Thanks for checking out the third episode of should you read and this is should you read Scott Pilgrim? This is available on Comicsology through their unlimited service. Also, you can just purchase it if you want to purchase it So off the bat so if people want to turn this video off right after seeing my recommendation You can go ahead and do it. Should you read Scott Pilgrim? Yes. Yes is what I would say But I'm gonna talk about it a little bit more. I'll give my star rating at the end Scott Pilgrim obviously there was a movie made about it So the writing had to be good enough to get the attention of people who wanted to make a movie out of it And that one's called Scott Pilgrim versus the world The actual series of comics is just called Scott Pilgrim One major minus to spot the Scott Pilgrim for me was the art style art style is very very simplistic It's not very high-brow. It's a very simple almost childlike artwork, but it works for the story because the story is very It's got a lot of dry humor to it and the story's goofy. It's about a kind of dorky-ish Guy's life and his love life in particular and It kind of fits for that reason. It's okay. I don't need it to be like super sophisticated super crisp super clean So I saw that immediately. I was like how this artwork is not really what I wanted it to be But then as I kept reading I was just like you know what? I'm totally over this after like the first few pages and it kind of fits with the story. So that was fine I am cool with that So that said you got to like the dry humor you have to like the characters the characters are really well put together They're all funny. I like every character adds a certain element of comedy to it So if you like comedic Comics and there's pretty much nothing really serious in it You're okay.  It seemed super Weird when at first did that it was just like normal story a normal story like oh this is funny And this could happen in real life Maybe it's someone's actual real life story and then they throw on this weird like video game style I'll mean I was like that's kind of out of nowhere, but then as they kept going with it. I'm like I dig it. I like it It's cool But it's very endearing the story is really interesting. It's a very endearing story It's interesting enough to keep you reading I've been through the first two volumes because that's what they'll allow through Comic psychology unlimited, and I really like it Debating whether I would purchase it or not just because I have seen the movie Therefore, I know the full story But I don't I mean there's a lot of extra stuff in the comic that obviously was not in the movie So that's why I'm kind of like torn on I'm like I kind of want to see what else is was missing from the movie and But all that said I also think that the movie was pretty faithful to the comics I mean as much as they really could and I think that their choice of Actors and actresses that they chose was really good for how the characters were written in the comic itself I Feel like that's pretty much all I have to say about Scott Pilgrim. I enjoyed it It's nice So if you're totally cool with what you heard you can handle a lot of comedy You're not super snobby about your artwork you can get past You know more simplistic art styles then this could very well be for you So that said should you read Scott Pilgrim in my opinion? Yes, you should and I think that should apply to pretty much everyone It's everyone likes to laugh here and there even if it's not out loud internally at least So in the star ratings that they do on comic psychology out of five stars. They gave it four stars Not like the most phenomenal comic I've ever read but quite good very good enough to keep me going back And I'm even contemplating if I want to purchase so any rate Thank you everyone for checking this out if you have ideas about comics You want to hear me do a review for or see me do a review for you can you know You don't have to actually look at me when you're listening to these you can look away because I'm just kind of sitting here with my Movies behind me and stuff You can send it to brutal battle podcast at gmail.com. You can also send movie and TV Suggestions because I might do those as well Anyway, once again brutal battle podcast at gmail.com brutal spell B. R. E. W. T. A. L Until next time well, please keep watching these videos and let me know what you think that's another thing But until next time keep it


Thank you, Mr. President. Mr. President of the Congress. Thank you, Chair. Chair of Congress, Director-General, Ambassador Hussein, Director-General-Elect, my dear friend Mr. Metoki, Deputy Director-General-Elect, my dear friend Marjan Oswald, delegates, friends, I address you all. There's no place for bitterness in defeat, particularly not the day when we celebrate victory. And I now turn to you, the family of the Universal Postal Union. And what I want to say to you is this, I've always served you and I will continue to serve you. My term of office continues until the 31st of December this year and then we will see what the future holds. I was a committed, serious candidate for the post that I was standing for. I knew how difficult the circumstances we are in are. I've already known defeats and difficulties in my life and I have no regrets whatsoever about the political campaign I waged because I had real ambitions for the Universal Postal Union. Of course, a verdict has now been handed down on my candidacy and some people are happy, some are not. But what's important today is that we join together. We must recognize the importance of the Universal Service that we provide. My campaign was difficult. It was difficult in terms of the resources available, the time available and the way that I could behave. I was very, very rigorous in my approach. I put forward proposals explaining my vision and my proposals. I put forward my arguments. I didn't manage to convince most of those who voted. But I remain deeply convinced of the arguments that I put forward. I wish to congratulate most warmly Mr. Metoki, the future director general of the UPU. I thank you for your campaign, Mr. Metoki. You waged a very correct campaign and a very friendly campaign with me. Japan and Switzerland have always got on very well and certainly this is not something that is going to trouble our friendship in any way. Now, my post of deputy director general will be handed over to another friend, Mr. Marjan Oswald, the pilot and I'm going to let him take over the controls at the end of this year. And it will be a new life for him and a new life for me too. But I hope that in that new life I'll be able to exert a positive influence elsewhere. But I'll never forget the wonderful years I spent at the helm of this organization taking it through a period of reform so that it can be where it is today. I've learned an awful lot from this unforgettable adventure. Yes, I had ambitions. I had a vision. I wanted justice. There was a kind of thirst for justice in what I did and my campaign now comes to an end as does that of the others. Tak, Vlad, Marcella, Eunus. I know how they're feeling and I think about them now. I've been lucky enough to know victory in UPU and I wish them in the future also victories here within UPU. I cannot conclude without turning to Ambassador Hussein, our director general. I have been at his side for many years. I have advised him. I have been loyal to him and at times I had to serve my vision of public service which involved being true to myself and being loyal to the situation in which I found myself. That's always been the values that I have upheld. The values of my family, my mentors, those who have helped me. Edouard Dian also entrusted me with many things because he too believed in those values. From what I have done from the 25 years I've spent in the international arena and in the postal arena, I have learned a great deal and I have always sought to uphold those values. I can say perhaps selfishly that I think we have all benefited from that. I've worked alongside the staff members of the UPU and Swiss Post. I thank them all for their work with me and I congratulate them on the wonderful results we have achieved as a team because no one can ever win alone. My life my life is focused on friends and family. My wife and my children. I've been very ambitious and perhaps because of that they've suffered sometimes, including if we look at what's happened today but I want to state here publicly that their support and their presence with me at all times is truly vital to me and to what I am. I also wish to thank Switzerland Switzerland for the trust shown in me, the confidence shown in me in all circumstances, even the most difficult circumstances. Over these 25 years I've been involved in politics in the widest sense of the world.  That's what's made me what I am. It's taught me resolve, yes but above all else, it's taught me humility in both victory and defeat. So it's time for me now to step back to others who will serve the cause of the UPU. Thank you for your kind attention. Thank you Thank you Pascal. Thank you. That was a very touching speech. Thank you very much indeed.


