and claw, or would it prove to be some skulking jackal, dangerous only to the weak and unguarded?


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[Assistant] In absolute silence we crouched amongst the bushes, waiting for whatever might come.


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[Assistant] At first the steps of a few belated villagers, or the sound of voices from the village, lightened


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[Assistant] But one by one these interruptions died away, and an absolute stillness fell upon us, save for the chimes of the distant church, which told us of the progress of the night, and for the rustle and the whisper of a fine rain falling amid the foliage which roofed us in.


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[Assistant] Half-past two had chimed, and it was the darkest hour which preceded the dawn, when we all started, as a low but sharp click came from the direction of the gate. Someone had entered the drive.


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[Assistant] Again there was a long silence, and I had begun to fear that it was a false alarm.


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[Assistant] When a stealthy step was heard upon the other side of the hut, and a moment later a metallic scraping and clinking, the man was trying to force the lock.


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[Assistant] This time his skill was greater, or his tool was better, for there was a sudden snap and the creak of the hinges


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[Assistant] Then a match was struck, and next instant the steady light from a candle filled the interior of the hut.


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[Assistant] Through the gauze curtain our eyes were all riveted upon the scene within.


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[Assistant] The nocturnal visitor was a young man, frail and thin, with a black moustache which intensified the deadly pallor of his face. He could not have been much above twenty years of age


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[Assistant] I have never seen any human being who appeared to be in such a pitiable fright, for his teeth were visibly chattering, and he was shaking in every limb.


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[Assistant] He was dressed like a gentleman, in Norfolk jacket and knickerbockers, with a cloth cap upon his head.


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[Assistant] We watched him staring round with frightened eyes.


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[Assistant] Then he laid the candle-end upon the table and disappeared from our view into one of the corners.


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[Assistant] He returned with a large book, one of the log books which formed a line upon the shelves,


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[Assistant] Leaning on the table he rapidly turned over the leaves of this volume until he came to the entry which he sought.


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[Assistant] Then with an angry gesture of his clenched hand he closed the book, replaced it in the corner, and put out the light.


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[Assistant] He had hardly turned to leave the hut, when Hopkins' hand was on the fellow's collar, and I heard his loud gasp of terror as he understood that he was taken.


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[Assistant] The candle was re-lit, and there was our wretched captive, shivering and cowering in the grasp of the detective.


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[Assistant] He sank down upon the sea-chest and looked helplessly from one of us to the other.


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[Assistant] Now my fine fellow, said Stanley Hopkins, who are you, and what do you want here?


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[Assistant] You imagine I am connected with the death of Captain Peter Carey. I assure you that I am innocent.


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[Assistant] We'll see about that," said Hopkins. First of all, what is your name? It is John Hopley Nelligan.


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[Assistant] If you have no answer, it may go badly with you at the trial. The young man winced.


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[Assistant] And yet I hate to think of this old scandal gaining a new lease of life. Did you ever hear of Dawson and Nelligan?


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[Assistant] I could see from Hopkins' face that he never had, but Holmes was keenly interested.


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[Assistant] You mean the West Country bankers? said he.


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[Assistant] They failed for a million, ruined half the county families of Cornwall, and Neligan disappeared. Exactly, Neligan was my father. At last we were getting something positive.


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[Assistant] And yet it seemed a long gap between an absconding banker and Captain Peter Carey pinned against a wall with one of his own harpoons. We all listened intently to the young man's words.


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[Assistant] It was my father who was really concerned. Dawson had retired. I was only ten years of age at the time, but I was old enough to feel the shame and horror of it all.


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[Assistant] It has always been said that my father stole all the securities and fled. It is not true.


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[Assistant] It was his belief that if he were given time in which to realise them, all would be well and every creditor paid in full.


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[Assistant] He started in his little yacht for Norway just before the warrant was issued for his arrest.


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[Assistant] I can remember that last night, when he bade farewell to my mother. He left us a list of the securities he was taking, and he swore that he would come back with his honour cleared, and that none who had trusted him would suffer.


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[Assistant] Well, no word was ever heard from him again. Both the yacht and he vanished utterly.


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[Assistant] We believed, my mother and I, that he and it with the securities that he had taken with him were at the bottom of the sea.


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[Assistant] We had a faithful friend, however, who is a businessman, and it was he who discovered some time ago that some of the securities which my father had with him had reappeared on the London market. You can imagine our amazement.


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[Assistant] I spent months in trying to trace them, and at last, after many doubtings and difficulties, I discovered that the original seller had been Captain Peter Kerry, the owner of this hut. Naturally I made some inquiries about the man.


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[Assistant] I found that he had been in command of a whaler which was due to return from the Arctic seas at the very time when my father was crossing to Norway. The autumn of that year was a stormy one.


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[Assistant] And there was a long succession of southerly gales. My father's yacht may well have been blown to the north, and there met by Captain Peter Carey's ship.


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[Assistant] If that was so, what had become of my father?


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[Assistant] In any case, if I could prove from Peter Kerry's evidence how these securities came on the market, it would be a proof that my father had not sold them, and that he had no view to personal profit when he took them.


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[Assistant] I came down to Sussex with the intention of seeing the captain.


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[Assistant] But it was at this moment that his terrible death occurred.


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[Assistant] I read at the inquest a description of his cabin, in which it stated that the old log books of his vessel were preserved in it.


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[Assistant] It struck me that if I could see what occurred in the month of August 1883 on board the Sea Unicorn, I might settle the mystery of my father's fate.


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[Assistant] I tried last night to get at these log books, but was unable to open the door.


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[Assistant] Tonight I tried again and succeeded, but I find that the pages which deal with that month have been torn from the book.


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[Assistant] Then how do you account for that?" cried Hopkins, as he held up the damning notebook with the initials of our prisoner on the first leaf, and the blood-stain on the cover.


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[Assistant] The wretched man collapsed. He sank his face in his hands and trembled all over. Where did you get it? he groaned. I didn't know. I thought I'd lost it at the hotel. That's enough, said Hopkins sternly.


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[Assistant] Whatever else you have to say, you must say it in court. You will walk down with me now to the police station.


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[Assistant] Well, Mr Holmes, I am very much obliged to you and to your friend for coming down to help me.


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[Assistant] As it turns out, your presence was unnecessary, and I would have brought the case to this successful issue without you. But nonetheless I am grateful.


