So for those of you who don't know, my name is McKenna Gott. My husband Kyle Gott was in the Air Force for six years and he decided to get out of the Air Force and now I am currently in the process of enlisting into the Air Force. I have gone to Mets, past Mets, swore in currently in the delayed entry program waiting for my job and ship date. But I figured I would finally sit down and kind of talk with you guys through my story and why I am finally joining at the age of 27. So to start from the beginning, we need to rewind to when I was about 18 years old, junior, senior in high school, living in small town, Southern Ohio.  I feel like a lot of people can relate to that. I knew I wanted to leave the area but I didn't know how and I just didn't know for sure. Like what I wanted to do in life. Now I had two grandfathers who were in the military and my dad was in the Army National Guard. My dad was in when I was still a kid but he got out when I was very, very young. So I didn't have anybody in the military that was around me as I was growing up. I don't know what the initial trigger was that made me decide on the military. I don't know like who it was or what it was. I had told some friends and family and I never really got a lot of support from anybody, unfortunately, which kind of sucks. I got a lot of just like, well, why would you want to do that? And I think more so in the way that I'm a petite female and they're like, you need to be this big, strong, tough guy to join the military. And I am probably the biggest people pleaser in the world. So when I have a lot of people around me not encouraging me to do something, it unfortunately like steers me away from it cause I'm like, well, I need to do what they want me to do instead of sticking with what I want to do for myself. So I still always had the desire but I would kind of like change my mind based on people around me like wanting me to do it or not. So I would still kind of mention it here and there.  So I went to Huntington, West Virginia which was the nearest recruiting station to me and my mom went up there with me and I talked to the recruiter. I did the practice as Vab and I think I did terrible on it. I feel like I got like a 34 if I remember correctly. It was really bad. And he also had to weigh me and I didn't weigh enough at the time for my height.  And then the next step is to get scheduled to take the ASVAB. So I got scheduled to take the ASVAB and when the day came, I had to drive two hours away to the nearest MEP station to take the ASVAB. So I drove two hours away and I go up to a door and somebody in uniform like opens the door and was like, can I help you? I'm like, yeah, I'm here to take the ASVAB. Our computer systems are down today. Do your recruiter not tell you that? And I'm like, no. And he's like, I'm sorry, you have a really terrible recruiter. After that, I had ended up finding out that I had a few medical things that I needed to get taken care of before I could be medically cleared to join the military. So I kind of stopped talking to my recruiter at the time just because I knew I had some other things that needed to get taken care of. But throughout all of this, Kyle and I were actually already talking at the time. And whenever I got medically cleared to join the military, I was kind of in this spot where it's like, do I go on with talking to the recruiter and trying to join? But then I was also debating on getting ready to start a program in school. I was wanting to take a ultrasound course that would get me an associate's degree. So it was a two year course, but the course that I wanted was actually full. There ended up being one opening in cardiac ultrasound. So I ended up just being like, you know what, I'm just gonna do that just so I could go to school for something, which is probably kind of dumb when it's not actually what I wanna go to school for, but I just felt like that's what you do.  So at the time it came down to doing the two year program or Kyle and I were gonna get married and I was gonna move to Japan. We ourselves had juggled a few different options. It was like, do I get married and move with him? Or do we wait till his tour in Japan is over and then get married? But then we were like, well, what if he gets stationed overseas again and then it was pointless to wait if we already know that we're gonna get married anyway. So at the time we chose to get married and I moved to Japan with him. I probably should have mentioned timeframes as well. So all of that whole beginning part was from about 2011, 2012, when like I said I was a junior senior in high school just having the desire to join until Kyle and I were talking in 2013 and we got married in 2014. But I flew to Japan with him after we had our wedding ceremony. He was stationed in Japan for three years but I was with him for the last year and a half that he was there. Once we moved to Okinawa, Japan I still had the desire to join and I was trying to get in contact with the recruiter there and the recruiter was really difficult to get in contact with. So it was by appointment only. The recruiter's office was actually like right the side of the apartments that we were in but the recruiter was never in their office and I would try to call and I would email and finally they emailed me back and told me to like fill out a whole bunch of papers so I filled out all the papers. But also during this time Kyle and I are talking about it and he was kind of starting to be annoyed with the military already. So he would kind of question me on my decision on if I should join or not. Kyle and I are two completely different people. So in his eyes he is just trying to question me to make sure like this is the thing that I want to do but for me like when someone questions me I'm like I probably shouldn't do it then you know so he's just trying to like make sure it's the right thing and then I'm over here second guessing myself. So then I had kind of pulled away from the decision to join at the time again. So then we moved to about 2016 when we were getting ready to leave Japan to be stationed in Las Vegas. And I was like you know what? I still want to join the military. You have active duty guard and reserves and I have bounced around with joining but also like which division of the branch that I'm going to join as well. So before in West Virginia I tried talking to active duty and then in Japan was going to be active duty and then by the time we're leaving Japan getting ready to go back state side to Las Vegas I was like well if we're going back state side to Vegas I think I want to join the guard and the closest guard base to Vegas was in Phoenix, Arizona and we have family in Phoenix as well. So it just seemed like something that might work out for us and I didn't have to go active duty and we could be stationed there and then I could just do my one weekend a month. So both Kyle and I were on board with this and I had called to talk to the guard recruiter in Phoenix, Arizona while I was still in Japan cause I was like let me go ahead and call and get everything set up so when I get there like we are good to go. And then he's like, oh, like you're not here? I'm like, no, not yet. I just wanted to get everything set up so it was easier for when I got there. And he's like, yeah, we can't start this process until you're here in person. Okay, no problem. I'll just wait till we get there. So then we had moved to Las Vegas in 2016 and actually that settled for a little bit. I was still considering joining the guard in Phoenix, Arizona, but Kyle and I started talking about different things that we wanted in life and we both loved travel. If I joined the guard right now, you have to do a six year commitment with the guard and the reserves. Active duty, you have the choice of four years or six years. So we're like, okay, Kyle has already been in for four years and has two years left but then he's gonna get out and we both wanna travel but then I'm gonna have to have the commitment of coming back and doing my one weekend a month. So we got to talking about it and we're like, well, that kind of interferes with our plans because what if we're over in Europe and then I have to leave to come home and do my guard duty. And I'm just like, you know what? That's just not what I want. Both of us had our hearts set on traveling and I'm like, okay, yeah, that's the route I wanna take. I'm not gonna join. That's it, like travel is the decision that I'm making. So we were stationed in Vegas and Kyle got out of the Air Force in 2018 and we actually have fallen in love with Vegas. We bought a house there. We still own a house there that we are renting out and we were gonna travel for a bit but we were gonna travel around, do a US road trip and make our way back to Vegas which is exactly what we did. Also, if you guys have noticed the airman vision shirt I have on, if you guys wanna get any airman vision merch the link is in the description of this video if you wanna grab something for yourself. So we make our way back to Vegas after traveling around the United States. One of the main reasons of our US road trip was also to see if there was anywhere else that we wanted to live because we hadn't really experienced like a ton of other states but when we got back we're like, no, Vegas is still home to us. We absolutely love it and we decided to settle down there for a while. So I started working at Ashley Furniture and we furnished our entire home because why not if you're gonna get a discount on furniture like that's what you do. So then with us being like, this is where we're gonna live for a long time. I was like, well, why don't I go talk to a reserve recruiter because here it is like that desire inside of me I still wanted to join and now I'm like switching divisions again. I've tried active, I've tried guard but now it's time for reserves because there's a reserves base in Las Vegas. I've got to talk to a reserves recruiter. Do you have any questions for me? And I was like, yeah, I just got my Invisalign on yesterday and they were like, oh yeah, you can't join with Invisalign. So with this being said, like technically you can but you also have to wait. Basically if you have Invisalign you can start the process of joining but you have to get a letter from your orthodontist stating the date that you're going to have them removed because you have to have them removed before you ship out to basic training. So for me, that wasn't really in the cards because I had just gotten them on the day before.  So I didn't continue with talking to the reserve recruiter at the time. Kyle and I are at the house and we got to talking again about how we were not done traveling and we both would be willing to travel some more. So we're like, okay, do we want to like take some vacations or would we be willing to kind of like uproot our life and move again? And we're both like, yeah, yeah, we would move again. That's fine. So Kyle is like, I can put my resume out on some of these contracting sites because he was out of the Air Force but there are job opportunities all over for the job that he had in the Air Force to do as a civilian contractor. So he put his resume out and we had gotten offers like that same week from places all over but we ended up choosing Huntsville, Alabama because the pay was good and the cost of living was low and the area is really nice. So a few months after furnishing our house, we had to sell all of our brand new furniture and we moved to Huntsville, Alabama and we were still paying off the furniture that we had just gotten for our house. Yeah, it was kind of crazy. We're crazy. Our life is always changing. Then we're in Huntsville, Alabama. The year is 2020. And I still haven't joined the military but of course, I'm still thinking about it. So we initially were planning on being in Huntsville for about a year but then Kyle's like, well, I might go to school and if I go to school, I don't wanna wait till we go somewhere else. I might just go to school here. So then we're like, okay, well, if you go to school we're probably gonna be here for like three years. And then I'm like, well, if that's the case if we're gonna be here longer and I still wanna join the military then why don't I talk to the guard recruiter here in Huntsville, Alabama. And by this point, Kyle and I had talked about me joining again and we were both on the same page with it and he was so supportive and it was really encouraging to me because like before when we were back in Japan and he would question me like, like I'm thinking that he wasn't supporting it when he's like, no, I was I just wanted to make sure that you were doing it.  