Well, first of all, thank you for inviting me here, very grateful. And I'm going to speak about small-scale, maybe a little funny experiment with anthropomorphic images, contemporary. Well, I will focus on rock features because I'm interested in them a lot and I'm interested in their roles in prehistoric landscapes. Well, what we know from historic record and ethnographical record that rock features or big stones, boulders usually have strong meaning. They have important roles for living communities in their religion, mythology, and so on. But we can ask why or we can ask since when the stones or the rocks had played these roles. So, since Paleolithic times, upper Paleolithic times, we can see that humans paid attention to rock surface as these two examples from the cave Altamira in northern Spain can show us here. And they combine the rock surface with their imagination or projection of animal shapes. Here's another case, another example from French cave called New York, also from the upper Paleolithic. Well, these two examples are from my country, Czech Republic, Bohemia and Moravia, and the picture on the on your left resembles very to human face and it's located on the edge of a big rock feature and it's well known by local communities, but there are no signs that this was made by humans, so it seems to originated naturally and the other face is located on the rock, sandstone rock. Also, it was not made by humans, but is widely recognized by contemporary humans living nearby. Sometimes rock features do not have a very clear resemblance to anthropomorphism or human shapes like this one. This comes from California and local tribe of Wintu people recognizes it as a back of bones, as you can see on the picture on your right, drawn by their shaman. But well, back to prehistoric landscapes in central Europe. When you have kind of men here or megalithic art, you can be sure that people paid attention to that stone, to that rock feature. But what about the stones that do not bear any traces of human modification? Can we also think about them as a part of the the landscape of prehistoric people? I think we can and I choose rock features because they are immovable and relatively speaking stable in their shapes or forms. But it depends on material and the local conditions, weather conditions and environmental conditions. Well, so I did a small-scale experimental study where I focused on processes by which the rock features can get our attention, attract our attention and to provoke our imagination or projection of our inner images to them. And I was curious if there can be some, let's say, patterns that can be shared within a community. So these are my more specific questions about my study. So I was curious if there are some parts of rock features that are the most attractive for human imagination or if there are some specific characteristics of rock surface that provokes our imagination most. Or I was interested also in various kinds of motifs that can appear when we are looking at the rock surface. And and so and so. Let's jump in. Okay. Okay. Sorry. I focused on two kinds of data because I asked people to draw what they can see on the rock surface. And so I have drawings, pictures of their inner images and they consist of, let's say, objects like human, animal and so. And these objects can be combined into motifs, like human being is sitting and holding a baby or something like that. And I tried to to search for patterns in the graphics of the pictures. And I also have interpretations because I asked people also to write some short commentaries about the meaning of their pictures. What do they think they draw? And this is one place that I was interested in.  And it's located on the southern slope of the mountain range dividing Bohemia and Germany and on a small promontory. And about 10 years ago some metal detector prospectors, Illigo, found Bronze Age X. Bronze, Bronze Age X. So me and my colleagues did some kind of a rescue survey with metal detectors and found other juicicles from Bronze Age, let's say late, final, late or final Bronze Age. They are almost the same shape. They were deposited nearby, that's all. We can find an X and juicicles. So it's possible that all the three artifacts were deposited at one moment. And also we found a piece of rock crystal of this size, which is very unique in our country. So we can, from the archaeological point of view, we can say this place was very important, at least in the late or final Bronze Age. But to get some, well, I should say simply, I was curious if people can see something in the shape of this rock or on its surface. So I took this photograph. This is the first one and this is the second one. Oh, sorry. And I can draw your attention to this part, this other part, which for me very resembles very well to human head, but it's white. And I asked people to draw, if I ask people if they see anything in these pictures, in these photographs. So I asked 100 respondents, 50 males, 50 females, and all the respondents draw something. Well, as you can see, three-quarters of my respondents were my students because I was teaching lectures on landscape symbolism, stuff like that. I asked also my friends and colleagues and most of the respondents were in their 20s because they were students. Well, you can see, let's say, fragrances of reactions, motives, objects and there is no big difference between males, females, well, but there was a big difference in various parts of the rock. As you can see on these graphs for the photograph A and photograph B, the whole surface of the rock was the most attractive for motifs for the inner images. Much more than the parts that I would like to see as the most attractive. Well, that's the same information. And here we can see some examples of the motifs and objects and mostly people would regard it as a two-dimensional object as they see photographs, print it on paper. But they were not on the side. Nobody was on the side except me and my colleagues. Well, here we can see that most of the objects were interpreted as human beings or some kind of non-human beings, sometimes resembling human beings, beings more, sometimes less. There also were some animals or natural motifs like rivers and so on. And yeah, here's a part that I was curious about and as you can see most of my respondents also see some kind of head in that.  And when I finished this experiment or my contact with the respondents, I took their drawings and put them above each other to search the patterns, graphic patterns. And here we can see the graphic patterns for the first photograph. There are 13 of them and the number one is the most frequent one of these. And about a third of the motifs can be divided into these patterns. Here you can see patterns for the second photograph and about 50% of them can be divided into some kind of a pattern. But there is a difference if you ask people what do they see and they tell you or if you ask them to draw what they see. And you can see in these graphs that for some patterns my respondents had different meanings, different interpretations. So I think it's important to engage both kinds of data. And to conclude briefly, so I found out that the rock surface also in our culture and for modern people has a strong capacity to provoke our projections or our imaginations, our inner images. Well, the relationship between the image as a symbol and its meaning is arbitrary. So that's why I think we should explore both drawings and the interpretations of the words. Well, it proved to me that we cannot expect everybody to see the same thing while in the rock, not the opposite, but nobody sees nothing there. And we may expect some kinds of patterns that can be shared among the community, but on the basis of their own experience. Well, that the people can agree on what they really see. But there has no... There doesn't need to be an authority to tell you what you shall see in the rock. And this one, I think, is very important, at least for me. Yeah. Well, by no means we cannot extrapolate these images into the past. It's impossible. It's just a picture of our thinking or our imagination contemporary. I do not want to relate these pictures to the past. And also the particular pictures or the precise numbers that are used in this presentation are not so important for me as these conclusions about the processes, how we can see the rock. Or how we can create our images because sometimes people draw... They had some image and they had to draw it. And sometimes they started to draw. But creatively, they changed their image as they were creating it. So it's not only about projection or quick, fast projection, but also about creativity. And, well, as my final words, I would like to say that let's test our assumptions or our question by some empirical study like this. Thank you for your attention.


Good morning. My name is Cole Bergman, profusionist by TREG, and currently the ECMO supervisor at Texas Children's since 2010. I would like to thank Texas Heart Profusion Department for asking me to present today. I will be presenting on Texas Children's ECMO history. I have no disclosures, and everything I'll be presenting is based on a one hospital ECMO experience in pediatrics. I have a title like past, present, and future of ECMO without a brief history lesson on the men that helped start it. In the beginning there were two, and ECMO wouldn't be what it is today without these two innovative physicians. Let's start with Dr. Given. His contribution wasn't necessarily ECMO, but his research and advancement and heart and lung bypass definitely paved the way. In 1931, he lost a patient to pulmonary hemorrhage, had nothing to offer her, which inspired him to develop the heart lung machine. But the irony is today, pulmonary hemorrhage is why we put patients on ECMO. So I think ECMO was actually what he had in mind, but his path landed him in the direction of bypass. In 1937, he was able to keep a catalyze for 26 minutes on bypass. Throughout the 1940s as research continued, finally in 1953, his invention of the heart lung machine was able to support a patient.


This coming Thursday on Winner Home, the competition gets cooking as the Designed Yoes start creating the heart of their home. With some of the most ambitious collaborations yet, will their designs be a recipe for success or will it all go up in flames? Well, we all about pushing boundaries, honey. The highlights of the space is going to be this unity at work. Catch the design drama on Winner Home Thursdays at 7.30pm on S.A.B.C.3. With a repeat on Saturday at 3pm, the stage is yours. Winner Home, proudly brought to you by Capitech and Private Property, with Samsung products designed for your connected lifestyle. Grand Prize Luxury Penthouse Apartment by Bowen Properties.


