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bilibili_data_1302898884_BV1uZ4y1C7SX_p90_BV1uZ4y1C7SX_p90_m4-dialogue_0518756
[S1] We are almost on land. [S2] Are you crazy? What are you doing? [S1] Saving your life. [S2] This is a race, you fool.
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bilibili_data_1302898884_BV1uZ4y1C7SX_p94_BV1uZ4y1C7SX_p94_m4-dialogue_0483358
[S1] 94, planted strength. [S2] Time to plant a tree. I have to put the shovel back in the shed. [S1] Come here, you little brat. Let me see your boy. I'm going to teach him a lesson.
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bilibili_data_1302898884_BV1uZ4y1C7SX_p96_BV1uZ4y1C7SX_p96_m4-dialogue_1040049
[S1] 96. Family photo. [S2] I like these costumes, Dad. You think this will work? [S1] Of course, my boy. Just play nice with the rabbits. There you go. That is the perfect shot.
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bilibili_data_1303874431_BV1ud4y17776_BV1ud4y17776_m4-dialogue_0896241
[S1] We already knew back then in the late 80s, 1990s, that the universe was expanding. [S2] Right. [S1] And we knew that to see the very first galaxies, and maybe even the first stars, that ever formed in the universe, because of the expansion of the universe, the light from those galaxies is likewise expanded. [S2] Mm-hmm. [S1] And it shifted from blue wavelengths
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[S1] And Uranus. I mean, I just knew that because I knew it would be big enough. I knew that because it was a space telescope, the images would be stable and pristine. And I knew that these wavelengths of light in the infrared had all sorts of interesting molecular signatures- [S2] Mm-hmm. [S1] ... so that we could learn about the upper atmospheres of these planets. [S2] Mm-hmm. [S1] And so I'm like, I'm in. [S2] [LAUGHS] [S1] You know, I, I'll do this. So in 2002, I wrote a proposal saying,
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bilibili_data_1303874431_BV1ud4y17776_BV1ud4y17776_m4-dialogue_0896243
[S1] I would like to be an interdisciplinary scientist for this program, to ensure that this telescope will be able to do solar system observations when it is launched. [S2] Mm-hmm. [S1] And in 2003, my proposal was accepted, and that- [S2] Mm-hmm. [S1] ... how it was how I formally became involved in this telescope. So Webb
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bilibili_data_1303874431_BV1ud4y17776_BV1ud4y17776_m4-dialogue_0896244
[S1] It's, it's different than Hubble. It's a different kind of telescope for a number of reasons. One is, it's a lot bigger than Hubble. [S2] Mm-hmm. [S1] So it's a six and a half meter mirror, the golden mirror of the collecting area, versus Hubble's 2.4. [S2] Mm-hmm. Um, I mean, it's so big that it couldn't be launched looking like that. It had to be all folded up. [S1] That's right. Had to be folded up. And that's why it's, the mirror is segments. [S2] Yeah. [S1] So that it could be folded up. [S2] Like a honeycomb. [S1] Like a honeycomb.
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[S1] Exactly. [S2] But then it had to unfold in space. And I, I remember how nervous people were about this process because it really was something that everything, every single step had to go right. [S1] Not only did the telescope have to fold up, but we, if you look at Webb, it's got this huge contraption underneath it, which we call a sun shield. [S2] Yeah. [S1] And that's crucial for this telescope. [S2] How did you feel as you were witnessing the deployment sequence?
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[S1] I sure was nervous, just like everybody else. Um, [CLEARS THROAT] there were several single point failures where if that thing didn't unbolt or unfold, we didn't have a, a, a working telescope anymore. [S2] Yeah. [S1] So it was extremely nerve-wracking. But we had many years of testing.
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[S1] Because we knew that there was no fixing this telescope. This telescope's not in low Earth orbit like Hubble. The James Webb Space Telescope is a million miles away at a point called the L2 point. [S2] Mm-hmm. [S1] And it was put out there deliberately because it needed to be cold.
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[S1] It needed to have a, the sun shield to protect the telescope from the warmth of the sun, the warmth of the earth, and even the warmth of our moon. [S2] Mm-hmm. [S1] So the sun shield is designed to be like a, an umbrella that protects it, a sun umbrella that keeps that telescope super cold. So we couldn't put it in low earth orbit because it's just too warm in that environment. [S2] Right. [S1] You can't sense infrared light when it's hot. [S2] Yeah. [S1] You have to have it cold. By the way, that's also why this telescope
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[S1] is completely exposed to the elements of space. Most other telescopes, um, have tubes that enclose them, and this one doesn't. The, the mirrors are just sitting out there. [S2] They're just out there. [S1] They're just sitting out there. [S2] So the first deep field from JWST, I think the analogy I heard was that the image itself covers about the amount of space as a grain of rice on a fingertip held at arm's length. Is that right?