I'm like, he is on board with this and I was on board with this, which is just exciting because of course, when you're in a marriage you need to consider like the best options for your family as well. So we're both finally on the same page and he was thinking about going to school and I'm like, okay, let me talk to the guard recruiter. So I talked to the guard recruiter here in Huntsville, Alabama for a little bit, things were going okay but throughout that time, Kyle and I were also talking about the options of guard and active duty and we're like, you know what? We both would be willing to kind of up and move again. I know like we're all over the place and things there is always changing and it's crazy. So I'm like, okay. So I stopped talking to the guard recruiter and I'm like, let me talk to the active recruiter and he was kind of going back and forth on like going to school or not but then he decided to get his license to be a mortgage broker and then we know somebody who's in that field who actually had offered him a job and he's like, I could do that job remotely. So if you go active duty, like I could still do that if I chose to. So we're like, all right, here we go. We've been married for seven years. I'm 27 years old and we wanna start a family in the future as well. And that's another reason why I'm like finally doing this because I want to, if I'm gonna join, I wanna join before I have kids. Not that people can't, like people have kids and join the military all the time but personally for me, I'm like if I have kids, like I don't want to leave to go to basic training and tech school and all of that. And I think it would just like prolong me joining even more and then like I might not end up doing it and I knew I would have that regret deep in my soul if I didn't do it. So I'm like, all right, I am going to give it my all this time and follow through because if by some chance something happens and the answer is no and I can't join then okay, I know my answer is no and I can move forward from there because like I finally got my answer. I called the recruiter and he set up an appointment with me two days later. I walk in and I was like, here's all my papers. And he's like, all right, let's get you set up to take the ASVAB and MEPs. So I had my appointment with the recruiter. I got my Invisalign off the week after that and I went to MEPs the week after that and took my ASVAB and passed MEPs and swore in on January 15th, 2021. So I finally have my answer of yes, McKenna, you can join the military and your spouse is supporting you to do so or both on the same page. We just, I mean, it's just fun like being able to have the flexibility to kind of up and go. And we just want to take advantage of that while we can. And I decided to sign a four year contract because Kyle was in for six years and about his like three or four mark, he had already decided like he wanted to get out. And like this whole time people were like, if he joined and he didn't like it and he got out like, why are you joining? But it's like, his experience is not my experience. So like how is that fair to even give me that compare? And I'm like, I will join and have a completely different experience. Like I may join and hate it, but then guess what?   This really works out for our family dynamic and I love my job and I'll sign another contract and we're gonna keep going with this life. But if I never try, then I'm never gonna have the opportunity to make that decision. I'm always gonna have the regret of not doing it and not fully trying to go all the way through with it.  Like proving it to myself and everybody else who didn't believe in me and didn't support me. Also just making everybody who does support me really proud. I'm excited for that. I'm excited to make myself proud with the decision because a lot of times in my life I've not joined because other people didn't want me to. And then like, I'm the one who is left like feeling sad and feeling regret. Like everybody else who didn't support me isn't feeling that like they're just telling me not to and then I listened to them and then I'm the one who's sad about it instead of like being confident enough to be like, you know what, I'm gonna do this for me. But I'm finally at that point Kyle is on board and we're both just really excited for me to finally have this opportunity and we're just excited to find out what my job's gonna be and where we're gonna be stationed and just whatever happens with the future.  Who knows? Only Kyle will tell and we will be documenting all of that on this YouTube channel. Kyle documented his experience while he was in and then now I get to have the opportunity to document my experience and share with everybody else and hopefully encourage those of you out there who have not been supported or just even thinking about doing it, like do this for you. Don't let anybody else tell you not to if it's what you wanna do, do it. As long as, like especially if you're married, as long as your spouse is on board with it and it works out for your family, you know. But if it is something you wanna do and your spouse isn't on board at the time, like keep talking about it, keep having the conversation with them about it because when you first bring it up, it might be unexpected for them and it's kind of like, oh no, like let's not do that. That doesn't sound like a good idea. But the more you talk about it, they might realize like, okay, they really wanna do this, like let's see how we can make it work. And I mean, there's benefits for your whole family with you joining the military. So that is my story of why I am finally joining at 27. Hopefully this encouraged those of you who are wanting to join. And I do wanna mention those of you who are still watching, if you want to become a channel member, it really helps us out as low as 199. It helps support us. And it's just like the tiniest amount. We have different tiers that you can join and you get a special rank by your name. And the longer you're a channel member, your emoji changes and ranks up over time, which is really cool. And you also have access to special emojis that you can use in the comment section and also on the live streams. They're unique only to channel members. And those of you who just want to support our channel, it would help us out so much and we would really appreciate it. But hopefully you guys enjoyed this video and I'll see you in another one.


Multi-level-modellinen terminologia on yksinkertaisesti yksinkertaiset. Niin, että se on yksi pari kertaa uusia kertaa, joita on käytössä multi-level-modellista. Onneksi, että pitää myös yksinkertaisuudesta, mitä on randominen effekt ja mitä on kertaa. koska nämä yksinkertaiset olisivat yksinkertaiset, joilla olisivat yksinkertaiset, mitä kirjoittavat nämä modelissa. Ja myös, että randomipäivät ja fiksipäivät ovat käyttäneet yksinkertaiset erilaiset jälkeen, kuten on, mitä literatuurissa olisivat yksinkertaiset. Tämä videossa järjestelmät yksinkertaiset erilaiset erilaiset randomipäivät ja fiksipäivät yksinkertaiset. Let's start with the random effect and fixed effects. What are those? And let's take a look at the basic recursion model. So we have a y, the dependent variable, that is a linear function of the explanatory variables x, multiplied by recursion coefficients b.  This model has a fixed part and a random part. The fixed part is the data and the recursion coefficients and the random part is just the random variation around the recursion line. So let's take a look at what this fixed part and random part are. The fixed part gives us the expected value and can be used to predict. So using the fixed part we can calculate a specific value for each observation. So the key here is that the fixed part, we have specific values for the recursion coefficients, we have specific values for the x's and we can calculate a specific predicted value for each of our observations. Then the random part on the right is uncorrelated with the fixed part. So that's an assumption and explains the variation around the recursion expected value. So whereas in the fixed part we can predict a specific value here in the random part, we can just say that the observations vary around the predicted value but we can't give any specific value for any observation based on this model. So that is just variation that we estimate. To be more precise, the random part, we don't estimate the specific value but we estimate the distribution. So normally we assume that the u, the error term in the Rikason model is normally distributed in which case this estimating, the u simplifies to estimating the error variance of the model. We could use other distributions as well with more parameters but normally we just use the normal distribution in which case we estimate this distribution by estimating its mean. So the random part is variation that we estimate, the fixed part specific values that we estimate. Let's take a look at how this relates to multi-level modeling because this really, the difference really becomes relevant only when we add more levels to the data. So here is the basic setup from multi-level model. See we have these indices so i is an individual, j is a cluster for example, i could be an observation, j is a person and we are repeated observation of its people or i could be a person and j could be a team so we have individuals nested in teams or i could be a company and j could be an industry so we have companies nested in industries. The level one equation is a normal regression equation with a catch. So we have the y that depends on the x's and we have betas that are regression coefficients. In the multi-level model this level one equation is like a normal regression model. What makes it multi-level is that we also have this level two equation here and we say that these level one coefficients are functions of level two variables. In this model we don't have any level two predictors that would predict the beta zero j and beta one j but we just have these gamma zero zero gamma one zero which are fixed effects and then we have these random effects u zero j and u y j. So we have three random effects in the model. We have the variation around the regression line, the level one error term. We have random intercept and we have random slope and this same kind of modeling approach is used also in panel data where we often have at least a random intercept model. If you read about random effects regression analysis then that could refer to having a random intercept in the model for example. So these are random effects. They are variance components. We estimate variances. We don't estimate specific values. The reason why we estimate variances is that we assume that these are normally distributed. Also other distributions could be used. This same model can be expressed in a single equation format. So we just write the equation for y as a function of these gammas from the level two equations and the absurd values and the error term from level one equation. It's called a mixed model because it has a fixed part and a non-trivial random part. So normally we don't refer to a regression model as a mixed model because there's just one error term but here we have a random part. We have three random effects that we estimate from the data and it's called a mixed model because it has this fixed part and a random part. So important things, fixed effects belong to fixed part. Random effects belong to random parts. Fixed effects are specific values that we can use to calculate predicted values for each observation and the random part is just variance components. We don't estimate specific values. We just estimate how much the case is vary. The fixed part and the random part are almost always assumed to be uncorrelated and that's called the random effects assumption and that will be explained in another video.


