Can't you understand that comparing animal slaughter to the nutty death camps was one step too far? It's the exact same thing. Strike of force! Force? You pay people to force knives in animals' throats. That's what you do. The thing is, you laugh in your van, I can't talk to you. You can't respond to what I'm saying to get angry.   It's pathetic!  There's a lift! Just close! Don't invade a restaurant. It's simply not fair. Do you want to talk about fairness and justice? It's not fair that we subjugate the most innocent beings on earth. That's not fair. Why are we doing it to them for? Welcome to another video. Now, I thought I would take this time to address something that I've been getting heaps of. I've got a lot of this since I started my advocacy. All these people out there saying to me, Joey, you're too aggressive. Now, the question has been raised because of my fiery debate. It was a very heated debate with a guy called Nick Ferrari. Don't know too much about him. Apparently, he's a bit of a big deal on the radio over there in the UK. They asked me for an interview regarding direct action everywhere. Direct action everywhere. They do some controversial stuff. I know we'll get into that whether I think it's effective or not. Last day of the tour. Last day of the tour. Big tour.  Very tired. I was questioning myself. I was like, oh, should I take on this interview? I'm a bit tired, a bit wound up. I've been at the front of slaughterhouses for three weeks. Okay.  Footage is coming soon. Very powerful. I was like, cool. Am I really in the right mental state to do this radio debate? And you know what? I thought take every opportunity because you never know how this is going to turn out. My conduct in the interview. I mean, there's many reasons for my conduct in that interview. He was mocking, mocking me. He was making me answer the questions that he had already set out. Trying to lead me into traps with his questions. Yes or no answers. I knew where he was going. Now, in terms of whether or not I think DXC actions are effective, it gets me on the radio to discuss veganism, doesn't it? Now, in terms of whether you think my approach, my aggressive conduct in this aggressive conduct in this interview, I think it was passion. I think it was passion. But I look, do you think it, do I think it was as effective as some of my interviews, some of my TV appearances? Probably not. Okay. Probably not. I'll agree with you there. But was it not effective at all? I don't know about that. And how the hell do you know about that? Now, I speak very directly, very directly. And I'm going to read you an email that I got just then. I just received that inspired me to make this video. Hi, Joey. I gave up being vegetarian at the age of 24, 10 years after I've decided to give up meat. The last two years of that decade, I was vegan. However, I went traveling and found it impossible to find vegan food in some countries. I gave it up. And since then, I've had nothing but health issues since she gave up veganism. I've been toying with the idea of veganism, toying with the idea of veganism for a while now. I wanted to let you know, I'm sure you get this a lot, that your conversation with Nick Ferrari on LBC radio convinced me it was the right thing to do. So she went vegan. She stopped the radio interview with Nick Ferrari convinced her. Now, not because I hadn't heard these arguments before. I'd seen the films, read the statistics, knew the facts. It doesn't seem to penetrate a meat-eating brain. Eventually, you forget the harrowing and revolting images of the sentient beings in agony. It's human nature to justify one's actions. However, listening to Nick Ferrari say they're just pigs in response to your passionate argument made me feel actually disgusted. Gives me pleasure to abuse the innocent? Pleasure to abuse? They are being abused. What did they ever do to you? It's a pig. It's a pig? I was disgusted to my core. They aren't just pigs. I know that. It gave me something to consider badly. I will try my hardest to make this work this time around. I can't stand the idea that I'm complicit in the murder of sweet animals. Wow. One more person has changed their mind. I got probably over 150 comments saying, Joey, you're too aggressive. Joey, you're too aggressive. Maybe I was. I was so passionate at this stage. You have no idea what I went through that three weeks.  I've wasted an opportunity on this radio show. Now, I get emails all the time from TV shows, radio shows. After this radio show, the day after, a very big TV program in the UK wanted me to come on. They're like, when are you coming back to the UK? We want you on for another debate. They want me on for debates, okay? Because I give them fiery, passion-filled debates that are big talking points. LBC radio listeners loved this. They loved it. I'll show you the screenshot. They loved this debate.  