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[Assistant] Rooms have been reserved for you at the Bramblety Hotel, so we can all walk down to the village together. Well, Watson.


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[Assistant] What do you think of it? asked Holmes as we travelled back next morning. I can see that you are not satisfied. Oh yes, my dear Watson, I am perfectly satisfied.


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[Assistant] At the same time Stanley Hopkins's methods do not commend themselves to me.


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[Assistant] I am disappointed in Stanley Hopkins. I had hoped for better things from him


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[Assistant] One should always look for a possible alternative and provide against it. It is the first rule of criminal investigation.


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[Assistant] The line of investigation which I have myself been pursuing. It may give us nothing, I cannot tell, but at least I shall follow it to the end.


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[Assistant] Several letters were waiting for Holmes at Baker Street. He snatched one of them, opened it, and burst out into a triumphant chuckle of laughter.


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[Assistant] Excellent, Watson. The alternative develops. Have you telegraphed forms? Just write a couple of messages for me.


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[Assistant] Sumner, shipping agent, Ratcliffe Highway. Send three men on to arrive ten to-morrow morning. Basil.


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[Assistant] That's my name in those parts. The other is Inspector Stanley Hopkins, 46 Lord Street, Brixton. Come breakfast tomorrow at nine thirty. Important. Wire, if unable to come. Sherlock Holmes.


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[Assistant] There, Watson, this infernal case has haunted me for ten days. I hereby banish it completely from my presence. To-morrow I trust that we shall hear the last of it for ever.


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[Assistant] Sharp at the hour named, Inspector Stanley Hopkins appeared, and we sat down together to the excellent breakfast which Mrs. Hudson had prepared.


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[Assistant] The young detective was in high spirits at his success.


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[Assistant] You really think that your solution must be correct?" asked Holmes. I could not imagine a more complete case. It did not seem to me conclusive.


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[Assistant] You astonished me, Mr. Holmes. What more could one ask for?


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[Assistant] Does your explanation cover every point?


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[Assistant] Undoubtedly. I find that young Nelligan arrived at the Brammelty Hotel on the very day of the crime. He came on the pretense of playing golf. His room was on the ground floor, and he could get out when he liked.


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[Assistant] That very night he went down to the Woodman's Lee, saw Peter Carey at the hut, quarrelled with him, and killed him with a harpoon. Then, horrified by what he'd done, he fled out of the hut, dropping the notebook which he had brought with him in order to question Peter Carey about those different securities.


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[Assistant] You may have observed that some of them were marked with ticks, and the others, the great majority, were not.


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[Assistant] Those which are ticked have been traced on the London market, but the others, presumably, were still in the possession of Carey, and young Nelligan, according to his own account, was anxious to recover them in order to do the right thing by his father's creditors.


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[Assistant] After his flight he did not dare to approach the hut again for some time.


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[Assistant] It seems to me to have only one drawback, Hopkins, and that is that it is intrinsically impossible.


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[Assistant] You must really pay attention to these details.


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[Assistant] My friend Watson could tell you that I spent a whole morning in that exercise. It is no easy matter, and requires a strong and practised arm.


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[Assistant] But this blow was delivered with such violence that the head of the weapon sank deep into


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[Assistant] Do you imagine that this anemic youth was capable of so frightful an assault?


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[Assistant] Is he the man who hobnobbed in rum and water with Black Peter in the dead of the night?


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[Assistant] Was it his profile that was seen on the blind two nights before?


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[Assistant] No, no, Hopkins, it is another and more formidable person for whom we must seek.


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[Assistant] The detective's face had grown longer and longer during Holmes' speech. His hopes and his ambitions were all crumbling about him, but he would not abandon his position without a struggle.


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[Assistant] You can't deny that Nelligan was present that night, Mr Holmes.


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[Assistant] The book will prove that. I fancy that I have evidence enough to satisfy a jury, even if you are able to pick a hole in it.


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[Assistant] Besides, Mr. Holmes, I have laid my hand upon my man. As to this terrible person of yours, where is he?


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[Assistant] I rather fancy that he is on the stair," said Holmes serenely. I think, Watson, that you would do well to put that revolver where you can reach it.


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[Assistant] He rose and laid a written paper upon a side table. Now we are ready, said he.


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[Assistant] There had been some talking in gruff voices outside, and now Mrs Hudson opened the door to say that there were three men inquiring for Captain Basil.


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[Assistant] The first who entered was a little ribston pippin of a man, with ruddy cheeks and fluffy white side whiskers. Holmes had drawn a letter from his pocket. What name? he asked.


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[Assistant] I am sorry, Lancaster, but the berth is full. Here is half a sovereign for your trouble. Just step into this room and wait there for a few minutes.


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[Assistant] The second man was a long, dried-up creature with lank hair and sallow cheeks. His name was Hugh Pattins.


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[Assistant] He also received his dismissal, his half sovereign, and the order to wait.


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[Assistant] The third applicant was a man of remarkable appearance. A fierce, bull-dog face was framed in a tangle of hair and beard, and two bold dark eyes gleamed behind the cover of thick, tufted, overhung eyebrows.


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[Assistant] He saluted and stood sailor fashion, turning his cap round in his hands.


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[Assistant] Your name? asked Holmes. Patrick Cairns.


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[Assistant] He took a sheaf of worn and greasy forms from his pocket. Holmes glanced over them and returned them.


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[Assistant] You are just the man I want," said he. Here's the agreement on the side-table. If you sign it, the whole matter will be settled. The seaman lurched across the room and took up the pen. Shall I sign here? he asked, stooping over the table.


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[Assistant] Holmes leaned over his shoulder and passed both hands over his neck.


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[Assistant] I heard a click of steel and a bellow like an enraged bull.


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[Assistant] The next instant Holmes and the seamen were rolling on the ground together.


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[Assistant] He was a man of such gigantic strength that, even with the handcuffs which Holmes had so deftly fastened upon his wrists, he would have very quickly overpowered my friend had Hopkins and I not rushed to his rescue.


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[Assistant] Only when I pressed the cold muzzle of the revolver to his temple did he at last understand that resistance was vain.


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[Assistant] We lashed his ankles with cord and rose breathless from the struggle.


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[Assistant] I must really apologise, Hopkins," said Sherlock Holmes. I fear that the scrambled eggs are cold.


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[Assistant] However, you will enjoy the rest of your breakfast all the better, will you not, for the thought that you have brought your case to a triumphant conclusion. Stanley Hopkins was speechless with amazement.


