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[Assistant] When we were near the inn, Holmes suddenly cried out, Ah! My foot! I can't stand on it! Help me, Watson! I took his arm.


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[Assistant] And we walked slowly to the door of the inn. A man stood there, smoking and watching us. How are you, Mr. Ruben Hayes? said Holmes. Who are you? And how do you know my name? said the man. He looked very unfriendly. Because it's on the door of the inn, over your head,


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[Assistant] Where do you want to go? asked Mr. Hayes. To Holderness Hall. Oh! Friends of the Duke, are you? Mr. Hayes laughed.


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[Assistant] Looking at our muddy shoes and trousers. Holmes laughed too.


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[Assistant] Well, we are bringing him news of his lost son, he said. The boy is in Liverpool.


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[Assistant] Mr. Hayes' face went white, then red. Oh! he said carefully.


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[Assistant] That's, uh, that's good news. I worked for the Duke once, but he wasn't good to me. I don't like him, but I'm pleased about the boy. We all went into the inn. Now, said Holmes, something to eat first, please. Then you can bring round the bicycle.


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[Assistant] I haven't got a bicycle, said Mr Hayes. Holmes put a pound on the table.


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[Assistant] I tell you man that I haven't got a bicycle.


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[Assistant] You can have two horses to take you to the hall. He brought us something to eat and we ate hungrily. Through the window


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[Assistant] Lots of cow tracks, but no cows?


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[Assistant] And do you remember those tracks, Watson? He took out his notebook. There were tracks like this.


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[Assistant] And sometimes like this. And sometimes like this. Do you remember that, Watson? No, I don't, I said. What does it mean, Holmes?


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[Assistant] It means that it's a very strange cow, Watson. Cows don't move like that. Now, let's go quietly out


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[Assistant] And have a look round these stables.


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[Assistant] There were two tired looking horses in the stables.


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[Assistant] Holmes looked carefully at one of the horse's feet and laughed. Look, Watson, old shoes, but new nails.


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[Assistant] Oh, this case gets more interesting every minute.


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[Assistant] I began to ask Holmes a question. But suddenly, we heard someone behind us. And there was Mr. Reuben Hayes. His face was red and angry. What are you doing in my stables? He cried.


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[Assistant] We're just looking at your horses, Mr. Hayes," said Holmes, smiling. Why, are you afraid of something? The man opened his mouth, then closed it quickly. His face was still red and angry. Holmes did not give him time to speak.


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[Assistant] I think your horses are tired, Mr. Hayes. We can walk to the hall. It's not far.


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[Assistant] Three kilometers by the road, Mr. Hayes said. His eyes still watched us angrily.


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[Assistant] We walked along the road for about a hundred metres. Then Holmes took my arm. Quick, Watson! Off the road and up the hill.


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[Assistant] Then we can come down the hill at the back of the inn.


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[Assistant] We can learn a lot more from Mr. Hayes. Ah, who's this? Watson, get down!


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[Assistant] There was a bicycle on the road. It came past us very quickly. And we saw the rider.


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[Assistant] Mr. James Wilder, the Duke's secretary. His face was white and afraid. Quick, Watson, said Holmes. We must watch him. We ran down the hill.


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[Assistant] And stopped when we could see the back door of the inn.


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[Assistant] Wilder's bicycle was by the wall near the door. For five minutes, nothing happened.


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[Assistant] Then a man on a horse rode quickly out of the stables and disappeared down the road. What do you think of that, Watson? said Holmes. Somebody's running away! Yes, but not James Wilder, because there he is at the door.


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[Assistant] We could see Wilder in the light from the door. He stood there looking out. And ten minutes later, another man came down the road and went into the inn. Then a light came on in a room upstairs. Come, Watson, we must get nearer, Holmes said.


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[Assistant] We went down the hill and walked very quietly to the back door of the inn. The bicycle was still by the wall. Holmes looked at the wheel and laughed quietly. A Dunlop tyre, Watson!


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[Assistant] I must look through that upstairs window, so I need your back, Watson. Holmes stood on my back, but only for a second, and then he was down again. Come, my friend, he said. It's a long walk to the school, so let's start at once.


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[Assistant] I can give you all the answers to this mystery tomorrow.


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[Assistant] It was a long, cold, muddy walk back to the school. I went to bed at once. But Holmes went out again. To Mackelton, I think. I was very tired.


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[Assistant] And slept all night like a dead man.


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[Assistant] That's right. An advanced lesson where we talk about investing in emerging markets.


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[Assistant] Well it sounds like the dad has missed out on a really big investment opportunity, hey?


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[Assistant] Yeah, yeah, yeah. So, for example, when there's a lot of turmoil in the market, that means stock prices are changing drastically from day to day.


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[Assistant] Let's move to our third phrase, aggregate demand.


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[Assistant] Yeah, and we want to listen to the dialogue one more time, but before we do, we have three words for you that we want you to listen for.


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[Assistant] That's right. So basically he wants to get a bunch of cash together so that he can buy a house or get married or whatever. It's that money you need to start your life, right?


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[Assistant] Inevitable basically means, uh, unavoidable.


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[Assistant] So this guy thinks that the recession is unavoidable.


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[Assistant] Yes, inevitable. You know, this word inevitable, if you apply the root words, you can get a noun, an adjective, or an adverb, right?


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[Assistant] So we've got some examples where you can see this word in action.


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[Assistant] Right, well inevitably we have to move on to our third words.


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[Assistant] We've got some examples of the phrase, hit up, let's listen.


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[Assistant] Actually, I'm not all that crazy about Italian food.


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[Assistant] I'm in the mood for something a bit lighter.


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[Assistant] Ella, you took me there last time I visited, and I got food poisoning, remember?


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[Assistant] Ella, you took me there last time I visited, and I got food poisoning, remember?


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[Assistant] That may sound ridiculous. Our bodies love to sit, right?


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[Assistant] The body's unique physical structure gives us the ability to stand up straight against the pull of gravity.


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[Assistant] Joints, muscles, and ligaments that are attached to the bones hold it all together.


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[Assistant] In areas that are the most compressed, your nerves, arteries and veins can become blocked, which limits nerve signaling, causing the numbness, and reduces blood flow in your limbs, causing them to swell.


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[Assistant] What effect does all of this stasis have on the brain? Most of the time, you probably sit down to use your brain. But ironically, lengthy periods of sitting actually run counter to this goal.


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[Assistant] Being stationary reduces blood flow and the amount of oxygen entering your bloodstream through your lungs. Your brain requires both of those things to remain alert, so your concentration levels will most likely dip as your brain activity slows.


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[Assistant] So what seems like such a harmless habit actually has the power to change our health?


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[Assistant] But luckily, the solutions to this mounting threat are simple and intuitive. When you have no choice but to sit, try switching the slouch for a straighter spine.


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[Assistant] But mostly, just appreciate that bodies are built for motion, not for stillness. In fact, since the video's almost over, why not stand up and stretch right now? Treat your body to a walk. It'll thank you later.


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[Assistant] Every year, campers work together to create something useful. A gift for future campers. Working toward this common goal is key to forming the strong bonds that will last well beyond your time here at camp.


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[Assistant] I still can't believe you talked gloriosa into having a fashion show. We're in the middle of the woods for crying out loud. We're supposed to be roughing it.


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[Assistant] At least the fishies are eating well. Let's salvage what we can out of the water. Maybe we can still fix this. We have to try! Can't ever-


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[Assistant] Wait, that dream could be a reality.


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[Assistant] Okay, why don't you lay off touching stuff for a while? Oh dear.


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[Assistant] It's nice to meet all of you too. Were you just talking to the birds? Uhm, yes.


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[Assistant] So much for my theory that leaving CHS would mean leaving any new magic business behind. Something at the camp must be making this happen. Uhm, Gaia Everfree?


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[Assistant] Twilight, there's no midnight sparkle. There's only you. How did you know what I was thinking? When I touched your hand, I could see things. I could understand why you were leaving.


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[Assistant] Come back, we embrace the magic. And make the magic part of you.


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[Assistant] Ah, this is all too much for you. You have to let it go. I knew it.


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[Assistant] It's Sunset. She says to meet her by the rock quarry. I thought we weren't supposed to hike out that far.


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[Assistant] Wait. I thought Timber was just faking there was a magical nature creature. Are you saying it's real? Timber? What does he have to do with any of this?


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[Assistant] I don't think I can lift something that big. It's our only chance of getting out of here and helping our friends.


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[Assistant] I don't wanna use too much. Midnight Sparkle could take over. Twilight! Our friends are in there!


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[Assistant] Up to you! You can use your magic to pull the brambles apart! No! There's too many of them! It would take too much magic!


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[Assistant] Yes, today we're going to learn a little bit about Chinese New Year in English, and we're also going to learn some language for describing things that we're excited about. Okay, yeah, I'm excited to hear the show.


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[Assistant] Yes, so it's basically small pieces of dough with maybe some meat or some vegetables inside.


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[Assistant] So if you know Italian food, they're really similar to a tortellini.


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[Assistant] So on Chinese New Year, there are millions of firecrackers.