I've had over 20. I don't even know. Over 20 big radio and TV debates last year alone. So you're playing word games. Let's talk about the app. Here's. Let him go. Let him go. I want to see you on. You'd be angry, too, if our dogs in the back of that truck. I'm going to tell you how many people just listen to that interview. Seven and a half million. I guarantee you next year, I'll have the same amount of opportunities. I create these opportunities. Now, in terms of my conduct, sometimes, you know, yeah, I agree. Could have been a little bit more, you know, chill. But what we're talking about here is animals being murdered. So sometimes it's an emotional issue. In terms of it being not effective, never effective. Look, I'll give you the best example of an activist you would deem. If my conduct in there was aggressive, you would deem this activist aggressive, too. Gary Urofsky. Gary Urofsky. Now, this individual is responsible for more conversions than nearly anyone else on Earth. A conservative estimate would be from between 100,000 to a million.  He uses all these words. He went to Israel, the victims of the actual holocaust and preached the animal holocaust. Don't you think that you may owe an apology for this comparison to the Israeli people? Absolutely not. The only apology that needs to take place is all human beings who treat animals like nothing. There's very controversial. He's on TV, very, very passionate. No holds barred with Gary Urofsky. Israel is one of the most vegan countries on Earth. Gary Urofsky actually assaulted a reporter over there. We're talking to us after coming back from police. Tell us what happened exactly. What happened was I got into a confrontation with some news reporter.    Okay, now his conduct over there, you would deem like maybe a little bit aggressive. Yeah, 100% it was. Did that hold the vegan movement back in Israel? Did it hold it back? No, it didn't hold it back. The message cuts through, and it means more than your conduct. If your message is true and it's strong, let me give you an example. If we're debating child abuse, I'm defending children, okay?   My daughter was abused by a child abuser, and I start getting aggressive. Maybe I throw in even an insult, which I never did in that interview. I don't throw insults. Nick Ferrari actually insulted me. He started to mock my voice. Protests such as this actually set your cause backwards. How do you know? Where's your data? Where's your data? I don't have any data.  No. No, not people with that I switched on. I'll give you an example of DXC actions not holding back the vegan movement because people are saying, you know, these DXC actions, even though I don't participate in them, sometimes I'm like, oh, that's a bit cringey myself and I'm a vegan activist. And that's me just being honest. Okay. Me just being honest. Okay, let me give you an example of some of the most quote unquote extreme. I don't think hacktivism is extreme compared to what happens to animals, but quote unquote extreme direct action on earth happens in Israel, the most vegan country on earth. Wow. Tal Gabola. Okay, you could consider her an aggressive activist as well. One big brother. She won the big brother show over there. A very famous vegan activist over there. Okay. A more aggressive conduct than me usually. Definitely. That's a very solid statement. Think of the actions that they were doing over there. ALF Israel, they were getting like baby, baby bobby calves that had died on a dairy farm. They were taking them out into the streets and doing like street theater where they would slaughter the bobby calf in public. They do very intense forms of direct action constantly over there. Now, there's also other activists working in the background. We've got vegan friendly doing their friendly um, outreach style activism. But all I'm trying to say is that the most aggressive the most extreme forms of direct action you could possibly find are in Israel and Gary Rofsky's two tours over there and his conduct where he assaulted a reporter stormed out, preached the animal holocaust in the land of the holocaust. Okay. And you were telling me that it held the vegan movement back over there? No, it didn't. There's more vegans in Israel per capita than anywhere else on earth. So don't tell me that my conduct in that interview is going to hold the vegan movement back. Nothing is going to hold the vegan movement back. Nothing is going to hold the vegan movement back. We have a very strong reality that we can show to people. You are paying for animals to be stabbed to death in a slaughterhouse and you claim to be against animal cruelty. Very strong reality. Very strong truth we have there. We have a lot of people who don't do activism themselves but they know all the answers. My form of activism would be better. You got to conduct yourself like this, Joey.  