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[Assistant] I don't know what to say, Mr. Holmes," he blurted out at last with a very red face.


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[Assistant] It seems to me that I have been making a fool of myself from the beginning. I understand now what I should never have forgotten, that I am the pupil and you are the master.


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[Assistant] We all learn by experience, and your lesson this time is that you should never lose sight of the alternative.


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[Assistant] You were so absorbed in young Nelligan that you could not spare a thought to Patrick Cairns, the true murderer of Peter Carey.


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[Assistant] The hoarse voice of the seaman broke in on our conversation. See here, mister, said he, I make no complaint of being manhandled in this fashion, but I would have you call things by their right names.


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[Assistant] You say I murdered Peter Carey. I say I killed Peter Carey. And there's all the difference. Maybe you don't believe what I say. Maybe you think I'm just slinging you a yarn.


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[Assistant] Not at all, said Holmes. Let us hear what you have to say.


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[Assistant] It's soon told, and by the Lord every word of its truth.


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[Assistant] I knew Black Peter, and when he pulled out his knife I whipped a parpoon through him sharp, for I knew that it was him or me. That's how he died. You can call it murder.


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[Assistant] Anyway, I'd as soon die with a rope round my neck as with Black Peter's knife in my heart. How came you there? asked Holmes. I'll tell it you from the beginning. Just sit me up a little, so as I can speak easy.


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[Assistant] It was in 83 that it happened, August of that year. Peter Kerry was master of the sea unicorn, and I was spare harpooner.


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[Assistant] We were coming out of the ice pack on our way home with headwinds and a weak southerly gale when we picked up a little craft that had been blown north.


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[Assistant] There was one man on her—a landsman. The crew had thought she would found her and made for the Norwegian coast in the dinghy. I guess they were all drowned. Well, we took him on board.


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[Assistant] And this man, and he and the skipper had some long talks in the cabin.


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[Assistant] All the baggage we took off with him was in one tin box. So far as I know the man's name was never mentioned.


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[Assistant] And on the second night, he disappeared as if he'd never been.


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[Assistant] It was given out that he had either thrown himself overboard or fallen overboard in the heavy weather that we were having.


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[Assistant] Only one man knew what had happened to him, and that was me, for with my own eyes I saw the skipper tip up his heels and put him over the rail in the middle watch of a dark night, two days before we sighted the Shetland lights.


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[Assistant] Well, I kept my knowledge to myself and waited to see what would come of it.


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[Assistant] When we got back to Scotland it was easily hushed up, and nobody asked any questions.


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[Assistant] A stranger died by accident and it was nobody's business to inquire.


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[Assistant] Shortly after Peter Carey gave up the sea, and it was long years before I could find where he was.


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[Assistant] I guessed that he had done the deed for the sake of what was in that tin box, and that he could afford now to pay me well for keeping my mouth shut.


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[Assistant] I found out where he was from a sailor man that had met him in London, and down I went to squeeze him.


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[Assistant] The first night he was reasonable enough and was ready to give me what would make me free of the sea for life. We were to fix it all two nights later.


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[Assistant] When I came, I found him three parts drunk and in a vile temper.


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[Assistant] We sat down and we drank and we yawned about old times, but the more he drank the less I liked the look on his face.


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[Assistant] I spotted that harpoon upon the wall, and I thought I might need it before I was through.


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[Assistant] Then at last he broke out at me spitting and cursing with murder in his eyes, and a great clasped knife in his hand.


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[Assistant] He had not time to get it from the sheath before I had the harpoon through him.


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[Assistant] Heavens, what a yell he gave. And his face gets between me and my sleep.


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[Assistant] I stood there with his blood splashing round me, and I waited for a bit, but all was quiet, so I took heart once more.


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[Assistant] I looked round and there was the tin box on the shelf.


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[Assistant] I had as much right to it as Peter Carey anyhow, so I took it with me and left the hut.


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[Assistant] Like a fool I left my backy pouch upon the table.


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[Assistant] Now I'll tell you the queerest part of the whole story.


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[Assistant] A man came slinking along, went into the hut, gave a cry as if he'd seen a ghost and legged it as hard as he could run until he was out of sight.


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[Assistant] Who he was, or what he wanted is more than I can tell.


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[Assistant] For my part I walked ten miles, got a train at Tunbridge Wells and so reached London, and no one the wiser.


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[Assistant] Well, when I came to examine the box, I found there was no money in it.


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[Assistant] And nothing but papers that I would not dare to sell.


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[Assistant] I had lost my hold on Black Peter and was stranded in London without a shilling. There was only my trade left.


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[Assistant] I saw these advertisements about harpooners and high wages, so I went to the shipping agents and they sent me here.


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[Assistant] That's all I know, and I say again that if I killed Black Peter the law should give me thanks, for I saved them the price of a hempen rope.


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[Assistant] A very clear statement," said Holmes, rising and lighting his pipe.


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[Assistant] I think, Hopkins, that you should lose no time in conveying your prisoner to a place of safety. This room is not well adapted for a cell, and Mr. Patrick Cairns occupies too large a proportion of our carpet.


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[Assistant] Mr. Holmes, said Hopkins, I do not know how to express my gratitude. Even now I don't understand how you attain this result.


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[Assistant] Simply by having the good fortune to get the right clue from the beginning.


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[Assistant] It is very possible if I had known about this notebook it might have led away my thoughts as it did yours. But all I heard pointed in the one direction—the amazing strength, the skill in the use of the harpoon, the rum and water, the sealskin tobacco pouch with the coarse tobacco,


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[Assistant] All these pointed to a seaman, and one who had been a whaler.


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[Assistant] I was convinced that the initials P. C. upon the pouch were a coincidence, and not those of Peter Carey, since he seldom smoked, and no pipe was found in his cabin.


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[Assistant] You remember that I asked whether Whiskey and Brandy were in the cabin. You said they were. How many landsmen are there who would drink rum when they could get these other spirits? Yes, I was certain it was a seaman. And how did you find him?


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[Assistant] My dear sir, the problem had become a very simple one.


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[Assistant] If it were a seaman, it could only be a seaman who had been with him on the sea unicorn. So far as I could learn he had sailed in no other ship.


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[Assistant] I spent three days in wiring to Dundee, and at the end of that time I had ascertained the names of the crew of the Sea Unicorn in 1883.


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[Assistant] When I found Patrick Cairns among the harpooners, my research was nearing its end.