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[Assistant] Well let's listen to our dialogue a second time, and this time it'll be a little bit slower so that you can understand the language a bit better.


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[Assistant] We have four phrases for you today. And the first one is, I'm so excited about.


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[Assistant] Or you can say, I'm really looking forward to seeing that movie.


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[Assistant] Well I guess we're ready to listen to our dialogue for the third time, and then when we come back, Dani's gonna tell us all about Chinese New Year.


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[Assistant] So I wanna know more about these fireworks and firecrackers on Chinese New Year.


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[Assistant] I've seen Chinese New Year three times in China and each time I've just been amazed.


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[Assistant] Well everyone, uh, we've just learned about how New Year's is celebrated in China, and we want to know how do you celebrate New Year's in your country?


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[Assistant] So come to our website at EnglishPod.com and leave us your comments.


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[Assistant] Ten minutes, you've got five minutes left. Now's the time to set up for that handover.


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[Assistant] Happy with that? Yes, good, good, good. That looks good.


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[Assistant] No, don't worry about it. I'll take care of everything.


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[Assistant] Thank you for coming. You look delicious. Uh, I mean beautiful. Please come in.


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[Assistant] No, don't worry about it. I'll take care of everything. I'll see you tonight. Come with an appetite. I know I will.


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[Assistant] Ladies. Thank you for coming. You look delicious. I mean, beautiful. Please come in.


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[Assistant] No, don't worry about it. I'll take care of everything.


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[Assistant] Thank you for coming. You look delicious. Uh, I mean beautiful. Please come in.


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[Assistant] No matter what they throw at us, I've just got to put my game face on and really slam this challenge.


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[Assistant] Cooking one chook over three rounds is gonna be really hard. Coming up with three dishes, uh, it's mind-boggling.


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[Assistant] Today I'm making a chicken sausage with an onion puree and a chicken jus. I'm gonna turn the breast meat into a mousse with herbs and wrap it in chicken skin.


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[Assistant] Thanks guys. I'm definitely taking a big chance of using so much of the chicken, but I think it's worth the risk.


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[Assistant] The 45 minutes is going by really quickly. I need to get my sausage cooked through perfectly. I just want that nice crispy skin. Just a good texture against the soft mission side.


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[Assistant] Chicken sausage with an onion potato puree and a chicken jus.


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[Assistant] Only the best two cooks out of the first round will be safe. Hopefully I've done enough not to go into round two.


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[Assistant] We don't have enough time to start again, so Jess and I are going to have to think quickly on what we can do to increase the flavour.


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[Assistant] Convincing a predator to attack might seem counterproductive if you don't want to be eaten. And getting them to attack your head might seem like the absolute worst idea ever. But that's exactly what these little guppies do. They taunt larger fish and get them to attack at their eyes. And that's actually safer for them.


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[Assistant] Let me explain. Trinidadian guppies are eaten by bigger fish called cichlids, which are ambush predators. When a cichlid is hungry, it hides and waits for a smaller fish to swim within reach. And then, boom!


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[Assistant] It's like a yummy fish dinner was delivered straight to its door. But these guppies have figured out how to make the cichlids attack on their terms.


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[Assistant] Allowing them to lure the predators into missing. First, they draw the cichlids' attention using conspicuous coloration.


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[Assistant] Highly noticeable colors that get the hunter looking where the guppy wants it to attack. But here's the thing. If the guppies were always conspicuously colored, they'd know where a cichlid would attack, but not when. Which is why they can change their color.


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[Assistant] And specifically, they can change the color of their eyes. Normally, their irises are silver, but they can turn them black. See, the color comes from cells that have sacs of pigment inside. Melanin, the black pigment that guppies use to change their eye color, is found in a special type of cell known as a melanophore. And when melanin is at the center of the melanophore,


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[Assistant] Hormonal and nervous responses signal their melanophores to rearrange. Proteins pull melanin from the center of each cell out across the entire thing. And the whole eye goes black in about three seconds. Those black eyes are much more noticeable.


[User] Please transcribe this text

[Assistant] So when a guppy changes its eye color, it's basically daring the cichlid to aim for its head. Which I know seems like the last place you'd want to be bitten.


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[Assistant] If the attack is aimed there, instead of its middle, where the cichlid would usually attack, the guppy can bend around its center to dodge the predator. So basically, they use their eyes kind of like a matador cape.


[User] Please transcribe this text

[Assistant] Luring danger into lunging at the wrong angle and allowing the guppy to twist away at the last second and escape. And the international team of researchers who wrote about this amazing tactic in a 2020 Current Biology paper


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[Assistant] Found that larger guppies are even better at this, as their center pivot point is even further from their eyes. So they think this adaptation may have allowed this species to evolve a bigger size overall. So next time you're faced with a stressful situation, consider tackling it like a guppy. Head on.


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[Assistant] That's why the animal world is full of adaptations to stop predators, like…


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[Assistant] Pretty much nothing eats them. Velvet ants aren't technically ants, they're wasps. The males can fly but the females don't have wings. What they do have is a massive stinger.


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[Assistant] In fact, relative to their size, they've got the longest stinger of any wasp.


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[Assistant] And some seriously painful venom, too. Still, they don't rely on it alone to deter predators.


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[Assistant] They also have a super tough exoskeleton. It takes about five times the force to crush a velvet ant


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[Assistant] As it does to squish a bald-faced hornet for example.


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[Assistant] They're round and slippery, making them hard to bite down on, something researchers realized firsthand while trying to crush these things. The crudders kept slipping out of their grasp. Of course, the velvet ant doesn't want it to come to that, so they employ an array of warning signals. Their velvet sections are brightly colored as a


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[Assistant] It seems to train other animals not to mess with them too. Like, in one experiment, lizards that had a run-in with a velvet ant still avoided them over a year later. And in another,


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[Assistant] Birds were wary of eating one of their favorite tasty treats simply because researchers had painted them to look like velvet ants. Predators don't even need to have encountered a specific species of them. Many velvet ants mimic each other's coloring in what scientists call mullerian mimicry. So if a predator encounters one, they're unlikely to mess with any of the others.


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[Assistant] Scientists have set up showdowns between velvet ants and many potential predators just to see what bites. They tried spiders, lizards, actual ants, birds, moles, gerbils, shrews,


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[Assistant] Almost all of them avoided the velvet ants entirely. And the few that did catch them mostly spat them up. As far as anyone can tell, toads are the only animals that occasionally…


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[Assistant] But they don't have an easy time of it. They swallow their food whole, and velvet ants can survive for over 20 minutes inside a toad's stomach. So even toads end up spitting them out more often than not. Velvet ants' extreme investment in defense likely has something to do with their lifestyle. Females can't fly away from predators.


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[Assistant] They spend lots of time on the ground looking for places to lay their eggs. See, these ants are parasites.


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[Assistant] To reproduce, they find nests of other bees and wasps, and lay their eggs inside. When the larvae hatch, they feed on the other species helplessly young. Oh, also, those nests are often well-defended by other stinging insects. So I guess if you're regularly that rude to your neighbors, you'd better be as tough as a velvet ant.


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[Assistant] Hi. I want to ask you guys a question. How many languages do you speak? This is not a rhetorical question.


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[Assistant] The definition at the bottom refers to specialized fields like medicine, science, tech. We know they have their own vernacular, their own jargon. But what most interested me was that definition right in the center there. The system of communication used by a particular community or country.


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[Assistant] And I'm not interested in altering this definition, I'm interested in applying it to everything we do. Because I believe that we speak far more languages than we realize. And for the rest of our time together, I'm going to attempt to speak in one language that is native to every single human being in this room.


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[Assistant] But that changes things a little bit, because then it's no longer a presentation. It becomes a conversation.


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[Assistant] And for any interaction to happen, there has to be a degree of willingness on both parties.


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[Assistant] And I think if we just are willing, we will see the magic that can happen with just a little bit of willingness. So I've chosen a relatively low-risk, common denominator that can kind of gauge if we're all willing. If you're happy and you know it, clap your hands.


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[Assistant] And look at a person sitting anywhere and start laughing.


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[Assistant] And I know that wasn't nice, and I'm sorry, but in that moment, some of us felt something.


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[Assistant] You see, we're often aware of what language does when we speak somebody's language, what it does to connect, what it does to bind. But we often forget what it does when you can't speak that language, what it does to isolate, what it does to exclude. And I want us to hold on as we journey through kind of our, uh, little walk of languages here.


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[Assistant] It has no equivalent in the English lexicon. The best definition would be something like an extreme grace or an extreme humility. But that doesn't quite get the job done. So I'm going to give you an example. If two gentlemen were walking by each other, it would be very common for the first one to look at the other one and say, which means, I am indebted to you.


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[Assistant] With new languages come new concepts that didn't exist before. And the other thing is sometimes we think language is about understanding the meaning of a word, but I believe language is about making a word meaningful for yourself.


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[Assistant] And for those of us that are in the know, we know that's text speak, or SMS language. It's a series of characters meant to convey the most amount of meaning with the least amount of characters. Which sounds pretty similar to our definition of language, a system of communication used by a community.