God, we all have all the answers, don't we? I think you should spend less time criticizing the work of other activists more time creating your own platform where you can spread this message in your own way. Now, I do my peaceful, socratic method most of the time. Sometimes people like this antagonistic speciesist can work me up, especially when I've been out the front of slaughterhouses for the last three weeks. You haven't seen what I've been doing the last three weeks. You don't know. Yeah, I know that I'm in the forefront of the vegan movement. I have to be careful of my conduct. But you know what? Sometimes things just happen. Things just happen. I get passionate. I get passionate. This means more to me than anything else in my life. I'll give my life for this cause. I guarantee you that my conduct in that interview did nothing to hold back the vegan movement. I guarantee you that those direct action everywhere actions are not holding back the vegan movement. There's many different types of vegan activists, health, environment activists, very peaceful advocates that are all working together. Yeah, it makes people cringe and it creates a little bit of a, you know, negative press. But as a result of that negative press comes discussion about animal rights. It creates discussion. It brings veganism into the headlines. Now, you do not know. You do not have the data or the data, however you want to say it. That says these actions hold back the vegan movement. I've got evidence in Israel more extreme direct action than anywhere else on Earth. Okay? And it didn't hold and it doesn't hold the vegan movement back there. Interviews like this are learning curve for me for sure. I've done plenty of them. I've done plenty of them. Yeah, sometimes I let my emotion get the better of me. But for the most part I keep cool, rational, calm and I'm passionate. People feel that passion. Always speak the truth with conviction for the animals. Never, ever withhold the truth of what's happening to them. Speak for them like you would want to be spoken for if it were you in their position. That is the advice of one of my mentors, Gary Arofsky and I'll always stick to that. Okay? Doesn't matter how you act compared to the truth of your message. Okay? The truth of the message cuts through and overrides and outweighs your conduct. Although having a better conduct and a rational, calm response type conversation with someone is a lot better. Yeah, I'm going to agree with that. I'm going to agree with that. But to say that my conduct in that interview is a missed opportunity. No, it's not. No, it's not. I took that opportunity instead of sitting at home and going hmm, maybe I won't. Maybe I won't I'm a bit tired. Maybe I should just sit this one out. No. No, I'm not sitting out opportunities like that. And I had a really good opportunity to show how insensitive this individual is by saying they're just pigs. They're just pigs. And as a result of that interview, someone's emailed me and said, you know what? I really realized that I should be vegan. That's what I got to say about that. I mean, everyone's got all the best advice. But you know, put it into action. Show us. Show us. Put it into action. I give my life for this movement every single day. You should be doing the same. If you've got a better way, do it. Show me how it's done. I want you to get online. I want you to do it. I want you to put yourself in the most uncomfortable situations where you're getting criticized constantly by the vegan movement, by meat eaters, by getting threats, constantly getting teased, mopped. Put yourself in those positions every single day for the animals. Okay. And then tell me how much better your activism and how much more effective your activism has been for the movement. Okay. Until then, have a little bit of perspective. Think about it from both angles here. All right. And you don't have all the answers when it comes to what's the most effective. Thank you all for watching. I'll see you all in the next video. Got a bit passionate there because it is true. It's a passionate topic.  Don't worry about that. Just keep doing your own. Keep doing your peaceful advocacy. That's your style. If you want to do something that resonates with your authenticity. Okay. Do that as well. All right. Thanks to all the activists who do their activism in many different ways. We need all different ways working together for the movement. Direct action. We need the peaceful advocates. We need the plant-based health arena too. Never forget the animals. Veganism is a moral principle. But all of us working together can help propel this movement forward. Less, you know, less of the negative stuff. You know, yeah, we have to uphold each other to a higher standard. But you know what? We're all just trying our best. We're all trying our best. Keep trying. Keep fighting. And together, we can make this happen. For real. After talking to 60,000 people, I've realized and learned that people are ready to listen to the message or they're not. No matter how you act, I can be as sweet as Gandhi or as radical as early Malcolm X. And it will not change one person's mind about the issue of veganism and animal rights. You support the very thing we're against. So, how could you be in favor of our cause?  I don't agree with it.