This is Cecil B. DeMille with a word from Hollywood for the soldiers, sailors, marines, and coast guardsmen of America. Once again, we have the privilege of bringing the Lux Radio Theatre to the men of our armed forces, wherever you may be. And tonight we have a thriller called Test Pilot, with a cast that's just as thrilling. Two fine actors, Bob Taylor and Bob Preston, and a young lady who, I understand, is the toast of all branches of the service. Miss Rita Hayworth. She'll say a word to you right now. Hello everybody. Naturally, I don't know where you're going to be when you hear Test Pilot tonight. But wherever that is, our hearts are with you. Good luck. Yes, good luck and good hunting. Lux presents Hollywood. The Lux Radio Theatre brings you Robert Taylor, Rita Hayworth, and Robert Preston in Test Pilot. Ladies and gentlemen, your producer, Mr. Cecil B. DeMille. Greetings from Hollywood, ladies and gentlemen. Tonight's play is the story of the most reckless gamblers in the world. Men who toss a coin with death to earn a living. For theirs is the business of taking aloft new, untried planes and straining them to the limit to see if they'll crash. But when these daredevils go to gamble in the clouds, they leave others on the ground. Others who can only wait and hope and pray. This is their story, too. But above all, there is great human drama in the Metro-Golden Mayor action hit, Test Pilot. And starring in it, you'll hear Robert Taylor, Rita Hayworth, and Robert Preston. Incidentally, we had to cover the town to get this cast. Bob Taylor from the Metro-Golden Mayor Studios, Rita Hayworth from the Columbia Picture, The Gay Senorita, and Bob Preston from a certain Paramount Picture called Reap the Wild Wind. Test Pilot is a great chapter in aviation history. A chapter about the pioneers of yesterday who helped to make American planes better and safer. And so helped to make the safety record of the United States Air Forces the best in the world. That record is being maintained right now, despite the enormous increase in the Army Air Force. We'll have thrills and romance tumbling over one another at breakneck speed in Test Pilot. A drama with a punch of a power dive, drama for you, and for our armed forces throughout the world, who hear these plays through short waves and certain other special facilities. We heard from one group of these boys a few days ago. Their letter was dated at a naval training station, and we discovered for the first time that part of the audience that Lux Toilet soap brings together every week listens in an igloo. They write, there are 12 men in igloo E17, and we listen to the Lux Radio Theatre religiously. To compensate for the enjoyment derived from your program, we thought that the proper thing to do would be to give your soap a trial. It's with pleasure we report that nothing other than Lux soap is now being used in our igloo. We salute igloo E17 and hasten to say they needn't buy anything to hear this program, but we're delighted that they've discovered how good Lux Toilet soap really is. Now the curtain rises, the motors rev up and here's Test Pilot, starring Robert Taylor as Jim Lane, Rita Hayworth as Ann, and Robert Preston as Gunner. At two o'clock this morning, Jim Lane, Test Pilot for Drake Aircraft Corporation, took off from Burbank Field in California in an attempt to smash the coast to coast record. He was last reported on Las Vegas, Nevada, 10 minutes ahead of schedule. Las Vegas, Nevada, 10 minutes ahead of schedule. Escalante, Utah, 15 minutes ahead of schedule. Swinging due east, a tiny plane roars high over the mountains of Colorado, streaking like a meteor through the night sky. Then, as the first rays of the sun flash on the propeller, it swoops low over the wheat fields of Kansas, 30 minutes ahead of schedule. Suddenly, the motor sputters a crop. The spray of oil hits back along the fuselage. With an angry whine, the gallant plane dies toward the ground. Pat, got your tongue? Outta my way, lady, I'm in a hurry. Something wrong with the motor, huh? No, I came down to look over the crops. Well, make yourself at home. I'm licked, see? I'm licked. I couldn't move this thing with a derrick. Oh, that's too bad. That's too bad, is it really? All I had was a coast to coast record and it's too bad.  I had it licked to death. Where are we? We are in Kansas. That's great. How near would you talk? About 20 miles. Tell me what you can do for me. Do you live around here? See that house? Right over there. You got a phone? Yes. All right, go call the air terminal at Burbank. Ask for Gunner Morris. When you get him, just yell down and I'll come. Johnny Morris? Gunner, Gunner, just ask for Gunner. Tell him I'm calling. I'm Jim Lane. That's all you have to do.  Listen, I've got to get these oil lines out of here. You don't think I want to be stuck in this dump all day, do you? Well, I don't care very much one way or the other. All right, all right, I'll pay for it. Don't worry about that. Listen, Swellhead, you're on private property and very uninvited.  Say, I'm just in the mood for a bull, sister. You go get him. I'm level to pick him up and throw him right back in your lap. Oh, I know you. You're the prince. Ah, what prince? A nice charming prince right out of the sky. A young girl's dream. And I've been waiting for you all my life. That's why no other man even touched the tip of my finger. I've lived for a prince. Yeah, a nice polite one. OK, sister, my apologies. Accepted. Are you a famous flyer, Mr. Lane? I'm Jim Lane. Oh, should I faint on that one? Say, where do you live? I still live over there. I haven't moved since I told you. Can I use your phone? Oh, it's all right with me if it's all right with a phone. Come on. What's your name? Anne Barton. We're near Wedgetar, are we, Anne? And it's still 20 miles. Oh, that's right. Tell me that before. What time is it? About six. Didn't ask you that before, did I? No. Tell me something. Do all the girls around here look like you this early in the morning? Hey, look at all the hay. That's not hay. That's wheat. Oh, wheat. The staff of life. Yeah, yeah. You know, it's nice here at that. I'm so glad you like it. What about some breakfast? Yeah, what about it? I'm starved. How many more waffles can you eat, Mr. Lane? Well, I'll tell you, Mrs. Barton, how many have you got? That's all I wanted to know. Say, Anne, where'd you get such a nice mother? Oh, I took my time picking her out. Fresh, isn't he, mother? Listen, lady, you're not being polite. I'm your guest here. You mean you're stuck here, don't you? Very smart. Very smart. I'll bet you went to school. Oh, she did. And graduated from State University with all the highest honors. Didn't care. Yep. Broke all the records. Did you go to college, Mr. Lane? Oh, mother. Don't embarrass him. Quiet, you. I broke some records, too. I entered high school as sophomore and came out a freshman. That must be your call, Mr. Lane. Oh, yeah, thanks. Don't talk about me while I'm gone now. He's very charming. Uh-huh. Hello? Yeah, put him on. Hello? Hello, Gunner? This is Jim. I figured it was. Where are you? The oil pump let go. I'm down on a farm near Wichita. Oh, Farwich. Listen, brother, it was his plane that folded up, not me. Bring along a whole new assembly and a set of lines. Where, too, Wichita? Wait a minute. I'll find out. Well, Anne, will anyone in Wichita know how to get here all right? Oh, sure. Do west of Wichita on the main highway. Everybody knows the Barking Farm. Yeah, hey, Gunner. Do west of Wichita on the main highway. Everybody knows the Barking Farm. I don't. Hey, what's all this Ann stuff? Forget it. What time are you getting Wichita? Well, I... Why, this isn't a stick, lad. This is the prettiest farm I ever saw. Where'd you see it? The wheat sways in the field like a silken sea. How's that? Sounds like a wing. We're calling it all afternoon. The oil pump, not Ann. Never mind, never mind. Well, I'll get in a bag. Okay, see you at the airport. Bye. Yeah. Say, Ann, have we got a car? Yes, why? Well, we gotta go to Wichita. Oh? We gotta meet the Gunner, don't we? Oh, when he arrives there, where? Around five this afternoon. And in the meanwhile? Well, I'll entertain you there. Oh, but I thought you had to work on the plane. Oh, no, no, no, that's hard work. Come on, pal, we're wasting time. Wichita is calling. Hooray. What do we do, pal? What do you want to do? Oh, anything.  Okay. You like baseball? Huh? Baseball. Wichita versus Omaha. Are you kidding? Say, have you ever been up in a plane? No, why? I'll take you up out at the airport. We'll hire a ship. Okay, sure. Try it again. No, no. Here he comes. Hey, Gunner. Gunner, over here. Take Ann's with Ann, Gunner. Gunner Morris Ann, the best grease monkey in the business. Hello. No, only one this time, huh? One what? One girl. He usually has two. Oh, that's nice talk. Now, one of them's usually named Mabel. Where's Mabel? Oh, uh, Mabel couldn't come.  Where'd he find you? I picked her off her cloud and got busy. The car's over here. This way, please. Your friend doesn't talk much, does he? Sour, of course. Yeah. Know what I'm thinking about? Am I in it? If you wish. Oh. What kind of a wish? I'm wishing that it was this morning. Did you do it all over again tomorrow? Could you? I never had a better time, man. What about you? The best. See, there's a picture show tonight. Where? Wichita. Oh, yeah. But what about your friend? You want him to go with us? No. Neither do I. Hey, Gunner, you're going to have a nice sleep tonight. Yeah. Did you get that pump off? No. Oh, I didn't. Well, that's fine. Glad to go to Wichita, didn't I? Oh, sure, sure. Had to meet you tonight. Yeah, yeah, sure. Is there any chance of getting out of here tonight? Nope, not a chance. Wait till you see where Ann lives. There's no house sailing along all by itself in the sea of wheat.  Now, don't give me that banjo.  Well, I'm ready whenever you are. Well, that's all I wanted to know. We're leaving early. Hey, there's a house, Gunner. How do you like it? Uh-huh. Oh, dear. What's the matter, Ann? There's Joe. I forgot about him. Who's Joe? My sweetheart. Oh. Oh, well, this is new. She's got a sweetheart. Yeah. And he's sweet, too. Hello, Ann. Hello. Hello, Mr. Lane.  Hi, Joe. Joe, this is Gunner Morris. Hello. Hello, Joe. Glad to see you. She had me worried, Ann. I thought you'd forgotten about tonight. Oh. Oh, is it tonight? Yeah. Did you forget? We're having a dance, Mr. Lane. Wouldn't you both like to come? Uh, no, no. I'm afraid we can't get away.  