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[Assistant] Anyone who's ever gotten to a argument via text can make a case for how it's maybe not the best method of communication.


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[Assistant] But what if I told you that what you saw earlier was a modern day love letter? If you follow along, for the time being, I love you lots. Because you positively bring out all the best in me. And I laugh out loud, in other words, let me know what's up.


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[Assistant] Every language we learn is a portal by which we can access another language. The more you know, the more you can speak.


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[Assistant] And it's something common that we all do. We take any new concept and we filter it through an already existing access of reality within us.


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[Assistant] And that's why languages are so important, because they give us access to new worlds, not just people. It's not just about seeing or hearing, it's about feeling, experiencing, sharing.


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[Assistant] And despite these languages that we've covered, I really don't think we've covered one of the most profound languages that there are, and that's the language of experience. That's why when you're talking with someone, if they've shared something that you've shared, you don't need to explain it much. Or that's why when you're sharing a story and you finish and the people you're talking to don't quite get it, the first thing we all say is, I guess you had to be there.


[User] Please transcribe this text

[Assistant] I guess you had to be here this week to know what this is about. It's kind of hard to explain, isn't it?


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[Assistant] And for the sake of our research, I'm going to close by asking that you participate one more time in this language of experience. I'm going to filter through some languages. And if I'm speaking your language, I'm going to ask that you just stand and you stay standing. You don't need to ask permission, just let me know that you see me and I can also see you, if you speak this language of experience.


[User] Please transcribe this text

[Assistant] When I was growing up, uh, in primary school, at the end of the year, we would have these parties. And we'd vote on whether we wanted to celebrate at an amusement park or a water park.


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[Assistant] I don't know about you, but sometimes when I approach a dressing room, my sweat glands start activating on their own, because I know the garment is not going to look like it did on me, like it did on that mannequin. Or how about this, when I would go to family functions or family gatherings, every time I wanted a second plate, and I usually did,


[User] Please transcribe this text

[Assistant] It was a whole exercise in cost-benefit analysis. My relatives looking at me like, I don't know, you really need that? Looks like you're doing OK there, bud.


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[Assistant] Do my cheeks have a big pinch me sign that I didn't see?


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[Assistant] And if you're squirming or you're laughing or you stood up or you're beginning to stand, you're speaking the language that I endearingly call the language of growing up a fat kid.


[User] Please transcribe this text

[Assistant] I want you to stay standing. Again, if I'm speaking your language, please go ahead and stand. Imagine two bills in my hand. One is the phone bill and one is the electric bill.


[User] Please transcribe this text

[Assistant] You gotta be resourceful. You gotta figure it out. And if you're standing, you know the language of barely making ends meet. A financial struggle.


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[Assistant] And if you've been lucky enough to speak that language, you understand that there is no motivator of greatness like deficiency. Not having resources, not having looks, not having finances, can often be the barren soil from which the most productive seeds are painstakingly plowed and harvested. I'm going to ask if you speak this language. The second you recognize it, feel free to stand.


[User] Please transcribe this text

[Assistant] I mean, my dad was hungry, we'd all rush to the dinner table to eat because that's what we did before, we ate together. So we were going to continue doing that.


[User] Please transcribe this text

[Assistant] And I didn't understand why we were losing this battle, because I was taught if you fight and you have the right spirit, you're supposed to win. And we weren't winning.


[User] Please transcribe this text

[Assistant] For any of you that stood up, you know very well that I'm speaking the language of watching a loved one battle cancer.


[User] Please transcribe this text

[Assistant] Any terminal illness is a derivative of that language. I want to speak one last language.


[User] Please transcribe this text

[Assistant] But I like to call it the language of disconnection. I don't mean disconnection, I mean disconnection.


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[Assistant] From where we are from our own thoughts, so we can occupy another space.


[User] Please transcribe this text

[Assistant] And now that I'm speaking your language, I'm going to ask you to go ahead and stand, since we're speaking the same language. Because I believe that language of being the minority is one of the most important languages you can ever speak in your life.


[User] Please transcribe this text

[Assistant] Because how you feel in that position of compromise will directly determine how you act in that position of power.


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[Assistant] Most of the girls in the world are complaining about it. Most of the poems in the world been written about it.


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[Assistant] Most of the broken hearts I know are walking without it, started to doubt it, or lost without it. Most of the shadows in the dark have forgotten about it.


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[Assistant] When I'm in it and I feel it, I be shoutin' about it. Everybody in the whole world knowin' about it. I'm hurt and broke down and be flowin' about it. Goin' about it wrong, cause I didn't allow it. Can the wound or scar heal without it? Can't the way that you feel be concealed about it? Everybody has their own ideal about it. Dream about it. Appeal about it. So what's the deal about it?


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[Assistant] Is the one we have the toughest time speaking or expressing.


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[Assistant] And I challenge you when you see someone to ask yourself, what languages do we share?


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[Assistant] And if you don't come up with anything, ask yourself what languages could we share? And if you still don't come up with anything, ask yourself what languages can I learn? And no matter how inconsequential,


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[Assistant] Okay, now you really have to film me in. What's it like?


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[Assistant] Well, actually, we had a fantastic time last night. He was amazing. Okay.


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[Assistant] He's quite tall, around 6'1".


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[Assistant] He's in his early thirties, and he's got the most beautiful dark brown eyes. He sounds hot! What does he do for a living? You know what? This is the best part.


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[Assistant] David is a junior investment banker at Fortune Bank, so he's got a


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[Assistant] He's quite tall, around 6'1", he's in his early thirties, and he's got the most beautiful dark brown eyes.


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[Assistant] He's really good looking. He's quite tall, around 6'1". He's in his early 30's. And he's got the most beautiful dark brown eyes.


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[Assistant] Okay, now you really have to film me in. What's he like?


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[Assistant] He's really good looking. He's quite tall around 6'1".


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[Assistant] Just taking in the scenery, Gloriosa Daisy. It's so... relaxing.


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[Assistant] In this video and in the video after this one, I want to tell you about some of the practical tricks for making gradient descent work well.


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[Assistant] In this video I want to tell you about an idea called feature scaling. Here's the idea.


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[Assistant] If you have a problem where you have multiple features, if you make sure that the features are on a similar scale, by which I mean make sure that the different features take on similar ranges of values, then gradient descent can converge more quickly.


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[Assistant] Concretely, let's say you have a problem with two features, where x1 is the size of a house and takes on values between, say, 0 to 2000, and x2 is the number of bedrooms, and maybe that takes on values between 1 and 5.


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[Assistant] If you plot the contours of the cos function j of theta,


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[Assistant] Then the contours may look like this, where, let's see, j of theta is a function of parameters theta 0, theta 1, and theta 2. I'm going to ignore theta 0. So let's forget about theta 0 and pretend it's a function of only theta 1 and theta 2.


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[Assistant] But if x1 can take on a much larger range of values than x2, it turns out that the contours of the cost function J of theta


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[Assistant] Can take on this sort of a very, very skewed elliptical shape.


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[Assistant] Ellipses, uhm, or these very tall, skinny ovals can form the, uhm, contours of the cos function J of theta.


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[Assistant] And if you run gradient descent on this sort of, uh, cost function,


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[Assistant] Your gradients may end up taking a long time and can sort of oscillate back and forth. It can take a long time.


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[Assistant] Before I can finally find his way to the global minimum.


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[Assistant] In fact, you can imagine if these contours were exaggerated even more, they would draw incredibly skinny, tall skinny contours.


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[Assistant] And it can be even more extreme than that. Then, you know, gradient descent can just, well, it turns out gradient descent will just have a much harder time taking its way, meandering around. It can take a long time to find its way to the global minimum.


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[Assistant] In these settings, a useful thing to do is to scale the features.


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[Assistant] Concretely, if you instead define the feature x1 to be the size of the house divided by 2000, and define x2 to be maybe the number of bedrooms divided by 5,


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[Assistant] Then the contours of the cross function j can become


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[Assistant] Much more, uh, much less skewed so that the contours may look more like circles. And if you run gradient descent on a cost function like this, then gradient descent


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[Assistant] You can show mathematically, you can find a much more direct path to the global minimum rather than taking a much more convoluted path where it's sort of trying to follow a much more complicated trajectory to get to the global minimum.


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[Assistant] So by scaling the features so that there take on similar ranges of values, in this example we end up with both features x1 and x2 between 0 and 1.


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[Assistant] You can wind up with an implementation of gradient descent. They can converge much faster.


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[Assistant] More generally, when we're performing feature scaling, what we often want to do is get every feature into approximately a minus one to plus one range. And uhm, concretely, you know, your feature x zero, that's always equal to one, so that's already in that range.


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[Assistant] But you may end up dividing other features by different numbers to get them to this range.


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[Assistant] And the numbers minus 1 and plus 1 aren't too important. So if you have a feature, x1, that winds up being between 0 and 3, say, that's not a problem, or if you end up having a different feature, that winds up being between, you know, minus 2 and 3.


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[Assistant] Positive 0.5. Again, this is close enough to minus 1 and plus 1 that, you know, that's fine, that's fine.