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[S1] I heard a grain of sand. [S2] Okay. [S1] Not a grain of rice. [S2] Okay. [S1] But it's the same concept, you know, uh, that, yeah, if you, the piece of sky you see in that picture, if you were, like, standing in your backyard and looking up in the sky, that piece of sky is about the same size as a, as a, as a tiny grain of sand. If you moved your grain of sand over to the left, you would see those more galaxies. And over to the left again, more galaxies. And anywhere you looked in the sky,
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[S1] It is filled with galaxies. [S2] Just thousands and thousands in that one image alone. [S1] Exactly. What I'm waiting for is the James Webb Space Telescope deep field where we stare for days at a dark spot that we don't know where anything is. [S2] Mm-hmm. [S1] What are we going to see?
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[S1] I just think about it appearing so far back in time, to the beginning of, you know, the primordial cosmic murk. [S2] Yeah. [S1] When stars and galaxies are just starting to turn on and...
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[S1] I view it as a, as an example of what humanity can do when we work for the greater good. [S2] Mm-hmm. [S1] You know, when we work as teams and we have a goal. [S2] Mm-hmm. [S1] You know, this, this project required thousands of people in multiple countries and multiple states to take this vision and turn it into a concrete thing, this telescope, and then launch it on a rocket. [S2] [LAUGHS] [S1] And then have the ability to use it to probe
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[S1] You know, from, from right in our local neighborhood, all the way to the edge of the known universe, and everything in between. [S2] Yeah. [S1] It's amazing to me. And everybody had a role to play. I mean,
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[S1] You know, both here and Europe, you know, we all worked t- Canada. Canada made the fine guidance sensor that allows us to point this thing. [S2] Mm-hmm. [S1] I mean, it's a truly international effort, um, and it all comes together to create this, this revolution in how we see the cosmos. [S2] Do you have a favorite among the images that have been released so far?
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[S1] Stars are being born. [S2] Yeah. [S1] And some of the little poke-y things that, that stick out that give it some of its dramatic structure, you know, those are like, that's star birth in the making.
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[S1] And I get, I think that's just so cool. And particularly when we use our infrared cameras, we can look inside some of those knobs and, and see the stars that are being born. [S2] Mm-hmm. [S1] And in some places, uh, just, uh, like the Orion Nebula, there was just an image released of the Orion Nebula. [S2] Mm-hmm. [S1] That's places where planetary systems are forming. You know, we aren't seeing the planets, but we're seeing the, the swirling disks of dust and gas where those planets are being born.
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[S1] What you learn from James Webb Space Telescope is that in the regions where they are interacting and overlapping, those regions light up in the infrared. Those are places where the dust and the gas and the existing stars of those other galaxies, when they are interacting, they are forming new stars. They are creating new realms of star formation. [S2] Hm. [S1] And they just light up in the infrared.
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[S1] in that image. So, yeah. [S2] And I just wonder, like, what are, what's missing from that picture? What is, what can JWST fill in? I mean, how much more color can it add? [S1] Um, what JWST adds to our ongoing story is it, it adds new wavelengths of light that we haven't had the sensitivity to study. And different wavelengths of light tell you different parts of this story.
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[S1] That tells you what molecules are there. [S2] Sure. [S1] Not only does it tell you what are there, it tells you their temperature. [S2] Mm-hmm. [S1] It can tell you their pressures. [S2] Mm-hmm. [S1] By tracking, um, carefully these lines in the spectrum, you can determine the motions of this material. And so we don't just have a static picture. We can actually do, like, three-dimensional tomography- [S2] Mm-hmm. [S1] ... of astrophysical objects by using this spectral light information.
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[S1] What's your favorite? [S2] What's, what's your favorite? [S1] Oh, I don't know. [S2] [LAUGHS] [S1] I've got a couple of favorites. [S2] Yeah? [S1] I think a lot of astronomers, a, a favorite system right now is the Trappist-1 system. [S2] Yeah, tell me about it.
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[S1] Yeah, Trappist-1 is, um, that's the name of the star. Well, it's, Trappist is the name of the survey, right? [S2] Yeah. [S1] But it looked at this star and, um, it discovered, um, that there are at least seven planets orbiting this star, and most of those planets seem to be Earth-sized. In the Trappist-1 system, several of the planets are the right distance from the host star.
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[S1] that water could be liquid on the surface of them. We call that the habitable zone. [S2] Right. [S1] And you and I can have a long talk about what habitability actually means. But, you know, in our solar system, at least on our Earth, the only place that we know life exists is a lot of water. [S2] Yeah. [S1] And so, when we're talking about looking for habitable planets,
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[S1] Okay, so let me answer the second question first. Um, this question of, is there alien life out there? I usually break it up into two things. One is a sp- thought experiment about the size of the universe, the scale of the universe, just how many stars there are in our galaxy. [S2] Yeah. [S1] And then how many galaxies. There's billions of stars just in our local galaxy, and there's billions of galaxies out there.