Jay Ward here at Mountain View Dodge and Olds just picked up my 2018 Ram SLT 3500 ready to go and ready to get back to work. Thanks very much Patsy. I appreciate it and we're gonna enjoy that


And political thugs invaded the APC's stakeholders' meeting in Jalingo, Tarrabah State, causing a confusion. The meeting, which was attended by six governorship aspirants, was haunted by the invasion. The commissioner of police, who confirmed the incident, said the police restored sanity. Immediately, it received an emergency call from the party's state chairman. Injured weapons were on top of the situation. No one can say that it was actually injured or in any way harassed by all these thugs. So there is peace in Jalingo. The chairman of APC called me that the environment was toxic, that it was quite potential of violence. I proceeded with the same, calmed them down and normalcy was restored at Shield Hotel Jalingo. Well, first and first, we arrived yesterday evening and we heard a series of meetings, ranging from security agencies, the critical state court, the aspirants, themselves. We heard a lot of series of meetings, which continues up to this morning. But so far, we had a lot of liberal issues as politicians. We are trying to sort it out and we are hoping that sooner or later, the election will commence. And like we told the aspirants, some of them are here, who told us here, the election will be conducted direct, primary, because as you know, we have three moods of the election, direct, indirect or by consensus. Thank you.


It's a strange animal, still a strange creature, this China. It has been for a long time. What I want to tell you tonight, today, is something I found that many people still haven't realized, at least in Germany, where I come from and in other parts of Europe, is that the China we actually grew up with and the China we have known for 30 or 40 years, the China of Deng Xiaoping, the China of reform and opening up the China that was curious towards the world and then the world was curious towards this country, like me, myself. This China doesn't really exist anymore. There's been a new China forming in the last six or seven years. But some things, here, this is a famous Reuters, actually a news agency picture from three years ago, I think it's from Chengdu. And what is this country actually? Is it capitalism? Is it socialism? Is it, I mean, calls itself a socialist country? At the same time, it's one of the most unequal countries in the world. There are more billionaires living in Beijing than in New York. You have Gucci stores, but always above all the commerce and the culture of shopping and is the Communist Party. It's always on top and it always has been there. Xi Jinping has changed the country in ways in these six or seven years that we really didn't think were possible. You know, there were a lot of optimists back then in 2012 who thought, yeah, everybody knew that China needed reform. There was a feeling of crisis. There was a sort of fan de siècle feeling actually, really, in the country. There was a lot of corruption. There was the inequality. The party was losing control and the party was losing its ideological core also. You know, nobody believed in Marxism anymore and all this stuff. And everybody knew that China needed reforms. But even in the party, many people thought those reforms, you know, people I spoke to at least, intellectuals, party members, think tank members thought, you know, maybe we need more of the sort of separation of powers, independent judiciary, these kind of things to get rid of corruption. And then along came Xi Jinping and made something completely different. He took back control for the party. With Xi Jinping, things are different anymore. Xi is not the new Mao. So Xi Jinping is the opposite.  But he quotes Mao frequently. One of the quotes he uses most regularly is, doesn't matter whether the north or the south, doesn't matter whether east or west or the center, the party controls everything. Suddenly the party has to be in control of everything again, which was not the case for 30, 40 years. The China that we got to know was a China where suddenly civil society grew up, people had room, you know. Of course, the economy got more freedom, but society also got more space and more freedom. And there were niches for people doing things that people had thought impossible before. But all these niches are gone again. Xi Jinping is sort of bringing repression back. He's bringing ideology back. Not only does he have a little red book, he even has a little red app. This is the Xue Xi Jianguo app. Study Xi, study Xi Jinping and make the country strong. This is an app where you find all the works of Xi Jinping. Obviously you will find other revolutionary movies and things. But most importantly you can do quizzes on this thing. And the party wants you to do that. And they have competitions. They have quiz competitions. And the good thing is, you know, as opposed to sort of the Renmin Rebao, the People's Daily, which you were supposed to read at home or in your office. But nobody really can control whether you just threw it in a corner and went to sleep.  And you get points and there are competitions.  And you get double points, for example, if you do the quiz between 8 and 10 in the evening.  But Xi Jinping is doing a second thing as well with his other foot. He's going straight into the future. Artificial intelligence, big data, the modern information technologies.  That starting with every single technology that came up, satellite TV, mobile phones, all these technologies were supposed to bring freedom into the last corner of the earth, you know. And of course it was the same with the Internet. And it was Bill Clinton who said, you know, good luck to the Chinese with your attempts to control the Internet. It's, you will be as successful as when you try to nail Jell-O to the wall. But here we are. We have the Great Firewall and the Jell-O is there, right there for everyone to see. You might have seen this picture. This went through a lot of media or pictures like this. There are, you know, with the facial recognition thing, they are doing the police in Shenzhen and Shenyang. They started, this is Shenyang in the northeast of China. When you're J-walking on the street, you know, immediately the camera will pick you up and the video screen on the other side will show your picture the moment you're still walking. And not only will it show your picture, it will show at the same time your name and your ID number. And this is the social credit system. This is the most sexy part of this whole new surveillance thing and it has been written a lot about. So you must have read about it, I'm sure. I just wanted to show you this picture. This is from the official credit China. I think it's the name of the website. So the official government website for the social credit system. And it shows someone who has landed on the blacklist of the social credit system. So he is a trustbreaker. What does the social credit system do? Maybe I should say this first. The social credit system is supposed to divide the people into trustbreakers and honest people, the trustworthy people.  And this is just a picture to tell you a cartoon to tell you what happens. If you are on a blacklist, this is a guy who wants a date with this beautiful girl. And he is sweating because he already knows probably what's going to happen.  I saw your picture on the big screen of the neighborhood in the streets. Nobody will ever have a date with you again. The social credit system. Maybe this is where I start with the social credit system. What is this? First of all, it's important to know that the social credit system, all the things you've read about are from pilot projects mainly and certain pieces of the puzzle that are already nationwide. But the actual introduction of the social credit system is only supposed to happen next year in 2020. So what is this? It starts, actually, you know, rating systems we also had in our own societies. And in Germany we call it Schufer. I know in England there's something called, what's it called, Experian. It's like this where your financial credit history is.  And then they decide whether you can have a loan and how high the interest is on this loan and so on. So the Chinese took that at a starting point. But then they said, you know, when I had my first interview with a professor from Beijing University, Professor Zhang Zheng, he's a high-ranking advisor to the system. He said, yes, Mr. Schufer, we studied all the systems.   So we want to collect everything, you know. The professor then told me, Mr. Schufer, if you really want to see how this is working, you should go to Rongcheng. You should go to the city of Rongcheng in Shandong because this is the pilot project where we think the system is working the best. So go there and visit the Office of Honesty. The Cheng Si-man, there is an office of honesty and I was like, what? So of course George Orwell comes up very often, you know, in this context, and so the ministry, what is it? The Ministry of Truth, right? The Ministry of Truth. George Orwell, by the way, is not banned in China. You can get him in every good bookshop. So people do read George Orwell. You just wonder sometimes whether they read him as a warning or as a manual. So in Rongcheng I went there, I visited the Office of Honesty, the whole, they divided up, there's a neighborhood with 11,000 inhabitants, they divided up the whole neighborhood into cells with 400 families to each unit. They watch each other and they report inappropriate behavior and this is how at the moment this all is fed into the system because obviously in the end it's supposed to be algorithms. This is what the framework, the national framework from 2014 says, in the end we want artificial intelligence to record all your behavior, your financial behavior but also your social, all your social actions and your moral behavior and it's supposed to be recorded in real time. If possible by algorithms it's supposed to be evaluated in real time and sanctioned, so rewarded or punished but at the moment they're still doing it the analog way. So the social credit system was often made out to be sort of the, this is the future of the Chinese surveillance state but it's only one puzzle, one piece of the puzzle. It's much bigger so the whole artificial intelligence complex it's much, much bigger and clearly the Communist Party has fixed on artificial intelligence as the key to its own survival and the perfection of its rule and it has done so. The latest from the spring 2017 where they brought out their big next generation artificial intelligence development plan and ever since they have jumped into this field with a sort of, with a passion and with resources and with money unseen in any other countries on the planet. There is no other government on the planet that spent so much money and pulled so much resources into this field like the Chinese one and of course part of the objective is to jumpstart the economy to sort of catapult the economy into the 21st century because the economy obviously is one of the main pillars of legitimacy for this party, it's no longer ideology. Some people also in the past years and decades very easily they use the word sort of totalitarianism to bash China and that was nonsense because China was a totalitarian state for some years under Mao Zedong but it was no longer after that. A state that really knows no, where the party knows no boundary on its controls where the state actually really tries to slip into the last really cell of your brain and go into your bedroom and slip under your quilt and under your pillow. This was the China under Mao Zedong, but they did it with relatives. That was the time when the wife was buying on her husband and when children were bringing their parents to the execution grounds actually. This was the Cultural Revolution. China was a totalitarian state back then. It was no more after that. The party actually it went back, it let loose, it gave the people more freedom and it was a dictatorship always, it was an authoritarian state, it was not a totalitarian state anymore but now with this totalitarianism is actually making a comeback in digital guise and it's a much smarter totalitarianism than the ones we see because the old totalitarianism, the one from Mao, the one from Stalin actually had to rely on terror and fear as everyday instruments. When you were living in certain years on a Mao or Stalin, you would go to bed at night shivering with fear and you would wake up the next morning with the same feeling. Of course, China now is not like that anymore, you know? And it's not when you step out of the plane, it's not the Orwellian sort of socialist Maoist barracks that you maybe expect if you have never been there. It's a wild, colorful place. It's a lot where people consume more than in the United States and where people actually, it's in the end at least as much Aldous Huxley brave new world than it is. George Orwell's 1984 and Aldous Huxley, he has this very good quote.  The real art of the ruler is to make the slaves actually love being slaves, you know? And this is what they're trying to do in China.