Oh, I don't think they'd like it. Well, you better get dressed, Ann. Yeah. I won't be long. Thanks for a lovely afternoon, Mr. Lane. I'll make it fast, Ann. You're picking up Willie and Jean. Yes, sir. Ain't no place like the country. Hear them sounds and smell them smell. Honey-suckle. Honey-suckle and raspberry.  Hello, Aunt Day. Oh, hello, Mr. Lane. You still up? Yeah. What have you been doing? Well, sitting around thinking. Nice out here, isn't it? Yes, it is nice here. And she's decided to stay at last. Haven't you, Ann? Yeah. Where was she going? I was going to the moon. I've been trying to win, Ann, for a long time, Mr. Lane. She very frankly told me she wanted someone better. From my understanding, that's probably why I won her tonight. We're going to be married. Oh. Well, that's it. It's nice. It's fine. Look, Joe, the prince has puzzled. What are you calling the prince for? Well, isn't he? They used to ride white horses over some hill, but nowadays they go so fast they can't see straight. Do you know what she means, Mr. Lane? No. I don't either. When she talks like this, I just let her go.  I'm tired. Sure. Good night. Good night, Mr. Lane. Goodbye. Good night, Joe. Good luck. Thanks. Night, dear. Night. He's a nice fella. Did anyone ever nickname you nice? No, why? Well, it seems to be your favorite word. Well, he's still a nice fella. Then you think I made a nice choice. Well, go ahead. Go ahead what? Go ahead and ask me. All right. What are you going to marry that guy for? Because he's a nice fellow. You don't love him? How do you know? Just the way you're behaving now, like a little flirt. I don't like you for saying that. That's tough.  One minute you're going to a show with me tonight. Next you get yourself engaged to him. Then the minute he goes, you're like this again. Sure. That's right. That's me. Yeah. And I rated you the best girl I ever saw. Rotten to be disappointed. You'll be gone in the morning. Soon be here. I wish I'd got out tonight. I wish I'd never landed. I wish I never saw you. But what do you think I wished? You think I like this? What are you trying to say now? Well, all my life I've waited for this morning to come. I thought it had come. Well, I was wrong. It was just a day to you. All right, you don't love me. What of it? What did you get engaged to him for, if that's the way you feel? Because I'm going to forget you. Because he's fine. Because I'm going to be a farmer's wife and a good one. Oh, I'm grateful to you for making me forget my dreams. You're giving me peace. Is that clear? What do you want me to do? Say I love you? Oh, not in a million years. If your heart were tearing for me, I'd like to see you get me now. Well, it was a thrill to see you come out of the sky. But it'll be a greater one to see you disappear in it. You better get up early, because it'll be early. All right, she's all set. Get going. Okay. Well, so long. So long. Get my regards to Joe. What'll I tell him? Oh, you don't need anybody to talk for you. Oh, and you can give my love to the Wichita team. I will. They don't win that league yet. Sure they will. Bye. Bye. Well, he got off all right. Yep, he got off. When do you go? Right away. Catch first plane to New York. Is he going there? Uh-huh. Well? Well, so long, Gunner.  You're going to be glad in the end, see? He's no good. He's the best friend I've got in the world, and he's no good. Well, you'll be glad in the end, believe me. Sure. So long, Gunner. So long. Yes, Mother? He was very nice, wasn't he? What's the matter, dear? Nothing, why?  Oh, I'll be glad in the end. What do you mean, dear? I don't know. Well, I'm sure I don't either. Listen, is that another plane? Well, it sounds like it. Well, for heaven's sake, he's coming back. He is? I think he's going to land again. Yes, there. He's coming down. He's coming back. He's coming back. And where are you going? I forgot my hat. Jim, you didn't. What? You didn't forget your hat. What did I forget? You forgot me. What are you talking about? Oh, you did. You couldn't go. You came back. You couldn't go. Well, then get in and don't ask any questions. Let's get out of here. Get in? Get in the plane?  Oh, yes, I do. Well, hurry up. And listen, you might as well understand one thing. You're going to be sorry for this. In just a moment, Mr. DeMille and our stars, Robert Taylor, Rita Hayworth, and Robert Preston, will bring us Act Two of Test Pilot. Now, I want to tell you a short, short story in words and music, a real success story. Our heroine, a woman who's far from wealthy, whose family budget must be thrifty, and what was taking care of her home and her lively young children all day. She's as busy as this. She rarely gets a chance to visit a beauty parlor. Yet everybody, and that includes her family, thinks she's beautiful. Her features aren't regular, but her complexion, her complexion. Yes, her skin is lovely to look at. So smooth and soft, it gives the appearance of beauty and freshness always. Yet her beauty care is a very simple one. You've guessed it, of course. It's active lather facials with lux toilet soap. Our clever heroine uses this fine white soap with active lather every single day. That creamy, rich lather swiftly removes stale cosmetics, every trace of dust and dirt, and gives her skin gentle protecting care skin needs to stay lovely. You know, it takes just a few minutes to give yourself a real beauty facial with lux toilet soap. Here's what you do. Pat the rich lather lightly into your skin, rinse with warm water then with cool. Then pat gently to dry with a soft towel. Now touch your skin. See how smooth it feels, how fresh it looks. Hollywood screen stars whose complexions must have the most explicit care. Tell you they depend on daily active lather facials with gentle lux toilet soap. We couldn't say more in praise of it.  Care that will help you keep it smooth, soft and lovely? Well, why not try regular lux soap active lather facials for 30 days? Then look in your mirror and see. Now, our producer, Mr. DeMille. Act two of test pilot starring Robert Taylor as Jim Lane, Rita Hay with his aunt, and Robert Preston as Gunna. The knight in shining armor has whisked down on his fiery charger and carried off the princess. The knight is a test pilot. The princess is a Kansas farm girl and the fiery charger, a low wing monoplane which has just landed in New York. Hey, Gunna, here we are. What do you mean we? Gunna, I want you to meet my wife. What? Oh, I've heard so much about you, Gunna. It's almost as if I'd seen you before. Now, wait a minute, wait a minute. I can't take any more today. Just tell me about it as it happened, will you? Well, I went back for her. We were married in Indianapolis and now we're with you again. Married, huh? Yeah. Where's Drake? He's in his office. I'm going to congratulate you. Well, hang on to her for me, will you? I got to get some dough. Make me the coffee shop. Ten minutes. You must be surprised, Gunna. No, no, no, I'm not surprised. I wouldn't be surprised if you got married in Indianapolis and divorced in Toledo. I'm surprised you didn't. You start out carrying with you the best we can give you and work and hope. You're due here in seven hours. An aviation is supposed to be advanced seven years and what happens? You arrive here 37 hours late with a girl. Don't call her a girl. She's my wife. All right, so she's your wife. You're going to test that Thompson racer on Thursday. Tomorrow's Tuesday. That'll give you a couple of days for a honeymoon. How's that? Well, how about a couple of hundred in advance? All right. Right. See you a week from Thursday. No, no, this Thursday. Yeah, I heard you a week from Thursday. I'm sorry, but the national air races won't wait for a honeymoon this Thursday. Right, week from Thursday. Lane? Yeah? Wait a minute. Hello? Yes, Mr. Drake. If Jim Lane asks you for any money, tell him he's no longer on the payroll. Yes, sir. Well, Lane, you can still change your mind. Who are you getting my place? Benson. You'll change yours. So long. Listen, Jim. You've got the idea in your head. You're the only test pilot in the world, aren't you? No, but you have. What are you thinking? Chocolate soda. Want a straw? No, never touch them. How are you gonna? Well, I got it. How much? The gate. Oh, Jim, you were fired. On my ear. Yeah, Drake's pulled a lot of beauties, but this one, he really dressed up for the ball. Jim, Jim Lane. I want to speak to you. Hi, Grant. Hi, Jim. I just heard you were fired. Yeah, that's right. Jim, fly for me. Fly my plane. I got the fastest ship in the world. Oh, go away, Skroy. Oh, listen, Jim, I've given three good years designing that ship. If I win the Thompson, I'll have a factor in a year. Hey, Grant, cut it out, will you? You know I'm broke, Jim. I can't give you any dough, but if you win, the whole 10 grand is yours. Beat it, beat it. Oh, Gunner, take a look at the plane, will you? I saw her. You said she was fast. You okayed all that dope. Remember, Gunner?  She's fast, and she's crazy.  It's a good boat. Oh, does that mean that you will or might or what? Oh, no, no, no. It's too fast.  Oh, yeah, okay. Okay, I'm glad to have met you. How do you like that, honey? Man wants to give me $10,000. Yeah, for breaking your neck. I don't need it. I got $10 in my wife. What more do I want? $10? Is that all you've got? Yep. Oh, lovely. Gunner, he buys a ring for $600, and he marries a girl. He has $10 in the world. He loses his job, and he comes out laughing. Yeah, it's all very funny. Hey, there's Al. I'll go put the bike on him for a couple of hundred. Well, I'll be getting along. Oh, one thing. Hey, Al. That guy ain't very easy to handle. I guess that. Yeah. And look, don't let him fly Grant's ship, see? It's dangerous. He didn't seem very interested. Well, he will be when he wants to dope. Well, it's in your lap now. Good luck. Okay. Thanks, Gunner. Hey, listen, Jim. Everything's going to be great. You can't lose in that ship of mine, can you, Gunner?  Now beat it and let him alone. Yeah, okay, okay, but the ship's in great shape. Yeah, yeah, and if you're not here when I come back, I'll understand. Yeah, okay. Okay. Hey, where's Ann? She's up in the grandstand. Hey, Jim! There's Benson. Hi. Hey, how are you? I'm fine. I'm fine. I'm fine. I'm fine. I'm fine. I'm fine. I'm fine. There's Benson. Hiya, Benson. Hiya, Jim. Let's see it. Gunner, have you met Mr. Drake's new pilot, the mighty Benson? Oh, yeah. You guys got good seats? Could be a nice race to watch. The battle for second place is going to be vicious. Yeah, my wife's sitting pretty. You know, you could buy a lot of seats for 10 grand, pal.  