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[Assistant] I argued that the man was probably in London and that he would desire to leave the country for a time.


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[Assistant] The tin box must be returned to him, but of course the securities which Peter Carey has sold are lost for ever.


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[Assistant] There's the Cab Hopkins, and you can remove your man. If you want me for the trial, my address and that of Watson will be somewhere in Norway. I'll send particulars later. End of The Adventure of Black Peter


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[Assistant] Had two cool parents, and loved all things science and superheroes. Everything changed though, when my dad was killed in the city hall bombing. I... I couldn't believe he was gone. But Peter Parker and his Aunt May, they were there for me. And so was Spider-Man, who I later found out was Pete. Crazy, right? Then when the Devil's Breath crisis started, things got intense. Seemed like all of Spidey's villains were on the loose.


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[Assistant] I managed to do my part to help him out. And after all that, believe it or not, a spider bit me. And I started to change. I didn't want to worry my mom, so I went to pee. And now, we're officially spider bros.


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[Assistant] I'm still learning to juggle this responsibility with everything else in my life. School, friends, a new home. I moved to Harlem a few weeks back. But I'll tell ya, I can't wait to see what the future holds.


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[Assistant] Maybe leave a little room for the new guy. Just in case.


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[Assistant] Okay, first we flush the core, then we wipe all data. You're sure they can't just make more of this stuff?


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[Assistant] I'll record us. Things go wrong, video uploads straight to the bugle.


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[Assistant] Triggering override in three, two,


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[Assistant] I was really glad you called. I needed a break. From what? Oh, just stuff.


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[Assistant] If that new Spider-Man hadn't shown up, everyone would have been fine. Please don't try to talk me out of this. I know what I'm doing.


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[Assistant] Good. So, that's my big secret. That's why I've been so busy. What's your excuse?


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[Assistant] You're always busy with stuff like that. What's the real reason?


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[Assistant] You know I'm not good with heights. You'll be fine. I'll be watching.


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[Assistant] You'll need to prove yourself to the underground. I'll show you how when we get to Fisk Tower.


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[Assistant] After he went to prison, the fed seized his property. They haven't gotten around to selling it, so we moved in.


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[Assistant] The underground. The tinkerer. Tinkerer's a knob to my roll.


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[Assistant] I built everything. The masks, the weapons. Programmable matter. Right.


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[Assistant] The underground tried to rob my granddad's shop and saw what I was working on. We made a deal.


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[Assistant] Notoriety. They wanna be so well known, they can get away with anything.


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[Assistant] Thanks for always having my back, man. Hey, I could use your help before you go. You got it.


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[Assistant] I want to cross-reference underground activity with buildings that can store new form. Maybe you could hack Ozcorp surveillance towers, or- I meant, it'll take a while to narrow down. That's alright. Thanks, man.


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[Assistant] It's Miles. I know I'm the last person you wanna talk to right now, but you need to listen. Krieger updated the specs on the reactor. If you plug unstable nuform into it,


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[Assistant] And I'm trying to save everyone else.


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[Assistant] Family? That didn't stop you from lying to me, manipulating me, fighting me? Being family isn't enough anymore.


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[Assistant] I don't either. But I can't be the person you want to turn me into. I can't turn my back when people need me.


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[Assistant] Museum closed for renovation, and the underground moves right in. Finn's gotta be inside.


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[Assistant] Finn! Come on! We need to finish this! You and me!


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[Assistant] Today, Oscorp Science Center. Tomorrow, every major museum in the world.


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[Assistant] Do you have tickets for the special exhibit? Oh, uhm, our project is on display. Didn't think we needed tickets.


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[Assistant] You do, and we're sold out. Can't let you go upstairs.


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[Assistant] The flashlights on our phones won't work. They won't reach.


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[Assistant] I'm not gonna vanish off the planet. We'll still hang out.


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[Assistant] Not that busy. I'm gonna make time for us. Seriously.


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[Assistant] Okay, okay, we'll get a picture. Love you dad, bye.


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[Assistant] You helped us get it working. Okay, okay, fine, fine, fine. Scoot over. Alright.


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[Assistant] You're breaking up. Where are you? Genki!


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[Assistant] If you can hear me, I'm on my way. Hang tight, man. Please!


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[Assistant] No! The reactor! Krieger changed the specs! You're not just gonna destroy Rockstorm Plaza! You're gonna vaporize all of Harlem!


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[Assistant] Roxxon did this uptown cause they saw us as disposable. Me. Rick. Finn. All of Harlem.


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[Assistant] Hey Pete, I'm working on a college application and it says I gotta tell them about myself.


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[Assistant] She's Councilwoman Rio Morales, and...


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[Assistant] There is a girl I like who's spectacular and inspiring, and I think is one of the best artists in the city. And I...


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[Assistant] Also got bitten by a radioactive spider that gave me superpowers. I learned how to be a Spider-Man from the OG. But I learned how to be a hero from my dad.


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[Assistant] He was killed by Martin Li in the city hall bombing.


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[Assistant] The good I try to do every day is the good my dad planted in me. But it's been hard.


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[Assistant] Welcome to the session on alleviating the habit of worry. Start by taking a comfortable position.


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[Assistant] Allowing your arms to rest gently by your side.


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[Assistant] Whenever you're ready, close your eyes.


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[Assistant] Let the weight of your body soften, releasing down into those places of contact and pressure.


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[Assistant] Then return your breath to normal so it's natural and easy.


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[Assistant] You can even say the word silently in your mind, to deepen concentration.


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[Assistant] It doesn't matter if they're healthy or even accurate.


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[Assistant] So part of this practice is bringing awareness to our automatic stream of consciousness. We get pulled into worry, and it's up to us to notice that happening so we can pull ourselves back.


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[Assistant] Otherwise our worries and ruminations become the soundtrack of our lives.


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[Assistant] Each time you notice you're caught up in thought, hold that thought in awareness and gently let it go, returning to the breath.


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[Assistant] Today we'll be discussing the habit of worry. Nearly everyone worries occasionally.


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[Assistant] And worry is a normal response to problems and the unknown. But here's the thing. There's productive and unproductive worry.


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[Assistant] If we're identifying problems and using effective problem-solving strategies, that's productive worry.


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[Assistant] But if we're worrying as a way of coping with problems we can't change, that's unproductive worry.


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[Assistant] This just adds worry and anxiety to our already unpleasant experience, increasing our suffering.