I'm going to be making the fairly controversial argument today that inequality is irrelevant, that inequality doesn't matter from an economic perspective, and that indeed the battle to establish economic equality is causing a lot of the problems that we associate with inequality. So let's start by the fact that recognizing that we have real problems. There are too many poor people. Absolutely. There's too little mobility in our economy where people are coming out of poverty and succeeding, rising to the middle class and into wealth. Absolutely, that is a problem. There's a problem at the top of way too much friendliness, you could call it, between business and government. Cronism would be the technical word I would use.  All of those problems exist. And I would argue, and I will argue today, that all of those problems are made worse by our attempts to deal with the gap. Inequality is just a gap. It's the difference between what poor people have relative to what rich have or between what the middle class has and the rich or any way you want to measure it, it's a gap. From an economic perspective, from a moral perspective, from a political perspective, that gap means nothing is irrelevant and too much energy and focus is put on that, instead of actually going and solving the actual problems. So let's talk a little bit about inequality and what it is. So let me ask, let me start by doing this, how many of you have read Harry Potter? Alright, good, love this audience already. This is good. Now Harry Potter is a real problem when it comes to inequality. Because I don't know about you, but I have calculated that I have spent thousands of dollars on Harry Potter. I mean you can do your own calculation, but I had two sons, they were about Harry's age. Every time a book came out, either I had to go stand in line at midnight and get two copies, or they, you know, and they got old, they got to stand in line and get two copies, each hardback copies, right, because they wanted the heart off the presses, they couldn't wait and they spent the night reading it. I also wanted to read Harry Potter, I loved the books, so I had to get them on audio tapes, a third copy, so that's three times seven, twenty-one, multiplied by about twenty-five, thirty dollars, do the math, then there's the movies. What are they, sixty-seven movies, because they turned every book into two or three movies to get as much out of us as possible, right? So take into account all the money you spent on the movies, and then add to that the Disneyland rides and all the other Harry Potter stuff that we have had a purchase to make our children happy. I spent thousands of dollars, I indeed, if you look at my bank account, got poorer by thousands of dollars because of Harry Potter. But the real evil here is not only did I get poorer, what happened to J.K. Rollins? She became a billionaire. I mean, give me a break, this is horrible. Inequality exploded. I got poorer, she got richer. This can't be good. We're told, we are taught, we read in every newspaper that inequality is a bad thing. Well, here's an example of inequality. She got rich, I got poorer, she got rich off of my back. My money came out of my bank account, straight, I mean, a few other people got rich in the meantime, right, in the middleman, but straight into her bank account. And yet, we all feel like there's something wrong with this example, right? Why? Why isn't it comfortable to say, you know, this is a bad thing, right? Well, because what happened, why did we spend those thousands of dollars of Harry Potter? Why did we spend it? Yeah, because we enjoyed it, because it gave us pleasure, because it gave us certain spiritual values. We benefited enormously. I'm thankful to J.K. Rollins. If I met J.K. Rollins on the street, I would say thank you for letting me spend those thousands of dollars. No, I'm serious. I'm serious, I would. That's exactly what I would say to J.K. Rollins. Wow, the pleasure you gave us is unimaginable. Very few authors have ever given us as a family, not just for me individually, as a family, so much pleasure. So did I really get poorer? No. I mean, I got poorer materially, but spiritually, I think I got richer. And I was happy to give up those thousands of dollars, because I had fun. I enjoyed it. So I am richer for the having Harry Potter, and I don't. I'm happy that she got to be a billionaire. She deserves it. She made all of our lives better. She made the world a better place to live. And she got rich. Who cares? Life's not about money. I have to remind my leftist friends of this, because the left seems obsessed about money. But I don't think life's about money. I would rather read the book than have the money in my pocket. I think most all of us would. That's why we gave up the money, because we believe, let's say the book costs $25, that the book, the experience of reading the book is more valuable to us as individuals than the $25 in our pockets. And that's how inequality is created. How do you become a billionaire? This is important, guys, because you could go out and if we figure out exactly how you become a billionaire, it's open to anyone of you. How do you become a billionaire? What's the secret? Have a great idea. Lots of people have great ideas. I think I have a few here and there, but I'm not a billionaire. What's that? Well, that's a shortcut to becoming a billionaire. So let's assume we become a billionaire in a free market where you can't manipulate the dictator to give you the money, right? Yes. So in a sense, there's something true there, right? What is it that takes to become a billionaire? Have an idea and put it into action, I assume. Create a value. Create something that how many people want? Everybody, hundreds of millions ideally, right? Want it. And are willing to pay you what for it? How much are they willing to pay for it? Well, not everything. What they think it's worth, which for you to become a millionaire needs to be what? More than it costs you to produce. So the secret of becoming a billionaire is very simple. Create a product that hundreds of millions or ideally billions of people want. And if they want it many times over, even better and are willing to pay you more than it costs you to produce. Now if you do that, that's every billionaire out there, except for the crooks who have used Putin and so on. But in the marketplace, every billionaire out there, that's exactly how he became a billionaire. Steve Jobs indeed created this product, which costs, this one costs about $6 when I go back to States to get the new one. It's $1,000. Why am I willing to pay $600 for this? I wanted, yeah, but why am I willing to pay $600? I want a lot of things. I want a Ferrari. Since I can't get it for $600, I'm not buying one, right? So it's worth it, which means this is worth more than $600 to me. It might not be to you. You might not have one of these. I doubt it though. I sure otherwise I couldn't buy this. If I didn't have it, I wouldn't buy it. And if I didn't have the $25 to spend on, on Harry Potter, I wouldn't buy it, right? But I have the money and this is worth more to me than $600. That's why I'm willing to spend it. And by doing that, I am richer because I have an iPhone. And by the way, almost everybody in the world has one of these. So almost everybody, not in the world, almost everybody in the West and in large parts of Asia has one of these. So almost everybody in the world can afford this. And almost everybody out there is better off having one. I have a super computer in my pocket. This is more powerful than the Kray computers you were in the 1980s or the computer that sent man to the moon. It's pretty amazing. And yeah, somebody became a billionaire making these. Thank you, Steve Jobs. Thank you. Because I get a lot more value than $600 out of this. This is worth to my life. Tens of thousands, if not more than that, of dollars. I can, I can, I can Skype with my kids from the other side of the world. I can read them a bedtime story, which I could not have imagined when they were born that I would ever be able to do that, given my travel schedule. I can stay in touch with work, family. I can look up every piece of music ever, ever composed. And it's right here available to me instantaneously for almost no money. What's a subscription to Spotify or subscription to Apple music is nothing as compared to how much you get in return. I can watch movies and I can look up an encyclopedia. You remember buying the encyclopedia Britannica. I don't know if any of you ever and getting volumes once a month or whatever. Oh my God, it's all here. Every single one of those articles is right here at a cost of basically zero. So somebody became a billionaire making my life better. Why would I resent that? Why would I resent that? Indeed, I'm thankful for it. I'm thankful to the billionaires of the world. They have made my life and whether you want to admit it or not, your life's better. They move civilization forward. They invent and have the ideas that we don't, we don't affect billions of people in the world. I don't, I don't make that much money because I'm a teacher. I've chosen not to make a lot of money because by teaching, I only affect a certain number of people. I can't reach hundreds of millions, maybe with the new technologies I'll be able to. But as of now, I can't, so I'm never going to become a billionaire. Who cares? I don't care. So inequality is an expression of a reality. It's a reality that we produce different values that are worth different to other people. If you produce something that's worth something to a lot of people, you get rich. If you could use something that's not worth a lot to a lot of people, you don't. That's the reality. It's not anything mystical. It's not an issue of exploitation. It's not an issue of fairness. It's the reality. We're all different. If you look around this room, if you look around any room, we are all different people. We have different skills, different abilities, different inclinations, different talents, different moral character, different characters. Some of us are lazy. Some of us are hardworking. Some of us love to listen to music. Some of us only watch movies. We're different. And as a consequence of being different, if you leave