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[Assistant] It's only if you have a different feature, say x3, that is between, say,


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[Assistant] That ranges from minus one hundred to plus one hundred, then, you know, this is a very different range of values than minus one and plus one. So, so this might be a less well-scaled feature.


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[Assistant] And similarly, if your features take on a very, very small range of values, so if x4 takes on values between minus 0.0001 and positive 0.0001,


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[Assistant] Then again, this takes on a much smaller range of values than the minus 1 to plus 1 range. And again, I would consider this feature poorly scaled.


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[Assistant] So you want the range of values, you know, it can be a bit bigger than plus one, a bit smaller than plus one.


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[Assistant] But just not much bigger, like plus 100 here, and not too much smaller, like 0.001 over there.


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[Assistant] Different people have different rules of thumb, but the one that I use is that if a feature takes on a range of values from say, minus 3 to plus 3, I usually think that should be just fine. Uhm, but maybe if it takes on much larger values than plus 3 or minus 3, I mean it's not to worry.


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[Assistant] And uh, if it takes on values from say, minus one-third to one-third,


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[Assistant] You know, I think that's fine too, or zero to one-third or minus one-third to zero or just, that's, that's typical range of values that I consider okay. But if it takes on a much tinier range of values like explore here, then again, I might start to worry. So.


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[Assistant] The take home message is, uh, don't worry if your features are not exactly on the same scale or exactly in the same range of values, but so long as they're all close enough to this, gradient descent should work okay.


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[Assistant] In addition to dividing by sort of the maximum value, when performing feature scaling, sometimes people will also do what's called mean normalization.


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[Assistant] And what I mean by that is that you might take the feature xi and replace it with xi minus mu i.


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[Assistant] To make your features have approximately zero mean. And uhm, obviously we won't apply this to the feature x zero, because the feature x zero is always equal to one, so it cannot have an average value of zero.


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[Assistant] But concretely, for other features, if the range of sizes of a house takes on values between 0 to 2000, and if, you know, the average size of a house is equal to 1000, then you might


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[Assistant] Use this formula, uhm, size, set the feature x1 to be the size minus the average value divided by 2000. And, uh, similarly if, you know, on average, if, uh, your houses have one to five bedrooms,


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[Assistant] And if, number of, and if on average a house has say two bedrooms, then you might use this formula.


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[Assistant] To, uhm, mean normalize the, uh, your second feature x2.


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[Assistant] And the more general rule is that you might take a feature x1 and replace it with


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[Assistant] of that feature and by range I mean let's say the maximum value minus the minimum value


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[Assistant] Or for those of you that know what the standard deviation of the variable is, setting S1 to be the standard deviation of the variable would be fine too, but taking this max minus min would be fine.


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[Assistant] And similarly for the second feature, x2, you replace x2 with this sort of thing.


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[Assistant] Subtract the mean of, of the feature and divide it by the range of values, meaning the max minus min.


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[Assistant] And uhm, this sort of formula will get your features, you know, maybe not exactly, but maybe roughly into these sorts of ranges.


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[Assistant] By the way, for those of you that are being super careful, technically, if we're taking the range as max minus min, this 5 here will actually become a 4. So if max is 5, min is 1, then the range of their values is actually equal to 4. But all of these are approximate.


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[Assistant] The feature scaling doesn't have to be too exact in order to get gradient descent to run quite a lot faster.


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[Assistant] So, now you know about feature scaling and if you apply this simple trick it can make gradient descent run much faster and converge in a lot fewer iterations.


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[Assistant] That was feature scaling. In the next video I'll tell you about another trick to make gradient descent work well in practice.


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[Assistant] Why aren't you with everyone else?


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[Assistant] She thought you'd talk her out of it. Because I would. Twilight, you can't leave.


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[Assistant] Ah, this is all too much for you! You have to let it go! I knew it! He wants her to get rid of the camp!


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[Assistant] Wait. I thought Timber was just faking there was a magical nature creature. Are you saying it's real? Timber? What does he have to do with any of this? Nothing.


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[Assistant] This camp has meant so much to so many people. My sister and me included.


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[Assistant] A shabby man named Estragon sits near a tree at dusk and struggles to remove his boot. He's soon joined by his friend Vladimir, who reminds his anxious companion that they must wait here for someone called Godot.


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[Assistant] So begins a vexing cycle in which the two debate when Goddor will come, why they're waiting, and whether they're even at the right tree.


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[Assistant] From here, Waiting for Godot only gets stranger, but it's considered a play that changed the face of modern drama. Written by Samuel Beckett between 1949 and 1955, it offers a simple but stirring question. What should the characters do?


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[Assistant] Such cryptic dialogue and circular reasoning are key features of the theatre of the absurd.


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[Assistant] A movement which emerged after the Second World War and found artists struggling to find meaning in devastation.


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[Assistant] The absurdists deconstructed plot, character, and language to question their meaning.


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[Assistant] And share their profound uncertainty on stage.


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[Assistant] While this may sound grim, the absurd blends its hopelessness with humor.


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[Assistant] This is reflected in Beckett's unique approach to genre in Waiting for Godot, which he branded, a tragicomedy in two acts.


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[Assistant] Tragically, the characters are locked in an existential conundrum.


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[Assistant] They wait in vain for an unknown figure to give them a sense of purpose, but their only sense of purpose comes from the act of waiting. While they wait, they sink into boredom, express religious dread, and contemplate suicide.


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[Assistant] But comically, there is a jagged humor to their predicament, which comes across in their language and movements.


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[Assistant] Their interactions are filled with bizarre wordplay, repetition and double entendre.


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[Assistant] As well as physical clowning, singing and dancing, and frantically swapping their hats.


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[Assistant] It's often unclear whether the audience is supposed to laugh or cry, or whether Beckett saw any difference between the two.


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[Assistant] Born in Dublin, Beckett studied English, French, and Italian before moving to Paris, where he spent most of his life writing theatre, poetry, and prose.


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[Assistant] While Beckett had a lifelong love of language, he also made space for silence by incorporating gaps, pauses, and moments of emptiness into his work.


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[Assistant] This was a key feature of his trademark uneven tempo and black humour, which became popular throughout the theatre of the absurd.


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[Assistant] He also cultivated a mysterious persona and refused to confirm or deny any speculations about the meaning of his work.


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[Assistant] This kept audiences guessing, increasing their fascination with his surreal worlds and enigmatic characters.


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[Assistant] The lack of any clear meaning makes Godot endlessly open to interpretation. Critics have offered countless readings of the play, resulting in a cycle of ambiguity and speculation that mirrors the plot of the drama itself.


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[Assistant] It's been read as an allegory of the Cold War, the French Resistance, and Britain's colonization of Ireland.


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[Assistant] The dynamic of the two protagonists has also sparked intense debate. They've been read as survivors of the apocalypse, an aging couple, two impotent friends, and even as personifications of Freud's ego and id.


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[Assistant] Famously, Beckett said the only thing he could be sure of was that Vladimir and Estragon were wearing bowler hats.


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[Assistant] Like the critical speculation and maddening plot, their language often goes in circles as the two bicker and banter, lose their train of thought, and pick up right where they left off.


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[Assistant] Beckett reminds us that, just like our daily lives, the world on stage doesn't always make sense. It can explore both reality and illusion. The familiar and the strange. And although a tidy narrative still appeals, the best theatre keeps us thinking. And waiting.


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[Assistant] While we have you, why not plunge into an existential vortex with this playlist? Or shake it off with a good old-fashioned cat video.


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[Assistant] Like the rhubarb got that nice kinda sourness to it and then the custard's just beautifully silky and the pastry's just amazing.


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[Assistant] Yeah, about five minutes ago. Oh, who's winning? The Bulls, of course.


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[Assistant] What? That wasn't a foul! Oh come on, ref!


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[Assistant] Don't worry, Shaq always screws up free throws.


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[Assistant] This ref needs glasses. Hey ref! Open your eyes! I can't believe you didn't see that.


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[Assistant] For nearly a decade, my collaborators and I at the Self-Assembly Lab have been working on material systems that transform themselves, assemble themselves and adapt to their environment.


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[Assistant] From our early work on 4D printing, where we printed objects, dipped them under water and they transform, to our active auxetics that respond to temperature and sunlight,


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[Assistant] To our more recent work on active textiles that respond to body temperature and change porosity,


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[Assistant] To our rapid liquid printing work, where we print inflatable structures that morph based on air pressure and go from one shape to another. Or our self-assembly work, where we dip objects underwater, they respond to wave energy and assemble themselves into precise objects like furniture.


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[Assistant] All of this research is about taking simple materials, activating them with forces in their environment, gravity, wind, waves, temperature, sunlight, and getting them to perform, getting them to transform, assemble, et cetera. How do we build smart things without complex electromechanical devices?


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[Assistant] But more recently, we were approached by a group in the Maldives, and they were interested in taking some of this research and ways of thinking and applying it to some of the challenges that they've faced in terms of climate change.


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[Assistant] And I actually walked away with a really different perspective on the future of climate change. Because you would imagine, you know, the Maldives are sinking, they're screwed, what are they going to do? But I walked away thinking they actually might be the model, the future model of the built-in environment where they can adapt and be resilient rather than our fixed man-made infrastructure.