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[S1] And we talk about whether or not life could have formed over the billions of years that our, our universe has existed with these billions of galaxies, each of which has billions of stars. I say life has to exist somewhere out there. [S2] Mm-hmm. [S1] Somewhere. Has to be out there. [S2] Mm-hmm.
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[S1] Does that mean that aliens have come to Earth and visited us? No. That's a totally separate question. [S2] Yeah. [S1] I just, they're not, it's not a related question, all right? That's a more psychological question. [S2] [LAUGHS] [S1] I'm more interested in the science aspect of the question. I, I think we need to start with terrestrial-sized planets that are the right distance to have water on them because those are the conditions
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[S1] ... orbital imaging, um, it's clear that there's evidence that at one time, there was liquid water on the surface of Mars. There's, you know, there's sedimentation, there's a chemical evidence, there's, you know, actually water trapped in the ices in the poles of Mars right now. [S2] Mm-hmm. [S1] And so, uh,
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[S1] It, it could very well be that at some time in the past, that planet had liquid water and may have had the conditions for life to form. We don't know. It could be that life formed there first and transmitted itself inward to us. We could be Martians. [S2] We could be Martians. [S1] I don't know. You know, we don't know the answer to that. Um, using our definition of looking at places where there's liquid water,
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[S1] Crazy. Think about it. [S2] It's kind of mind-boggling to think about. [S1] Yeah. Um, the question is, could life form in that water? And, and it gets back to what are the ingredients you need for life? You need water, but you also need some kind of an energy source. You need some kind of a surface on which life can do its, uh, chemical thing to form. I don't, I'm not an astrobiologist, so I don't know what the right lingo is, but you need to have a surface for stuff to happen. [S2] Mm-hmm. [S1] Um,
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[S1] And we also know that Europa is warm. [S2] Mm-hmm. [S1] Now why? Why would this moon out there at Jupiter's distance, why would it be warm, right?
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[S1] And that repeating warms the planet. Um, I used to illustrate this for kids with, um, like old credit cards. If you- [S2] Oh, yeah. [S1] ... I took an old credit card and you bend it, bend it, bend it, bend it, bend it, and you feel where you're bending, it's warm. [S2] It gets warm. [S1] It's really the same process. It's that flexing is what warms these. So for Europa, in orbit around Jupiter, we have the water,
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[S1] We have the rocky surface deep inside, and we have warmth. You know, we've got this energy source thing. So, is it possible that life is formed there? [S2] What? Man. [S1] Sure.
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[S1] My favorite moon is Triton. [S2] Oh, it's a pretty good one. [S1] It's not the right one, though. [S2] I was gonna say Iapetus. [S1] Oh, no, no, no, no, no, no. We're gonna have to have a long conversation about that. [S2] Okay. Okay. Tell me why Triton is better than Iapetus. [S1] All right, so, Triton. Triton is such a cool moon. It goes in a retrograde orbit backwards around the planet. We think it was actually a Kuiper Belt object that got too close. [S2] Too- [S1] To Neptune, and was captured by Neptune.
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[S1] And it's a big moon. I mean, if you want Pluto to be a planet, I don't know where you s- stand on that issue, but Triton is a twin to Pluto, all right? So it's like a planet in orbit around another planet. [S2] But it's going backwards. [S1] But it's going backwards around the planet. And when Voyager flew by in 1989, it, it actually flew kinda close, so we got
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[S1] a good view of one half of it. And it's got remarkable terrain. [S2] Hmm. [S1] And it has active cryovolcanoes on it. There are volcanoes, ice volcanoes erupting on Triton, like in real time. So that's pretty amazing. [S2] [LAUGHS]
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[S1] So, I asked my history teacher instead, and she did write a letter, and I did get into MIT. [S2] Mm-hmm. [S1] And when I brought back my acceptance letter and showed it to my chemistry teacher, look, I got into MIT, he said, "It's only because you're a woman. They have quotas to fill."
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[S1] This is in 1978, when people said things like that to your face. Um, that made me angry, more than anything. [S2] I'm super- [S1] So, I was determined to go to MIT and graduate, you know. [S2] What are some of the most nagging, unanswered questions in your mind that exist in astronomy, any field in astronomy? Could be anywhere in the universe, close to home, far away. What bugs you? What keeps you up at night?
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[S1] is an area that is very, very interesting right now. And of course, that's why James Webb Space Telescope was built, to add to a, to a piece to that story. [S2] Mm-hmm. [S1] I think I'm also interested in how our planetary system that we live in, how did it in particular come to be- [S2] Mm-hmm. [S1] ... and how did it come to be habitable? [S2] Mm-hmm. [S1] We know this is the only one
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[S1] The only system that we know is inhabited, right? This, our solar system. [S2] Right. [S1] Is it required that you have giant planets in the outer system and small planets in the inner solar system to make habitability, or is it just by happenstance? Did you have to have a Jupiter to make it habitable? Did you have to have a Neptune to sweep out through the Kuiper Belt and deliver volatiles to the inner solar system, water and stuff?