us free, if you just leave us free, what will happen? We're not going to become the same. We're going to stay different. So if you leave us free, we're going to have different outcomes. We're going to produce different things. We're going to have different interests. We're going to follow different paths. So inequality is just a feature of freedom. When people are free, they're always going to be unequal. Now what do I mean by freedom? I mean freedom from coercion, freedom from force, freedom from authority, freedom from somebody telling you how you must live, what you must do, what values you must consume, and what values you must produce. The freedom from authorities and from coercive elements. That's the freedom I mean. And with that kind of freedom, you're going to have inequality. Now I'm not willing to give up that freedom for the sake of equality, for the sake of anything. I can't think of anything more valuable, certainly politically. Then my freedom to make decisions about my life, to do what I want, and to let other people do what they want. I don't want people telling Steve Jobs that he couldn't build an iPhone, or that he should just send an amount for the iPhone, or they should have certain features that it doesn't have. I want the genius that is a Steve Jobs to build the iPhone based on his vision. We all have benefited from that. I want J.K. Wallace to write the novel. She wants to write. Not the novels we vote to have written. I don't want the people who have real ability to change the world, the people who have the ability to actually make our lives better. I don't want them to be told, to be forced, to be forced into doing what somebody else wants. I don't want any of us to be cursed into doing what we don't want to do. You don't want to buy an iPhone? Don't buy an iPhone. You don't want to read J.K. Wallace? Don't read J.K. Wallace. That's the beauty of freedom. In freedom, you get to decide what you do.  But in order to achieve equality, if we value equality, if we think equality is a good thing, equality of outcome, then how do we get there? What is the only way to get there? The only way to get there is through coercion. The only way to get there is by limiting people's choices, by telling them what they can and cannot do, by reducing people's freedom. So to achieve equality of outcome, you have to trade off freedom in order to achieve it. So I would rather have my freedom. I think freedom is more important for individual human beings and to let us all flourish and be successful. Again, I don't want to be cursed. I don't want to be told what to do. There's one form of equality that I think is crucial and essential for human success and flourishing and prosperity. And that is equality of rights, equality of liberty, equality before the law, if you think of law appropriately. Not equality of outcome, but the equality to live your life as you see fit, free of coercion, free of force. And that is exactly the equality that gets destroyed when we try to move towards the idea of equality of outcome, any kind of equality of outcome. Because the only way to get people to become more equal is to do what? What's that? To standardize, to limit, to reduce opportunities and to take from some to give to others. And to take physically, forcefully take in order to give to others in order to somehow bring about this equality. But they created it. J.K. Wallens wrote the books. What right do I have to come and take her stuff away? She provided a value. I've already, you know, I chose to provide her with those dollars in exchange for the value she gave me. By what right do I come to her and say, by the point of a gun, you have to give up more because what? Because there's equality, and it's an ideal, and we love it, and we want to achieve it. We call it a tax, yes. I know. We make it sound like it's not cursive, and it's not violent, and there's no gun involved. But try not paying that tax, and you'll see how much a gun is involved, and how much coercion is absolutely there. Yes, we call it a tax. But why? Why do we tax those who change our lives more at a greater rate than those who change our lives less? What does need have to do with it? And what, how do you categorize need? Does anybody need an iPhone? I think so. I think you need an iPhone. I need an iPhone. And who are you to tell me what I need? Who gets to the side? Do we need houses? We used to live in caves. So as human beings, as an animal, we don't need a house. We can live in a cave. Do we need a car? We used to ride horses. So do we need a car? And who is, who is anybody to tell Jeff Bezos what to do with a hundred billion dollars that he has? Not just one, he has a hundred. But I think it's a beautiful thing, because you know what it makes possible. It makes possible for Jeff Bezos to dream in a way that none of us can dream. It makes it possible for Jeff Bezos to think about how does he invest his money to take humanity to Mars? And wow, I think that's a beautiful dream, and it's his money, and it's he's taking the risk with it. And who am I to say no, don't do that? If it was up to me, Steve Jobs probably would have never invested an iPhone, because I would have said, ah, who needs a super computer in your pocket to waste of time. Now I can't live without it. Why would my limited imagination, limit the imagination of Jeff Bezos or Steve Jobs? I benefit enormously from Amazon.  They mail you books, right? But it's changed my life. So instead of allowing people to be free and imagine and create and not telling them what they need and what they don't need. And if Jeff Bezos, if he wants to go to Mars, needs a lot more than a hundred billion dollars, and luckily for him, he's probably going to make it, right? And luckily for us, he's going to make it, because if he can achieve going to Mars, we will all, I think, our children or grandchildren will benefit from that fact and the science created around that and everything else that's involved. And instead of NASA deciding what should be done about space, let individuals decide with their own money what should be done without space. Instead of taking my money and I don't want to go to space, you're taking my money to send a man to the moon. That I don't need. I don't need my money going to sending a man to the moon. Amazon's money, Jeff Bezos' money, I don't care. Good for him. But you know, we talk about these things as benign, but if we want equality of outcome, why only in money? Money is just one type of outcome. There are many outcomes. We're all different. What about equality of good looks, or equality of intelligence, or equality of education, or equality of a million different parameters that we could have out there? Why only equality of money? Why is money so central? Indeed, if you really take your egalitarianism seriously, you wouldn't just want equality of money.  And I'll give you one example. Granted, a pretty extreme example, but a true example, nevertheless, of what the striving towards equality can generate. So in the 1960s and 70s, a small group of intellectuals went to study in Paris. And they studied under the great philosophers, the Camus, and the Satras, and the Foucaultes, and all these great egalitarian philosophers who taught them that equality was the only thing that mattered. And what really matters in life is to achieve equality of outcome. They went back to their home country and they achieved political control. And now they could actually apply these things in reality. They looked around their country and they saw some people live in cities and some people live in the countryside. How do you make them equal? How do you make them equal? Cities have huge advantages. There's infrastructure and the people in the cities would tend to be richer. People in the countryside were subsistence farmers and struggling. How do you make the two equal? Move one to the other. You moved everybody from the city out of the city into the countryside and they literally did this. This is in recent history. They moved everybody out. But even in the countryside, all these people in the countryside, some people were educated, some people were not. Some people were smart, some people were not. Some people were good forages for food and some people were not.  But these people in a hurry, they wanted equality now. They didn't have time to wait generations to bring people up. They wanted to establish an equal society. So what do you do? What do you do with the fact that some people are educated, some people are smarter, some people are more knowing.  This is the killing fields of Cambodia. If you wore glasses, they shot you. If you had a college or high school degree, they shot you. If you were good at foraging, they shot you. Two million people, 40% of the population was killed in the name of equality because they didn't settle for just monetary equality. Why settle for just that? They wanted complete equality. So in my view, I can't think of an idea given human nature, given how different we all are. I can't think of an idea more evil than the idea that we should all be equal. And if the idea of all of us being equal is bad, then why are we even trying to strive towards it? And the fact is that the inequality we have is not, as I said originally, in and of itself a problem. If the people who are getting rich are getting rich by producing values for all of us. And yes, when economists looked at my bank account, when Piketty, the famous French economist who wrote that wonderful book, 21st Capital in the 21st century, or it's like I like to call it Das Kapital in the 21st century, it's just German pronunciation for exactly the same title. When he looks at my bank account, I got poorer, they got richer. But I got richer for having read the books. And this is true of all of that phenomena. We get better when we are free. We get better when we allow the J.K. Wallins and the Steve Jobs and the Jeff Bezos to do what they do and allow us to do what we do. And if you want to solve the problem of poverty, then create lots of opportunities, create lots of jobs, create lots of opportunities for people to find work and rise up.  So in the trade-off, the inevitable trade-off between freedom and equality, I'm 100% on the side of freedom. Thank you.