My wife's here with the kids. What do you want to disappoint all of them for? Attention, pilots for the Thompson trophy race. On the line now. Well, that's us. Come on. Good luck, Benson. Same to you. For second place. The Thompson trophy race for the 10 fastest planes in America. All set, Gunner. Let it go. Oh, well, it's Annie. Yeah. I think I left Kansas for this. Hey, I wonder what Joe's doing now. Just giving me the laugh. Uh-huh. Well, there's a sucker born every second, pal. Not anymore. I broke the mold. All clear. All clear. Well, baby, you can sing a song of 10 grand in a pocket full of dough. I'll see you at the bank. Don't do anything I wouldn't do. I won't. Oh, darling, wait. Yeah? Jim. Yeah, what? I got a telegram from the landlady. Yeah? What'd she say? She hopes you win. I will. So long. So long. A little fire. You don't know how cold it gets up there. Besides, the guy's made of asbestos. Oh, how can you talk like... What do you think this game is, anyway? Married him without giving you the fuck, didn't you? Well, if you can't take it, get out. Go on, beat it.  Go on. Bless you, Gunner. He's got a good chance, Sam. He's awful good up there. Are you giving an exhibition? Good, Jim. Are you burned? Oh, not a blister. I don't have a hand. Ten thousand bucks, baby, all for you. Mrs. Benson, or would you rather I didn't? It's all right. I don't feel the way out. I guess I was so sure it would happen. How's the... how's the bill situation? Oh, we'll be all right. You're lucky in one way, Mrs. Benson. I mean, lucky that I won. You see, Benson and I were splitting if either of us came through, but I suppose he told you. He what? Yeah, didn't he tell you? No. Well, we were. So I got it cashed. There's five grand in the envelope. Mr. Lane, please. No, no, no. You don't owe me to Welch on a guy because he's not here to collect it, do you? Mr. Lane, you're lying to me. But it's so beautiful up here. I... I do need it so terribly. I mean, the children... Sure, sure. Listen, he died at his trade, see? That's a lot. Take my word for it. He died in the air. The air was Benson's business. Yes. Yes. Come on, Jim. Hand it over. Where is it? I'm right here, pal. I'm right here. Come on, the dough, the dough. Oh, never mind the dough. Waiter! Listen, Anne, this guy started with 10 grand all in cash and he's on a bender. Now grab some of it, will you? I can't grab any. He's too big. Come on, let's drink. Let's drink to Benson. Fred Benson. Give me the dough, will you? Go away. Fred Benson. What license did that guy have to fly? He didn't have any. Jim. Too tough, baby. This guy looks sweet. He wears a pretty blue dress, doesn't he? Yeah, well, don't kid yourself. She lives up there.  A nice guy like Benson. Don't think, Anne. I'm not thinking, honey. I'm just telling you that Benson wasn't good enough for her.  I don't like you. Sure, that's her. Don't let her fool you when she looks soft and sweet. She sits in your lap and purrs, doesn't she? Yeah, well, she don't fool me, none. Fire is still fire. Stuck her little tongue out of me today, didn't she? All nice and red. Kissed from Cinderella. She didn't get away with it, did she? Did she, Kansas? She got kissed right back.  Dirty, scheming wife. Darling, stop. Please. Yeah, I'm not thinking, honey. Waiter. Hey. Jim, listen. Let's go home, huh? Come on. Oh, baby, who are you? A girl. Yeah, who told you so? You did? I don't even know your name. I know yours. I'm a famous guy. Yeah. I want a blue dress. Blue? She wears a blue dress up there. Who does? Miss Uphead. I look nice in blue. No good. No good. Waiter. Gunner, will you take me home? Sick? No. No, I'm just tired. Yeah, yeah, take her along home, Gunner. She's tired. Good night, Gunner. Thanks. Good night. Now, don't worry about him. No. Well, I met her, didn't I? Who? My rival. Oh, yeah, sure, sure. You met her. Oh, don't just sure me like that, Gunner.  She rides with him when he's up there. Oh. Yeah. And it's hard to cut out a girl a man loves when he's alone. He never looked at me the way he looked when he said he slapped her back into place. I met her all right. Take care of him, Gunner. Don't worry. I'll stay right with him. And Gunner. Hmm? I want to be slapped, too. Hello? Hello, Ann. This is Gunner. Now, listen, he got away from me. I don't know. I've been making the rounds all night looking for him. Yeah, I'll find him. I don't know where, but I'll find him. Come on. Come on. Wake up, sunny boy. Don't shake me. I'm awake. I'm awake. Well, you should be by now. You know what day it is? I know it's day. It is night. It's enough. You know where you are? No, I was in Detroit. Hmm? Well, now you're in Chicago. Chicago. Chicago, Chicago. Oh, I don't feel like doing that. You've been in every city but Indianapolis. Hey, where's Ann? Well, the last time I saw her, she was in Cleveland. That was four days ago. I had just enough dough to wire back to New York. Oh, yeah, and speaking of dough, I suppose you've got my share right here with you, huh?  I did. Even the handkerchief was blown. And the vest. Ain't no vest. Or is it? Ask the vest. Well, Pal, it was a great race. I'm glad you won it. No dough, huh? I'm going home, isn't it? I don't know. Anyway, it's an idea. Fine. Fine. How are you, bad boy? Pretty bad boy. Feeling low? Been up higher. Sure. I'm glad to see you, Ann. I'm glad too. Is Gunnar out there? Yeah. Come in, Gunnar. Howdy. You look fine, too, Gunnar. Feel great. Hey, what have you been doing? That's just like him to say that like that, isn't it funny? Well, dear, you've had more fun than I have. Well, I've tried. And I've tried for five days to think of some way to be cross with you. Oh, Jim, if I could only hate you. What do you want to hate me for, baby? Oh, won't the landlady be glad to see you, though? Why? She likes you. Yeah? She kept asking me, when in the world will Mr. Lane be home? Oh. Say, how much do we owe her, darling? Oh, about $200, darling. Oh, well, that's nothing, is it? No. But I'll bet you haven't got all of that 10,000 left, have you? I'll bet you haven't got over six or 7,000 left, have you? Well, no. Not over that, dear. No, not over that. Well, suppose you give me a little, darling? I'm sorry, Ann. I'm broke. I know you're broke. I was only teasing you. But I know Mrs. Benson isn't broke. That was lovely of you, pal. I'll bet you were funny when you were giving it to her. I wish I'd been behind a screen. Hey, you knew? I guessed. Say, you're some girl. Oh? I see. I see now. You do? What? I see what you are. You're all right. And listen, do you know what I'm going to do?   What a surprise. I'm drinking to a woman.  Now, don't go away. Well, I've been around him a long time, and that's the first time I ever heard him praise anything but himself. But you got it coming, it was swell. Why? What else do you do when there's nothing to do? It's easy to be gallant when you're doomed. What do you mean, doomed? You should ask me that. I've had five days to think, haven't I? And don't you think, Mr. Gunner, I've tried to walk out? I've got a ticket in my pocket, but I didn't go. Anne, you shouldn't think like that, because there's no way to think, it's crazy. Well, this is crazy. Three roads faces, and there's doom at the end of each. Suppose he didn't drink, he slapped her back again, and he sits around, his nerves screaming. He doesn't want a drink, but he can't help it. The second road is worse than that. He's retired from flying and works on the ground. Imagine a man with his heart in the sky, living with a woman on the ground. He wouldn't like himself very much, and I wouldn't like him either, Gunner. Oh, no. No, he's in love with a woman with wings. She's got him, and I've no way to cut her out. I can't fight the sky. Well, there's another road. Yeah, there is, and we're on it. We go on as if nothing had happened. He goes on the next race, another bat, another race, until someday, when he's not quite so young and quick, she slaps him out. You know, don't you? Oh, I don't know. I've only had it for 10 years, and you hit her right in the nose, too. You just sit and wait for it. What do I do it for? Because there's nothing else to do. He gets you. There's no fun being with anybody else. Well, what's fun about waiting for someone to die every tick of the clock? Still living, still living, still living. What for? I won't do it. I won't love him that much. Haven't I the right to live my life without being tortured every second? Haven't I? Yeah, well, sure. And you know what you'll do, don't you? You'll stick with it. You'll hook. You can't get away no matter how hard you try. You know that, don't you? Yeah. Yeah, I know. I know, Gunner. Now, for station identification, this is the Columbia Broadcasting System. After a brief intermission, Mr. DeMille presents Robert Taylor, Rita Hayworth, and Robert Preston in Act 3 of Test Pilot. And now, here comes our young friend Sally. Hey, Sally, isn't that a song from Maytime? Yes, it is, Mr. Ruick. And now's the time of year to be singing it. Everything looks so fresh and lovely. You mean everything has that springtime look. Well, you know, Sally, that's a good way to describe a lady with a luxe soap complexion. Well, it's just right, Mr. Ruick. And you might add that luxe toilet soap helps a girl to keep that springtime look the year-round. Well, Sally, that's why smart girls use luxe toilet soap regularly. It's a real beauty soap. It's mild and as gentle as... As a morning in May. Thanks, Sally. Yes, everyday care with this gentle soap is certainly a real investment in beauty. Well, luxe toilet soap is a quality product. You can depend on its mildness, its purity. When you unwrap a cake, notice how white it is, how satin smooth to the touch. Then, compare the rich, abundant lather with that of other soaps you used. Active lather. It's so creamy and smooth, it's like a caress to the skin. Nine out of ten lovely screen stars, you know, use luxe toilet soap as a complexion soap and as a delightful bath soap, too. Luxe toilet soap is luxurious to use and it's thrifty as well. Millions of cakes are sold each year and so this fine white soap with the flower-like fragrance costs you only a few pennies. Why not let the whole family enjoy it? Get three cakes of luxe toilet soap tomorrow. Now, Mr. DeMille returns to the microphone. Curtain rises on the third act of Test Pilot starring Robert Taylor, Rita Hayworth and Robert Preston. Jim Lane has a