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[S1] I mean, I, that's so interesting. And, um, it, it, it touches us as humans. Like, how did we come to be? It's, it's part of our story. It's part of our life story. So I'm very interested in that question as well. And we still have so many observations left to make. [S2] [LAUGHS] [S1] Both within our solar system and in the greater universe. I think astronomers will be busy for a long time to come.
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[S1] I'm beside myself. [S2] Yeah. [S1] Really. Um, yeah, it's, it's actually, uh, it's a concept record, but it's my first directly autobiographical album in a while because the last album that I put out was, um, a re-record of my album Red. So that has some space. You know, you, I wrote that stuff a decade ago. Folklore and Evermore, I was, it was like story time. It was like mythology. Like I'm creating a character. They went and did this and felt this way. [S2] Yes. [S1] So I'm feeling like, I'm feeling very overwhelmed.
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[S1] He is. [S2] Wow. [S1] And, uh, you know, not a lot of people know that. [S2] I did not know that. [S1] And now they do. [S2] Yeah. [S1] But I liked, I really, I love to make things with my friends. I love to work with my friends. I think that the experience of making something is, is just as important as how proud you are of it in the end. And I think it really informs how proud I am of something. If I had a really joyful experience making something. This is a pretty dark album, but I'd say I had more fun making it than any album I've ever made. [S2] Isn't
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[S1] Interesting. [S2] It's, and I, 'cause I don't think that art and suffering have to be holding hands. [S1] Yeah. [S2] All the time. I think you can, I think you can write songs about pain or grief or suffering or loss or hard things that you go through in life. Uh, shame, you know, love to write about that one. Um, self-loathing, I could go on. [S1] [LAUGHS] [S2] But I think there's- [S1] Please stop, yeah.
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[S1] No, I- [S2] And so very lucky to have collaborated with her on that. And Dylan was actually in the studio with me and Jack because we re- a lot of the time we record at his place and, um, and Dylan was just hanging out, like drinking wine with us and listening to stuff. And, and he was just trying out the drum kit there. He wasn't, he wasn't serious. [S1] Yeah.
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[S1] So, no, I didn't. I reached out to him to, um, to be in the short film for All Too Well because I had always really loved his work. I, I also felt like he seemed like a very quick-witted person and I knew that this- [S2] He's funny. [S1] I wanted the character to be, uh, charming. I wanted, I wanted that sort of charming, quick cleverness to, and the charisma to be why we love the character because there's a lot of, um, complexity to that character that makes us not love him as much. So I wanted
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[S1] Dylan to bring something. [S2] His layers, his, yeah. [S1] To, uh, the character to make, to make us, you know, love him. And I do think that was achieved in this short film. Meanwhile, I mean, Dylan and I become really close friends. Jack becomes really close friends with Dylan. We all start hanging out all the time. Like, it's the, it's the same with Sadie Sink, who was in it. Like, we're just- [S2] You, you have that. [S1] I just, I think very-
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[S1] I miss it. I really miss it. I miss, you know, uh, when you write songs and you're proud of the songs and you have the, the fans reacting. [S2] Yeah. [S1] The, the most potent way that you can see them react is when you're looking into their faces. Do you know what I mean? I miss that a lot. I really miss that, that connection. [S2] They're looking at you right now. They're looking at that. [S1] I know, right? [S2] Yeah. [S1] So it's like,
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[S1] My favorite besides some of the casting, uh, my favorite is when you're, like, I feel like a giant coming in and, like, kind of ruining the party and coming in and not, and you, you sneak in and you're a giant at this dinner party and they're all freaking out, screaming. [S2] Yeah. [S1] But then you eat some of the- [S2] Too big to hang out. [S1] But then, yeah. But then you eat some of the food with this tiny fork.
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[S1] Follow the laser pen. It's a scary monster. [S2] And that's you, yeah. [S1] And then, um, and then we had a teeny, tiny little room with a teeny, tiny table. We just had the most ama- We had the most amazing production design and we had the most incredible crew. [S2] Oh, man. [S1] And they just got me those tiny little forks. [S2] Yeah. A tiny little- [S1] And a little wine bottle. [S2] A little, a tiny wine bottle. [S1] It was just incredible. [S2] It's so well, uh, well done. And you, uh, cast some, uh, great people in here to play. [S1] Oh, yeah. [S2] Yeah. [S1] I was really
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[S1] Are they fun? And are they nice? And are we gonna have a fun time on set? Obviously, like, talent, that's number one. Like, do you fit the part? [S2] Yeah. [S1] But then there's also this sort of caveat of like, well, like, we're gonna be on set for a while. Like, is this gonna be a blast or is this, do you know, is this person have, like, this internal struggle with what they do and they can't stand acting but they're good at it. Like, it's, I meet a lot of people out and about and that's how I'll cast things. So,
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[S1] You had a pizza party. [S2] Mm-hmm. [S1] And I went to it, and I ended up in a corner talking to Mike Birbiglia and his wife Jen, who's a poet. [S2] Yeah. [S1] All night, they're the most wonderful people. And I just remember thinking, 'cause I'd seen Mike in things, and I'd seen some of his, you know, he does these amazing shows. He just makes such thoughtful, um, performances and- [S2] Yeah. [S1] ... and comedy. [S2] He has a new one coming out on Broadway. [S1] Yeah, he has one that's, that I, I can't wait to see. [S2] Yeah. [S1] And so I was talking to them, and I was just thinking,
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[S1] They approve. [S2] Yes. [S1] So basically the first video, Anti-Hero, I was like, "This is going to be the first single." And I knew that, but I was like, "I want to make a video that is just for the fans who like certain things like glitter and Easter eggs."