Hi everyone. Asalaamu alaikum. My name is Maury Turner. I am the representative for Oklahoma's 88th House District, and my pronouns are they and sometimes she. I think it's important to note that I am not a woman, but the good people of SOCAP have asked me to share a little bit about my journey with politics, and I think this is a wonderful space to be able to do that. The abridged version of why I got into politics and why now is that quite honestly my community was asking me to. I had the ground running, doing community organizing here in Oklahoma, and it was focused on the holistic kind of justice reform that we need, right? And it's not reform so much as reimagining it and rebuilding it. And so when I did that, I wanted people who looks like our communities to be able to represent us. And I saw that there was a lack of that at the Capitol. And so I started looking for people who had experienced the worst parts of the system, right? People that looks like me, people that had to navigate food stamps or housing insecurity. And there are so many hurdles outside of just the stipulations for being able to run for office that prevent people from running, right? It's not politically connected. If you don't come from money, it's really hard. And so the folks of House District 88 started to ask me when they could expect me to run for office, and I was at a place where financially I was just able to get a little financially stable. And quite honestly, if we didn't have those stimulus checks, then I probably wouldn't have been able to make it through. But the important thing about running for office was also that visibility, right? That is the underlying thing is that when we have experienced parts of the system, we are able to see things, we are able to navigate, we are able to reimagine and rebuild a system. And I think that's really important to note, especially when we're talking about how we are continuously creating new power structures for people to be able to show up fully as themselves, which is something that I think women, specifically women of color and specifically women of color, who are also a part of the LGBTQ plus community are really good at is creating a space where people can fully show up as themselves. And that is how we continuously create a new power structure, right? Continuously reimagine and rebuild a world that has a vision for everybody to be able to show up fully as themselves. I think one of the ways that we continuously empower women, right? And because this is specifically women's history month, I think it's important to note that a lot of the times I think on average a woman has to be asked at least seven times to run for office before they start to take themselves as seriously as their community is taking them, right? And that's because of I think electability politics. Sometimes people say, it's a great, she's a great candidate, right? But I don't think she's going to win. So I'm not going to work for her. I'm not going to make the phone calls. I'm not going to knock the doors. I'm not going to vote for her, right? And we have to unlearn that thought process all together. So in continuously educating and continuously empowering women, we have to unlearn some of the most difficult parts about the patriarchy that is ingrained in us, right? And I think that's so important as we are fostering a new generation that is politically inclined in a way that is so remarkable. In all this work, it gets really heavy, right? And so we also have to make sure that we are practicing self care in a real deep meaningful way. And for a lot of people, it looks very different, right? So for me personally, how I find joy, I've just started riding my bike again. I've just started painting again. And it's so cathartic and I love it. A little known fact about me is that every painting in my house is an original minus one. And that was a gift that someone gave to me. But I think it's so important to make sure that you're finding joy in the everyday life, right? And in resting, right? Because this work gets very, very heavy. And so we can't show up to do it if we aren't taking care of ourselves, right? And in last words, I think it's really, really important to note that we have to keep going. Rest is really beneficial, right? But understanding that our liberation is tied to one another, right? Whether we are women, we are non-binary folks, whether we are inside or outside of the binary, it's important to note that our liberation is tied together. We don't get to pick and choose who crosses that finish line with us. So I hope that you will join me on this work and I'm so excited for every place that we're going together. Okay. Bye-bye.