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[Assistant] And quickly escalates into a whole storyline. Whether we're worrying about our finances, career, family, or health.


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[Assistant] We play out hypothetical scenarios in our imagination, often in the form of a what if question. Like, what if I lose my job? What if I fail my exam? What if I get injured?


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[Assistant] And just like anything else, if you worry often enough, it becomes a habit.


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[Assistant] Worried thoughts become a hardwired response pattern in the mind. So when problems arise,


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[Assistant] Rather than observing them calmly and objectively, we fall into habitual worrying. This can interfere with sleep and concentration and our general well-being.


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[Assistant] So it's helpful to have tools to fall back on when worries pop up and take us on a ride.


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[Assistant] As usual, the first step is awareness.


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[Assistant] Then stop and pay attention to those thoughts.


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[Assistant] Notice yourself getting caught up in a storyline full of imagined projections of the future and say to yourself, ah, I know this pattern. This is me getting swept away again.


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[Assistant] Is it likely that what I'm worrying about might have varying possible outcomes? And that everything's not so black and white?


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[Assistant] And can I find a way to breathe in this space of uncertainty, since so much of life is uncertain? We take a few breaths and gently pull ourselves back to presence, breaking the string of worried thoughts. This is the practice, noticing the patterns of our mind


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[Assistant] It serves us to alleviate worry whenever possible. All we have is this moment.


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[Assistant] After careful thought, Piglet was comforted by this.


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[Assistant] You have to get to work. Dinner tomorrow?


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[Assistant] Hi, my name's Pete, or Mr., Mr. Parker. Uh, and we are all very lucky today, because this is physics class, and physics is awesome.


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[Assistant] How some insects, and uh, birds, reptiles can just run right across a pond? Two words. Surface tension. Bathroom!


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[Assistant] F divided by the length, L, of the line over which the force acts. Can anybody, uh, I, I need your help.


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[Assistant] Uh, Mr. Morales, is it? Uh, are you sure this isn't something you can handle yourself?


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[Assistant] Feel angry after all these years, Marco? You should try yoga!


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[Assistant] I don't know. I left in a hurry this morning. I'll just meet you there.


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[Assistant] I had the whole semester planned out. Next week, we were gonna make a potato-powered helicopter.


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[Assistant] Oh, well, you'll be fine then, because you're the best reporter they have.


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[Assistant] Oh man, I've been wanting to play this. Just need to find the time.


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[Assistant] I don't know. To be honest, I'd like to take some time off, but I can't really afford to.


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[Assistant] No, no, I can't let you do that. Plus, you said Jonah might clean house.


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[Assistant] I think that was in my bedroom. Why did she take a picture of that? Balance. What does that mean? Wonder if this is still there. I'm gonna go take a look.


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[Assistant] Don't worry, May. I'll keep your wheat cake recipe alive and well.


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[Assistant] Oh man. I see like a rogue wave sometimes.


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[Assistant] Alright, let's get started. We have three weeks left in the class and we'll be doing for the next three weeks.


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[Assistant] is really a series of applications of what we've learned so far, uh, to sort of help you understand how we add some richness to what we've learned and sort of take it to some more real world applications.


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[Assistant] So we're gonna start that today by talking about something we've really ignored in the course so far, which is uncertainty. And how uncertainty affects your decision making.


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[Assistant] So we've done so far in this class is we've sort of said, look, we've assumed whatever you make decisions, you make them with full knowledge and full certainty. But many, many decisions in life are made under conditions of uncertainty.


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[Assistant] Okay, so consider your decision to study for the final in this class.


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[Assistant] In our model so far, you would, you could optimize your studying across different units of the class. So our model so far, you'd know on the final which unit would be represented with what proportion. You'd optimize your studying appropriately. But of course you don't know that.


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[Assistant] You face uncertainty about what will be covered in the final and what proportion. You know the whole course is, you're responsible for the whole class, but obviously allocate your time, you're uncertain about how to allocate your time across the different subjects on the test. So how do you make that decision?


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[Assistant] Nothing, we need to bring our tools to bear on thinking about these kinds of decision making under uncertainty situations.


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[Assistant] And this isn't just about the test, you know, I decide whether to bring my umbrella today.


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[Assistant] If I bring my bell, there's a chance I'm going to lose it, but I don't want to get wet. I have to think about whether it's going to rain. It all depends on how certain I am it's going to rain, etc.


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[Assistant] There's decisions about uhm, you know, uh, whether to bet on a sporting event. That's decision uncertainty. And that's all the fun stuff in your life. We get to the anxiety ridden adult life.


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[Assistant] You've got things like whether to buy a 7 year mortgage or a 30 year mortgage, uh, whether to buy health insurance, what school to put your kids in. All these things involve a huge amount of uncertainty.


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[Assistant] And we have not yet developed the tools to deal with this. What's really cool


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[Assistant] Is that economics has a very useful tool to think about exactly these kinds of situations. That much like the other tools we've developed this semester, is pretty easy once you understand it. But it has a huge amount of power for explaining the world.


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[Assistant] And that's the tool of expected utility theory.


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[Assistant] And that's what we'll focus on today. That's what we'll learn today. The tool of expected utility theory.


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[Assistant] Okay, now, I'm gonna ask you a question. As always, I don't want you to try to outsmart me. I just want a quick gut reaction. Okay? I'm gonna offer you a bet. Not really, but imagine I was. I'm gonna flip a coin.


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[Assistant] Heads, you get $125. Tails, you give me $100.


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[Assistant] So you win 125 vs lose 100. How many of you take that bet?


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[Assistant] Okay, so, yeaah, you're a slightly more aggressive class than usual. About 40% of you taking the bet usually get more, about 20-25%. Okay? Now, uhm, yeaah. Uh, no, it's a one-time bet.


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[Assistant] Uhm, okay, so basically, uhm, now how do we think about this? Whether it's a good idea or not. Now those of you who raised your hand,


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[Assistant] Probably quickly did the math and did in your head what we call an expected value, expected value calculation.


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[Assistant] What's the expected value of any gamble? The expected value of any gamble is the probability that you win.


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[Assistant] Times what you win, plus the probability that you lose, times what you lose.


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[Assistant] So you did that calculation in your head. You said as long as he's not cheating using a fair coin, there's a 0.5 times 125.


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[Assistant] So those of you who raised your hand probably did that calculation quickly in your head and said yeah, this is a positive expected value. This is what we call in economics a more than fair bet.