Good afternoon. My name is Nara. I'm from Brazil. I'm from the city called Taguachinga. It's next from Brasilia, the capital. It's the suburb of Brasilia. Me and my colleague Fareed have a studio, a design and audiovisual studio named Gunga. We created it about 10 years ago and we work with free and open source software since then. I am a graphic designer. Fareed is a programmer and video maker and web developer. I'm here today to show you my work and our work. Today we have more people working with us and make a showcase and tell you about the history of Gunga. Feel free to ask questions because I think questions will make this thing more rich. This is Gunga logo. This is me. You can see me. Fareed is 10 years ago. We just rented our place by that time. We are with these funny heads. I don't remember why. We are in a place called Mercado Sul. The translator is self-marketed. It's an antique market that was not unmarketed anymore. Today it's like a lot of cultural collectives. There are squads there. There are many different and crazy things going on there. It's like a community. It's very little streets like here. Everyone knows everyone and everyone uses free software because a lot of people use free software there. We are kind of a place that people go to install and people go to solve problems. We are studio too, but we are working with the community. It's like something like this. Some photos of there. I'm doing it on Inkscape because I feel it's easier to do a presentation on Inkscape. I bring some photos. This is some of the events that go on there. This is the streets of South Market. Our place is right here on these brushes. This is Faridhi. There are a lot of cultural things going on like Kapoeira. This is one of workshops that happens in there. This is inside the stores on the second floor. This is one of the squad activities that we contribute. This is another party. There are two. This is me talking in the streets. This is like Carnival. And other cultural stuff. This is like Samba. This is our friends who work there with us. It's a lot of people working there. This is another little workshop. This is us in the fair, like fruits. This part of some work that we do, like a team. This is like where we are today. We begin like me and Faridhi. But today we have another two people working in Gunga. They are two of our journalists. One of them work with photograph and design. This is Webert. This one here. And the other is Haissa, who is a graphic artist and a journalist too. And works with social media too. We added this service recently. Working with social media. We didn't have social media. But about two years ago we were in nothing. We only have a website. But we are starting to lose a lot of jobs. Because we don't offer the service of working with social media and design. We just offer design and web service. This two here is Davit and Kayani. They are co-working. And there are two other companies. That are journalists who work with culture. And Tomada, who is another company. He is two girls here. Who work with cultural projections. Like events and fairs and this kind of stuff. This is our team in an event. In a movie festival. In our city. This is like Cunga today. This is like inside and outside. I take this picture just before I came here. Now I'm going to show you some of my projects. I use a lot of software. I mix them in my process. Krita, my paint. In scribbles. Inkscape. And a lot of other ones. And I'm going to show you some of the works. This was the movie festival of Taguatinga. This is our city. This is on the 12th edition. And the team was like our woman first person. Our woman part. Something like that. We all have a woman part in everyone. Like this was the team of David. We made web. We made printed. We made both doors. Outdoors. Everything in free software. This was like more the shows. And the workshops. Other shows. And things like to the Facebook and Instagram. This year the festival is already beginning. The 2018 edition. I just started. This is like the first thing that I made just before I came here. Like the new identity. This year the team is like the movement on us. Like Brazil is getting through a political, social, ethical crisis. So the festival is like inviting movies that talk about that. That inspires people to make things different. Like this thing, like what we're doing here and other stuff. I just started the posters. The first campaign is just to call the video makers to subscribe their films. We are in that part now. You are understanding? My English is... Yes. Not the one that I'm going to show you. This was a simple job that I made. It's like a logo for animation studio. Online animation school. This was what I showed to the clients to the options of logo. I was trying different typographies and different images. They chose this first one. And after it changed a little. This was the final one. They work a lot of with motion graphics and liquid design, liquid motion. So it was one of the inspirations for the logo. I want to show one part of this. This is like my mess when I'm part of the creation. Here you can see how the logo was created, like the curves. It looks like something that you just draw, but it's something that... It's like a lot of lines and you have to make this work very fine when it's big and when it's very little. So it's like part of the process here of the creation. This is an app of... We are called to contribute in this app because they are... It's all made with free software. It's like a Foursquare for cool things and responsible consumption in Brazil and organics and agrofoilers and stuff. I create the logo and some icons for it. This is like something that I do for the marketing. But I also have some mock-ups. To do an app was like a big challenge. I studied it, but it's my first app that I work on it. You make lots of mock-ups to understand how it's going to work and just take a minute. But in the end it's kind of different from the beginning because you think and the software is... When you come to the end, to the cell phone, a lot of things change. But it's important to think the process. So you have to design every step that I use and could do inside the app if he's going to make this type one. You have to trace it. Everything that the user is going to do, you have to design in the different ways that he can go there. So like this is the... I know not the first mock-ups, but it was part of the process. So you like the beginning when you enter and they show you... You pick some places, they show you the information of that place, where it's in the map, some people talking about that. You can write something... Oh, I like this place, I don't like. This place doesn't exist or something like that. Well, you can download it in... Google? No, App Store, no, the other one. Google Play, yeah. You can download it, it's responsive. It works in smartphones. This is some screenshots of the real thing, not the mock-ups. Like when you... For download it? Oh, just like step-by-step how to download and use it. You can write your number, receive a code, enter in the app and find initiatives of responsible consume, like there's... I don't have so much time to... But you can see all initiatives in a map or in a list and get inside them, like... Works like a Foursquare. I showed this in the next LGM, but I'm going to show it again because we are proud of it. We redesigned the logo of Cadden Life, so the old one, let me see if I can... This is the old logo, and we offered to contribute in this part, creating, making a redesign of the logo of Cadden Life, and this is the new one, so we changed it a lot of things, but mainly the... Maintaining the concept of the software and of the logo. We made versions for... This is like one version, it has another four icons that are very little, so we have to make a different logo for use for very little applications. This is something like the process. I started, oh, this is the old logo, and okay, let's do something like that, but no, that makes something different, and this is not entirely here in this archive, that's okay. So this is the little version of it, tiny version. I was making some templates for the website that are online now. This is how I work with Harid, like he's a web developer, so I make the elements in Inkscape, export them to him, and make some mock-ups of the site to see how, more or less, this is what I want the site to be. We work in the same place, so I think we have a very fluid workflow. We don't have a lot of documents, and we just sit one by the next other and do the things. There's something you know and you want me to show, like how you do that project. This is Malaika, this is an animation 3D movie that we are doing right now. This is the main character. I made the characters and all the drawing parts of the animation and contribute with the, like, when you draw everything, like the storyboard. This is some sketches that I made. This is like the 3D versions of the characters. This is the part of the process, the main character. It talks about the history of the quilombos in Brazil, which are, like, African tribes that remains until today in Brazil. So they are missing their lens and the animation talks a little about that. This is like the drawings that we used to do the 3D characters. Most of the characters are here. The bad guys and the good guys. We started the scenery. We have another big scenery. It's just two houses and some flowers. We think maybe, like, the animation is going to be, like, five minutes, but we are trying to do these five minutes to get founds to do something longer episodes, something like that. Yeah, this was, like, how much time I have? This was a DVD, a music DVD. It is in a world of best DVD, like, in a... like, music awards in Brazil. This is the cover. Okay, that's fine. This is, like, the cover. It's, like, Brazilian music. It's very mixed. I can't explain it to you. It's, like, the CD, because it has a deluxe version and a low-cost version. This was the low-cost, just the CD in a paper label. We do some work on the Internet to communicate the DVD. So this is the artist, the band. There's a lot of things that I could show you. I can talk with you if you want to see more things and open the files and see how I work and how I use the programs, the software. And I bring... I bring some things that were the printed jobs and I tell you to see. It's a lot, but not a lot, but some... Maybe I just put in here and you can see. I think it's better than to pass over. And questions? I suppose you started with the software before... I started using... Yeah, like Adobe or... Yes, yes, I started. I was still studying design. So I use it, provide software for like two years or three years. So I have more time using free software than private software. How do you think free software has improved the design or how improved the general practice of design? In the beginning I have lots of problems and headaches and I want to throw the computer from the window and oh my God. But today I'm very okay. I can... I send something to the... to print like, okay, go print. I'm going to travel. But in the beginning it was a very problematic thing. I sent something. I have to go to the printer shop to... No, I don't have a... Illustration or a Coral Draw Archive. This is... You have to work with this. So... But today I think it's like... I'm really naturalized with the workflow of free software. So I think when someone new gets in Gunga I actually question, what do you think it has to be to improve the software? Because I am no longer... have more comparative because it's been so much years that I don't use proprietary. So I don't have... In the beginning I have. But now it's only what I use. But I think it's improved. Some software is most than others. But today I can do what I have to do with no problems. Thanks, you can contact Gunga in the website or my email and Twitter, Instagram, Facebook, etc. Thank you.