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[S1] Well, yeah, I mean, she's just the greatest and she's, um, I mean, I don't, I don't, it's, I don't even believe I'm saying things like this. And then, and so then we have, um, one of my favorite performers who I think has been so influential in pop music, um, and I've, I've nicknamed this character, not the Fairy Godmother, but the Fairy Goddess, and that is played by Dita Von Teese. [S2] Oh, yeah. [S1] Who is, I think, one of the most iconic performers, and it's so exciting to get to see her do what she does in this. [S2] Yes. [S1] Um,
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[S1] ... survive or die with a given disease. So it's a very commonly occurring problem and very important. So we're going to spend some time today on this, actually in the, in the next, uh, set of lectures on classification. And Trevor and I are both here. Trevor's going to give the m- uh, most of the talk and I'm going to pipe in and, uh, correct him when he makes mistakes and make fun of his accent and things like that. [S2] That means we won't hear much from you. [S1] [LAUGHS] We'll see. [S2] Anyway, let's go to the slides. Um,
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[S1] The first thing we do is just show you what, what categorical variables look like. I'm sure you know. So for example, eye color, that takes on three values, brown, blue, and green. Those are, those are discrete values. There's no ordering. They're just three different values. Email, we've talked about already, is spam and ham. I like that word, ham. [S2] I like ham, I suppose. [S1] I hate
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[S1] Oh, you tell me, Rob. [S2] Okay. Well, let's see, a box plot, what's, what's indicated there, Trevor, you can point, the, the black line is the median. [S1] It is a, it is a black line, that's a median. [S2] So that's the median, the medium for the, the yes, for the people, the median income for people who have defaulted. And then the top of the box, the, where are they, the quartiles, that's the 75th quartile, 75th percentile, quartile, and the 25th is the bottom of the box.
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[S1] So really a good summary of, of the distribution, um, of income for those in category S. What about these, these things at the end, Rome? [S2] Okay, I think they're called hinges. [S1] They are called hinges. [S2] And those are the ranges, are they, or the, approximately the ranges of the data?
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[S1] Who invented the box- [S2] John Tukey. [S1] John Tukey, one of the most famous statisticians. He's no longer with us, but he's left a, a big legacy behind.
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[S1] Well, the popular way is to use maximum likelihood. Maximum likelihood was introduced by who, Rob? [S2] Me, actually. [S1] Oh, yeah. [S2] Just last week. [S1] Did you reinvent it, or? [S2] I didn't realize it was actually, yeah. It, um, I, the correct answer is Fisher, back in the 1920s, Ronald Fisher. [S1] Fisher. Ronald Fisher, very famous statistician, um, invented a lot of the tools that we use in, in modern applied statistics, and maximum likelihood is one of them.
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[S1] And in this case, this is what it produced. The coefficient estimates were -10 for the intercept and .0055 for the slope for balance. That's beta and beta zero. It also gives you the, so they're the coefficient estimates. It also gives you standard errors for each of the coefficient estimates. It computes a Z-statistic, and it also gives you p values. [S2] Oh, I, I think I just realized something. So you had a picture a couple of slides ago of the- [S1] Yes.
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[S1] ... the, a curve? [S2] Yes. [S1] And is that how you found the ... I was wondering how you found the parameters for that curve. Is that how you found them? [S2] That's exactly right, Rob. [S1] Oh. [S2] So, this curve over here is the curve corresponding to those estimates that we just produced in the table. And you might be surprised because the slope is very small here. [S1] Mm-hmm. [S2] Rob. Yet it, it seemed to produce such a big change in the probabilities. [S1] There may be a typo or ...
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[S1] So before, when we just measured student on its own, it had a positive coefficient. But when we fit it in the multivariate model, the coefficient's negative. Do you think this is an error, Rob? [S2] Uh, I don't think so. [S1] So how could that happen? [S2] Well, we remembered last time we talked about in regression models, how difficult it is to interpret coefficients in a multiple model, but well, it's a regression model because the correlations between the variables can affect the th- the signs.