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[Assistant] So a fair bet is one with an expected value of zero. So a bet with a positive expected value is more than fair.


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[Assistant] And you in your head said, I did that through, it's more than fair.


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[Assistant] Uhm, uh, and uh, that's why some of you raised your hands. But many of you didn't. And that doesn't mean you were wrong. It just means this is not the right way to think about it.


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[Assistant] Okay, the right way to think about it is that what you care about is not dollars. What you care about is utility. Dollars are meaningless. What you care about as a consumer is your utility.


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[Assistant] And ex- and so we don't want to think about expected value. We want to think about expected utility.


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[Assistant] Now what is expected utility? It's the same kind of formula as this, but with one change. Expected utility is the probability that you win times your utility if you win, plus the probability that you lose times your utility if you lose.


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[Assistant] And the reason is because utility is not a linear weighting of dollars. Utility is a concave weighting of dollars. Okay?


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[Assistant] As such, because utility is a concave weighting of dollars, it exhibits diminishing marginal rate of, uh, diminishing marginal utility or diminishing marginal rate of substitution.


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[Assistant] Diminishing marginal rate of substitution, as we talked about at adenosium in consumer theory. Okay?


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[Assistant] That means that the next dollar is worth less to you than the previous dollar. Okay?


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[Assistant] The next dollar is worth just think of diminishing utility. The next slice of pizza is worth less to you than the previous slice of pizza. Likewise, the next dollar is worth less to you than the previous dollar.


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[Assistant] As a result, losing a dollar makes you sadder than winning a dollar makes you happy.


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[Assistant] There's a nonlinearity that comes from diminishing marginal utility, diminishing marginal rate of substitution.


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[Assistant] So for example, let's think about our typical utility function that we used previously to consumer theory. Utility equals the square root of consumption.


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[Assistant] And let's just say you consume all your income as we always did. We've talked about savings the last couple lectures. Let's put savings aside again and just assume people consume all their income.


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[Assistant] Okay, and so utility is the square root of consumption. Okay, and let's say you start your initial consumption, C0, is 100. You start with $100 of consumption. Okay? Okay, your C0 is 100. So your initial utility, u0, is 10.


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[Assistant] I give you, I offer you this bet. What's the expected utility of this bet? Well, the expected utility of this bet is the probability you win 0.5 times utility if you win.


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[Assistant] Well utility if you win is the square root of your consumption if you win. What is your consumption if you win?


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[Assistant] If you win the bet, what's your consumption? So raise your hand and tell me. Starting with a hundred, and I made this bet with a yeaah.


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[Assistant] 225. You started with 100 and you won 125. If you lose the bet, what do you have?


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[Assistant] What do you have if you lose the bet? Zero. Okay? So you're expecting utility.


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[Assistant] Is 0.5 times this utility of what you get if you win. Plus 0.5 times the utility of what if you lose. Now if you do that math.


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[Assistant] You will find that that is 7.5. Your expected utility of this bet is 7.5. Which is less than your initial utility. So you should not take the bet. Which is, through the mechanism of psychology, why many of you didn't. Okay? You should not take the bet. Okay? And the reason is because


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[Assistant] You are what we call risk, and humans are what we call risk averse.


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[Assistant] That risk is inherently negative value to us. That a certain dollar is worth much more to us than an uncertain dollar. Just like a dollar today is worth more than a dollar tomorrow, a certain dollar is worth much more than an uncertain dollar.


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[Assistant] To see why, the best way to do this intuition here is graphical. So let's go to figure 20-1. And just sort of slowly walk through this. A little confusing graph.


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[Assistant] On the x-axis is your wealth, your total consumption or money you have. You consume everything you have. So it's wealth or alternatively consumption. On the y-axis in figure 20-1 is your utility. This is a graph of how much you consume against your utility.


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[Assistant] And as you can see, this is a concave graph. It is, it's exhibiting diminishing margin utility.


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[Assistant] Okay, each dollar, each dollar of wealth adds utility, but less and less over time.


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[Assistant] Just like a slice of pizza makes you happier, but less and less over time.


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[Assistant] Okay, you get that, so the shape of this curve,


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[Assistant] It's true for any utility function that features diminishing margin utility. That's pretty much any utility function we have used this semester. Except we're trying to trick you. Okay? Has diminishing margin utility. So as a result, it has this shape.


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[Assistant] Okay, now with the utility function of this shape, let's evaluate the gamble I just gave you. You start


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[Assistant] With wealth of a hundred. So you see in the x-axis the hundred point.


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[Assistant] That corresponds to utility of 10.


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[Assistant] Right, so you can trace up that 100 to utility curve, and then you go over to the y-axis. So that corresponds to the utility of 10. Okay? Now, think about what the gamble does.


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[Assistant] What the gamble does is say, look, there's two possible outcomes with 50% chance each. One is wealth of 225. That is the point all the way to the right. That leaves utility of 15. The other is wealth of zero. That's the point all the way to the left. That leaves utility of zero.


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[Assistant] What is the average of those two? Well, it's just a linear combination. Right? It's a 50% chance of each. So the average of those two is a wealth of 112.5.


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[Assistant] But an expected utility of 7.5. So you take, you draw a chord between those two points, between the zero point and point B. You find the midpoint of that chord.


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[Assistant] That's 12, 112.5, but then you trace that over to utility function. And you see the expected utility is only 7.5.


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[Assistant] And that's because we're not using a linear combination, we're using a nonlinear combination. A nonlinear concave combination, which means that moving up in terms of wealth makes you less happy than moving down in terms of wealth makes you sad. And you're really sad at zero.


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[Assistant] So it's going from 100 down to 0, makes you way sadder. They go from 100 up to 225, makes you happier. And that's all because diminishing March utility of income.


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[Assistant] So it's natural that this gamble would make you worse off, even though it's more than fair.


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[Assistant] Because yeaah, you're somewhat happier if you win. If you win, utility goes up from 10 to 15. That's great.


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[Assistant] But if you lose, it usually goes down from 10 to 0. That's really bad. So you don't want to take this risk.


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[Assistant] Okay, which is why, although you may not realize it, many of you, uh, wouldn't want to take that, that gamble. So using this graph, we can ask, okay, are there questions about that? Yeah.


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[Assistant] Well, uhm, you've answered, it's the same, the answers to those two questions are the same, it just depends on the probabilities. If the probabilities are .5 each, then those two answers, two questions are exactly the same.