This is a course I've been wanting to make for a long time. We're going to talk about linear algebra. I'll put these courses out one at a time. It's something that I'm making at home while away from work. Mathematics is a beautiful subject. Linear algebra is at the heart of so many things that we do with mathematics. And I'm specifically thinking about something like deep learning where we can use tenses, matrices, vectors, to build models to predict some outcome. So linear algebra really at the heart. And I think if you understand linear algebra, you understand a lot about mathematics. And it's really a beautiful part of mathematics. And I really would like you to be as enthused as I am about it. I'm going to use a computer language together with the explanation. And I really think that's a modern way that we should approach teaching mathematics. We are going to use code. Most of us are going to use code when it comes to the mathematics that we are using. And just to be exposed to that as soon as possible is great. So this is not about teaching you a computer language. I do have courses for that, both on Udemy and on Coursera. So you can get a university certificate even from one of the courses that I do teach. And what we're going to use is the Wolfram language. The Wolfram language is really built around symbolic mathematics. And that's what we're going to do. We use symbols. And it really is the language that works best that you can write your own code. You can do that in a browser, just open a free account with Wolfram on the Wolfram cloud. Or you can buy a small subscription. And with that, for instance, you could get a desktop version of the Wolfram language that you can use on your own system. But otherwise, you can just use it free of charge. This is not about the code. You'll see the code, but the code is there to draw something to the screen or to check on some result of a calculation, just to show you how easy it is to do with a code versus what we do by hand. And we're going to do it by hand. By that, I mean, it is written on the screen. So not to worry about that. It is about the linear algebra. But I'm just going to bring the code in it as a modern form of teaching the subject. So in this very first video, we're just going to talk about points and vectors. Either one understands what a point is on a 2D plane, or perhaps even a point somewhere here in space. It has three components to it. X, Y and Z component. But from there, we can very naturally move on to what a vector is without wasting any further time. Let's go have a look at points and vectors. So from points to vectors, I think most of us are familiar with points. And if we look at this flat surface that we have in front of here we can just put a point anyway. And if we have this Cartesian coordinate system where the bottom of your screen is the x-axis and the left side up of your screen is the y-axis, we can denote a point. There's a pixel and that pixel will have a position. And we usually, it's important in mathematics, of course, how we write things down. And there's certain rules that we stick to. So I think in most textbooks you are going to see something like this where we have a point, like you see there, 3, 2. So the 3, 2, that's a two-pole, two-tuple. And as much as the two values there, they're separated by a comma, the inside of parentheses, and they go directly after the name of the point. And we can also use the subscript notation. So yeah, we have 0.0 being at x sub 0, y sub 0, or 0.1 at 3, 2 and 0.2 at 0, 1, etc. That's just a point. And that is how I'm going to write a point. The subscripts, of course, are elements of the natural numbers. So if I have points I just have, let's include 0 with those numbers as well in that set. So 0, 1, 2, 3 as the subscripts. So here we have our first function in the Warframe language. I'm going to reiterate this. It's not about learning the the Warframe language, but it certainly helps. Remember, you can run this in the cloud, free of charge. It's going in your web browser, to the Warframe cloud, sign up for a free account. You can do all of this yourself. I've got courses available to you. All the links are down below for you to learn the Warframe language should you want to. I'm going to use it as something to illustrate the mathematics. I do think it is important to do that in a modern world. So it's a functional language. So we're going to have functions. And there you see the function there. Function is a keyword. And Mathematica, or the Warframe language at least, has more than, I think, 5 or 6,000 of these. After those, you'll always see a set of square brackets. There's my opening square bracket, my closing square bracket. And inside of those go parameters or arguments. And all arguments are separated by commas. So you see these commas there. And that gives information to the function so that the function actually do something. And when you bake a cake, you put it in the oven, but there's lots of ingredients that go inside of that and out pops a cake.  There's your function. So all I'm specifying here is something about a point. And because I want to specify more than one thing about a point, I put those things inside of a set of curly braces, which you're going to see there and there. And they've also got commas between them. And between curly braces is something that we call a list. So I'm saying point size. And again, point size is just going to be another function. So I can pass functions as arguments to other functions. And because it's a function, we see the open and closed square brackets and 0.05. That's going to be the size of the point that I have. You can see the point down there. You can see what it's going to be. I want it to be red. And then the position of it. And there we go. There's my 0.3 comma 2. So if we go down the x-axis on this side, we get 2, 3. And if we go up 2, we get to that over there. And that's how we get the point 3 comma 2. And then comma outside of that list, I just put, have some attributes, axis, I set to 2 so that we can see the x and y-axis. And I have axis labels. And again, there's a pair of them. I pass them as a list so that you can see the word x-axis there and y-axis there. And that comes from there. So it really is as simple as that. The point is, I'm not going to teach you the Wolfram language here. I think it's very easy to pick up when you look at it like this instead of trying to learn how to use the language after a while. It'll just come to you in a quite a natural way. The point being here is linear algebra. And we've got a point. And we can denote a point by its address on the surface or within the volume that we are talking with here. We have a surface so we can give it an address. 3 on the x-axis, up 2 on the y-axis, 3 comma 2, there's our point. And to illustrate the point, I've got quite a few points here. And here I've just given them computer-variable names, p underscore 1, p underscore 2, up to p underscore 4. And I've given them their coordinates instead of a set of curly braces denoting a Wolfram language list. But that would be the same as us writing in a mathematics textbook, point 1, 3 comma 2. That's exactly what we're doing. So we're doing them all in red again. And in the point, instead of a single point, I'm passing a whole list of points. So the list goes inside of curly braces. And it is pretty much the same, although I haven't said x-axis and y-axis as the axis labels there. But once again, the point being, I can clearly see this is point number 1, and it's at 3 comma 2 because that 3 goes down to the x-axis and the 2 goes to the y-axis. And it's quite simple to see here. We see point p4 because it is at 2 comma minus 1. And you can work out what these other points are going to be. So that's really simple enough. And as I've written here, let's change our point of view now. We all know about points. So let's just change them to vectors. And here we can see that we are trying to get to this same point. If you think about that, if I put a dot there, that's the same point, p3 comma 2. So I'm still going 3 on the x-axis up 2. But now I can just imagine walking there from the origin. And we call this the origin. The origin will be a point 0 comma 0. This is two-dimensional space or two-space. And I just walk 3 along the x-axis. And I denote that by a long arrow of which the tail, I have a tail of my green arrow here. And I have a head on this side. So there's the head. And here by the origin is the tail. And then this green one will also have its own tail at the bottom here and its own head there. So if I do this little walk indicated by these arrows or vectors, I get to the same point. And that obviously becomes quite important to us when we talk about that. So instead of these two walks along the x-axis up the y-axis, I can just walk straight to the point. And this green thing is indeed a vector. We will call this a vector. And we've just seen though that a vector does have components. We sort go along the x-axis and we sort go up the y-axis. So immediately you should have this intuitive understanding that I can add these two things somehow, these two walks. And that will just give me this resultant walk, this resultant vector. And you can see the code here. Again, it's just a graphics function there. I'm making a slightly smaller point size. It's still in red. It's still a 3, 2. And then though I want a green thick arrow. And the arrow goes from the origin. There's my 0, 0 at the origin. And there's the final point that it goes to. That was my point. And it goes to that point. And everything else is quite self-explanatory. So a point and a vector is just two ways to represent basically the same spot on the plane. But I can do so much more with a vector than I can do just with the points. So that brings me just to how we write these things down. Here you see one notation. This is the angled bracket notation, as you can see here. And you can also see that I broke this down into two separate ones. V, first of all, you see the underscore there. Let's say V with an underscore. So many textbooks will have that. And that denotes that this is a vector instead of a point or anything else. So we put that little underline on it. V with an underline. And then also we use these little angled brackets here. And it says 3 comma 2. But what it is really there, it is the x value and the y value. And I've done just that. Remember the two green vectors initially. That would be the first one that went along the x direction. And this one that went along the y direction. And I can write the two of them separately as well. Because the V sub x vector went along until point 3 comma 0, 3 on the x axis, 0 on the y axis. And y went from 0 to 2. But that might look a bit strange to you because it didn't start at 0. It started at 3. So what's going on here? For now, just these little angled brackets, you'll see them all over the show. But you can start to see that there's something going on here. Because if I add 3 and 0, I get 3. And if I add 0 and 2, I get 2. So there's this intuitive idea of adding vectors. And it also brings us to this y is at 0 comma 2. Because you see these two green vectors here. First of all, you'll see the tail of this one here. And the tail of this one is at the origin. And the head is up there. And the head is up there. And these two vectors are exactly the same vector. There's no difference between the two. Just because we've displaced it laterally here, it is still the same vector. So that's something that you should really get used to. This vector on the left-hand side is just called the positional vector. Sometimes called the positional vector. That just means take any vector and just sort of transport it so that its tail is at the origin. We just want to place this at the origin. But no matter where we move this tail, these two are still the same vector. I