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[S1] We're not really trying to predict the probability of getting a heart disease. What we're really trying to do is to understand the role of the risk factors in, in, you know, in the, in, uh, to, in the risk of, of heart disease. And actually, this study was, uh, was an intervention study aimed at educating the public on healthier diets, but that's a, that's a whole other story. [S2] Did it work? [S1] Um, I think it might have worked a little bit, but this, this crowd is really hard to get them away from their meat. [S2] Okay.
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[S1] Um, you know what they call a barbecue in South Africa? [S2] No. [S1] Brie Flakes. [S2] Okay. [S1] Every South African loves a brie flake and their bull tongue. So here's the result of GLM, um, for the heart disease data. And here I actually show you some of the code used to fit it. And we get it, we'll get into the code session later, but, um, it's just interesting to see that it's a, it's pretty easy to do. There's a call to GLM, um,
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[S1] Hi, I'm Trevor. No, I'm Rob Tipshrani. [S2] And I'm Trevor Hastie. And welcome to our course on statistical learning. [S1] This is the first online course we've ever, we've ever given, and we're really excited to tell you about it. [S2] And a little nervous, as you can hear. [S1] So, uh, by way of background, what is statistical learning? Um, Trevor and I are both statisticians. We were actually graduate students here at Stanford in the '80s. We've known each other for about 30 years. [S2] Oh, my goodness. [S1] And, uh, back then, uh, well, we did applied statistics like a lot of statisticians did. Statistics have been around since about 1900 or before.
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[S1] Um, but in the 1980s, people in, in computer science developed their field of machine learning. Uh, especially neural networks became a very hot topic. I was at University of Toronto and Trevor was at Bell Labs. [S2] And one of the first neural networks was developed at Bell Labs to solve the, the zip code, uh, recognition problem, which we'll show you a little bit about in, in, in a few slides. [S1] So around, around that time, uh, Trevor and I and then some colleagues, Jerry Friedman, uh, Brad Efron, uh, Brad-
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[S1] Uh, very, uh, very well. Matter of fact, he got all the, the, the, the Senate races right, and the, uh, the, the presidential election, he, he predicted very, very accurately using statistics, using carefully div- uh, carefully sampled data from various places, some careful analysis. He did an extremely accurate job of predicting the election when a, a lot of places where a lot of news outlets weren't sure who was gonna win. [S2] Pretty nerdy looking guy, isn't he, Rob? [S1] Yes, but he's very famous, and, uh- [S2] He's like a rock star these days.
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[S1] And this is looking at, this graph has the, a log periodograms of, uh, for two different phonemes, the power at different frequencies for two different phonemes, uh, A, A, A and A-O. How do you pronounce those, Trevor? [S2] A-A is odd and A-O is ought. [S1] As you can tell, Trevor talks funny, but hopefully during the course you'll be able to- [S2] How could you say- [S1] Odd and ought? Okay. [S2] Okay.
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[S1] And these, these data come from a region of South Africa where the heart, the risk of heart, uh, disease is very high. It's over, uh, over 5% for this age group. The people, the, the, the, especially men around, they eat lots of, uh, these were men, um, they eat lots of meat. They have meat for all three meals. And in fact, meat so prevalent, chicken's regarded as a vegetable. [S2] Poor chicken. [S1] Rob loves it too. [S2] I used to love that job.
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[S1] Our next example is email spam detection. Now, as everyone who uses email, and spam is definitely a problem. Uh, and so, um, spam filter is a very important application of Cisco machine learning. The data in this, on this table actually, um, I think it's from the, the, maybe the late '90s. Is that right? [S2] Before, before, yeah. Late '90s, exactly. [S1] It's
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[S1] It's from Hewlett Packard. So this is a, a person named George, who worked at Hewlett Packard. So this was early in the days of email where, as well, spam was also not very sophisticated. So what we have here is data from over 4,000 emails sent to an individual named George at HP Labs. Each one's been hand-labeled as either being spam or good email. And the goal here is to try to predict- [S2] Actually, they call good email ham these days, right? [S1] Mm-hmm.
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[S1] Uh, remove. Okay. So I guess it probably said something like, "Don't remove." Is that right? [S2] I think it says, uh, if you want to be removed from this list, click. [S1] I see. [S2] That's usually a spam. [S1] Right. So the goal was that in, if it, and we'll talk about this example in detail, to use the, the, the 57 features, and here's, these are seven of those features, as a classifier together to, to try to predict whether an email is spam or ham.