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[Assistant] As more than 40 percent of the world's population is living in coastal areas, as sea levels rise and as storms get worse and worse, we're going to be more and more underwater. So it's imperative that we solve this pretty demanding problem.


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[Assistant] The second is that we can build barriers, we can build walls. The problem here is that we take a static solution, trying to fight against a super-dynamic high-energy problem, and nature is almost always going to win.


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[Assistant] So that's likely not going to work either. The third approach is using dredging. So dredging is where you suck up a bunch of sand from the deep ocean and you pump it back onto the beaches. If you go to any beach around the northeast or western coast, you'll see that they use dredging year after year after year just to survive. It's really not a good solution.


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[Assistant] In the Maldives, they do the same thing, and they can build an island in a month, a brand new island they build from dredging. But it's really, really bad for the marine ecosystem, and then they become addicted to dredging. They need to do that year after year.


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[Assistant] So what we're proposing is to work within forces of nature to build rather than destroy.


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[Assistant] And in my lab at MIT, we set up a wave tank, a big tank that's pumping waves, and we placed geometries underwater. We tried all sorts of different geometries. The waves interact with the geometry and then create turbulence and start to accumulate the sand.


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[Assistant] So the sand starts to form these sandbars on their own. Here's an aerial view. On the left-hand side, you'll see the beach that's growing. In the middle, you'll see the sandbar that formed. So these are geometries that collaborate with the force of the wave to build. We then started to fabricate one. This was in February in Boston.


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[Assistant] Large rolls of canvas, it's a biodegradable material, it's super cheap, easy to work with. We then sew it into these large bladders, and then we flew over there. And I know what you're thinking, this is not the fire festival.


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[Assistant] It's real life. It's real. And we flew there with these canvas bladders in our suitcases. We got sunburned because it was Boston winter. And then we filled them with sand and we placed them underwater. These are exactly the same geometries that you saw in the tank. They're just human scale.


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[Assistant] Large objects filled with sand. We place them underwater. They're just really simple geometries. In the front of them,


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[Assistant] You'll see it's clear water. The waves are crashing over. It's quite clear. And then on the back side, there's turbulence. The water and the sand is mixing up. It's causing sediment transport, and then the sand is accumulating. You'll see some friendly stingrays here that visited us.


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[Assistant] On the left is day one, the right is day three. You'll see the sand ripples in the light areas where the sand is accumulating just after two days. So this was last February, and it's very much ongoing work. This is just in the beginning of this research.


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[Assistant] Over the next year and longer, we're going to be studying this through satellite imagery and bathymetry data to understand what the short-term and long-term impacts are of natural sand accumulation in the environment. And the bigger vision, though, is that we want to build submersible geometries, almost like submarines that we can sink and float.


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[Assistant] Like adaptable artificial reefs, you could deploy them if there's a storm coming from one direction or another, or if the seasons are changing, you can use these adaptable reef structures to use the force of waves to accumulate sand. And we think this could be used in many coastal regions and many island nations around the world.


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[Assistant] But when we think about building smarter environments, think of smarter buildings or smarter cars or smarter clothing. That typically means adding more


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[Assistant] Power, more batteries, more devices, more cost, more complexity, and ultimately more failure. So we're always trying to think about how do we build smarter things with less? How do we build smarter things that are simple?


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[Assistant] And so what we're proposing at the lab and with this project specifically is to use simple materials like sand that collaborates with forces in the environment, like waves, to accumulate and adapt.


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[Assistant] We'd like to work with you, collaborate with us to develop this, to scale it and apply this way of thinking. We think it's a different model for climate change, one that's about adaptation and resilience rather than resistance and fear.


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[Assistant] This episode was brought to you by the Music for Scientists album, now available on all streaming services.


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[Assistant] Theft in nature isn't exactly a novel idea. I mean, animals steal stuff from each other all the time. Squirrels steal food. Burrowing owls steal burrows.


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[Assistant] In other words, the toxin puts holes in the target cells, which can cause them to rupture. And when that happens, the cell loses critical nutrients. Even worse, those pores also give other toxins a way in. So even if the pores themselves don't cause a cell to die,


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[Assistant] They take them from cnidarians and use them for their own defense. Take eolid nudibranchs, for example.


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[Assistant] Commonly called sea slugs, these animals are some of the few that can successfully wrangle a stinging cnidarian, like a coral or anemone. After they catch their prey, the nudibranchs eat the animal's tentacles, including the nematocysts.


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[Assistant] The part that delivers the venom. Somehow, they do this without getting stung themselves, but that's still not the most impressive part. Once the slug has ingested the pneumaticists,


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[Assistant] They travel through its digestive system to special glands in its serrata.


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[Assistant] The detached cerata could sting the predator, but could also just distract it while the slug makes its escape. Next up, we've got cyanogenic glucosides, which are toxins produced by plants for self-defense. Chewing or digesting a cyanogenic glucoside releases hydrogen cyanide.


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[Assistant] And that can ultimately cause cell death. Except, these glucosides are also found in some plants that are regularly eaten by herbivores. So in many cases, like for the bird's foot trefoil, these compounds don't protect them from large animals.


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[Assistant] Cows can pretty happily munch on this stuff. But the glucosides do provide protection against smaller predators like snails and insects. That is, except for the six-spot burnet.


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[Assistant] A moth that depends on bird's foot trefoil as a larval host. Like cows, the brunette's larvae can eat trefoil all day without suffering ill effects.


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[Assistant] Despite being much, much smaller than our bovine friends. And to pull this off, the larvae have a few tricks. For one, they eat fast.


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[Assistant] Which limits the amount of time they're in contact with the cyanogenic glucosides. But most importantly, the environment in their gut just doesn't break down those compounds. In an acidic gut like ours, those molecules would be digested and release hydrogen cyanide.


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[Assistant] But the brunette larvae has a gut that's more basic than acidic. The brunette isn't the only member of the moth and butterfly family that doesn't digest these molecules.


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[Assistant] But what happens next is the special part. See, the brunette larvae don't just leave the glucosides alone. Instead, they move them into their own tissues. Scientists don't know much about how they do this, but they know that once the glucosides are in place, they act as a powerful defense mechanism. In fact, the intact molecules remain in the insect's tissues even after it turns into a moth. The moth keeps the glucosides in defense droplets inside cavities in its skin.


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[Assistant] And then when the moth tangles with a predator, it releases the droplets. In small doses, this means the moth tastes bad.


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[Assistant] But in large doses, it might be deadly. Most predators never find out, though, because they know better than to bother a six-spot burnet. Up next are the cardenolides. These are cardiac-active steroids, which broadly means they mess with the heart. Once inside your body, they block the sodium-potassium pump.


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[Assistant] Blocking them can cause an irregular heartbeat, and if it's severe enough, can lead to heart blockage or even cardiac arrest. Cardenolides are found in plants all over the world, including the African acocanthara tree, which has a cardenolide called wabean in its bark and roots. Indigenous Somalis use this toxin to poison their arotips and make it easier to bring down big game-like elephants. And the usefulness of wabean hasn't been lost on the African crested rat, either. It deliberately steals the tree's toxin by chewing its roots and bark,


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[Assistant] Mixing it up with its saliva. Then, the creature applies this mixture to the specialized guard hairs that cover its body, kind of like how you might slather on a conditioner or a styling gel. The guard hairs absorb the toxin and then deliver it to any predator that's foolish enough to bite the rat. What's especially wild is that cardenolides are the same toxins used in rat poison, yet they don't seem to harm this particular rodent.


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[Assistant] Scientists don't really know why, but it might be because their salivary glands are unusually large and may produce secretions that can somehow process the toxin. Now, like cardenolides, bufodenolides are steroidal toxins, and they also affect sodium-potassium pumps. They cause an increase in sodium and a decrease in potassium in the cell, which prevents the cell from conducting electricity. That can lead to a heartbeat that's too fast or too slow,


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[Assistant] And again, in severe cases, it can cause cardiac arrest. But don't tell that to the tiger keelback. This snake keeps bufadenylides in special glands on its neck called nuchal glands. But again, it doesn't make these toxins itself.


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[Assistant] This time, it gets them from the toads that it eats. Luckily for the snake, it's resistant to bufadenylides. In fact, a lot of snakes have a natural resistance to these toxins, including ones that don't even eat toads. Studies have found that these snakes seem to get their immunity from unique amino acids on the part of the


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[Assistant] suggesting that the toxins are transported there in blood plasma. And when the snake doesn't eat toads,


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[Assistant] It also doesn't have bufadenylides in its glands at all. Instead, they fill up with really benign stuff, like water, lipids, and carbohydrates. So, toad eating isn't just about food, it's also important for self-defense. And as a nice bonus, mother snakes can pass the toxin along to their offspring as well. And finally, batrachotoxins are poisons that affect the nervous system.


[User] Please transcribe this text

[Assistant] These toxins affect the sodium channels in nerves and muscles, changing their sensitivity to voltage and their ability to choose which ions to transfer across membrane.