Today I want to talk about machine learning, a very cool topic that's getting used more and more these days. Part of the reason that machine learning seems weird is that we have this idea of machines as being this sort of rigid and unadaptable kind of thing, just sort of blindly doing whatever they do. But the whole idea of learning is that you take in some data, some observations about the world, and try to find patterns in them that you can then exploit to do better next time. So a machine for a machine to learn means it has to be able to, number one, change its behavior and number two, observe and find out things about the world, which is sort of the opposite of blindly doing the same thing. There's a lot of different ways that we can sort of look at learning problems. Here's four of them and you already know all of them. Unsupervised learning is you get some input and then a teacher, a supervisor tells you what they are. Like, you know, this is a fleab and this is a gloob and okay, so now here's a quiz, you know, what is this? It's a fleab, supervised learning. Unsupervised learning, there's no teacher. You're just sort of seeing stuff and saying, oh, this thing and this thing, oh, these are pretty similar. I'm going to put them together. Oh, this other thing, that's very different. I'm going to put it in a separate category. So unsupervised learning, you just observe some data and sort it into groups based on your sense of similarity amongst the things that you see. Reinforcement learning, you're actually out doing things, not just looking, but acting in the world. I wonder what happens if I do this, oh, got a shock, negative reinforcement or, ooh, tasty, positive reinforcement. And then you're trying to learn to do things that get positive reinforcement. Temporal reinforcement learning, same as reinforcement learning, except there's sort of like a big time delay. It's like, oh, I shouldn't have eaten that mushroom yesterday. Games, chess, checkers, whatever, are typically examples of temporal reinforcement learning tasks. You have to take a whole bunch of moves, you win or lose and it's not clear how the combination of moves were necessarily responsible for it. In these problem formulations, there's lots of different learning algorithms, specific things to have the machine do to change its behavior in response to its observations and try to do better. Nearest neighbor in K-means clustering, those are unsupervised learning algorithms, the other ones are mostly supervised. This is a current area of research, there's lots of different algorithms here, lots of different ones that could be put in, which is good. Also there's a lot of activity happening, but it also kind of suggests that this is definitely not a solved problem, and there's a sense in which the whole idea of learning is not really a solvable problem. It depends on making assumptions about the world that some pattern that used to hold will continue to hold. So regardless of what learning algorithm or which problem formulation really you adopt, there's some things that come up over and over again. I want to talk about two of them here and try to do demos. The first one is this idea of exploration versus exploitation. If you need to explore out in the world to find out what your options are, to find out what's good and what's bad, then a question comes up, okay, this thing seems to be pretty good, should I just cash out and keep doing this thing? Or should I try doing some other stuff in hopes of finding something better, which may cost me to give up, pay off, reward good things that I could have had by doing what I already knew? Trying new stuff is exploration, cashing out the best thing that you know so far, exploitation, their inherent trade-off between them. All right, let's try an example. This is the chili monster, is an alien robot chili monster, I think maybe it's a zombie too. And the way it works is you poke this guy in the eye and he gives you a cookie. So there, plus one, that's a good cookie, that's a payoff. And so the question is, well, so should we punch him in the red eye again or should we go for green? I'm going to go for green, green, okay, that was bad, minus one. So here we are, we're now the learning creature. We've got a good one from red, a bad one from green, figures will do the red one again, oh great, so two, all right, well so two and one, do this guy maybe a little more, now we're two and one either way, okay, so what choice do we want to go with next? Who knows, pick a red one, okay, three and one, all right, that's worse, okay. So here we are with a learning problem, do we want to just commit to red and do that all the time, or do we want to try green some more and see if it catches up? As humans we have a real tendency to try to make up immediate explanations for everything like, all right, so we'll try red again, okay good, so red is just better, we'll try green, well green was better too, so maybe we're just being extra lucky today and we should alternate back and forth, well I guess not. So one way that we can avoid sort of trying to say, well the reason that red is better is because I'm wearing my lucky red socks, is instead of making up explanations immediately we should lay back and collect data, we need to keep count of how many things went well and how many things went badly, I mean one of the mistakes that we can make as people is to only count one side, if we're sort of optimist we can count the good side and pessimist we can count the bad side, well so we've got a little collector cup here that we can use, then the way it works we just sort of put it here and it vacuums up whatever it is, so so far from the red side we've got four good ones and two bad ones, got a guy for the green side, he's paying off at three and two, they're both pretty good, okay, so you know which one should we pick, well we've got this guy we've got a learning creature that is connected to our cup so he's aware of the data that he gets here and he doesn't have a mouse so he throws water balloons like that, so he threw it at green and got a got a negative payoff, right, so if he goes again, well he got a negative payoff on that side, so the learning algorithm for this guy has to decide what to do, which way is he gonna go, let's just let him run for a while, goes red, got a payoff, so he's focusing on red, why is he focusing this on red, well red is 160 something percent of the time, green, well now green's up at there too as well, he's going back and forth between the two, so how does this guy work inside, and here it's pretty cool actually, it's very simple and it's an algorithm that is being used out in the world, we'll talk about that in a sec, let's turn them off, okay, alright, so here this graph, I'm not gonna explain it in complete detail because it's a little bit involved, it's called a beta distribution and what the way it works is, you know, so how much is that red guy worth, we've tried him 31 times, we got 16 wins and 15 losses, how good is that, well we know the average, you know, we divide it out 51%, whatever it is, but is that really what it's worth, could it actually be sort of just paying off 50-50 and we haven't seen it yet or could it even be paying off like 55% and it's just we're getting particularly low, well this thing called a beta distribution, it comes out as statistics, you can feed in the two numbers, the number of wins and the number of losses, I'm fluffing over some details here and it gives you back this curve and the curve doesn't say what the worth of the choice is but it says the distribution of it, so right now we've got this green curve corresponds to the fact that we've got 17 wins and 13 losses, which is actually a little better than the red curve at 16 and plus 16 and minus 15, but both the curves are very broad, meaning we're not really sure how much this thing is worth at all, I mean like the green guy, he has, you know, some height all the way out at like 0.7 and all the way down to, I don't know, maybe 0.3 or something like that, so the white guy is a little demo rod and he's completely flat, so if we've never tried him at all, it's completely flat, but as we try it and like start to get wins, the curve gets sharper and sharper toward the wins, so if we had 11 wins and zero losses, we'd start to think wow, it's pretty likely that this thing pays off all the time, but then the instant we get a loss, well we know it can't be paying off all the time and so on, so the beta distribution you feed in the wins and losses and it gives you this estimate of how much the distribution of possible values of the choice, and so now the nice thing about this is that it's better than just saying the average number of times it won, because, you know, if we had three wins and three losses, that's 50-50, but if we had 300 wins and 300 losses, that's also 50-50, but we know more about it when we have 300 wins and losses than we have three, so you see, as we try to like go from zero-zero, it's completely flat, as we increase the number of wins and losses, if I can go straight here, it stays at sort of 50-50, but the distribution gets narrower and narrower, because we got more and more data saying it's really likely that it's 50-50, so what this guy is doing is he's got those two curves, let's get rid of the white guy here, he's got the two curves for the data that he's seen, and every time he makes a choice, the one curve that gets more data gets updated, and what he does is he throws a random number weighted by the green curve, and then throws a random number weighted by the red curve, and whichever one comes out higher, he picks that, so let's let it run, okay, so now at the moment, the red and green curves are sort of overlapping quite a bit, which means he's going to pick one, pick the other, and so on, but as we get more data for these things, the distributions start to get more narrow, and that if they don't overlap less, then it's going to pick one over the other, okay, so green is paying off 54%, something like that, red's paying off 51%, I can tell you now that I programmed this so that one of red and green pays off 48% of the time, the other one pays off 52% of the time, but I don't even know which is which, the program scrambles them randomly when it starts, so I mean if I had, well I don't know, I was going to say it was probably green, but now they're very similar, and in fact they're both paying off more than their actual pay off, just because of random variations, just because of luck, and actually speed this up a little more, I just figured this out the other day, if we can get two of them going at once, see if I can get it going, there we go, okay, so now he's throwing the next one before he even got the cookie from the previous one, which means he's making his decisions about what to do next based on the throw from two ago, but you know we're trying to get lots of data, so who cares, and now it's looking like the green is significantly better, so the learning algorithm is choosing to exploit, to dump it into the green guy, still trying the red one every so often, because might be wrong, still exploring a little bit, but shifting more and more towards exploitation, this number in the middle here is its total payoff over all choices red and green put together, so it's up 33, 31, whatever it is, this kind of problem where you've got to do something out in the world and you have two goals, one is to get knowledge about what's happening in the world, that's why you explore, and the other one is to actually make something good for yourself, that's the exploit, is a fundamental problem of learning algorithms, and this kind of algorithm, this kind of learning problem, this is really not called the alien robot chili monster problems, more often called the two-arm bandit problem, or the multi-arm bandit, where each action you've got is like a different slot