date again with his lady in the sky. This time it's a power dive and his orders are to rip the wings off the ship. On the field, Gunnar watches the sky anxiously. Why would you say it was, Gunnar? About 18,000. He'll turn the nose down in a minute. Gunnar? Hey, I thought you were going to stay home. Oh, it's worse. I'd rather see it. Do they always go that high? That's the idea of it. You've got to get a start. How bad is it? As bad as I gather? Remember, we don't act. I don't know, Anne. That's right. Don't kid me. What's he going to do? Power dive. He's got orders to tear it wide open and if I know Jim, he'll try. Here he comes. He's on his way, Anne. Oh, no, I wish I'd stayed home. Oh, no, I don't either. Oh, come on, Jim, come on. How much longer, Gunnar? Depends. He'll pull out when he gets ready or when the wings fall off. Let her come, Jim. Straight down. Straight down. Still living. Still living. There it goes! Gunnar! He's cracked it. It's breaking up. Feel out, Jim! Feel out! Why does he get out? Why does he get out? He will give him a chance. There. There he goes. Come on, Jim. Pull that cord. Let's go, boy. Come, Gunnar. It's okay. Shoot's open. It's okay, Anne. Still living. Still living. Anne, snap out of it. Anne! Jim! Jim Lane to test new ship. Still living. Jim Lane silent on record flight. Still living. Lane flies mercy ship to Arctic. Still living. Still living. Still living. Right on the roller coaster. Oh, do you think you should, darling? Remember, you're weak hearted. Oh, yeah, that's right. Anne, you ought to remember you're testing a ship tomorrow. Don't be morbid, Gunnar. How can you think of business at a time like this, Gunnar? Oh, Jim, I want some peanuts. All right, peanuts? Coming up right away. It's wonderful to be silly, Gunnar. You can't keep this up, Anne. What's the matter? I've never felt such pain. It's like a sharp edge of a knife. I'll get used to it. You'll be dead before he is. That's all right, too. I'm grabbing what I can, Gunnar. What do you want me to do? I don't know. Oh, it'll be all right. I'll be okay, too, when the baby comes. Baby? Yeah. He doesn't know yet. Don't tell him, Gunnar. Why not? Don't tell him, please. Okay. And don't ever fall in love, Gunnar. Don't ever fall in love. Here we are. Here you are, peanuts. You know what goes good with peanuts? What? Outside of you. Champagne. Oh, yeah. Try and get it. Having a good time, darling? Pressure. Enjoying yourself, Gunnar? Adorable.  Too many roads. What? Three roads. Three roads? You're going crazy. I guess maybe I am. Maybe you're drunk, huh? No. But I think I'm gonna be. There's your ship, General. Pretty, huh? Pretty doesn't count, Mr. Drake. The army wants to know how she'll fly. Don't worry about her. Say, how much heavier do you figure this new bomb load will run? Oh, three or four times. That's enough. See if you met Lane's wife. Hey, Kansas, come here. Hello. How are you, Mr. J? General Ross, this is Kansas Lane. Hello, Kansas. Hello, General. Hey, your plane looks like Grand Hotel. Can you see a poster?  See all that loading they're doing? Those sandbags represent the weight of the bombs and the crew. The height record for a war boat of that size is just under 20,000 feet. Well, we're up to 30. 30,000 feet? That's a way up, Kansas. Six miles. Hi, General. Hello, Lane. Hi, you darling.  Yeah, you're jealous. Yes, darling. I'd love to take that high ride with you. I've never asked you before. Can I be a bomb? I'd be twice as quiet.  What would I be? A little icicle. With you there? When do you take off, Lane? Right away. Give me 28,000. We'll call it a day, Jim. Right, General? Certainly. Well, they give me for everything I get over 30. I feel informed. Now you just get 28 and stop feeling so good. And those are orders. Okay. See you around, Kansas. Yeah. Come on, get those sandbags in there. We ain't gonna have to noon. Get a move on. Take that time, Gunner. We're ready.  Now listen, you do the flying. We'll do the loading. Now don't give me any of your lip-wrap. Busted wide open seat. Oh, yeah? Yeah, you want to see me? Yeah, yeah, yeah. What's the matter? Ah, tell that guy to lay off me. What happened? What's the matter with you? You're not the guy I know anymore. Drinking and fighting? Yeah, and I'll tell you why. You're gonna listen and like it. And then maybe you'll see. See what? Come on, see what? I'm shooting my mouth. I don't know what I'm talking about. I'll snap out of it, sweetheart. Come on, let's go. All set there. Get in, Gunner. All set, Jim? Let her go. For a nice fellow, you've certainly turned into a crab. I never saw anything like it. She lifts nice. You better if you didn't have so much weight in her. You're heavier than lead these days. Let them know how we're doing. Calling WSR from Lane, 12,000 feet starting up through overcast. Going on instruments north beam. There she is. There's the sky, Gunner. We're coming, honey. Little Alice moved down. WSR Lane, new record for weight, 26,200. Manifold pressure falling. Hey, we're about washed up. Not yet. Turn the heat full on. WSR Lane, 29,350. Get up there, baby girl. Get up. 29350. Hey, we're about through, Jim. She's washed. Oh, no, she's not. She's choking to death. Next thing you know, she'll fall off into a spit. 30. 30, I tell you. Listen, this is high enough. What more do you want? I want 30. I want to take an inch under it. WSR Lane, 29950. 50 more. Squeeze. Squeeze. Hey, look, Jim, with all those sandbags back there. Squeeze. Come on. What's it read? It's almost there. A little more. Up, baby. Squeeze. Here it is. It's coming up. There. 30,000 even. She's over. Add up, baby. Hurray. Now, look out. She's fallen off. Now, don't let it get into a spit. Don't worry.  It's okay. Where do we get down with this some air? You feel all right, don't you? Oh, I feel charming. I hope those sandbags hold together. I hope we hold together. WSR from Lane. WSR from Lane. We're spinning. Come on, ladies. Straighten out. Hey, when do we hit that thick air? We're dropping like a light. You handling your controls? I'm not touching them. Stay. Just leave your hands off. I'll pull it out, sweetheart. Fine. When? Take your time. Take your time. I'm just a little impatient. That's all. Oh. What's the matter? See those bags? They're breaking loose. They've got me in the back. Move over here. Quick. I can't. There's too much weight. It's pinning me. Stay clear of the controls. I can't move. I can't. All right, all right. I'll get the bags out. You never make it, Jim. You squeeze away from the controls just a little? No. Jim, bail out. Listen. I have it. Jim, please get out.  Forget what I tell you. No time. Now, Jim. There. Can you move? No. An inch, just an inch. Come on, Gunner. Wait. Is that it? One more? There. It's okay. Jim, can you get it out? Hang on, Gunner. I'll bring it down flat. Watch it. Hang on. Jim. Hey, can you move any? Sure. Just taking it easy. It feels good not to try to move. Listen.  What? Just listen. I've got so many words. Listen. Don't take anyone in my place.  You don't know how good I was. I was awful good. See? You've had a kiss, will you? Gunner, look at me. Here's a break for me, though. I won't ever have to go home and break the news to her. I'll leave the roads first. Three roads.  For my sake, Gunner. That's all I'd come back for. Hey, Gunner. I heard. He's dead. Gunner's dead. Why wasn't you? I couldn't have been you, could I? Oh, no. I've got more coming to me. I've got to get all that's coming to me. Another year maybe. I'll go crazy first. Ann, look at me. I've got a kiss for you, Ann. For him. Go on. What else? What are you going to say? Your heart's bleeding? Aren't you going to say that? My heart isn't bleeding a drop. My memory of Gunner is beautiful. I believe you. You have no heart. You don't know what pain is. He died at his trade, didn't he? What more do you want? Oh, that's great. Go back up in the sky. That awful sky.  Go on. Don't leave me alone. Sit down, Jim. How'd you take up at the hospital, huh? Yeah, I'm okay. I had a thing wrong. Did they tell you that? No, but I'm okay. I'll take the sister ship up tomorrow.  Well, how else could you figure it? Listen, I haven't started yet. I'll go back up there. I'm going back up there and pay the sky back for what you did to me. I'll pay her back. I'll ring her neck. Jim, you're not taking that plane up tomorrow. You're not going to ring her neck either. No, why not? I've just had a report from the hospital. You're grounded, Jim. Grounded? Me? Well, they can't do that. They... Why?  Grounded. That's great. That's fine. There's still a spot for you. Here, if you want it. Find a desk. It's great. Or the army. The army needs men on the ground, too, now. Yeah, I guess that's it. I don't know. Talk it over with Anne and let me know, huh? Yeah, sure. So long, Drake. So long, Jim. Oh, yeah? Jim, I said some awful things. I didn't know what I was talking about. I was just jealous, darling. Jealous? That girl of yours up there. Well, I'm not anymore. She can have you when you're flying. But when you're down here, you're mine, Jim. And don't be jealous.  You cadets, I've been talking for 30 minutes to you boys, and you're probably looking wise and giving me the bird. Anybody got any questions? All right, good luck. Get up there and fly. Hey, what are you doing here? I brought a friend. Hello, Jim. Oh, well, hi, son. Mother said I could watch the airplane. Why, sure. There they are, son, just taking off. Gee, look, mother. Come on, Barney. Get up there. Oh, why can't I get in there and show them? Look at me. A man spends all his life getting somewhere, and where'd he end up? On the ground, just where he started. Jim, when I grew up, I'm gonna be a pilot. I'm going way up in the sky. Way, way up. Well, you'll have to ask your mother about that, son. Four years old.  