[User] Please transcribe this text

[Assistant] The result is that nerves can no longer send signals to muscles, which is pretty bad news, especially for the heart. Humans famously steal batrachotoxins from poison dart frogs,


[User] Please transcribe this text

[Assistant] So named because the toxin can be used to make darts a whole lot more lethal. But other animals steal these toxins too, though not necessarily from frogs. New Guinean passerine birds get batrachotoxins from the malaria beetles that they eat. Like poison dart frogs, the birds aren't affected by the toxins.


[User] Please transcribe this text

[Assistant] Possibly because they have special sodium channels that have evolved resistance to them. Regardless, somewhere along the evolutionary road, the birds developed the ability to store these toxins and secrete them in their feathers and skin.


[User] Please transcribe this text

[Assistant] Instead of, you know, just digesting them. Scientists aren't completely sure how they do this, but the result is clear. The birds themselves become toxic.


[User] Please transcribe this text

[Assistant] See, feathers in general act as a barrier between a predator and a bird's flesh. For most birds, it isn't a super effective barrier, because the predator can just


[User] Please transcribe this text

[Assistant] But if you're a passerine, predators that mess with your feathers will get a nasty surprise. The toxin dose isn't usually large enough to kill, but it can cause respiratory irritation and other unpleasantries. The toxin also seems to help the passerine ward off parasites, like lice. In fact, a 1999 study found that lice seemed to deliberately avoid the feathers of toxic birds. Lice that do come into contact with the toxin also had shorter lifespans.


[User] Please transcribe this text

[Assistant] So, fewer lice to start with, and a shorter irritation from those that do attach. Some studies also suggest that the passerine may be able to transfer batrachotoxins from their feathers to their eggs.


[User] Please transcribe this text

[Assistant] Potentially protecting the eggs from nest robbers. So whether it's something they do deliberately or a bit of a happy accident, nature's thieves can be pretty crafty. Also, toxin stealing is still an active area of research, so it's probably a lot more common than scientists even realize. Still, there's a lot to appreciate about what we do understand.


[User] Please transcribe this text

[Assistant] How these animals sequester and use toxins can teach us important things about how structures in their bodies evolved and how species interact. Just, you know, make sure you handle with care.


[User] Please transcribe this text

[Assistant] If all of these toxin-stealing animals have got you pumped up about the wonders of the world, you might want to check out Music for Scientists after this. It's an album that was inspired by the beauty of science.


[User] Please transcribe this text

[Assistant] The songs were written and recorded by Patrick Olson, and the whole project is an homage to people of science. If you want to check it out, we recommend starting with Aristarchus in the Rain, which is a bit of a bop. You can start streaming at the link in the description.


[User] Please transcribe this text

[Assistant] I bake bread a lot and we usually eat it fresh. So it's a bit of a funny challenge trying to incorporate bread into food as a ingredient.


[User] Please transcribe this text

[Assistant] I'm happy with something that I just came up virtually on the spot.


[User] Please transcribe this text

[Assistant] Yeah, the lime's perfectly cooked. I got worried for a tick that I left it too long, but it's, it looks beautiful.


[User] Please transcribe this text

[Assistant] In this video, I want to give you more practical tips for getting gradient descent to work.


[User] Please transcribe this text

[Assistant] The ideas in this video will center around the learning rate alpha. Concretely,


[User] Please transcribe this text

[Assistant] Here's the gradient descent update rule, and what I want to do in this video is tell you about what I think of as debugging, and some tips for making sure that gradient descent is working correctly. And second, I want to tell you how to choose the learning rate alpha, at least how I go about choosing it.


[User] Please transcribe this text

[Assistant] The job of gradient descent is to find the value of theta for you that, you know, hopefully minimizes the cost function J of theta.


[User] Please transcribe this text

[Assistant] What I often do is therefore plot the cost function J of theta


[User] Please transcribe this text

[Assistant] As gradient descent runs. So the x-axis here is the number of iterations of gradient descent, and as gradient descent runs, you hopefully get a plot that maybe looks like this.


[User] Please transcribe this text

[Assistant] Notice that the x-axis is number of iterations. Previously we were looking at plots of j of theta.


[User] Please transcribe this text

[Assistant] I'm going to run gradient descent for 100 iterations, and whatever value I get for theta after 100 iterations, I'm going to get, you know, some value of theta after 100 iterations, and I'm going to evaluate the cost function J of theta.


[User] Please transcribe this text

[Assistant] For the value of theta I get after 100 iterations and this vertical height is the value of J of theta.


[User] Please transcribe this text

[Assistant] For the value of theta, I got after 100 iterations of gradient descent. And this point here,


[User] Please transcribe this text

[Assistant] For the theta that I get after I've run gradient descent for 200 iterations.


[User] Please transcribe this text

[Assistant] So what this plot is showing is it's showing the value of your cost function after each iteration of gradient descent, and if gradient descent is working properly, then J of theta should decrease after every iteration.


[User] Please transcribe this text

[Assistant] If you look at the specific figure that I've drawn, you know, it looks like by the time you've gotten out to maybe 300 iterations, between 300 and 400 iterations in this segment, it looks like J of theta hasn't gone down much more. So by the time you get to 400 iterations, it looks like this curve has flattened out here, and so


[User] Please transcribe this text

[Assistant] Way out here at 400 generations it looks like gradient descent has more or less converged because your cost function isn't going down much more.


[User] Please transcribe this text

[Assistant] By the way, the number of iterations that gradient descent takes to converge for a particular application


[User] Please transcribe this text

[Assistant] So maybe for one application, gradient descent, we converge after just 30 iterations. For a different iteration,


[User] Please transcribe this text

[Assistant] For a different application, gradient descent may take 3,000 iterations. For another algorithm, for another learning algorithm, it may take 3 million iterations. It turns out to be very difficult to tell in advance how many iterations gradient descent needs to converge. And it's usually by plotting this sort of plot.


[User] Please transcribe this text

[Assistant] Calling the cost function as we increase the number of iterations is usually by looking at these plots that I try to tell if gradient descent has converged.


[User] Please transcribe this text

[Assistant] It's also possible to come up with automatic convergence tests, namely to have an algorithm try to tell you if


[User] Please transcribe this text

[Assistant] Gradient descent has converged, and here's maybe a pretty typical example of an automatic convergence test. And such a test may declare convergence if your cost function J of theta decreases by less than some small value, some small value epsilon, some small value 10 to the minus 3 in one iteration.


[User] Please transcribe this text

[Assistant] But I find that usually choosing what this threshold is, is pretty difficult. And so in order to check your gradient descent is converged, I actually tend to look at plots like these, like this figure on the left, rather than rely on an automatic convergence test.


[User] Please transcribe this text

[Assistant] Looking at this sort of figure can also tell you or give you an advance warning if maybe gradient descent is not working correctly.


[User] Please transcribe this text

[Assistant] Concretely, if you plot J of theta as a function of the number of iterations, then, and if you see a figure like this where J of theta is actually increasing, then that gives you a clear sign that gradient descent is not working.


[User] Please transcribe this text

[Assistant] And uhm, a figure like this usually means that you should be using a learning rate alpha. If JfData is actually increasing,


[User] Please transcribe this text

[Assistant] The most common cause for that is if you're maybe trying to minimize the function that maybe looks like this.


[User] Please transcribe this text

[Assistant] But if your learning rate is too big, then if you start off there, gradient descent may overshoot the minimum and send you there. And if the learning rate is too big, it may overshoot again and send you there, and so on.


[User] Please transcribe this text

[Assistant] So that, you know, what you really wanted was for it to start here and for it to slowly go downhill.


[User] Please transcribe this text

[Assistant] Alright, but if the learning rate is too big, then gradient descent can instead


[User] Please transcribe this text

[Assistant] Keep on overshooting the minimum so that you actually end up getting worse and worse, so sort of getting to higher values of the cost function J of theta so that you end up with a plot like this. And if you see a plot like this, the fix usually is to just use a smaller value of alpha.


[User] Please transcribe this text

[Assistant] And to fix for something like this is also to use a smaller value of alpha.


[User] Please transcribe this text

[Assistant] I'm not going to prove it here, but under mild assumptions about the cost function J, which does hold true for linear regression, you can show, mathematicians have shown that if your learning rate alpha is small enough, then J of theta should decrease on every single iteration. So if this doesn't happen, it probably means alpha is too big and you should set it smaller.


[User] Please transcribe this text

[Assistant] But of course you also don't want your learning rate to be too small, because if you do that, if you were to do that, then gradient descent can be slow to converge. And if alpha were too small, you might end up starting out here, say,


[User] Please transcribe this text

[Assistant] And you know, end up taking just miniscule, miniscule baby steps.


[User] Please transcribe this text

[Assistant] Right, and just taking a lot, a lot of, taking a lot of iterations before you finally get to the minimum. And so if alpha is too small, pre-intercent can make very slow progress and be slow to converge. To summarize, if the learning rate is too small, you can have a slow convergence problem.


[User] Please transcribe this text

[Assistant] And the learning rate is too large, J of theta may not decrease on every iteration, and it may not even converge.