machine, you're trying to figure out which is the best slot machine, if there are any different, and this problem comes up all over the internet, it comes up with advertising, and now the actions are what ads should you put on a webpage say, and the chili monster is you, it's trying to get you to click on one of those ads, that's a plus one, and if you don't click on an ad, that's minus one for all of them, so the system behind the ad system, or like in the video website, when you're watching videos, you get to the end of videos, you get this little grid of other ones to watch, same thing, those choice of which ones to put up there are based on this kind of algorithm, it's trying to make the ones that on the one hand you'll pick, and you'll watch, but on the other hand it's also trying to get knowledge about is this particular video one that people like, all right, so still not completely clear, we can let this go a little bit more, and then we'll come back when we do the next demo, all right, so exploration versus exploitation, even when we're in other problems, other versions of learning, that's still behind the scenes, I mean in supervised learning teachers just telling you do this, do this, do this, it's not so obvious how there's the explore exploit trade-off, but once you learn something, you're still going to have to go out and do it in the world, and then that comes back again, okay, so you know, if the video site is showing me a set of videos that I might want to watch, it's like I'm going to make one choice and then I'm gone, it's not like I'm the chili monster sitting there getting treated over and over and over again, so in fact really I'm just a teeny little piece of the chili monster, all the other people who are looking at videos and getting presented with choice screens and so forth are all more parts of the chili monster, which raises the question, you know, I don't like the same videos that somebody else does, and if they show me something that someone else likes, it's not necessarily going to work that well for me, I mean they might be able to pick the videos that everybody likes, you know, Gangnam, Azalea or whatever it is, but you could do better if you could recognize that I am similar to other, you know, geeky, computer-y, whatever I am, and somebody else is similar to that too, so what we can try to do is that we want to do a categorization task and based on some knowledge that we have we want to make a distinction between one versus the other, and this ultimately leads into this question of knowledge representation, how do we divide up things that we see in the world into categories that we can make predictions about them, the things in this category we're going to tend to like these videos, things in this category we're going to tend to like those videos, okay, so let's do an example of that, well let's see how the learning guy is doing, they're still both extremely close together, and as a result, and this is good, as a result it's still trying both of them, looks like red's got a little bit of the edge here, 52%, and green is falling away a little bit, although did we lose our double, yeah we lost our double clocking there, so we weren't going as well, well I guess we're not going to know this story for sure exactly which one ends up better, maybe if there's time we'll come back to it at the end, don't know, but we're going to have to stop him for now, and all right let's look at this, one of the earliest learning algorithms for making distinctions, supervised learning now, we're going to get input, teacher's going to tell us this is this, this is that, and we have to learn it, in this case we're going to learn pictures, okay, I went out and I found on the web a bunch of news photographs that were used for face recognition research, it took a dozen pictures for President Bush, and I looked in my camera and I got a dozen pictures of cats, so we're going to try to learn between former president and cat, all right, and the way it works is this, up here we've got our input, this is 250 by 250 individual pixels that make up a black and white picture, so they can be zero which is black, they can be one which is white, anywhere in between which is gray, down here at the bottom we have another whole set of 20, 250 by 250, 62,000 something, weights, numbers that represent what we've learned, and if we start this thing up, all right, so at first, the first thing we do is clear out the weight, so this level of gray is a weight value of zero, and if the weight value goes negative, it's going to be darker than that, if the weight value goes positive, it's going to be brighter than that, so the way this machine works is we put in a picture, all right, there's a picture, former president Bush, and in order to evaluate this we take each pixel in turn, 250 by 250, multiply it by the corresponding weight and add them all up, and if it's greater than zero, we say the category is president, and if it's less than or equal to zero, we say the category is cat, okay, now at the moment, all the weights are zero, so no matter what picture it is, we're going to get time zero plus something time zero plus something time zero, the whole result is going to be zero, so the first prediction is the sum is less than or equal to zero, in this case it's equal to zero, so what the perceptron says is cat, and the supervisor says wrong, okay, and now the perceptron learning algorithm, what it does is saying, oh okay, you're saying this thing should be greater than zero, it should have a sum greater than zero, so it goes through each of its weights, and all the weights that are sort of big, it moves them to make, all the inputs that are high, it makes the weight more positive, all the weights inputs that are low, it makes them more negative, as a result the whole sum goes up, and I didn't actually even really expect this when I first implemented this, but all right, so now we're going to modify our brains to make this thing look, produce a more positive sum, and it actually makes kind of a shadow of the input that we're in, because the brighter spots get more positive weights, the darker spots get more negative weights, all right, now here's a cat, but since we just changed the weights to make everything positive, it comes out some greater than zero, so again it makes the wrong guess, now we do the same learning, except now we want to make the sum smaller, less than or equal to zero, so it's like we memorize a negative of the picture in order to kind of cancel it out, like that, so now we've got sort of half of one picture in positive, half of the other picture in negative, and so on, so we can go through, we've got a dozen, one category, a dozen of the other category, and we're just going through them in a random order, whenever we get the answer right, okay, cat, we don't change the weights, we don't have to learn, we didn't make a mistake, but when we do make a mistake, then we update the weights again, okay, we go all the way through all 24 cases, we see how well we did, if we got them all right, we're done, otherwise we shuffle them again and go back to the beginning, so let's speed this up, so it's getting some right, getting some wrong, all right, so now we're at the end of the pass, and we got half right, same thing we would have gotten by flipping coin, or always saying cat, but let's see what happens in the second pass, all right, yes, well, no, still making some mistakes, nope, yes, yes, yeah, uh-huh, yes, yes, starting to learn, okay, so if we let this go a few passes, and because the actual pattern of the weights depends on the order of presentation, because we only learn when we make a mistake, and if we just got went in one direction so that it gets us several more right, then we don't do any learning, it can take a different number of passes before we actually categorize all the inputs correctly, and there we got it, okay, so is that cool, we learned all these things, now one of the things that people got excited about the perceptron way back when in the 50s when it was first studied, was that there was a proof that if it was any way for it to learn something it would learn it, so in this case it learned it no problem, but we would like more than having it just memorize a bunch of pictures that we showed it, we want it to learn the concept of former president versus cat, so that we could feed in new pictures, maybe pictures that the supervisor hadn't even categorized, and get useful answers out of this thing, so that's called how well the algorithm generalizes, so not just learning, not just getting it right, you know, teaching to the test, but then being able to apply knowledge to other cases, so I've got a couple of other inputs here that the perceptron never saw, so a generalization test, so here's a different picture of the cats that the perceptron never saw, what do you think? Is it going to get it right? No, got it wrong, another picture of a cat, got it right, 50-50, another picture of the former president never saw, no, sorry, not so good, okay, the perceptron as we've used it here is not very good at generalization, because really if we look at these weights, you know, it's learning extremely specific little details about the pictures that we happen to show it, and there's really no reason to expect that it would actually apply to other pictures, I mean even if we took one of the same pictures we trained on which sort of moved it a little bit, it would line up with different weights and get probably a different answer, so the knowledge representation problem is how do you actually build algorithms that are like the perceptron, they're making categorizations, but they make better characterizations, they make better categorizations that are more like the way we do it, okay, and one thing we do is that one of the algorithms that was mentioned, so in the beginning the deep belief networks is, it's like got a whole bunch of perceptrons, but instead of going straight from the input to the output, it's got layers of them and trying to get more and more general abstract things, and a lot of this stuff is working pretty well now, as we go forward, one of the things that in fact is driving machine learning getting used now is the combination of two things, computers are much more powerful than they used to be, number one, and because everything is connected to the internet in particular, there's tons and tons of data to learn from, there's lots of pictures, there's people typing stuff, there's people speaking and doing speech recognition, there's tons of data, and just like if we had many, many more pictures that we were trying to make a distinction between, we'd have a better chance that our learning algorithm would sort out what's really important and what isn't, assuming our knowledge representation and the way we built the learning algorithm is even capable of representing the concepts that we wanted to learn. In the general case, the Explore, Exploit trade-off does not go away, the theoretical framework that's studied in is called Minimizing Regret, in the learning algorithm world, there's really the idea of no regrets isn't possible, the only regret means if you could predict everything perfectly, you'd get some amount of payoff and whatever you get less than that because you had to explore is your regret. And finally, knowledge representation sort of goes to the core of what learning needs to produce in order to be successful, and also even how we see things, how we understand the world as a result of our experiences.  It's totally happy to make a judgment of any possible input you give it. So for example, if we give it something that's not a cat or a president, like this is my dad at Sky City years ago, and what do we say that is? We said my dad's a cat. And here's a picture of a dentist's light that looks like a robot. So I took a picture of it. There you go.