could have moved this one up on the right-hand side. Further up, further left, further right, further down. But as long as it's the same length, and you can clearly see that this is the same length. So length is going to be very important to us with vectors. And it also has the same direction because from physics, it's really intuitive. It's an intuitive way to understand vectors that it has this idea of there's a physicality to it. It is something that has a length and a direction. And anyway, where you go, when you walk now, you're going to walk for a certain distance and in a certain direction. And of course, you can change directions many times. And that is just the addition of a bunch of little vectors. And I can bring all of them where they tails back to the origin. And that'll be exactly the same thing. And you'll soon see that. So remember this idea of the positional vector, which means we can also write it in this as far as linear algebra is concerned in a much better way. These we call column vectors. This is a column vector. Where's my n column vector? And we're going to have a lot to say about column vectors. You can clearly see it's written as a column. And they're two rows to my column, two rows to my single column. So there's row number one, row number one, and there's row number two. So there's two rows in a single column. This vector v sub x is then what we would call a two by one vector. It's always a row. And then column always in that order. So it has two rows in one column. And because it has one column, we call this a column vector. And that means v sub y is also a column vector. And it is written like that zero and two. The x component is zero. So it's not moving along the x component at all. But it's moving plus positive two on the y component. And that's exactly the two vectors that you see here. Both of them are v y. And both of them are zero two. It's the same column vector that we see then, both representations. And now it makes it very easy for us to see this idea of the addition of vectors. Because if I add these two column vectors on the left hand side, the v sub x and the v sub y, I get exactly that. Because what we see here is actually called a linear system. And we're going to talk all about linear systems. But let me write down the word a linear system. This is a different way of writing a linear system. And as much as what it says there is that I've got two equations. It says three plus zero equals three. And zero plus two equals two. It's just a succinct way of writing a linear system, a system of linear equations. And we're going to talk all about that. And sometimes people just start off with those things. And it's not always that intuitive to understand where it comes from. But if you see it this way, I think it actually makes a lot of sense. There's nothing difficult here. It's very intuitive. So of course we need to stick to the plain surface here. We can go up in another dimension. And here we have vector w. And it's in three dimensional space. So it has an x value. It has a y value and a z value. So we're going up. So not only do you have to walk on the floor, but you can get in the lift and go further up. And these vectors live in a certain space. And before when we only had two elements in our column vector, we were in R2. And we write R there. It's the set of real numbers because we are denoting here that the elements are real numbers. We can also have something like C2. And that will be a vector where the elements can be complex numbers. But we're not going to get into that anytime soon. So let's take that away. The R there just refers to the fact that we're talking about real number entries in three and two and one. Okay, they are integers, but they're also, that's a subset of the reals. So if we go to three dimensional space, of course this will be a vector in R3. So you can see there.  We can only imagine three dimensions in our heads. But of course, there's no limitation on that. We can let n be much larger than three. And we get into what we call hyperspace. So different ways to look at vectors, the physicality of it is something that has a length and a direction. But we can also view it in slightly different way. Instead of having these three components, we can look at it in this way. So here trying to represent doesn't really fit on the screen. Three dimensions. So you see the x-axis moves down here to the side. The y-axis is there. And then the z-axis goes all the way up. And then we have still this origin at the bottom. Right here's our origin. And this vector comes out in three dimensional space. This is a right hand coordinate system. Because imagine that you can contort yourself putting your right hand's palm at the origin pointing towards the x-axis.  So this is a right hand. And it's a bit difficult the first time to go from x down the bottom of your screen and y straight up to this contorted view. But it actually, it's the best way. Just trust me on that one. It's the best way to do. So we can deconstruct this vector a little bit. Because imagine we look straight down, we can look straight down onto the floor. So imagine the x and y-axis are down on the floor. And I'm looking straight down at the origin, straight down the barrel of the y-axis, the z-axis. I should say that vector that comes out has this projection down onto the floor. And this is this, let's call it projection from now, although we'll get to projections. And that is this representation right down here, this little one down here. It is the projection of this one down onto the x-y plane. And it has a length of r, as you can see there, we can do that. It will have this vx component here for sure. It will have a vy component, which we see back there. A vy component back there. And it also has a height. And the height will be down from the floor up. So we have our vz component there. And you can see where we've indicated them here. It also has a length, like any other vector. And you can quickly see how we're going to write the length. It's quite a cumbersome way. That is the length of a vector. We're going to call it a norm. It has a length. But there's some other things here too, the two angles that we're talking about. So here's our positive x-axis, our positive x-axis on this side. And we can see this angle theta, it swings out from the positive x-axis to this projection. To the projection on the x-y plane. And then we also see this angle phi up here. And that is just an angle from the z-axis. And how much does it lean across? From straight up, how much does it lean over? So you can see that the interval on which we can find that angle is from 0 less than or equal to phi is less than equal to pi radians. Because you can only go straight down to the bottom here. And then the theta is going to go all the way to 2pi. It can go all the way around the circle. An actual factor can go many times around. And there's some lovely peculiarities about that as well. And we'll certainly get to those too. So you can see the intuition here of how we describe this vector. It's head here of the vector. How can we describe it as a positional vector? In other words, the tail is at the origin. Yes, it has an x, y and z component. And I can write it like that. But I can also write it in terms of this radius r. And I can write it in terms of this angle theta. And I can also write it in terms of this height. Or alternatively, as this angle. So we have this idea that we have a multivariable calculus where we can use cylindrical coordinates or spherical coordinates. None of that matters now. I'm just hoping that this makes intuitive, really intuitive sense. So let's get to this idea of the norm of a vector. And you see we've got vector v here. Well, there's again the notation. And I try to put things that I just want to, if I view my documents quickly, I want to see all the important terms. I put those in green. Which means in that area of that green, I'm defining that term. So that when you see green like this, that's the way my head works. And when I do use highlighters, very sparingly. But every color means a different thing. I don't just go for any color all over the show. Anyway, so we see vector v here. It's represented in two different ways with the angle brackets or as a column vector. And we're going to stick to this column vector notation, not in the physics notation, but in linear algebra notation. And we're going to get the norm of that vector with this ugly notation with the with those double lines on both sides. And it actually makes intuitive sense. So let me try and get a ruler here. There we go. I'm going to have my ruler again. And there was just the axis that we were dealing with. Remember, there's my x axis and y axis. So we're only dealing with R2 here. That's a vector in R2. And there's our little vector going out there. Remember, it has an x and a y component. So there's going to be my x component. There's going to be my y component. And there's a little angle there theta. And this is a right angle triangle. So Pythagoras to the rescue, what is the length of that vector was the right angle triangle. So if this vector is V, it is just going to have a length or a norm just of the square root of x squared. It's x component and it's y component. It's as simple as that. So if we have three and two there, it's three square plus two squares. That's 13 square root of 13. It's the length of my vector. So it really is as simple as that. And if it was out in three dimensions, I'm just going to add plus z squared to that. So I'm just adding the squares of its components. And that's just Pythagoras. So nothing there. Not difficult to imagine that a vector really has a length. Now I can specify a vector in the Wolfram language. We've seen that. So I'm giving it a name. That's how computer languages work. So it can't be one of the 5,000, 6,000 odd keywords or functions. So it's usually this lowercase letter that we give it. And the equal sign in a computer language is not an equal sign. It's an assignment operator. It assigns whatever's on the right hand side of it to whatever's on the left hand side of it. So on the right hand side, I have a list object. And it is a list because they're the set of curly braces. And I've got two elements in there, three comma two. And I'm assigning that to a computer variable. So V is called a computer variable.  