Item number SCP-100 Object Class Euclid Special Containment Procedures SCP-100 is to have six guards patrolling the interior of the perimeter's fencing and two guards dedicated to the monitoring of the interior and exterior of both warehouses and the residential building, with rotations to occur every three hours. Any unauthorized personnel found within SCP-100 are to be detained for questioning prior to amnestic administration and release. Three guards are to remain within the storefront of SCP-100, with rotations to occur every eight hours. The storefront front entrance is to remain locked at all times, with keys provided to necessary personnel. Private property and no trespassing signs are to be posted on the front of the storefront to deter any drivers from stopping at SCP-100. Any constructs SCP-101 creates are to be removed from SCP-100 and melted down into slag, with the exception of SCP-102A and SCP-102B. Should SCP-101 become uncooperative, SCP-102A and SCP-102B may be removed from SCP-100 until the time that SCP-101 becomes cooperative again. The largest of the two warehouses within SCP-100 has been converted into a basic research facility. All objects created by SCP-101, excluding SCP-102A and SCP-102B, may be used for research purposes. Testing on SCP-101 itself may only be conducted with written permission from the Acting Head Researcher. Description SCP-100 is an abandoned scrapyard, 80 kilometers from South Carolina, known as Jamaican Joe's Junkyard Jubilee. The scrapyard covers roughly 5,000 square meters of fenced-off land, consisting of two warehouses, a storefront, and a small residential building, as well as neglected land and land used for storage. SCP-100 holds roughly 1,500 vehicles, both pressed and un-pressed, as well as roughly 1,400 kilograms of separate scrap, estimated to be worth $5,000, or 3,870 euros. SCP-100's anomalous effect manifests through SCP-101 in its constructs, including SCP-102A and SCP-102B. Autonomy is lost when SCP-101 or one of its objects cross the fenced perimeter of SCP-100, remaining in this state until reintroduction. SCP-101 is an autonomous, sapient, humanoid construct, consisting mostly of copper piping, uninsulated copper wiring, and aluminum cans. SCP-101 lacks the ability for written or verbal communication. However, it possesses the ability to communicate using rudimentary sign language. SCP-101 is largely uninterested in conversation outside of sales, and information gathered from it has been limited. SCP-101 appears to possess skill and craftsmanship, demonstrating the ability to operate tools such as arc welders, drills, and power saws, as well as heavy machinery such as car compressors and forklifts. SCP-101 possesses the ability to create autonomous constructs similar to itself, using material available within SCP-100. SCP-101 tends to create four specific animals, iguanas, crocodiles, turtles, and flamingos. However, SCP-101 has been known to craft other species, such as domestic pets. To maintain compliance, SCP-101 has been allowed to keep two objects, labeled SCP-102A and SCP-102B. SCP-102A and SCP-102B are constructs superficially resembling insects, assumed to be created by SCP-100, as they have occupied SCP-100 since the initial discovery of SCP-100. The names Ramon and Beatrice are welded into the backs of SCP-102A and SCP-102B, respectively. They appear to operate as both companions as well as guards for SCP-100, as they patrol the perimeter of SCP-100 except during intervals of interaction with SCP-101. SCP-101 appears to follow a ritualistic schedule, repeating the same actions daily. From 0800 to 1500 hours, SCP-101 enters the storefront of SCP-100, seating itself behind a counter and attempting to bargain with any humans within the storefront. Occasionally, SCP-101 will return to the yard prematurely for reasons unknown. From 1500 to 1600 hours, SCP-101 interacts with SCP-102A and SCP-102B, communicating using vague hand and arm gestures. Interaction tends to consist of grooming, repair, and activities resembling fetch and hide-and-seek. From 1600 to 2100 hours, SCP-101 performs various tasks, including taking stock of material within SCP-100, cleaning and maintaining tools and heavy machinery, and cleaning the interiors and exteriors of buildings present within SCP-100. From 2100 hours to 0100 hours, SCP-101 performs what is assumed to be leisurely acts, ranging from creating new constructs, interacting with SCP-102A and SCP-102B, and patrolling SCP-100. From 0800 to 0800, SCP-101 enters the residential building, where it remains seated at a desk for the duration of this time. In the event that a human enters the storefront of SCP-100 during the interval of time SCP-101 is seated behind the counter, SCP-101 will attempt to bargain with them, using