Welcome back to episode five of Math 1050, College Algebra. I'm Dennis Allison here in the Math Department at Utah Valley State College. And today we're going to talk about two big topics. The first one is using functions as models. And the other one is on direct and inverse variation. So let's begin by looking at functions and models. And let's go to the first graphic that says the graph of a function can tell a story. In this case, it becomes a, quote, model for the application. Now let's take an example and go to the next graphic here. We actually saw this same problem several episodes back. But I just want to remind you how this goes. This is a graph of a salesman's distance from home. So you see it starts off at 8 AM. He's at home. And by 9 o'clock, he's a certain distance away from home. And it looks like between 9 and 10, he stopped. Maybe for breakfast. Maybe he stopped at his office. But then he travels on between 10 and noon. He travels in a linear fashion, we might point out. And he stops between 12 and 1. Perhaps he had lunch. Then he's traveling again between noon and 5 o'clock. He gets a little closer to home. Then he travels further away. And then he stopped between 6 and 7, perhaps, for dinner. And then he comes home in a hurry. So you see, here's a graph of a function that is a model for a story. And when you look at the graph, you can interpret the story. We don't know that we have all the details right. We don't know if he stopped for dinner from 6 to 7, but it looks like he was stopped anyway. Let's go to the next graphic. Here's a new one. This one says, a homeowner mows the lawn every Wednesday afternoon, sketch the graph of the height of the grass as a function of time over a four week period, beginning with Sunday. Well, you see, beginning on Sunday, the grass has some height to it, but it keeps growing until Wednesday. And that's when the homeowner mows the grass. And then the height drops back down. And then the grass starts growing until the next Wednesday. Then it gets mowed again. So you see, this graph is chopped up into pieces. Does that graph, would that graph be a function? Does it represent a function? Well, let's see, it has to pass the vertical line test. Does it pass the vertical line test? Yes, every vertical line seems to intersect it no more than once. Why is it that the graphs, those little branches don't start off at zero? What would be your explanation for that, Jenny? You don't shave your grass off completely. You have to leave about a half an inch there. Yeah, exactly. So you have to leave a little bit of grass. You don't cut it right down to the ground. So the graph starts off, those branches start off a little bit higher than zero. But then it seems to grow in a linear fashion. Now, of course, when I say a function as a model, this is not an exact model of the grass because I doubt if grass grows in a perfectly linear fashion. If you get rainfall, grass grows faster. If you're in a drought, grass may grow slower. So this model is supposed to represent, but not perfectly, the growth of the grass. By the way, it's said to grow this or to represent this for a four-week interval. And actually, it looks like I've only drawn about a three and a half-week interval. So I should put an extra short branch coming out of the right-hand Wednesday if I were actually going to show four weeks. Okay, let's go to the next graphic. Here's a quite different problem. This time, we have an illustration, but we don't have a graph. It says a property owner uses 120 feet of fencing to make a rectangular garden beside a garage. So you see the garage is represented. We're sort of a bird's eye view. The garage is on the left. We have the rectangular garden. We come out X yards on each side. And the perimeter of the three sides is 120 feet. Now, the questions say, first of all, find the four-sided perimeter. We'll call that function P of X, P for perimeter. And then find the area, A of X. So we're gonna choose the function, name the function A for area. So let's try solving this on the greenboard. I'm gonna draw that illustration up here. Here's the garage. We're going to come out, down, and back. And we know that we have 120 yards all together of fencing. And I'm gonna call this X, call this X. So if I put X yards here and X yards here, how many yards are left over for this side? Stephen? 120 minus 2X? 120 minus 2X, yes. And I think I'm running out of room there, so I'll put it, I'll write it over here. 120 minus 2X. So part A asks us to find the function P of X, which is the perimeter of the garden. Now that's for all four sides. So the perimeter, I'd have to add up X and 120 minus 2X and X, and another 120 minus 2X, even though there's no fencing here, it's part of the perimeter. So that's gonna be X. Actually, I'll have two of those X's. Why don't I put 2X there? And I also have two of the 120 minus 2X's. Two times 120 minus 2X. Now that is the function P of X, but it's just begging us to simplify it, so let's go ahead and do that. So that'll be 2X plus 240 minus 4X. And that's a total of 240 minus 2X. And what units would I put on that? Yards. Yards, okay. So that would be 240 minus 2X yards. So that is the function rule for the perimeter. Now you see what this means is, if you tell me how much X is, like if you tell me X is 10, if I plug in a 10 here, that'll tell me what the perimeter of the garden is. Let's just see. P at 10 would be 240 minus 2X 10 minus 20 is 220 yards. That's the total perimeter. Now you remember, we only have 120 feet of fencing, but the perimeter of the garden is 220 yards. That would be 10 and 10. How much would this side be? 100. 100, and this would be 100. So 10 and 10 and 100 and 100 is 220 yards. On the other hand, what if we chose X to be 50? Well, then this would be 240 minus 2X. That'll be 100. And I get 140 yards for the total perimeter. That would be 50 and 50. And what would this be? 20. 20 and 20, 50 and 50 and 20 and 20. Sure enough, that's 140 yards. And you might say, well, Dennis, look, if you can figure out those answers just by pointing at it, 50 and 50 and 20 and 20, what's the purpose of this? Well, now I have a general representation for all possible, for all perimeters, for all possible Xs. By the way, there is a restriction on the domain of this function, because X can't just be any number. One restriction, for example, is that X can't be negative. So we know that the Xs here have to be positive numbers, because you can't have a negative dimension on a garden. On the other hand, what's the biggest X could be? That's kind of a tricky one. Let's see, we have 120 feet of fencing.  60. It'd be 60, so X can't be bigger than 60. If I go out 70, I don't have enough fencing to even come back. So the biggest X could be, would be 60. And as a matter of fact, we might even argue that 60 isn't allowable, because that's not really a rectangle. If you go out 60 and back 60, you just have a line segment with zero area enclosed. But we'll include those as sort of the extreme possibilities. And I would say that the domain of this function is restricted, and that is the domain is zero to 60. The reason I point that out is we mentioned in the first episode, I think it was, that if there's no mention of a restriction on the domain, we assume the domain is every allowable number. Well, you see, this function allows every possible number to give you an answer. It just, it doesn't make sense in this physical application. So we have this smaller domain. Part B of the same problem says, find the area of that garden. So let's do that now. We call this function A of X. Once again, the garden looked like this. We come out X, and we said that this side was, oh, this is X down here. We said this side is 120 minus 2X. So what would be the area of the garden? Susan, what would you say is the area? X times 120 minus 2X. Exactly, X times 120 minus 2X. Now, we could leave the answer like that, but why don't we multiply it out? And this says that A of X will be 120X minus 2X squared. If you wanna turn that around and put the X squared first, you could say minus 2X squared plus 120X. It doesn't really matter which way you write it. But in either case, this is not a linear function because it's not in the form F of X equals MX plus B. It has this X squared term in it. So this sort of a function is called a quadratic function. You remember you've solved quadratic equations before. Well, this is a quadratic function. Can anyone tell me what would be the area of the garden if we chose X to be 15? That was not my calculator. Well, let's see. Let's see how we'd do that. Now, we could plug in a 15 here and here. We'd have to square the 15. We'd have to multiply 15 times 120. We could plug in the 15 here and here. That would be essentially the same thing. Or we could plug in the 15 up there. So why don't we go to that first version because I think it'll be simpler to multiply. If I put in a 15 for X and then if I put in a 15 here, that'll be 120 minus 30. How much is that? 90. 90, okay. So what I need to do is take 90 times 15. Let's see, 15 times 90 is going to be 0, 5, 1, 3. So that'll be 1350, 1,350. And what are the units on that answer? Yard squared. Yard squared, exactly, because we're talking about area. So this gives me yard squared because it's an area function. You notice that the name of the function is not f of X because f is sort of a generic name for function. In this case, the area has, or the function has a certain meaning. So what I choose is a letter to allow me to remember what this function is. P for perimeter, A for area, 1350 yards in this case. Okay, let's go to the next graphic. This next problem is actually a rather famous one. It was first solved by Galileo. Let me write his name up here, Galileo. Galileo was born in 1564 and he died in 1642. And Galileo was the first mathematician to notice that the height of a projectile, if you throw it up into the air, would obey a quadratic function. Here's what he discovered. If we go back to that graphic, you see if we have a building, let's say we're standing on top of that building, and let's say the building is H sub zero tall. There's a H sub zero in that equation that you see there. That's how tall the building is. And let's say you throw the object up in the air with an initial speed, which I call V sub zero, then the height of the ball can be calculated by the formula you see on the screen. Let me just write that up here. Capital H of T. Why do you think I'm calling the function capital H? For height. For height, okay. Is equal to minus 16 T squared plus V sub zero T plus H sub zero. Now, the number H sub zero is your initial height. That's why it's H sub zero. It's your height that times zero when you first release the object. V sub zero is the initial speed. If you throw the object up in the air, the initial speed is positive, and if you throw the object down, I'd call this negative, in which case it's actually velocity. And the minus 16, well now that's the strangest part of all, this has to do with the acceleration of gravity. If I were to solve this problem, let's say on the moon, where the acceleration of gravity is different, because you're way less on the moon, I'd put a different number there. The minus 16 stays the same because we're doing all of our problems here on the earth, luckily, so we don't have to worry about other accelerations of gravity. Okay, let's go to the problem that follows the graphic of the building. It says that a ball is tossed upward from a 240 foot building at a speed of 32 feet per second. And there are three questions that we ask. First of all, find the function H of T. Well, we have the general form of the function here on our green board. Part B says, how high will the ball be after four seconds? Part C, when will the ball strike the ground? And part D, what is the domain of the function H? Okay, let's come back to the green screen and take a look at those one at a time. The first question was to find the function H of T for this particular problem. So this function is going to be a model of that problem. Let's see, so we start off minus 16 T squared plus the initial speed V sub zero. Do you remember what the initial speed was? 32 feet per second. 