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[Assistant] Because .5 each would be gain out weighing, loss is the same as on net positive. But if the probabilities aren't .5, you want to use this equation.


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[Assistant] So you basically want to say, is the weighted, it's about the weighted average change in utility essentially. Where the weights are these probabilities. Yeaah.


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[Assistant] Hold on, I'm gonna come to that. We're gonna come back to Gamble. We'll talk all about the lottery at the end. Okay? So uhm, okay, but do people understand the basis of this graph?


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[Assistant] Okay, so, using this graph, tell me the following. How much, answer the following, uhm, answer the following question. Okay, uhm,


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[Assistant] How much, let's say, this is a hard question, see if you can get this.


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[Assistant] Let's say that I said, you know what class? I'm going to force you to take this gamble.


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[Assistant] I'm gonna come in here and I'm gonna tell you I'm locking the door. You're not leaving.


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[Assistant] Without taking this gamble, unless you pay me not to force you. So I'm gonna offer you a more than fair bet.


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[Assistant] Would you be willing to pay me to get out of that bed? And how much would you be willing to pay me?


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[Assistant] Uh, okay, you're thinking about, sort of right, but you're still thinking in a linear world, not a non-linear world. Look at the graph. Okay, yeaah.


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[Assistant] But in a nonlinear world, you've got to account for the curvature. So the way to think about it is, right now, your utility from that bet, if I force you to take it, it leaves you a utility of $56.25.


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[Assistant] Okay, you can see that, just go backwards from the 7.5 utility down to what level of wealth that's equivalent.


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[Assistant] What that means is you would rather pay me.


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[Assistant] $43.74. Then take that bet. Think about how crazy that is for one second. I'm offering you a bet that is more than fair.


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[Assistant] And you will pay me almost half of your entire wealth to avoid taking that bet. And that's only with our standard utility function we always use.


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[Assistant] That's risk aversion. And the reason is because zero sucks so badly.


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[Assistant] Okay. The reason is because you're so sad going to zero that you really don't want to be in that situation. And so you will actually pay me $43.75 to avoid a more than fair bet. That's what's crazy. Okay. So another way to see this, let me ask you another question.


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[Assistant] How large, let's say I have for you the same bet, flip a coin, tails you lose a hundred, heads you win X. How large would X have to be for you to take the bet?


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[Assistant] Because then your expected utility is 10. Right, exactly. If it's 300, then I'm doing the square root of 400, which is 20, and the square root of 0. You average those, and you're gonna get expected utility of 10. So for you to take that bet, I would have to say, tails you lose 100, heads you in 300. I'd need to give you like a monstrously more than fair bet. And that is due to the principle of risk aversion.


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[Assistant] That basically because of diminishing marginal utility, risk conversion is something like made up, it's not some crazy concept. It just falls naturally out of diminishing marginal utility.


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[Assistant] Because making you sad, uhm, because losing, because moving down makes you sadder than moving up makes you happier. Okay? Any questions about that? Yeah.


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[Assistant] Great, okay, stop there. Let's go to the next section. You guys are way ahead of me as always. Let's go, let's talk about a couple extensions.


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[Assistant] Let's talk about a couple of extensions. First extension change utility function.


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[Assistant] Okay, suppose your utility function was of the form u equals 0.1 times c.


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[Assistant] Now I've chosen this particular form because the initial conditions are the same. With C0 of 100, u0 is still 10. So I'm starting from the same point as I was before. But now, would you take the bet and why?


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[Assistant] If that's your utility function, would you take the bet and why?


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[Assistant] What's your expected utility of that bet? Your expected utility is 0.5 times your utility of 225. So it's times 0.1 times 225.


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[Assistant] And solve it, you get 11.25. Which is greater than 10. So you would take the bet. Does anyone, any question about the math? I just did the expect utility evaluation. So you would take the bet. What's the difference? Why do you take the bet here? Yeah.


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[Assistant] If you're a linear utility function, what you care about is expected value. So you can see that. Do I have that? Yea. In figure 22.


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[Assistant] This is the case we call risk neutrality.


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[Assistant] With a linear utility function, you're risk neutral. Because a linear utility function does not have what?


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[Assistant] As a result, you're, you're just, you just care about expected value. Okay, there's, there's no difference between expected value and expected utility.


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[Assistant] It's all just now, the number's a little bit different because of the functional form, but it gives the same outcome. You'll always take a more than fair bet, and you reject a less than fair bet.


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[Assistant] So as people become moved from risk averse to risk neutral,


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[Assistant] Or as utility features less and less diminishing marginal utility, there'll be more and more willing to take gambles. But it doesn't have to stop there, we can go further.


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[Assistant] Imagine that I wrote utility of the form.


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[Assistant] Utility was of the form c squared over a thousand.


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[Assistant] A weird utility function, but once again created so that if c0 equals 100, u0 equals 10.


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[Assistant] Well, if you take the gamble, there's a 0.5 probability that you win. So then you would have, utility B would be 225 squared over 1000, and a 0.5 probability that you lose. So you just get 0.


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[Assistant] Okay, and the expected utility in that case is 25.3.


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[Assistant] The expected utility equals 25.3, which is way bigger than 10. So you take this gamble. Why? Because now you're risk loving. Because what does this say about diminishing marginal utility of income?


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[Assistant] This actually says you have increasing marginal utility of consumption. A utility function like this says the next slice of pizza makes you even happier than the previous slice of pizza. So look at figure 20-3. This is the risk-loving case.


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[Assistant] Okay, we don't really talk about this case because it sort of doesn't make sense. But just to understand how this works.


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[Assistant] Okay, same calculations before you start at a point like A.


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[Assistant] If you win, you go to B. If you lose, you go to zero. Well this shape utility function


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[Assistant] Going to B makes you way happier than going to zero makes you sad. So you love the gamble. Okay?


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[Assistant] In fact, you, with this utility function, you would take an unfair bet.


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[Assistant] Okay, so for example, imagine I change the gamble to one where it's win 100, loo- I'm sorry, win 75, lose 100.


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[Assistant] So I changed the gamble now. Win 75, lose 100. I made an unfair bet. The expected value is negative.


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[Assistant] Okay, well this person will still take that bet. If you do the math, if they win 75, they get 175. You do, just replace this with 175. And you do the math.