A thrilling play had a thrilling performance at the hands of Robert Taylor, Rita Hayworth, and Robert Preston. And right now, we'll ask them to step into the spotlight again. Thank you, CB. One look at the sky will convince anyone that aviation is the most exciting topic of the moment. The records show that there are more planes in the air now than ever before. Sounds like we might have a traffic jam up there before long. Yes, what about accidents? Now, in spite of all the planes in the air, Rita, America's safety record is still the best in the world. The figures prove it. Even though the Army has cut the length of time spent in training pilots, I believe they've also cut the accident rate. It was done through new methods of training, methods that ensure greater safety. And that record is something we're all proud of. And now, Mr. DeMille, if I may, I'd like to say just a word about the product back to this theater because luck soap is an old friend of mine. I use it every day. It's the finest way I found to care for my complexion. We're glad to hear that luck soap is at a part in one of Hollywood's greatest success stories, Rita. I mean the story of your career, of course. Well, what's happening here next week, CB? I think you'll be interested, Bob. To begin with, the play is the Samuel Goldwyn hit Ball of Fire. And our stars are Barbara Stanwyck and Fred McMurray. Why didn't somebody tell me these things? Well, it's one of the comedy successes of the year, Bob. The romantic story of a professor, that's Fred McMurray, who is studying slang and learns more than he bargained for from a dancer named Sugarpuss O'Shea. That's the part Barbara Stanwyck played in the picture, of course. Well, it should be a great show, CB. Fred McMurray is one of my favorites.  Forgotten? Oh, yes, Barbara Stanwyck. She's good, too. They, CB, I know you're at work on a Mexican picture, but I think you should let us all in on that other drama you've been whispering about all week. Well, it's no secret any longer, Bob. The agreement was made in Washington the other day. I'm going to film the story of Dr. Wassell. Oh, that's the Navy doctor that the president told the nation about on the radio a couple of weeks ago, isn't it, Mr. DeMille? Yes, Rita. The humble man of medicine who single-handed evacuated nine wounded and helpless naval heroes from Java, ran the Japanese blockade, and brought them to safety in an Australian port 1,500 miles away. Dr. Wassell has been awarded the Navy Cross. It's a great story, and part of every dollar paid at the box office will go to Navy relief. Well, that'll be good news to all Americans, Mr. DeMille. Good night. Good night. Good night. Good night. Happy landings, good night, and every night. You are American airmen. Our sponsors, the makers of Lux Toilets Hope, join me in inviting you to be with us again next Monday night when the Lux Radio Theatre presents Barbara Stanwyck and Fred McMurray in Ball of Fire. This is Cecil B. DeMille saying good night to you from Hollywood. The Current Look magazine has an article of great interest to all our listeners. The story and pictures of Cecil B. DeMille's 30 years in Hollywood, along with scenes from Lux Radio Theatre rehearsals. Heard in tonight's play, where Cy Kendall is Drake, Fred McKay is Joe, B. Benadiric as Mrs. Benson, Verna Felton as Mrs. Barton, Charles Seal as announcer, Howard McNeer as Grant, and Triss Coffin, Tudor Williams, Warren Ash, and Bobby Larson. Tune in next Monday night to hear Barbara Stanwyck and Fred McMurray in Ball of Fire Our music was directed by Louis Silvers and your announcer has been Melville Rory. This is the Columbia Broadcasting System.


In the last lecture, we have discussed Newton-Raphson method for approximating an isolated root of a non-linear equation. We have also stated the convergence theorem of the method in the last class. In this lecture, we will prove the convergence theorem. As a first reading, you may skip this lecture. However, I advise you to carefully understand the proof of the convergence theorem of the Newton-Raphson method, because the mathematical tools used in this proof is very important for you, especially if you want to train yourself as a numerical analyst from the research point of view. Let us get into the theorem. Let us first state the theorem, which we have already stated in the last class. Let F be a C 2 function. Recall, to set up the Newton-Raphson iteration, we just need F dash of x n. That is, we just need the first derivative of the function F, but for the convergence, we need one more order of smoothness of F. That is why we have assumed that F is a C 2 function. And also, we will assume that the root R, which we are interested in is a simple root. It means what? It means F dash of R is not equal to 0. If these two conditions hold for our function F, then the theorem concludes that there exists a small neighborhood of the root R. That is what we meant by saying that there exists a delta such that R minus delta to R plus delta is a small neighborhood, delta neighborhood of R. And if you start your iteration, that is, if your initial guess is taken in this small neighborhood, remember, we have to find this neighborhood delta. There exist means we have to find this delta neighborhood such that if you start your iteration with your initial guess x naught in this neighborhood, then everything will go nicely. That is what the theorem says. What is mean by everything will go nicely? Let us see. First thing is each term of the Newton-Raphson sequence is well defined. What is mean by this? Well, what happens if you started with a x naught, then you went to x 1, then you went to x 2, like that you kept on going.  Then what happens? Well, then the Newton-Raphson iteration sequence is not well defined. The theorem says that if you start your initial guess pretty close to the root, then this will never happen. That is what it says. Well, the question is when such situation will happen? Let us see. Suppose, we are working with a function f whose graph is like this. You can see that it is a nice smooth function. At least visually, you can see that and suppose we are interested in capturing this root r. Now, you started with some x naught, say and you started computing x 1, x 2 and so on. At some n, say x n is this, then what happens? Your f of x n is this and now x n plus 1 is nothing but the point of intersection of the tangent line with x axis. What is this tangent line? Tangent line is parallel to the x axis and therefore, it never intersects x axis.  This is a geometrical illustration. What is happening analytically? You see in this case, you will have x n plus 1 is equal to x n minus f of x n divided by f dash of x n. What is f dash of x n here? That is equal to 0. So, this becomes 0 here and that will give you infinity. This is how the Newton-Raphson iteration sequence may fail to exist. The theorem says that I can find a small neighborhood of r as long as I start my initial guess within that neighborhood, then such a situation will never occur. That is what it says. Suppose, you see if you restrict yourself to this neighborhood and start your x n here, x naught here, then you see your x 1 will be somewhere here and your x 2 will be somewhere here and your x 3 will be somewhere here. Everything will lie in this interval only. That is, all your x n's will lie in this interval only and they all will be well defined. So, that is what we are going to see. So, as long as you start your iteration with the initial guess x naught in a small neighborhood like this, then your Newton-Raphson iteration sequence will be well defined. The sequence x n will remain within this interval. This is what I have shown geometrically in the previous slide and the important point is that the sequence will also converge to the root and finally, this gives us the quadratic convergence of the Newton-Raphson method. Well, it means what? This quantity is equal to constant. Some finite number, that is what we have to show in order to conclude that the sequence converges with this order. You can see now here it is 2. Therefore, the order is 2. Why this term is finite? Because we assumed f dash of r is not equal to 0 and f double dash is a continuous function. That is what we assumed here that f is a c 2 function and we are always restricting to a closed and bounded interval. Therefore, this is a finite quantity. This is also non-zero finite and therefore, this entire thing will be finite. So, if you prove this expression, it precisely means that the Newton-Raphson iterative sequence converges quadratically. Let us see how to prove this theorem. The proof of this theorem is much simpler than the proof of the secant methods convergence theorem, but the idea goes more or less the same. First, we have to establish this relation for some xi which is very close to x n and this we have to establish for each n. Let us see how to prove this expression. It is not very difficult. You start with the Newton-Raphson method formula and now what you do is you take r minus on both sides. So, you will take r minus this equal to r minus this term. Now, this right hand side can be rewritten like this. It is very easy to see that the right hand side with r minus x n minus f of x n divided by f dash of x n can be rewritten like this. Now, let us see how to deal with this expression for that. First, we will go to the Taylor's theorem and try to expand the Taylor's theorem around x n at the point r. If you recall, you are taking a equal to x n and you are writing the Taylor's formula for some x equal to r here. What is r? r is precisely the root of the equation f of x equal to 0. Therefore, the left hand side is 0, right hand side is precisely the Taylor formula and this is the reminder. Now, you can see that this term that is the linear term is precisely what you have here. This is quite natural because in the Newton-Raphson method, we precisely did the linearization and took that expression, right. That is why this and this are just coinciding. Now, what I will do is this term is equal to minus of this term, right. So, I will take this reminder term to the other side and I can replace the numerator in this expression by minus of this, right. So, that is what I am going to do. I will replace this with minus of this one. I hope you understand this where xi n lying between r and x n, which is coming from the reminder term of the Taylor's theorem. Once you do that, you get this expression. This is precisely what we wanted to show, right. Therefore, we have obtained our claim. That is, we wanted to prove this and we have derived this expression right from the Newton-Raphson method. Now, we can use this expression to prove all our conclusions. Let us see how to do that. First of all, if you recall, we have assumed that the root r is a simple root and also if you recall, we assume that f dash is continuous. In fact, we assume that f double dash is also a continuous function. Why we assumed? First and foremost, we want this Taylor formula to hold. For that, we need f to be c 2, right. We already used that hypothesis that f is a c 2 function. Now, we are only using a part of it. That is f is a continuous function. Therefore, we will combine these two results. That is, f dash is not equal to 0 at the point x equal to r. It means what? When f crosses the x axis at r, f dash of r is not equal to 0. Therefore, it will either cross like this or it may cross like this and so on, right.  