32 feet per second, exactly. And you remember what the height of the building was? 240. 240 feet, yes. By the way, before I go on, let me just mention, for those of you at home taking notes on this, all of these problems are worked out in detail on the website. So if I give you a value like the height of the building and you say, wait a minute, I don't remember what you said the height was. If you look on the website, you'll see a full discussion of this problem and all the others that we've done. And you can check the numbers and you can look at that more slowly than listening to me explain it here verbally. Okay, so this is the function that describes the height of the ball at time T. Now, the second question was, how high is the ball after four seconds? Well, T represents time in seconds. So I'm gonna substitute in a four for T and this answer is gonna be given in feet. That's gonna be the height of the ball in feet. Well, if I substitute in four, that's gonna be a minus 16 times four squared, that's 16 plus 32 times four plus 240. Now, we just have to simplify that. 16 times 16 is 256, that's a minus 256 plus four times 32 is 128, thank you, plus 240. Well, why don't we combine those two together? Those are real easy to combine. Negative 256 plus 240, that's a minus 16 plus 128. And so 128 subtract 16 is how much? 112. 112, right. So that's 112 feet. So the ball is 112 feet in the air. Now, let me just erase some of this and let's just look at the illustration of that building. I'm gonna draw the building here on the graphic. Let's keep in mind that after four seconds, the ball is 112 feet in the air. And so if this is the building and if this is where we're standing initially at h sub zero, we throw it up in the air and then it comes back down and it's on the way to the ground. So this altitude, if I make a vertical axis right here, this would be 240 because that's our initial height. Now, of course, the ball goes higher than that for a while but then it comes back down. After four seconds, it's 112 feet off the ground. 112 would be, I'll estimate it right about there. So after four seconds, the ball is right here. I'm gonna say t equals four, which means that it has already got up to its maximum. It's on the way back down, it's traveling downward but it hasn't reached the ground yet because it's height is in zero. So the ball's right about there. Now, if you were to actually carry out this experiment, if you went to the top of a building that was 240 feet high and if you could throw the ball up in the air at exactly 32 feet per second straight up and if you'll let it come down the side, it probably wouldn't be exactly there. Do you know what other effects would influence the progress of the projectile? Air resistance. There'd be air resistance. So you know what happens is the ball actually slows down. It probably wouldn't go quite that high because of air resistance and it would probably accelerate not quite at the acceleration that Galileo predicted because his formula is actually intended to work in a vacuum but we're not in a vacuum when you throw the object in the air. There's air resistance but this is a very close approximation. That's why I'm saying this function H of t is a model for the application. It's not the exact representation of it but it's close enough for our purposes say in a physics course. The next question we asked related to this problem was when does it hit the ground? Let's see, let me just write in our function for this particular situation. We said it was minus 16 t squared plus 32 t plus 240. Now how are we gonna find out when it hits the ground? That's question C. Any suggestions? Ginny? When H equals zero? Exactly, when the height is zero it's on the ground. So I'm gonna put a zero right here and what I have now is a quadratic equation. We had a quadratic function. Now we have a quadratic equation. There are several ways to solve this but if we can factor it I think that's the quickest way to do it. Trouble is there's a negative 16 coefficient. Why don't we divide that out? I think 16 divides all of these. I'm gonna divide by a negative 16. Of course even divide the zero by negative 16 and I get a zero. This would be a t squared, what will this be? Negative two. Negative two t, yep. And this one will be a negative, let's see, 16 into 24, one, 16 to 85. That's a minus 15. That looks a whole lot nicer. Now of course this equation is different than the previous equation. But what they have in common is they have the same solution. So I've actually made a transformation in the equation to a simpler form and now I'm gonna solve this one. Just like last time we made transformations in graphs, here I'm making a transformation in an equation. I can factor that into, let's see, t, t. This sign's a negative. That tells me something's positive, something's negative. Has anyone figured out what those numbers would be? Three and five. Three and five, yeah. I think we wanna put the five with the negative but the three with the positive. And if this product is zero, one of the factors is zero. So either t plus three is zero or t minus five is zero. So either t equals negative three, hey, what's that all about? Or t is equal to five seconds. Of course, this is the answer that we'll wanna choose. It hits the ground in five seconds. You remember it was 112 feet off the ground after four seconds. In one more second it should be on the ground. Now, why did we get a negative three? What does that mean? Well, you know, if I go back and draw the illustration of the building, I think we can see where that comes from. In this problem, the algebra doesn't know that the problem begins when t is zero. So we said we released the ball at time t equals zero, it goes up and then it comes down to the ground. Well, for all the algebra knows, we released it prior to time zero. We released it at maybe negative one second, maybe negative two seconds, maybe negative three seconds we were on the ground. So three seconds prior to the release of the ball on the top of the building, we could have been on the ground and thrown it much faster and it would have followed the same path and it would have gone up to that peak and come back down. So the algebra gives us every possible answer and it asks us to figure out what answer we want. So we're gonna take the answer t equals five and we're going to reject the answer t equals negative three seconds because we know this problem began at the moment when t was zero. But the algebra doesn't know that we don't want that so it gives us every answer. Now, we have one more application I'd like to look at. This one involves an interview with an oral motorcycle policeman. So let's go to that tape. War class, we've been discussing how functions are used as models in our college algebra class and so I've called Officer Gaines from the Orem Police Department who's gonna show us how his radar gun works and we'll go back to the classroom and we'll talk about how we can make a mathematical function that models the radar gun. So Officer Gaines, thank you for coming. Thank you. Basically we use two different types of radars. One is one that we use in our car which uses radio frequencies. The other one is the one I have here which uses laser or light frequencies to figure out the speed. Basically, the difference in the two is with the radio frequency that's sending the radio frequency out. It's hitting the object and coming back into the radar. The radar's taking the change in that frequency or the change in that wavelength to figure out the speed in miles per hour. We can use that unit when we're either moving down the road or when we're stopped. If we're moving down the road the speed we're traveling plays an effect in the way it figures out that speed. It needs to take that speed out of there so it comes up with an accurate speed of the target vehicle. With the LiDAR, the big difference is, one, it's using a light wave and it's sending out pulses of light at about 600 pulses per second. It's hitting an object and returning back into the unit. When it returns, the unit uses that time it laps to calculate the speed and convert that into miles per hour. The one disadvantage to this unit is that we have to be stationary or stop to use it so we can't be driving down the road to use it. The other benefit of this one, obviously when you're using a radio frequency it's going out there and getting wider and wider. There's some other steps as an officer that you have to use in order to make sure you're getting an accurate reading. With the LiDAR, the beam width at 1,000 feet is only about 12 inches wide so we can place the LiDAR unit on a particular object whether it's a person, bike, car, whatever, and we know that's the reading we're getting is from that particular object. Okay, with this unit, it tells us both the speed and the distance the object is from us and then you'll see either a plus or minus next to that number which lets us know if the vehicle's coming towards us or going away from us. What I'm using inside this unit here is just a small red dot so that I can use it to point it at the object or what I want to get the speed from. And you can see as the speed changes in the unit it changes in the speed here as well as it giving us the distance and again there's the plus sign which is telling us that object was coming towards our location. Okay, now you notice you said there are actually two different types of radar guns. The one that's mounted in a police car you can actually be traveling while you're using that radar gun and it's tied to the speedometer of the car so it makes an adjustment for the speed of the police car and they can clock you whether you're going away or toward them. But with this radar gun that he has works on a different principle and he has to be sitting stationary and he has to be looking right at you you have to be coming right at him if he moves off to the side like at a 30 degree, 45 degree angle then your speed will be registered as too slow. So that's why they step out in the middle of the street and they look right at you to get an accurate reading and if you think well if they're on the side maybe I'm gonna be they're gonna think I'm going faster no actually they'll think you're going slower so there'll be a difference there and in fact that uses something he calls the cosine effect that we'll talk about in math 1060. Well let's take a look at the radar gun that the motorcycle officer is using and the principle is that it sends out pulses of light he said 600 per second and that light bounces off the car comes back to the radar gun so it takes two different readings first it sends out a pulse see how long it takes for it to come back then it takes another pulse sometime later and bounces off the car comes back and now it's not gonna take as long if the car's coming toward him and so by measuring the change in the time intervals of those two pulses he can determine what your