a variety of gestures to convey meaning. Most attempts by SCP-101 are to sell scrap, figures of its own creation, or repair services. However, it has been known to purchase scrap. Despite SCP-101's inability to read, it possesses the ability to perform basic mathematics, as demonstrated by sales. Sales made by SCP-101 are typically met with some degree of unfairness. SCP-101 has been known to intentionally use faulty scales and contaminate scrap piles with cheaper metals, and has demonstrated knowledge of the area of effect within SCP-100, as SCP-101 has sold constructs repeatedly, despite the loss of autonomy when exiting SCP-100. Efforts to confront SCP-101 about this have been met with both distress and indifference, with referral to a side post on the wall reading, No refunds, man, happening regardless of SCP-101's emotional response. SCP-101 was discovered on 1109-76, following reports of strange machines operating from within the scrapyard. These rumors were discredited as urban legends, and a Foundation agent was sent to SCP-100 to act as the landowner until containment was performed under the guise of property sale. A wooden privacy fence was built along the former perimeter of SCP-100. One-way windows were installed in the storefront, and a highway now running through the nearby town of... redirects the majority of civilian traffic. Addendum 100A Records show the property is owned by one Joseph DeVall, with the mailing address sharing the same name. Local utility companies report billing had stopped approximately three months before the discovery of SCP-100, which was found abandoned, save for SCP-101, SCP-102A, SCP-102B, and several avian and canine figures, presumed to be made by SCP-101. The initial sweep of the buildings revealed the residential building to be mostly bare, with the only sign of former occupants being a note found taped to the door of the storefront. Incident 100A On 060305, SCP-101 created a humanoid, autonomous construct, 10 cm in height, the first time SCP-101 has done so. Significant effort was put into this construct compared to others, with greater detail applied to the construct, including facial features, and JJ welded into the back of the construct, in stainless steel making up the majority of the construct. SCP-101 placed the construct on the counter of the storefront for the duration of the scheduled interval, both using vague gestures to seemingly communicate with one another. Following the confiscation of this construct, SCP-101 remained seated within the residential building of SCP-100 for a total of 10 days. Document 100A The following is a copy of the note recovered upon discovery of SCP-100. Out to lunch. Please see Assistant. JJ Lesson complete. If you missed the previous orientation, go watch SCP-099, the portrait, right now. Or for the complete course, watch this playlist.


Today, we're planning a pre-boarding time, we're writing all important information, like location of a ship, members of the team. It's important because if you go out to sea, somebody might get injured. Usually it's the boarding team leader who does all the planning. And we sometimes assist him in planning. We're a team, so we think like a team. We have to brainwash everything and we put it to a plan and make a perfect plan.


Hi, Foxes! Hello, everybody! E here. Welcome back to another book tag video. I know I went forever without doing one, and then this is the second one in a week, so don't mind me. We just gonna jump right into it. Many thanks to Richard Reads. I will link to his channel down there in the doobly-doo. Today's tag is the mid-year book freak-out book tag stuff. So I probably got that all wrong. Mid-year freak-out book tag, something like that. Book freak-out tag, whatever. Number one is a best book you've read so far in 2019. This is a tie. I don't know if one of them is gonna fall off or not, but right now it is a tie between Recursion and Westlake Soul. Recursion is by Blake Crouch. Westlake Soul is by Rio Yewers. I'm not sure. I apologize. I love both of them equally right now, but I don't know if one of them is gonna fall off or not. If anything, Recursion might fall off, so we might just go ahead and go with Westlake Soul there. The more I think about it, the more I'm leaning towards Westlake Soul. The only reason why I'm throwing Recursion on this list is because Westlake Soul is on this list again later on. And I don't like repeating myself. So number two, best sequel you've read so far in 2019. This is a cheat because I've only read one sequel that I know of. So that's gonna be Black House, but I absolutely loved it. So of course it would probably be on the list anyways. And no, this is not the last time you're gonna hear Stephen King's name in this video. My apologies. And maybe that's some repetition like I said I wasn't gonna do, but it's whatever. It is what it is. So number three. A new release you haven't read yet, but want to, Wanderers by Chuck Wendig. I am not a Chuck Wendig fan. I dig the guy. I follow him on Twitter. He's a lot of fun. I don't like his writing. You can yell at me down there in the doobly-doo. But I checked out Wanderers and I got an electronic advanced readers copy. And I got past the first chapter and I was like, this is like nothing else he's ever written before.  