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[S1] Actually, I remember the first time, Trevor, that we worked on a machine learning problem. It was, it was this problem, and you were working at Bell Labs. I visited Bell Labs. And you'd just gotten this data, and you said, "These people in artificial intelligence are working on this." And that we thought, "Oh, let's try some statistical methods." And we tried, uh, discriminant analysis, right? [S2] That's right. [S1] And we got an error rate of about 8.5%, and the best error rate- [S2] In about 20 minutes, is it? [S1] Right. And the best error rate anyone else had was about 4 or 5% at that point. We thought, "Oh, this is gonna be easy." We're already at 8% in 10 or 15 minutes- [S2] [LAUGHS]
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[S1] So here we see the, the three, three of the variables that affect income. And again, the goal is we'd use regression models to try and understand the roles of these variables together and see if there's, you know, if there's interactions and so on. [S2] And the last example is, um, Landsat images of, of land use, uh, area in, in Australia. So this is a rural area of Australia. [S1] Those are harsh colors, Rob. Did you, did you choose those colors? [S2] Uh, you probably did, Trevor. You're the, uh, color, color- [S1] This is before. [S2] ...
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[S1] This is before it's developed taste. [S2] When did that happen? [S1] [LAUGHS] [S2] I didn't, I didn't see the, uh, news memo. Okay. So, um, here are, uh, these are from landslide images. So let's start here in the, in this panel. So this is, uh, again, uh, a rural area of Australia where the, uh, land use has been labeled, I think actually by, um, by graduate students or, or, uh, researchers into one of one, two, three, four, five, six. [S1] They don't have to pay- [S2] ...
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[S1] And- [S2] Pixel by pixel, right? [S1] Pixel by pixel. [S2] Yeah. [S1] Although we might want to use the fact that nearby pixels are more likely to be the same land use than ones that are far away. And we'll talk about classifiers. I think the one we use here is actually nearest neighbor. It's a very simple classifier, and that produces the prediction in the bottom right. And you can see it's quite good. It's not perfect. There's a few mistakes it makes, but it's, for the most part, quite accurate.
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[S1] The other thing- [S2] You're going to give my, going to give my entire lecture? [S1] Oh, I'll try not to, Rob. Just in case you miss out some of the salient points. The other thing we're going to look at is standard errors of estimators. Sometimes our estimators are quite complex and we'd like to know the standard error, which means what happens if we've got new samples from the population over and over again and we re-computed our estimate and at the standard error is the standard deviation of those estimates under re-sampling.
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[S1] about fitting a polynomial with higher and higher degree. [S2] Right. [S1] You can see our model complexity increases with degree. [S2] So we move to the right, we'd have a higher complexity, higher order of polynomial. The prediction errors on the vertical axis. And we have two curves here, the training error in blue and the test error in red. So what do we see? Let's first look at the blue curve. On the, on the left, the model complexity is low. For example, we're fitting a small number of parameters, maybe just a, a single, a single constant.
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[S1] This is simply a, a one stage process. We divide it in half, train on one half, and predict on the other half. [S2] It seems a little wasteful if you've got a very small data set, right? [S1] Yeah, that is wasteful. And, uh, as we'll see, it's cross validation will, uh, remove that waste and be more efficient. But let's first of all see how this works, uh, um, in the, uh, the auto data where we're trying, we call, we're comparing the, um, linear model to higher order polynomials in regression.
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[S1] Um, and that's likely to be quite a bit higher than the, uh, the error for a training set of size N. And- [S2] Why, Rob? [S1] Why? [LAUGHS] That was my question. Okay.
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[S1] So here's the cross validation error rate. Um, basically, this is the mean square error we get by applying, uh, the, the, we, we fit to the, the K-1 parts that don't involve part number K. That gives us our fit, Y-I hat, uh, for observation I. [S2] It's four-fifths of the data in this case. [S1] Right. And then we add up the error. This is the mean square error that we obtain now on the validation part using that model.
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[S1] ... a tenfold cross validation. Now, again, it's, it's also showing the minimum around two, but it's, uh, there's not the, what we're seeing here is the tenfold cross validation as we, as we, uh, take different partitions in, uh, into ten parts of the data, and we see there's not much variability. They're pretty consistent. In contrast to the, uh, when we divide into two parts, we got much more variability. [S2] And those get averaged as well, those curves on the right. [S1] Right.
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[S1] This is figure 5.6 from the textbook, and this is the, uh, simulated data example, which was figured from figure 2.9 of the book. Um, just recall that this is, uh, smoothing splines in three different situations. In this case, the true curve, true error curve is the blue curve. Uh, and again, these th- three different functions that we're, we're examining. This is mean square error for simulated data. [S2] The true error curve. How do we get that, Rob? [S1] Well, it's simulated data, so we just, uh-
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[S1] So we can get a, we can get a, a very big test set. [S2] Exactly. [S1] And estimate the error exactly. [S2] Um, Lee-Van-El cross validation is the, uh, the black broken line and the orange curve is 10-fold cross validation. So we can see, what do we see? Well, here we see that, um,
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[S1] and the, the true error curve is minimized around, I guess maybe three. [S2] Although those, those error curves are fairly flat. [S1] Yeah. [S2] So, there's obviously a, a high variance in, in where the minimum should be. [S1] Right. And then- [S2] It doesn't really matter where, you know. [S1] That's right. It's not gonna matter much if you choose a model with flexibility two or maybe even 10 here, 'cause the error is pretty flat in that region. And then the third example, the, the two cross-validation curves do a, quite a good job of approximating the test error curve, and the minimum's around 10 in each case.