speed is. Okay let's say the officer is standing right here where sort of a bird's eye view the officer standing along this line and your car is over here moving toward the officer so the officer points the radar gun at you sends out a radar beam that goes out hits the car and comes back in a total of T1 seconds and let's say at that moment you're a distance of D1 miles away and then in a short length of time you've moved closer to the officer you're still moving toward the officer and now the radar gun sends out a second pulse that goes out and hits the car comes back but this time this will be a little bit shorter so we'll call this T2 seconds and let's say at this moment you're D2 miles away. Now clearly T1 is bigger than T2 because it takes longer for the first pulse to go out and hit the car than the second pulse and also that D1 is bigger than D2 and let's say for the sake of argument that the second pulse is sent out let's say 1 tenth of a second after the force pulse is sent out so I'm gonna assume 0.1 seconds is the delay for this second pulse Okay, so let's see now why is D1 bigger than D2? Well, your car has moved a little bit closer in that time interval in the time interval of 1 tenth of a second so I'm gonna use the formula rate times time equals distance you've used this formula a number of times in other courses, algebra courses and maybe some science courses as well so I'm thinking that this distance could be measured by the rate of the car which is your velocity times the amount of time that's lapsed between this moment and that moment and that's the same as the difference between the two pulses pulse emanations and that would be 1 tenth of a second so that would equal the distance travel I'll call that delta, delta D Okay, so how can we put all of this information together? Oh, there's one more thing I wanna mention let's say that C is the speed of the light or the speed of the radar Now, if this is actually the speed of light then this would be 186,000 miles per second and that is, I would assume to be the same as the speed of the radar beam in the gun at the same time Okay, so what can we say about this? Well, I know that D1 is equal to D2 plus the distance traveled by the car and the distance traveled by the car was 0.1 times V V being your velocity in this case so if I solve for V I'll need to subtract D2 from both sides so let me turn this all around and say 1 tenth V is equal to D1 minus D2 Now, I know that D1 can also be computed by the formula rate times time is distance D1 would be the amount of time it takes for the radar beam to go from the officer to the car times the speed of the radar gun so if I substitute in here the amount of time it takes for the beam to go from the officer to the car would be T1 over 2 Now, why am I taking half of that? Well, you see T1 is the total round trip time so T1 over 2 is the time it takes to travel strictly to the car and I multiply it by the speed of the radar beam and we're assuming that's C down here minus D2, well, let's see, now D2 that would be distance times or that would be rate times time and the time would be D2 over 2 times C once again so if I simplify this a little bit I have 0.1 V is equal to C T1 over 2 minus C T2 over 2 and if I get a common denominator I can put it all over 2 and if I factor out the C then I have T1 minus T2 C times T1 minus T2 all over T Now, the difference between those two time amounts I'll call delta T and so this is C times delta T over 2 Now, delta T is the difference in the readings between the first impulse coming back and the second impulse coming back we call that delta T Okay, and over on this side this is 1 tenth times V so if I multiply both sides by 10 then I have V is equal to 10 times this quantity and let's see the two will cancel out so I'll get 5 C times delta T now you see C is a constant it's the speed of the light and therefore my velocity is a function of only one variable and that's the difference between the two time readings on the radar gun so I assume what happens is when the radar gun first sends out a signal and it comes back it measures the distance or it measures the time the time it takes for the first radar beam to come back and then it measures the time interval for the second radar beam to come back and it takes a difference in those two times and that's what we're referring to here as delta T Okay, you know maybe we can distract the police officer next time you get pulled over with an argument like this but for now I think we better move on to a new topic let's look at variation as a matter of fact here's direct variation there are three types of variation there's direct variation which you see on the screen there's also inverse variation and then there's compound variation so let's discuss these one at a time two quantities X and Y if they're related by the equation Y equals K times X where K is a non-zero constant those two variables are said to vary directly with one another let me just write that on the screen if I have two variables X and Y and if I tell you that Y is just some constant multiple of X this is where K is not zero but it's a constant then I say that Y varies directly with X there's an abbreviation for that you may have seen this in some science books before if I put a little Wiggly sign in here Y is proportional to X then what that means is there's a constant I can multiply X by so that Y is equal to a constant times X and the constant K in this case K is the constant of proportionality the constant of proportionality let's go to the next graphic and I'll show you some examples of things that vary directly first of all suppose a car is driven at a constant speed then the distance D that it travels varies directly with the time T that you drive the car in other words T is equal to K times T D is equal to K times T now in this case K represents the speed of the car or the rate because distance equals rate times time you see if you drive at a constant speed then your speed is constant that's what the K is D equals K times T in another example this is called Hooke's law Hooke's law says that force is equal to K times X this has to do with two weights suspended from springs and I'm going to set up a model that demonstrates this that demonstrates Hooke's law from our physics lab I'm going to hang two springs from these hooks there's one and there's one and at the moment you'll if the camera can zoom in on this you'll see that there's a gradation I think maybe I better turn this one around so we can see those better you'll see that there's a scaling along here that goes from zero then point one point two point three down to two point oh I think it is and there's a little marker on this on this spring if you can see that right there going up and down and that comes up to zero same thing on the other one now I'm going to take two masses and hang them from these springs this first mass is a hundred grams and that pulls the spring down I think you have to look a little higher to see the scale it pulls it down to a mark just above one point zero right here there's a mark right here not quite one point zero the second mass I hang on the second spring has twice the mass it's two hundred grams and it pulls the spring down twice as far this time the marker comes down to just above two point oh that one was just above one point oh this one's just above two point oh now you see what's happened is when I put on twice the mass I get twice the stretch now the mass is equivalent to saying I put on twice the force or the weight over here and so twice the force stretches it twice as far now this relationship is called Hooke's Law let's go back to the green screen and I'll show you how to represent this mathematically as a matter of fact let's go to the next graphic I think we have an illustration of this that would be helpful uh... on the left there we see a spring that's unstretched and then on the right we see a circle that represents a force f suspended from that spring and it stretches it stretches at a distance x now the fact is that the force is proportional or direct or varies directly with the distance x so if I were to double the force I would double the stretch if I triple the stretch I would triple the force so I can make this an equation by saying f equals kx this is where k is a constant and so therefore f becomes a function of x it's equal to a constant multiple of x now the constant in this case in this application is referred to as the spring constant k is called the spring constant and every spring has a different constant to it uh... for example if you look at the springs in the back of your car so that if you go over a bump the springs absorb the shock there uh... those have a very high spring constant because it takes a huge force to stretch it just a little bit on the other hand the springs that we have right here it didn't take that much force or weight to stretch it fairly far so the spring constant on these springs is relatively small okay let's look at another uh... application of direct variation and we have this on a with an interview another interview this with one of our physics professors dr paul mills of the physics department let's let's show that interview well college algebra students uh... we're in the sacred halls of the science building here at uvse and uh... this is dr paul mills of the physics department and he's going to show us some uh... applications of our recent discussion of variation direct and inverse variation so paul i'm gonna turn it over to you uh... newton pointed out that uh... object that starts moving has an inertia as he called it or perseverance in trying to keep going and the mathematical way of describing that perseverance that the object has in wanting to keep moving is in the the perseverance of this thing is equal to the mass times the velocity or we call it the momentum is equal to the mass times the velocity in this kind of a relationship if you increase either one of these you have a lot of perseverance in wanting to keep going and we have a range for a little demonstration of this we're gonna start with a very small mass of ping pong ball and we're going to get it moving really fast and will look at its perseverance this is what i call a mosquito killer uh... it's got a cap in here that's going to ignite and it's going to expect produce hot gases which will then expand really fast and that will drive this ping pong ball at the end mosquito killer and it will take off moving at really high velocity okay this goes right it will not hit you okay you better get a little closer i'm not that good of a shot he's lined up and hope you don't fall into the plant are we ready okay hold your papers up you can see that that ping pong ball just wanted to keep going it didn't want to stop it coasted right through both pieces of paper and it kept going until it hit the wall over on the other side momentum is equal to mass times velocity okay now you know that's the same principle uh... that uh... you might have uh... heard a reference to say after a hurricane say if a hurricane goes through florida sometimes these they find straw embedded straight into a telephone pole you wonder how could you take a piece of straw and stick it into a telephone pole like that but the straws going so fast it has very little mass but it has such high velocity that if it hits the telephone pole straight on rather than shattering the straw it actually sticks into the telephone pole so they they see examples of these things now and then uh... the formula that he wrote was that perseverance he called it