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[Assistant] Okay, you're gonna find that the expected utility in that case is 15.3.


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[Assistant] Which is greater than 10. So even an unfair bet.


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[Assistant] Lose 100, win 75 will still leave these risk-loving people better off than if they hadn't taken a bet. Yeah.


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[Assistant] Okay, great, I'm gonna come to that next. That's in these examples, but you've called me on an important assumption I'm making.


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[Assistant] Okay, these examples I have. Let's make sure we understand risk, neutral, risk, loving. Do people understand that? Okay, so now...


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[Assistant] Let's, uhm, now you actually have raised another issue. Let me ask a new question, once again.


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[Assistant] Forget everything you've learned. Got instincts. Here's the bet I'm offering you. Flip a coin.


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[Assistant] Heads, you win $12.50. Tails, you lose $10. Who takes that bet? Raise your hands if you take that bet. Okay, that's backwards. More of you should take that bet, not less of you. Okay, and why is that? Because of exactly what you just pointed out.


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[Assistant] It's because basically, if you think about that, uhm, think about that bit. Think about, let's go back to our old utility function, u equals square root of c. Okay?


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[Assistant] You're still risk averse. This is the guy who would have paid me 44 bucks to avoid the other bet is now happy to take this bet. Same person. What changed? What changed? Yeah.


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[Assistant] Exactly, because ultimately, infinitesimally, it's a linear curve. So if you go back to figure 21,


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[Assistant] At any given, for any given epsilon change from point A, it's linear.


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[Assistant] So essentially as you get small, as gambles get smaller and smaller relative to your starting point, you become more and more risk neutral.


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[Assistant] And remember it's linear, you just take the, so if I did a pen, if I did 12 and a half cents versus 10 cents, then unless you were crazy risk averse, you should take that bet.


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[Assistant] Because essentially you only care at that point it's so tiny relative to your wealth, you might as well use expected value.


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[Assistant] Okay, so as gambles become smaller relative to your income, utility function becomes locally flatter. Okay, utility function becomes locally flatter. And as a result, you become more and more risk neutral.


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[Assistant] Last point, why did so many of you still not take that bet?


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[Assistant] Well the answer is that even the model we've taught so far misses an important psychological phenomenon.


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[Assistant] So now I'm stepping out of standard micro and fundamental behavioral economics. Unfortunately, due to time semester, I'm not going to get to my lecture on behavioral economics. But if you guys want to learn, I'll talk a little bit about it in the next few lectures. I'll sprinkle it in. But course 11.13 is a fascinating course we offer here about how you build psychology and think about economics. And here's one example.


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[Assistant] Why is it that even with this gamble, even if I'd done the twelve and a half ten cent gamble, a bunch of you still wouldn't have taken it?


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[Assistant] Why is that? That's because humans not only feature risk aversion, humans also feature loss aversion.


[User] Please transcribe this text

[Assistant] Which is we have an irrational behavioral bias that losing by itself makes us sad relative to winning. Taking away something we have makes us sadder than getting something new. So here's a standard experiment that's run.


[User] Please transcribe this text

[Assistant] They take, they make, they get, they get a bunch of like $5 mugs, mugs worth about $5. They take people, and randomly half of the people, they ask, how much would you pay for this mug?


[User] Please transcribe this text

[Assistant] And half the people, they give them the mug and say, how much would you sell your mug for?


[User] Please transcribe this text

[Assistant] Half the people, they say, here's a mug, how much did you pay for it?


[User] Please transcribe this text

[Assistant] How people say, here's a mug, it's yours, but I want to buy it back, how much do you sell it to me for? The average person will pay three dollars.


[User] Please transcribe this text

[Assistant] But the average person wants $7 to sell it back. That makes no sense.


[User] Please transcribe this text

[Assistant] Either way, it's a mug, it's just a mug, it's trivially relevant to your wealth. It's just a mug, it doesn't really matter. But once people have it, they feel like, no, that's already mine, I don't want to sell it. That's loss aversion. People are biased by their starting points.


[User] Please transcribe this text

[Assistant] Okay, your very starting point dictates your willingness to take a gamble.


[User] Please transcribe this text

[Assistant] Which is not true in a standard economic model. But it's true in all laboratory experiments in psychology.


[User] Please transcribe this text

[Assistant] So, not only, so the reason people like gambles are not only, uh,


[User] Please transcribe this text

[Assistant] Because they're risk averse, but even more they're loss averse. So for example, this great economic studies, which show that there's a massive


[User] Please transcribe this text

[Assistant] Bias against selling your house for anything under the price you paid for it.


[User] Please transcribe this text

[Assistant] The people sort of, they're very sort of linear in the middle of the sale house above the price you paid for it, but there's this huge notch at the price you paid for it. They simply don't want to sell unless they paid for it. And that's this loss aversion idea. Okay, this comes up in many other contexts.


[User] Please transcribe this text

[Assistant] So that's, so there's two reasons why people are risk averse. People won't take gambles. The standard reason and the sort of extra psychological bias. Now.


[User] Please transcribe this text

[Assistant] This raises, this leads us naturally to the next section I want to go to, which is to talk about applications.


[User] Please transcribe this text

[Assistant] Of this theory and why it's important. And the first application I want to talk about is insurance.


[User] Please transcribe this text

[Assistant] Insurance is big business in America. Individuals in America.


[User] Please transcribe this text

[Assistant] Pay individuals, forgetting the government, just people.


[User] Please transcribe this text

[Assistant] Spend 1.5 trillion dollars a year on insurance products. Almost 10% of GDP.


[User] Please transcribe this text

[Assistant] This happens in our entire economy, it's people buying insurance. Health insurance is the biggest, life insurance, casualty and property insurance, auto insurance, etc. Add it all up, it's almost a tenth of our entire economy. Okay, why?


[User] Please transcribe this text

[Assistant] Because they're risk averse and also loss averse. I'm gonna put loss aversion aside and just use the standard framework. That just strengthens the argument. But it's because they're risk averse. So let's, let's do the math.


[User] Please transcribe this text

[Assistant] Okay? Imagine you're a single 25 year old male. I just, I'm only being gender biased here because there's no risk of pregnancy. Okay? If you're a single 25 year old male, in perfect health.


[User] Please transcribe this text

[Assistant] So the only risk you face health-wise is getting hit by a car.


[User] Please transcribe this text

[Assistant] Okay, that's basically a risk, otherwise you're basically not going to go to the doctor.