It gives it a name. And that's the name V. And it assigns an object to that little piece of memory. And at the moment I'm adding, I'm putting a list object inside of that piece of memory. I call it V. But that's how we represent a column vector as a list object in the word from language. And now I can just use the norm function. And I pass it that little piece of memory, which contains my list object and out pop square root of 13. So norm. And then just the name of that. So I could also have this written if I didn't want to save it as a name, I could have written norm, and just pass the three comma two there. Exactly the same thing. By the way, this semi the semi code on you see there, that just means don't print the result back to the screen. Just keep it to yourself, please. And that's all it does. So there I just show you, if I have another dimension, I just keep on adding the squares of the components. And again, then the norm of a vector in three space, three comma two comma one is going to be 14, which brings us to the point of the unit vectors. And we write a unit vector with that little hat on top of it. So instead of the underline, the unit vector of V would be V with a little hat on it. And what does a unit vector mean? It means I'm taking my original vector and it's still pointing in the same direction. So if I look at it in three space, the theta and the phi is still going to be the same. But I wanted to have unit length, unit length, meaning a length of one. And how do I do that? Well, it's actually very simple. I just take a vector and I get its length. And in the end, this is what I do. I divide the vector by its norm, which means each component is going to be divided by the length of the whole vector. So there's some fancy notation for the norm of a vector, get used to that one, because that's much neat a way of writing it. It says the square of the sum of all the components squared. And the components is one to n, n being the number of components. It's exactly what we did if we have a long vector, we had to write all those squares out, but that's just a succinct way of writing it. So if I take every component of a vector and I divide it by the norm of the vector. So look at that. If I have a vector that is one, three, and four, and we had the vector one, three, and four up here, the vector, oh, we didn't. We'll have to do, we'll have to do that one by hand. But anyway, it's square root of 26. So the norm of this vector is going to be the square root of one squared plus three squared plus four squared. And if we do that, that's the square root of one plus nine plus 16. And that's the square root of 26. So that's the norm. And what we're doing here on the inside here, we're just taking the vector and we're dividing it by the norm of the vector. So each component gets divided by that norm. So it's going to be one divided by square root 26. That's going to be my unit vector v hat. And then we have three divided by square root 26. And then four divided by square root 26. And that's exactly what we see here. We just see a cleanup there of the square root 26 there. And you might be told never to express something like that. Just multiply it by that. So that would be the square root of 26 divided by 26. And of course, you can try and clean that up a bit as well. And as I mean in the case of this one. And the thing about a unit vector, if you think of its norm, it's going to have a length of one. It's really just going to have a length of one. So if I were to take the norm of this unit vector, it's going to be the square root of one over square root 26 squared plus three over square root 26 squared and then four over square root 26 and those squared. And if you work that out, this is going to be one by the nature of the beast because we've divided it by that. So if we square all of those, we're just going to get to one. That means the length of one. So all we're doing in this instance, that was ugly, is if I have my vector out here, it's going to be exactly the same vector, but it's just going to have a unit length. So it's going to be one long, but the direction is still exactly the same, which brings us to the standard unit vectors. And that is where we just go one in the direction of my, if we look, if we had this idea of our three dimensional vectors, so there's my X, there's my Y, there's my Z. So I'm going to go along each of these, I'm going to go along each of these, and they each going to have a length of one. And we usually call these I hat and J hat and K hat going along those components. And that makes it very easy for me to express, you can see them express this column vectors one zero zero one in the X direction, nothing in the Y, nothing in the Z. And here with I, with J, nothing in the X direction, one unit along the J and zero and then zero zero one. As simple as that, which also means I can express any vector as this linear combination of the standard unit vectors. So if I had a vector three comma two comma one, that I wanted to express, that will be three times the I hat one plus twice the J hat plus the K hat. That'll be exactly the same, because this is going to be three zero zero. This is going to be zero two zero. And this is going to be zero zero one. And if I add them up, remember my linear system, that's going to be three to one. Exactly what we want. So we can use these constant multiples of a unit vector. And now we already see scalar vector multiplication in the go. This and I multiplied by three, it means each component is multiplied by three. And in this instance, it's going to make this I hat just three times longer, because that's going to be three zero zero. And if you take the norm of that, it's going to be three times longer than the unit vector or very simple and intuitive. Let's just then also talk about the direction of a vector. And once again, if I look just in two dimensional space, let's have that. Let's have our vector up here. And down here, again, that's our x component, our y component, this is a square. That's our angle. And because that's a square right side of triangle, you just use trigonometry, the tangent of theta. Well, that's this opposite divided by adjacent opposite is y adjacent is x. And which means that theta is the arc tangent, the arc tangent of y of x. And that's as simple as that. And the only problem with trigonometry, you really have to be careful in what quadrant you are in. So what I've done has just looked at these quadrants. Here is my first vector. It is at this is a vector one, square root of three, you can write it like that. That's that vector. And which means my x component is one, my y component is square root of three. It's in the first quadrant. And if I take the arc tangent of that, I'm going to get pi over three, which means this angle right here with a positive x axis is pi over three, theta equals pi over three. So it's easy then to do the arc tangent. And the arc tangent has a function, as you can see there in the Wolfram language, arc in uppercase tan. And that is my y and that is my x. And the result comes back pi over three. So let's shift this along to the second quadrant. In other words, my x axis is now negative square root of three. So what I'm doing here is the arc tangent of one over negative the square root of three. And the arc tangent of that is minus pi over six. So that looks a bit difficult because what we're interested in really is this angle. That's what we're interested in. So really, when you get that, remember that that must be subtracted from pi. This whole straight line is pi and I'm just subtracting this a little bit from the whole, from the whole thing. And that gives me this angle that I'm interested in. So that's five, six pi.  And what quadrant is this? What am I looking for from the positive x axis to the vector? If we move on another pi over two radians, I'm now negative one comma negative square root of three. And if I take the arc tangent of that, I get pi over three. But this time I've got a subtracted from pi. Because what we usually do here is that let me just fill this in for you. So those two axes, we go from the positive x axis, but we usually, we just stop there at pi radians. Once it goes over pi radians, we actually can express it as a negative. So on this side, we'll express it as a negative and on this side, we as a positive. But that's this convention and this is something you've got to get, you just got to get used to. So in this instance, it's pi over three.  So I get my negative two thirds pi. So this angle here, the one that I'm really interested in is that one. And that's what I'm going to get. And then in the fourth quadrant, again, now we're still interested in this as a negative angle. And in the fourth quadrant, you can just use arc tan. You don't have to involve pi with that. So I hope that made intuitive sense what vectors are and how I think everything that you're going to learn about vectors has come from this very basic thing. They're very simple to understand as some simple concepts just to get used to. And there's nothing, there's nothing much to it. We can do some very exciting stuff with them. In Sydney, that's what we're aiming for.


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What's up everyone takedown here welcome back to another video today. I'm gonna be showing you guys how to factory resets your Nintendo switch lights This is really easy to do you can do one of two things you can either navigate using at your arrow keys or The sticks or the Nintendo switch is also touch screen.  So you can hit the red button here to initialize it and this here will take some time it could take anywhere from a couple minutes to 10 15 minutes depending on how much you have saved on your Nintendo switch and how much needs to be erased So it is loading up here. You do now see the Nintendo switch logo up here on the screen and This is the setup for a new Nintendo switch So from this point on you would go through and set it up as a brand new Nintendo switch since I am gonna be selling This Nintendo switch lights now it is perfectly set up for the new owner whenever I do go and sell this So this is how you factory reset your Nintendo switch lights Very very simple and pretty much the same thing as the regular Nintendo switch and the OLED So very very similar to that and it's very easy to do this one here did not take too long Just a couple of seconds But sometimes you might have to wait like I said 10 to 15 minutes on average Depending on how much you have to erase. Okay, so enjoy this video. See you guys in the next one. Please take care. Peace


I would turn back to this this summer you know I would reiterate that you know I thought Aaron Boone was part of the solution wasn't a problem or the problem and listen I think Baron brings a lot of great qualities is a great baseball mind comes from an amazing family that has a history of you know in this industry for quite some time but his ability to connect to communicate to be open-minded he's had a lot of success here despite obviously our postseason you know ultimate results you know because our our big goal happens to be a world championship but that doesn't mean there's a lot of goals that you know are getting accomplished or things to be proud of along the way to be quite honest if he was entering the the free agent market I believe he'd be the number one managerial candidate in baseball and there's a number of different vacancies and and we would be going to market looking for someone like him and so I think he's a you know has been a good hire and he's going to be a continued good hire in that position I think you know as I said you know if you if you lead follow the breadcrumbs from the past you know I think I publicly stated how I feel about him this is a manist manifestation of that and it's not just me you know as this is an organization that obviously has a lot of input from a lot of people and most importantly the owner with the final say and I think there's a you know a great deal of respect for what Aaron Boone brings to the table and what he's certainly capable of and and and so why the delay we had to wait for the season to end ultimately and then and then have a lot of dialogue above and then ultimately you know like anybody they have an agent we had you know so I was negotiating with with his agent and representation of Adam Katz and and then clearly we had some changes in the coaching staff too so there's a lot of discussions to have whether it's you know contract term adjustments along the way and so I think you know everything all all in due time you know it's you know like anything else it's not like it's as quick as just flipping a switch and you just get it done there's a lot of a lot of details to work through conversations to have and and boxes to check along the way but like I at least from my perspective there was never a doubt or an intent to have Aaron Boone back here it just came down to working through it and making sure that you know it was going to get the sign of the cross from from other powers that be at the same time and and when we actually got together after a little bit of a time and delay you know we had a conference call discussing all things and all parties were 110 percent on board as well and alignment on that