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[S1] like a weighted average in that formula, right? There's NK over N. [S2] Well, do you want to explain that? [S1] Because the, the, each of the folds might not be exactly the same size. So we, we actually compute a weight which is proportionate to this, which is the relative size of the, of the fold, and then use a weighted average. [S2] Right. And if, if we are lucky, the, the K divides, the N divides by K exactly, then that weight will just be one. [S1] One over K. [S2] One over K. [S1] Right.
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[S1] Well, I wonder why. Well, the thing is we, we, we compute in a standard errors if these were independent observations, but they're not strictly independent. Error sub K, um, overlaps with error sub J because they share some training samples. [S2] Right. [S1] Um, so there's some correlation between them, but we use this anyway.
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[S1] And then we, we, we use 100 predictors with the cla- uh, uh, we use them as, in a classifier, such as a, a low-jump model using y- uh, only these 100 predictors, and we omit the other 4,900. So that's not unreasonable. We have a building a classifier. For example, maybe we don't want to have to deal with 5,000 predictors. We just want a small number of them. The question we address here is, how do we get an idea of the test set error of this classifier? [S2] Cross-validation. [S1] Okay, thank you. [S2] [LAUGHS]
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[S1] leaving out the first filtering step and giving it a very, uh, cherry-picked set of predictors in the second set. [S2] Is it- [S1] In the second step.
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[S1] And now we can do whatever we want on the other four parts. We can filter and fit or however we want. And fi- when, the, when, when, uh, when we finished our fitting, we'd then take the model and we'd predict the response for the left out part. The key point being, though, that we, we form the folds before we filter or do, or do, or fit to the data in order to get a, uh, to, so that we're applying cross validation to the entire process, not just the second step. So this is the right way to do it. [S2] So- [S1] So- [S2] ... cross validation. [S1] So-
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[S1] He didn't agree, and his supervisor didn't even agree, who also, I will not name the person. [S2] Wasn't me. [S1] It wasn't you. Well, the supervisor said, "Well, maybe you're right, but you're really being picky. You're splitting hairs here. It's not gonna make much difference." And I said, "Well, I think it might make a difference. You really have to go back and do it." So a few months later, this dude knocked on my door, my office. [S2] Did he pause?
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[S1] Uh, that was, again, it's, it happens and Trevor and I have talked about this a lot and other people have written papers about this error, but people continue to make this error in cross-validation. [S2] So that's a big heads up. [S1] Yeah. [S2] And of course another heads up is not have Rob Tipton- [S1] [LAUGHS] [S2] ... be on your oral committee. [S1] Okay. Okay, so that, that completes our discussion of cross-validation. We, we spent quite a bit of time on that topic 'cause it's a very important technique for all, all the methods we'll see in this course. In the next session, we'll talk about a, a closely related idea, but a different one called the bootstrap.
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[S1] Welcome back. In the last section, we talked about cross validation, um, for, for the estimation of test error for supervised learning. Now we'll talk about a closely related idea called the bootstrap. [S2] It's a powerful method for, for assessing uncertainty in estimates. In particular, for getting, getting idea of standard errors of an estimate and getting confidence limits. [S1] Wow, it sounds like a powerful technique, Rob. Are there any good books on the topic? [S2] [LAUGHS] As a matter of fact, no. [S1] Rob, Rob is
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[S1] ... the best amount, um, proportion to put into, uh, into X, and the remain goes into Y, to minimize the total variance. Okay, so- [S2] Those are population quantities, aren't they? [S1] Those are population quantities. So-
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[S1] And we do this a thousand times. We take the standard, standard error of those. Well, actually, let's, if you do this a thousand times, we'll go to the, look at the histogram in a couple of slides. This, this histogram on the left shows the 1,000 values over 1,000 simulations from this experiment. Each one is a value of alpha hat, and they average around 0.6. [S2] It's called a sampling distribution of that estimator. [S1] Right.
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[S1] Now, um, unsupervised learning is another thing, topic of this course in which- [S2] That's how I grew up. [S1] I see, that's the problem. Okay. Well, so in, in unsupervised learning, now in the kindergarten, now Trevor's in kindergarten, and the child was not, Trevor was not given examples of what, uh, house and a bike was. He's, he just sees on the ground lots, lots of things, right? He sees maybe some houses, some bikes, some other things. And so this, this data is unlabeled. There's no why. But- [S2] Oh, it's pretty sharp, right?
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[S1] And so you can think of this as having a, a very big matrix, um, which is very sparsely populated with ratings between one and five. And then the goal is to try and predict, as in all recommender systems, to predict what the customers would think of the other movies based on what they'd rated so far. So Netflix set up a competition, um, which, where they offered a $1 million prize for the first team that could improve on their, on their rating system by 10%. [S2] Right. [S1] By some measure.
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