is equal to mass times a velocity now if we think of uh... the masses being the constant your member uh... we had uh... why equals k x so if we think of this is being the constant then we can say that the perseverance is directly uh... varies directly with the velocity so as the velocity gets bigger so does the perseverance now in this case when he fired the ping pong ball out of that little gun it had such a high velocity even though it didn't have that much mass it had such a high velocity it had a lot of perseverance and it persevered with the effect that it went right through the two sheets of paper it didn't split them from top to bottom it just split them open in one little little spot so that was his example for perseverance uh... okay now another type of variation is inverse variation let's go to the next graphic we have this for the screen instead of direct variation inverse variation says that if x and y are related by the equation uh... y is equal to x uh... y is equal to k over there should be x not a p y equals x over uh... y equals k over x where k not zero is a constant then y varies inversely with x i probably had p on my mind when i wrote that because i've just seen the perseverance uh... here's an example if total sales s let's say you have a company total sales s varies inversely with the unit price p if that happens then we say uh... s equals k over p now uh... as you might imagine what if you're selling uh... what if you're selling cds and what if you double the price of the cds wouldn't that make the sales probably go down now if it goes down in such a way that when you double the sales price you cut the sales in half if you triple the sales price you cut the sales down to one third in other words as one goes up the other one goes down and then that said to be inverse variation in this case i said that the sales would equal k over sales price now it's not always the case that just because the price doubles the sales prices cut in half but if that were to be the case then we would say that s varies inversely with p with p now we have a physical model that will demonstrate this for us so uh... let's just take a break while i set up this demonstration and we'll come right back okay uh... we had to take a break there so we can set up this apparatus but now i want to demonstrate a property of pendulums and uh... in this case the pendulums are basically two strings with masses hanging from the ends one of them is very short one of them is fairly long uh... actually when i set this up i should have gotten two masses that were exactly alike but uh... the mass appears a little bit smaller but it turns out the mass doesn't affect the period of the pendulum when it oscillates it's the length of the string that affects how long it takes the pendulum to go back and forth so uh... the first string is twenty centimeters long the first pendulum the other one is eighty centimeters long so in other words this one is four times longer than the other one and we're going to see how that affects the period now you notice when i displace this one it has a fairly short period it only takes a short time for it to make one complete oscillation that's what i mean by the period on the other hand this one when i just place it a small amount it has a longer period it takes a longer amount of time to make one complete oscillation now how are they related well it turns out that these two quantities very directly these very directly uh... okay so let's see what happens if i pull these out i'm going to release them at the same time uh... the one up above i believe will make two oscillations in the amount of time this one makes one oscillation so here we go uh... i didn't quite release it straight one two one two whoops i touch that one sorry about that but i think you are i think you will see that this one let me turn this like so and uh... i think this camera in front of us may be able to pick it up uh... okay so one two one two one two one two and uh... that should progress indefinitely so what we have here if we go to our green board is that the if i call t the period of a pendulum then uh... and if i let l be the length of the pendulum that would be the length of the string actually it's the distance from the pivot down to the center of gravity of the weights is not just to the end of the string but to the center of gravity so that would be the length of the pendulum then the period varies directly with the square root of the length so it's a bit more complicated because i have a square root now but it's still a direct variation so what that says is the period is equal to a constant multiple of the square root of the length this would be my constant proportionality and uh... so if i put a if i if i multiply the length of the pendulum by four if i put a four in here four l because see the longest the longer pendulum was four times as long then that should be the period of the new pendulum but when i reduce this that four comes out as a two two k square roots of l now if k square roots of l was the original period of the shorter pendulum then when i when i when i quadruple the length of the pendulum i get two times k square roots of l so that says the period has been doubled because i have two times the previous period so this is a direct variation but it involves a square root okay now the last type of variation involves both direct and inverse variation and uh... the example i'll use is the law of gravitation the law gravitation and this was first proposed by isaac newton by the way isaac newton was born in sixteen forty two that was the year that galileo died just a moment ago uh... and uh... he died in seventeen twenty seven now isaac newton said that if you have two masses for example if you have a small planet and if you have a big planet maybe let's say the sun and they have masses little m and big m and if there's centers of gravity which i'll just take to be the center of each object if the distance between them is called r probably r for radius is what he what he meant then there's a force of gravitation that attracts the small planet to the big planet and it also attracts the big planet to the small planet so there's a certain force uh... there's a certain uh... certain force of gravity that attracts these two uh... if these weren't planets this could be you and the earth there's a certain gravitational force attracting you to the earth and there's a gravitational force attracting the earth to you and uh... this would be your mass this would be the earth isn't the earth's mass and the r would be the distance from your center of gravity to the center of the Earth, so that'd be a little over, or right around 4,000 miles. Now here's what Isaac Newton concluded. This force is directly proportional to the mass of the first object, the mass of the first planet, the mass of you, whatever the two things we're considering. But you know also this force is directly proportional to the mass of the second object. It's inversely proportional to the square of the distance between the two. You know in the pendulum problem we had a direct variation with the square root of the length. This is an inverse variation with the square of the radius. Now if I put these three things together I can make one compound variation out of it.  The force is directly proportional to, or it's proportional to, or varies with little m big m over r squared. Now the way I make that an equality, so now let's go back, the way I make that an equality is I put in a constant of variation.  And this is called the gravitational constant. So let me just write that on the side here. G, I'm not using k, but g is the gravitational constant. And it's the constant that makes the variation into an equality. It's the gravitational, gravitational, let's say, let me get that right here, constant. And the way you normally see this law written is to have g in the numerator, so it's big g little m big m over r squared.   Same thing with big m.  On the other hand, if you double the radius so that you move the objects further apart, the force will not get greater, the force gets smaller, and if you double the radius, the force will be one fourth of what it used to be. So if you want to lose weight, what you do is just get further away from the earth and you'll weight less. It doesn't mean your mass will change, but you just need to go further away from the earth, that's the problem. Go up to the top of the mountain, top of a mountain, and you may weight slightly, slightly less. Okay, that's called Newton's law of gravitation. Let's see, let me work one example of inverse variation because we really didn't get to, we didn't, we saw an example of direct variation, but I didn't work an example of inverse variation. Suppose I tell you that x and y vary inversely, very inversely. Now what that means is y is equal to k over x, or if you want you can say k times 1 over x. Now what if I told you a particular value that say when x is equal to 4, that y is equal to 10. So when x is 4, y is 10, the question I might ask is, what is k? Well I think if we substitute n 4 for x and 10 for y, we can solve for k. So if I put a 10 here, k over 4, then solving for k, I get k equals 40. So if I have one reading of an x and a y, I can figure out the constant of proportionality. So what this tells me is that the relationship is y is equal to 40 over x. Let's take a different one. Suppose we have a joint, rather a compound variation, where I have products and quotients. Suppose I have three variables, a, b, and c. And what if I tell you that a varies directly with b, and a varies inversely with c? Now if I put those two things together into one statement, I would say that a varies with b over c. And this is what I refer to as a compound variation. Compound variation. I can make that an equality if I just multiply by a constant of proportionality, which we could write as kb over c. Now if I have one reading of a corresponding a, b, and c, I can calculate the k. If we say for example that a is equal to 2, at the same time b is equal to 5, and c is equal to 20, then the question is, what would be the corresponding, the corresponding value of k? Well now that I have my relationship, I can plug in the numbers 2 equals k times 5 over 20. And that says that 40 is equal to 5k. Let's see, I'm running out of room. What is k going to equal? k is going to equal 8. k is going to equal 8, exactly. Now if I go back up here to this relationship, a is equal to kb over c, I can now say a is equal to 8b over c. Some of your homework problems are going to be such that they will describe the proportion by telling you how a is related to two other variables, let's say, and they'll ask you to find k. And to do that, you'll have to have one set of readings that corresponds to each other, so you can substitute those in. Well, if we summarize what we've done today, we started off by looking at functions as models for applications. We saw two examples of graphs that are used as models, and those graphs represented functions, although we didn't know the exact rule. There was the traveling salesman problem, and there was the, there was the graphs on the lawn growing example. And you see from those illustrations, those graphs told a story, from the story we could tell what was happening. Then we looked at some very specific functions that modeled the perimeter of a garden, the area of a garden, at the radar gun model. And then we looked at, at the very end of the episode today, we've looked at some variations, at various variations. We'll see you next time for episode six.