[User] Please transcribe this text

[Assistant] In some cases, if the learning rate is too large, slow convergence is also possible. But, uh,


[User] Please transcribe this text

[Assistant] The more common problem you see is that just that j of theta may not decrease on every iteration. And in order to debug all of these things,


[User] Please transcribe this text

[Assistant] Often plotting that J of theta as a function of the number of iterations can help you figure out what's going on.


[User] Please transcribe this text

[Assistant] So these are factor of 10 differences, and for these different values of alpha, just plot J of theta as a function of number of iterations, and, uh, then pick the value of alpha that, you know, seems to be causing J of theta to decrease rapidly.


[User] Please transcribe this text

[Assistant] In fact, what I do actually isn't these steps of 10. So this is, you know, this is a scale factor of 10, if each step up. What I actually do is try this range of values.


[User] Please transcribe this text

[Assistant] And so on, where, uh, this is, you know, 0.001. I'll then increase the learning rate threefold to get 0.03. And then this step up, this is another roughly threefold increase point from 0.003 to 0.01. And, and so these are roughly, you know,


[User] Please transcribe this text

[Assistant] Trying out great in the sense with each value I try being about 3x bigger than the previous value.


[User] Please transcribe this text

[Assistant] So what I'll do is try a range of values until I've made sure that I've found one value that's too small and make sure I've found one value that's too large and then I sort of try to


[User] Please transcribe this text

[Assistant] Pick the largest possible value or just something slightly smaller than the largest reasonable value that I've found and, uh, when I do that, usually this gives me a good learning rate for my problem.


[User] Please transcribe this text

[Assistant] And if you do this too, hopefully you'll be able to choose a good learning rate for your implementation of gradient descent.


[User] Please transcribe this text

[Assistant] No, I don't really do bolognese at home. My kids don't like bolognese. They find it a bit, uh, a bit mushy, the mince. But steaks and, uh, lamb I cook a lot at home. I'm making pan-fried rum with anchovy butters, smoked carrot puree, and caramelized onion.


[User] Please transcribe this text

[Assistant] The sashish touch is always flavors. So, I'm using goncalo to render the fats to give the extra flavor to my caramelized onion.


[User] Please transcribe this text

[Assistant] For my anchovies butter, I put heaps of anchovies. Anchovies give the umami to the butter.


[User] Please transcribe this text

[Assistant] Today I use a rum with anchovy butter, carrot puree and caramelized onion. The rum start to have nice grill marks on it. It looks very beautiful. The color is amazing. I'm sharing the sides also very well. It looks very good. I hope the judges like it all together.


[User] Please transcribe this text

[Assistant] Also, what protects you if your insurance company goes under? Well, the regulator is supposed to have checked that they're doing things right.


[User] Please transcribe this text

[Assistant] But what if the regulator messes up and you buy insurance and now there's some big catastrophe and the insurance company goes bankrupt and can't pay you?


[User] Please transcribe this text

[Assistant] So, the state governments have set up insurance guarantee funds. There's a lot of complexity to this whole business. It's not so simple and easy.


[User] Please transcribe this text

[Assistant] So the first step, it wasn't until the 20th century that these even set up.


[User] Please transcribe this text

[Assistant] It's like deposit insurance when you have a bank. When you go to the bank, you'll see FDIC insured, Federal Deposit Insurance Corporation. But we have similar insurance of the failure of the insurance companies. Uh, but not until 1941.


[User] Please transcribe this text

[Assistant] There was no insurance guarantee. So here's our local insurance guarantee fund. Connecticut Life and Health Insurance Guarantee Association. It was created in 1972. That's not that long ago. It's kind of remarkable that before 1972, if your insurance company failed in Connecticut, you were just out of luck.


[User] Please transcribe this text

[Assistant] But now they will, uh, insure your insurance against, uh, a maximum death benefit of fifty thousand, five hundred thousand dollars.


[User] Please transcribe this text

[Assistant] Uh, it's still not big enough because if you are as a young person, what is your present value, your lifetime present value? It must be several million dollars. Uh, so five hundred thousand dollars just doesn't cut it, but at least it's something.


[User] Please transcribe this text

[Assistant] Other countries have insurance. The China Insurance Regulatory Commission has set up a state-owned non-profit called China Insurance Protection.


[User] Please transcribe this text

[Assistant] See, one thing I like, this is a course in financial markets and I like this institutional detail because to me it's what makes things work.


[User] Please transcribe this text

[Assistant] Well, the uh, financial crisis of 2008 took everyone by surprise.


[User] Please transcribe this text

[Assistant] That's a concern, and it's been a concern of lawmakers. Part of the issue though is that AIG was bailed out, but the stockholders did not do well. They didn't enrich the stockholders. It was a disaster.


[User] Please transcribe this text

[Assistant] The US government took over securities regulation in the 1930s after the Great Depression. They formed the Securities and Exchange Commission to regulate stocks and bonds from the federal level. They never did that for, uh,


[User] Please transcribe this text

[Assistant] In fact, the McCarran-Ferguson Act of 1945 delegated insurance regulation to the states. So there's 50 different state regulators, all different. Now this is chaos because companies like to operate nationally, but they have 50 different regulators, one for each state.


[User] Please transcribe this text

[Assistant] So there was a non-profit called National Association of Insurance Commissioners, NAIC, which is not government.


[User] Please transcribe this text

[Assistant] It's set up by the insurance industry and they have regular meetings creating suggested laws for insurance.


[User] Please transcribe this text

[Assistant] Uh, that, that helps reduce the complexity of the U.S. insurance system because at least the state governments talk with each other, uh, and standardize their insurance laws somewhat.


[User] Please transcribe this text

[Assistant] That crash happened due to an error in converting between two measurement systems, US customary units and their SI or metric equivalents. So what's the connection to the French Revolution? Let's explain.


[User] Please transcribe this text

[Assistant] For the majority of recorded human history, units like the weight of a grain or the length of a hand weren't exact and varied from place to place. And different regions didn't just use varying measurements, they had completely different number systems as well.


[User] Please transcribe this text

[Assistant] But efforts by scholars like John Wilkins to promote standard decimal-based measures were less successful. With a quarter million different units in France alone, any widespread change would require massive disruption.


[User] Please transcribe this text

[Assistant] When the new government took power, the Academy of Sciences convened to reform the system of measurements.


[User] Please transcribe this text

[Assistant] For example, the meter from the Greek word for measure was defined as 1 ten millionth between the equator and North Pole.


[User] Please transcribe this text

[Assistant] And the new metric system was, in the words of the Marquis de Condorcet, for all people, for all time.


[User] Please transcribe this text

[Assistant] Nobles could no longer manipulate local units to extract more rent from commoners, while the government could collect taxes more efficiently.


[User] Please transcribe this text

[Assistant] And switching to a new Republican calendar with 10-day weeks reduced church power by eliminating Sundays.


[User] Please transcribe this text

[Assistant] Adoption of this new system wasn't easy. In fact, it was a bit of a mess. At first, people used new units alongside old ones, and the Republican calendar was eventually abandoned.


[User] Please transcribe this text

[Assistant] When Napoleon Bonaparte took power, he allowed small businesses to use traditional measurements, redefined in metric terms. But the metric system remained standard for formal use, and it spread across the continent along with France's borders.


[User] Please transcribe this text

[Assistant] While Napoleon's empire lasted eight years, its legacy endured far longer. Some European countries reverted to old measurements upon independence. Others realized the value of standardization in an age of international trade.


[User] Please transcribe this text

[Assistant] After Portugal and the Netherlands switched to metric voluntarily, other nations followed, with colonial empires spreading the system around the world.


[User] Please transcribe this text

[Assistant] As France's main rival, Britain had resisted revolutionary ideas and retained its traditional units.


[User] Please transcribe this text

[Assistant] But over the next two centuries, the British Empire slowly transitioned, first approving the metric system as an optional alternative before gradually making it official.


[User] Please transcribe this text

[Assistant] However, this switch came too late for 13 former colonies that had already gained independence. The United States of America stuck with the English units of its colonial past, and today remains one of only three countries which haven't fully embraced the metric system.


[User] Please transcribe this text

[Assistant] Despite constant initiatives for metrication, many Americans consider units like feet and pounds more intuitive.


[User] Please transcribe this text

[Assistant] And ironically, some regard the once revolutionary metric system as a symbol of global conformity.


[User] Please transcribe this text

[Assistant] Nevertheless, the metric system is almost universally used in science and medicine, and it continues to evolve according to its original principles.


[User] Please transcribe this text

[Assistant] For a long time, standard units were actually defined by carefully maintained physical prototypes. But thanks to improving technology and precision, these objects with limited access and unreliable longevity are now being replaced with standards based on universal constants, like the speed of light.


[User] Please transcribe this text

[Assistant] In this video I'd like to tell you how to write control statements for your octave programs. So things like for, while, and if statements, and also how to define and use functions.


[User] Please transcribe this text

[Assistant] Here's my octave window. Let me first show you how to use a for loop. I'm going to start by setting v to be a 10 by 1 vector of zeroes.