It's obviously been quite an interesting week in the press. There's been some there's been some smack talk going on back and forth. Obviously Trent Alexander-Arnold came out yesterday and made a pretty outrageous quote. I don't have the quote verbatim in front of me, but he was pretty much saying that the trophies that Liverpool have won mean more, mean more because of the way that they did it. Now I couldn't for one tell you what that's meant to mean. He said the two financial situations of the club, which again feel like there's a bit to unpick there. But he said that he feels like Liverpool are actually more successful even though statistically City more successful because of the inverted commas way that they've done things. What are your thoughts on that? I mean it's mean more FC, innit? They've invented caring now. Brilliant. Yeah, you did that. Thanks. I'll go try and care now. They've invented having fans who like winning trophies now. Yeah, it's just a mad comment to make before we play each other. Some of that's going to rifle things up, obviously. I just don't agree with it in the slightest. Really? That surprises me. I thought you said it actually didn't mean a lot to you when we were on the treble. I just think I don't agree with anything that you're saying. It means more to them like why? Why would it mean more to them? Why? Like it doesn't make any sense. I saw a tweet that said something along the lines of when Rodgers scored that goal in Istanbul, I quickly got out of my XL app on my phone, went through all the Manchester City's finances for the past 15 years before deciding what my barometer of celebration will be in accordance with the financial records. It's like, is that what you think City fans are doing? Yeah, we have to go through it. How much money do we spend to get to this point? Right, okay. That's that much per goal, which means I can be this level of happy. A bit too much for me to be eccentric. I've got not a cry, not a cry. I've not quite got to that point yet. Like auditing the goals. Can't quite take my shirt off because we're putting in a bid for Gavadil, so can't do that. Can't do that. We'll have to rein it in a little bit so we can afford that Gavadil. It seemed to me like a really row common, which you don't expect in this day and age because plays are generally so media trained to say the appropriate thing. It seemed to me like a comment from days gone by when like Thurgy and Venge used to throw shade at each other at every single press conference. It seemed like that. And to be honest, I'm kind of all for it because obviously we'll get on to there's been a bit of a retort today on that from a city player, but it kind of builds the tension around the game. I don't agree with the comment itself.  Like we've got some stuff to talk about. We're speaking about it now, right? I like it. I like the animosity that it kind of brings. It adds a little spice to games. Like Derby Day is now, for an example, the not as fiery. It's all they'll hug each other after a match. It's all nice, nice Derby Day nowadays. When we're Manchinian, it's all kicking off with Fergie on the touch. I remember when Mark used it. Yeah, yeah, I kind of lost Tevez doing little, what was it like talking? Yeah, yeah, see that kind of stuff, it's that adds to it. It adds so much to it. Like, and then so yeah, the trend doing that, like I say, I agree with you. I don't agree with anything that I said. I think he's chatting, but I'm here for it. Yeah, you keep talking like that. I want to fuel that fire. Yeah. And speaking of fuel on the fire, we'll obviously get to the quote that came out today from Harland, which was cold as ice. He pretty much got told about the comment from a journalist for the first time. He hadn't heard it. He was read the comment and his response was, well, I've been here one year. I won a treble, which was pretty nice. I'm pretty sure he wouldn't know how that feels. Which is it's peak. It's like, I love it. I love it. I love it. Well done, Harland. I love that so much. What I do love now, and I'm not, I'm not about to like take the side of United fans in any way, shape or form, but I do love just being able to pull a treble out your pocket. Yeah. Like a little trump card. It's like a new, no reverse card. Anything you say, but everyone in trouble.  But now I do. Now we can do it. You get it. Oh, yeah. It actually feels good doing that. Anyone get, you know, any Liverpool fans, Arsenal fans now start going, oh, you're rubbish at the weekend or they start making comments or 115 charges or whatever.  Oh, treble. Oh, treble for you. Where's yours? Where's yours? Come on with these, mate. You're not going to treble. You're not going to get invited. And Harland literally did that. And Harland did that in the press. He did that in the press. He was just like, Trent Alexander, Trent Alexander, under Arnold said X, Y, Z. He just went, no treble. Basically did that. It's great. That's what I mean. That's going to add to the weekend. Everyone's, everyone's just both seen these quotes, both quotes from both players.  But you should love the fact that they're both saying it because it's just, it's tension for the game. It's because it just adds a lot to the weekend. Like rather than being, oh, nice and nice and Trent being like, oh, I respect everything man city have done. The guy came out and started shooting and I'm glad that Harland fired shots back. Because when I seen that quote from Trent, I was like, yeah, I don't agree with it. I did not expect anyone to respond to it. And I thought if they didn't even get asked, say Pet got asked or anyone got asked, it would be played down so much. But how to come back and say that is just, it's almost like he's gone off the rails a little bit. I think city be like, whoa, we shouldn't have said that. What I love about his voice, watch the clip. So cool and calmly says it. He doesn't like, he doesn't bite. He's not like getting angry. He's not like, that's rubbish quote. Like you should think about the fact that we want to treble. He literally sits and he goes, well, I've been here a year, I want to treble. It's quite nice. Can't imagine how it feels. The thing is the best way to come back to it is the success that we've had. That is the best way. Like us pulling out that treble card is just the best way of coming back to anyone. And when it gets to the weekend now, and we see a crunch in tackle from Trent, or we see Harland makes him and score a goal or whatever else, like we know we know it's going to mean something. Yeah, the tension is there. But Harland would be scores to celebrate in Trent's phase or just do anything. Or Trent's scores and then we'll have to be sat there thinking, oh gosh. I mean, he scored against us last time. So that's on the cards now. Like I say, as a level of excitement for the game at the weekend. Yeah. Yeah. What are your thoughts going into the weekend in terms of, I guess, if we're going to win? If you think we have it in us to win, what you think in Liverpool at the moment? Liverpool getting the results. I still think, I think Liverpool fans are degrees. I still think we are the better side. I just think they're getting the results, which is showing champion form, which is great for them. And that's why they're currently sitting top of the Premier League, because they keep getting clutch results. Norwich, sorry, not Norwich. Forrest. Forrest, and you've got lute and like kind of games and things like that. They're getting good results, which fares. I mean, I'm all for it. They're doing it in a similar way that they have done before, which is scrappy games, but they'll grind out the results. They keep getting a lot of like 80 plus minute goals. Yeah. But I feel like when you win the Premier League, I feel like you do kind of, it's not all these 5-0, 6-0 kind of thing. You do have to grind out the results where you're not particularly playing well. They're doing that. I think we are the better team. I think going into the weekend, I do feel like we're going to have to be playing at a high level, but it's something that we all know. We've not won at Anfield with fans in the stadium, which is the Anfield curse. Although people say, no, it's gone because we won there in the Covid year. For me, and I'm a Man City fan, I feel like there's a bit of an asterisk next to it. Yeah, because not the fans out there. Or it's in brackets like we won, but there was no fans. I feel like it's we won, but the curse is not broken. The curse still remains. It's still a thing. The Anfield curse is fully there, and it's something that we're going to have to overcome this weekend. I back us to do it because I'm looking at what we did last year. I know I go back to them kind of games, but we had to get to a level to beat the big dogs. If we want to win this Premier League, anti and then players, you need to go there and you need to beat them. Yeah, obviously we can draw against them, but I say the Liverpool driving point from now to the end of the season is far and few between. I don't know where it's going to be. So we need to get up there. You've said for a few weeks now, like you feel like we're going to win, but you feel like we'll get that result. I'm really not on the same boat. I genuinely feel like we'll do it. I'm really not on the same boat. I hope we will and I want us to win, obviously. Yeah, but I don't have this sort of like assuredness. Big Steve was saying when he was last here, that he feels the same. Like he just has this feeling that we're going to win. Yeah, I don't know what I can't even explain it. I just have a feeling that you don't have to do it. We're going to get up for it and we're going to win that game. I was like that last season when the Champions are going to feel like a lot of City fans were, from day dot, from the day the season, the Premier League season started, I was saying to all my mates, City will win the Champions League this year.  I was like, I can't really explain it. I just have this feeling that this is the season that we win the Champions League. And we did. So I hope your feelings are right. I hope my feelings are right. I hope you feel it's all right. Now, does it mean that I'm going to be nervous going to, not nervous going to it because I have this assuredness? No, not at all. I'm going to be, I'm going to be just as scared as any time that we play these kind of games. I think it's going to be difficult and... It's going to be horrible. It is, it is, but I'm just hoping we get the peak of these players. We've had a few players in midweek who got a bit of a rest, which is nice to see you, Kevin Abroins, Phil Forden getting a rest, Rodney getting off at halftime. I think it will kind of walk again a full rest. John Stones getting a majority rest and that's clutch. So to pull it back to the Champions League game last night, that's pretty much what we said, wasn't it? Is we just wanted injury free. We said that was the biggest thing in this game. Yeah. Injury free resting players and going through. Yeah. Yeah. That's it. Yeah. I mean, again, without being disrespectful, going through felt quite assured, especially after the first 10 minutes. After that, we just said... At 10 minutes, I said subs. Yeah, yeah. Subs at 10 minutes. I was thinking there's not quite even keeping any of these players on the pitch. Rest up. Some people were asking why we bought off Rodney at halftime and it's like we don't need him. We just don't need him at this point and we need the rest ahead of Sunday. So fingers crossed. Fingers crossed it goes well for us, but it's mad to think that on Monday's episode, we could be top of the Premier League. We could be. We could be top of the Premier League. Or we could be third. No. No. Don't tell me that. Top of the Prem. That's all you can see. Top of the Prem. Top of the Prem League is where it's at and it's where we will be on Monday. I believe... You know what? You're making me believe more. Good. Which is good. You're inspiring me, which is good.