That is what we meant by saying r is simple. Once f dash of r is not equal to 0, then we can find a small neighborhood of r in which f dash remains non-zero, right. So, in this interval f dash of x is non-zero. How we get this? This is by the intermediate value theorem. So, intermediate value theorem says that if the continuous function f dash is non-zero at r, then you can find a small neighborhood say delta naught neighborhood. That is r minus delta naught to r plus delta naught such that f dash will remain non-zero for all psi in that neighborhood. That is what the intermediate value theorem says. Remember we have to capture a delta neighborhood, right. But this is not the neighborhood that we want. We want further a small value delta from where we pick up. We should choose this delta which is less than delta naught such that this quantity is less than 1. What is this? Well, capital M is the maximum of f double dash and small m is the minimum of f dash. So, minimum of f dash is always greater than 0 because we are restricting ourselves to this neighborhood where f dash is not equal to 0. Therefore, this will always be positive. Well, why should f double dash and its maximum should be positive? Well, that can be assumed without loss of generality. This may not be true, but we can assume this without losing any generality. Why? Just see if m is equal to 0, it means f double dash of zeta is 0 for all zeta in the neighborhood. That is this delta neighborhood. It means what? It means f dash of zeta is constant for all zeta in this neighborhood. It means what? f is a linear polynomial. It means its graph is a straight line. f graph is a straight line. So, what it means? If you take any x naught and apply the Newton Raphson method, if you recall Newton Raphson method, we will take the tangent line at the point x naught and see the point of intersection of that tangent line with the x axis. In that sense, you can see that if f is itself a straight line, then the Newton Raphson method will capture the exact root at the first iteration itself. Therefore, there is no question of convergence and there is no question of the existence of the Newton Raphson iteration or anything. Everything becomes trivial. Therefore, we will not consider the case that f double dash of zeta is equal to 0. It means we will assume that f double dash of zeta is not equal to 0. Therefore, without loss of generality, you can assume that M is greater than 0. We choose our delta which is less than delta naught. You should also think and observe that such a choice is possible. I will leave it to you to see why such a choice is possible. Therefore, you have to choose like this and the corresponding delta you take. Now, let us see that this delta will work very nicely for us. How? Let us see that choose x naught in that smaller delta neighborhood, not the delta naught. Delta naught we are not going to take. We are going to take the delta which is smaller than delta naught such that this holds and this will work very nicely for us. Let us check that you choose x naught in this neighborhood. Remember, in this neighborhood f dash is not equal to 0. That is something which is already there because it is there for the bigger neighborhood itself. Therefore, it will be there for this smaller neighborhood also. Now, let us take this formula which we have derived as the first claim of our proof. We will use this how? Take modulus on both sides. Take modulus on both sides. You can see that this term is less than or equal to. Now, what I am doing is I am taking modulus and putting maximum for this that is this one and minimum for this. Therefore, this will be less than or equal to m divided by 2 small m into this I am keeping as it is. So, I am not taking modulus here because I am squaring it. So, we got this inequality. Let us see what we can do with this inequality. In this inequality you take n equal to 0. Now, what you will get? The first left hand side will be mod x 1 minus r and that is less than or equal to m by 2 m into mod x naught minus r square. That is what I am taking like this. Now, this is less than delta and this is less than 1. Why? That is how we have chosen our delta. Therefore, as long as x naught belongs to this interval, this first term will be less than 1 and the second term obviously will be less than delta. Therefore, the both together will be less than delta. What it means?  So, it means if you start your x naught from this neighbor root, we have shown that x 1 will also belong to that neighbor root. So, that is what we have shown. Now, you can use an induction argument to show that all x n's belongs to this neighbor root. That is very easy for you to show. So, what we have shown? We have obtained a delta neighbor root. Remember how we obtained? We obtained this delta such that this inequality holds. That is always the demand. So, once you choose such a delta, we have seen that all the x n's belong to this neighbor root. That is what we have seen and also you can see that as long as x n belongs to this neighbor root, all x n will exist. Why? Because the only way they do not exist is when x dash of x n minus 1 is 0. But that can never happen because in this interval, in this neighbor root, basically we have chosen this delta such that if dash is not equal to 0, therefore all the x n's will be well defined. Therefore, we have also shown this property. Let us now prove the convergence. It is not very difficult. Let us start with the inequality that we have already derived in our previous slide. First thing is you can see that x n minus r is less than delta because x n belongs to the delta neighbor root. Therefore, one term in this square I will take and put it. In fact, this can be put as strictly less than delta and remaining m by 2 m into x n minus r is kept as it is. Now, let us go to apply the same inequality for x n minus r. See, this kind of recursive idea is used in many places. So, once you use this inequality for x n minus r, you will get delta m by 2 m square into mod x n minus 1 r. Again, you use this inequality for mod x n minus 1 minus r. That gives you less than or equal to, well it is strictly less than delta into m by 2 m cube into x n minus 2 minus r. Like that, you can keep on going till what? Well, you will go till you hit x naught minus r. At that level, you will have this constant as delta m by 2 m to the power of n plus 1. Now, you see what is this constant? You can show that this constant is less than 1. Why it is so? Well, we have chosen our delta such that m by 2 m into mod x naught minus r is less than 1. What is mod x naught minus r? That is less than delta. Therefore, this implies delta into m by 2 m is actually less than 1. Now, you see you have this constant which is less than 1 and that constant is given with power n plus 1. Now, what can you say about this right hand side as n tends to infinity? That is the question. Well, as n tends to infinity, this term goes to 0 right, because this constant is less than 1. That is precisely what we want to show because once this side goes to 0, then left hand side will also tends to 0 and that is precisely the convergence of the sequence x n right. So, we have proved the convergence also. Now, all reminds is to prove this order of convergence that is not very difficult. Again, you start with this expression which we have derived as the first step of our proof. Now, you can see you want to show limit n tends to infinity mod x n plus 1 minus r. You see that is there already with you divided by mod x n minus r square that is already there. So, you bring it to the left hand side and that will be equal to limit n tends to infinity f double dash of xi n divided by 2 into f dash of x n right. That is what is given here. Now, you see x n tends to r. We have just now proved the convergence. Therefore, this is converging to r. Similarly, xi n lies between r and x n. Therefore, you use the sandwich theorem to conclude that xi n also converges to r as n tends to infinity because x n is converging to r and xi n is lying between r and x n. Therefore, xi n will also converge. Therefore, your numerator will converge to f double dash of r. This is what precisely we wanted to show in the order of convergence and that is also achieved. By this, we have proved the convergence theorem of Newton-Raphson method. The Newton-Raphson method converges if you start your initial guess pretty close to your root. That is what the theorem says and the important take away of this theorem is that if the sequence converges then it converges quadratically. With this, we will end this lecture. Thank you for your attention.


Evidently not completely satisfied with the scientific rigor of the dietary trial presented in Daniel 1, 8 through 16, researchers in Tennessee published two papers recently detailing a series of parallel experiments on a 21-day, all-you-can-eat diet, devoid of animal products and preservatives, and inclusive of fruits, vegetables, whole grains, legumes, nuts, and seeds. In other words, food intake in accordance with a stringent vegan diet. The purpose of the studies were to determine the effect of a 21-day Daniel Fast on both biomarkers of antioxidant status and oxidative stress, as well as the efficacy of the Daniel Fast to improve markers of the lion's den of metabolic and cardiovascular disease risk. No surprise that a diet composed of whole plant foods improves several risk factors for metabolic and cardiovascular disease as well as an improvement in selected biomarkers of antioxidant status and oxidative stress, including metabolites of nitric oxide, which I've talked about before. Participants experience meaningful improvements in blood pressure, cholesterol, insulin levels, insulin resistance, C-reactive protein. We're all lowered to a clinically meaningful extent. And this was in a young, healthy population. Imagine the miracles it could do for people who are really hurting. This study extends the findings of other plant-based diets by documenting the impact of a strict vegan diet on multiple measures of oxidative stress and antioxidant capacity. Of course, if instead of a biblical Daniel Fast, they had called it a strict vegan diet, they probably would not have gotten a compliance rate of 98.7%, especially in Tennessee.