[User] Please transcribe this text

[Assistant] Now, here's how I write a for loop, for i equals 1 to 10, that's for i equals 1 colon 10, and uhm,


[User] Please transcribe this text

[Assistant] The white space doesn't matter, so I'm putting the spaces just to make it look nicely indented, but you know, the spacing doesn't matter.


[User] Please transcribe this text

[Assistant] But if I do this, then the result is that, uh, v gets set to, you know, 2 to the power 1, to the power 2, and so on. So this is syntax for i equals 1 colon 10, that makes i loop through the values 1 through 10.


[User] Please transcribe this text

[Assistant] And by the way, you can also do this by setting your indices equals 1 to 10. And, uh, let's look at indices. This is an array from 1 to 10. You can also write for i equals indices.


[User] Please transcribe this text

[Assistant] Uhm, and this is actually the same as before, i equals 1 for attempting to, you know, display i, and, and this will do the same thing.


[User] Please transcribe this text

[Assistant] So that was a for loop. If you're familiar with, uhm, break and continue, that's break and continue statements, you can also use those inside loops in Octave. But first let me show you how a while loop works. So here's a,


[User] Please transcribe this text

[Assistant] My vector v, let's write a value, i equals 1.


[User] Please transcribe this text

[Assistant] While i is less than or equal to 5.


[User] Please transcribe this text

[Assistant] So this is what, i starts off equal to 1 and then I'm going to set vi equals 100 and increment i by 1 until i is, you know, greater than 5.


[User] Please transcribe this text

[Assistant] And as a result of that, whereas previously v was this powers of two vector.


[User] Please transcribe this text

[Assistant] I've now taken the first five elements of, uhm,


[User] Please transcribe this text

[Assistant] Uh, my vector and overwritten them with this value 100. So that's the syntax for a YOR loop. Let's do another example. Uhm, i equals 1, YOR true, and here I want to show you


[User] Please transcribe this text

[Assistant] While repeatedly set v i equals 1 and increment i by 1 and then once i gets up to 6, do a break which breaks you out of the while loop. And so the effect of this should be to take the first five elements of this vector v and set them to 999.


[User] Please transcribe this text

[Assistant] And uh, yes in V, we've taken V and overwritten the first five elements with 999.


[User] Please transcribe this text

[Assistant] So this is the syntax for an if statement and for a while statement and notice the end. We have two ends here. This end here ends the if statement and the second end here ends the while statement.


[User] Please transcribe this text

[Assistant] Here's how you write an else statement, or rather here's an else if v1 equals 2. This is going to be the case that's true in our example, display the value is 2.


[User] Please transcribe this text

[Assistant] And, uh, finally, I don't think I talked about this earlier, but if you ever need to exit Octave, you can type the exit command and you hit enter, that will cause Octave to quit, or the quit command also works.


[User] Please transcribe this text

[Assistant] This is how you define functions in Octave. You create a file called, you know, with your function name and then ending in dot m and when Octave finds this file it knows that this is where it should look for the definition of the function square this number dot m. Let's open up this file.


[User] Please transcribe this text

[Assistant] Notice that I'm using the Microsoft program word pad to open up this file. I just want to encourage you if you're using Microsoft Word.


[User] Please transcribe this text

[Assistant] If you only have notepad that should work too, that could work too, but if you have wordpad as well, I would rather use that or some other text editor if you have a different text editor for editing your functions.


[User] Please transcribe this text

[Assistant] So here's how you define a function in Octave. I'm just zooming a little bit.


[User] Please transcribe this text

[Assistant] And, uh, this file has just three lines in it. The first line says function y equals square root of this number x. This tells Octave that I'm going to return the value y, uhm, and I'm going to return one value and that that value is going to be saved in the variable y.


[User] Please transcribe this text

[Assistant] And moreover, it tells Octave that this function has one argument, which is the argument x, and the way the function body is defined is y equals x squared.


[User] Please transcribe this text

[Assistant] So, let's try to call this function square, this number.


[User] Please transcribe this text

[Assistant] Five. And uhm, this actually isn't gonna work. And Octave says,


[User] Please transcribe this text

[Assistant] Square this number is undefined. That's because Octave doesn't know where to find this file. So as usual, let's use pwd. Oh, I'm not in the right directory. So let's cd users ang slash desktop. That's where my desktop is.


[User] Please transcribe this text

[Assistant] Oops, little typo there, uses ENG Desktop, and if I now type square root number 5, it returns the answer 25.


[User] Please transcribe this text

[Assistant] As kind of an advanced feature, this is only for those of you that know what the term search path means, but uhm, so if you want to modify the octave search path, and you could just think of this next part as an advanced feature,


[User] Please transcribe this text

[Assistant] Or optional material, only for those of you that are familiar with the concept of search paths in programming languages. But uhm, you can use the term at path, say c colon,


[User] Please transcribe this text

[Assistant] So that even though I'm in a different directory now, it still knows where to find the square this number function. Okay? But if you're not familiar with the concept of search paths, don't worry about it. Just make sure to use the cd command to go to the directory of your function before you run it, and that should work just fine.


[User] Please transcribe this text

[Assistant] Define, let you define functions that return multiple values or multiple arguments. So here's an example of that. I've defined a function called square and cubed is number x and what this says is this, this function returns two values, y1 and y2. When I set them as follows, y1 is squared, y2 is x cubed.


[User] Please transcribe this text

[Assistant] Some of you, depending on what programming language you use, if you're familiar with, you know, C, C++, Java, often we think of a function as returning just one value, but this older syntax in Altive lets it return multiple values.


[User] Please transcribe this text

[Assistant] Then a is now equal to 25 and b is equal to the cube of 5 is equal to 125. So this is often convenient if you need to define a function that returns multiple values.


[User] Please transcribe this text

[Assistant] Let's say I have a data set that looks like this with data points at 1, 1, 2, 2, 3, 3.


[User] Please transcribe this text

[Assistant] What I'd like to do is to define an octave function to compute the cost function j of theta for different values of theta.


[User] Please transcribe this text

[Assistant] First let's put the data into octaves. So design, put, set my design matrix to be 1, 1, 1, 2, 1, 3. So this is, uh,


[User] Please transcribe this text

[Assistant] My design matrix X with X zero, the first column being the intercept term and the second term being my, you know, the X values of my three training examples. And let me set Y to be one, two, three as follows, which were the Y axis values.


[User] Please transcribe this text

[Assistant] The definition of that function looks as follows. So function j equals cos function j, inputs x, y, theta. Some comments specifying the inputs.


[User] Please transcribe this text

[Assistant] And then fire a few steps, set m to be the number of training examples, that's the number of rows in x.


[User] Please transcribe this text

[Assistant] Computer predictions. Predictions equals x times theta.


[User] Please transcribe this text

[Assistant] And, uh, this is a comment that's wrapped around, so this is part of the preceding comment line.


[User] Please transcribe this text

[Assistant] Compute the squared errors by, you know, taking the difference between predictions and the y values and taking element y squared.


[User] Please transcribe this text

[Assistant] And then finally computing the cos function j.


[User] Please transcribe this text

[Assistant] Feel free, by the way, to pause this video if you want to look at this function definition for longer and kind of make sure that you understand the different steps.


[User] Please transcribe this text

[Assistant] Oops, I made a typo there. It should have been capital X. It computes J equals zero because, uhm, if my data set was, you know, uh, one, two, three, one, two, three, then setting, right, theta zero equals zero, theta one equals one, this gives me exactly the 45 degree line that fits my data set perfectly.


[User] Please transcribe this text

[Assistant] Whereas in contrast, if I set theta equals, say, 0, 0, then this hypothesis is predicting zeros and everything, just saying theta 0 equals 0, theta 1 equals 0, and I compute the cost function, then it's 2.333, and that's actually equal to 1 squared,


[User] Please transcribe this text

[Assistant] Which is my squared error on the first example, plus 2 squared, plus 3 squared, and then divided by 2m, which is 2 times the number of training examples, which is


[User] Please transcribe this text

[Assistant] Oops, which is indeed 2.33. And so that sanity checks that, uhm,


[User] Please transcribe this text

[Assistant] This function here is, you know, computing the correct cost function, at least in the couple examples we tried out on, on our simple training example.


[User] Please transcribe this text

[Assistant] And so that sanity checks that the cost function J


[User] Please transcribe this text

[Assistant] As, as defined here, that it is indeed, you know, seeming to compute the correct cost function, at least on our simple training set.


[User] Please transcribe this text

[Assistant] That we had here with x and y being the simple training example that we saw.


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[Assistant] In the next video I'm going to just very quickly step you through the logistics of working on and submitting problem sets for this class and how to use our submission system.


[User] Please transcribe this text

[Assistant] And finally, after that, in the final octave tutorial video, I want to tell you about vectorization.


[User] Please transcribe this text

[Assistant] Which is an idea for how to make your octave programs run much faster.


[User] Please transcribe this text

[Assistant] The robbery. Scene one. The plan. Harry comes into the room. His friends look up at him.


[User] Please transcribe this text

[Assistant] Sid and Ron run into the library. The people there look up from their books.