It felt like an actual novel and I am there for that. But I stopped reading it just probably about 10, 15 pages into it because I want to read the actual book.  If you want to do a buddy read with me, let me know. It comes out July 2nd and I plan on reading it as soon as it comes out. Okay, so number four, we have most anticipated release for the second half of the year. The Institute by Stephen King, duh, if you're a fan of the channel, you know I am a massive Stephen King fanboy. I am hoping it is good and not another elevation. We can hope. We can have big dreams, okay? We can do that. Biggest disappointment was the talisman because I remembered liking it more than I liked it this time. I re-read it, but it was just a horrible, horrible slog to get through and I thought I was going to enjoy it this time because usually when some Stephen King books are just okay for me, on a second re-read they get better because I catch more and whatnot and it's still great as far as the Thursday Thursday stuff is concerned. Me finding all the connections and everything, but I just didn't like that book at all. Also did elevation come out this year? I like blocked it from my memory. If it did come out, that one is my biggest disappointment. But if it didn't, if it came out last year, I kind of think it came out this year. It's terrible. I literally blocked that book out of my mind. I hope I don't forget that it was terrible and end up trying to re-read it anytime soon. Oh lord Jesus. Okay, so the biggest surprise was Aether Christ by Kirk Jones.  If I may also add, it's not really a surprise because I knew he was good, but Chad Lutsky has been killing it this year. Everything I've read by him has been fantastic and he's a new to me author kind of deal. He's also become a bit of a friend of mine. So yeah, Chad Lutsky is on there, but definitely Aether Christ. That just came out of nowhere. I bought it. It was a cover buy. Usually when I buy things based on the cover, I'm disappointed because nothing lives up to a great cover usually except for maybe like regulators by Stephen King or Richard Bachman. But yeah, Aether Christ by Kirk Jones. If you haven't read it, check out my review. It's on the channel. Just search Aether Christ, Edward Lorne and it'll come up or just go read my review on Goodreads. Terrific book. Big surprise. Let's see here. Favorite new author. Debut or new to you. Christopher Buhlman of Those Across the River. I went out, actually it's around here somewhere, but I got those across the river. Reddit loved it and I went out and bought another one of his novels. I should be getting that one pretty soon. I'm going to try and get it in before the end of summer and it's called Necromancer's House. I'll be in this month's book haul video. You'll see that. Let's see here. Newest fictional crush is Westlake Soul. I remember falling in love with that dude while I was reading that book and that's just, I mean, my heart was all for him. I just wanted to give him a hug.  You know, it's also okay if you leave, man. I fell in love with that dude reading that book. It was just fantastic for me. And again, Wayne Fenlon, thank you so much for sending me the book and introducing me to Rio, yours, Yours, whatever his name is. Rio's, right, Rio. Rio's work. Sorry, but thank you so much for sending me that book and introducing me to that author is a fabulous character, fabulous book. Once again, number nine is newest favorite character. Again, I'm going to put Westlake Soul on there. Yeah, I know I said I wasn't going to repeat myself, but here I am repeating myself. So, Westlake Soul, again, he's my newest crush, favorite book of the year so far, and my newest favorite character. Let's see here. A book that made you cry was Lot by Brian Washington. It's probably the only one this year. There's a lot of books last year that made me cry, but this year definitely Lot. There was a lot of very passionate, heartbreaking stories in there. A lot of very near and dear subjects, subjects that are near and dear to my heart. A lot of stuff in that book that really hit home, and the writing was beautiful, fantastic, just an all-around terrific book. If you haven't read Lot by Brian Washington, I suggest you go out and grab it. Next up, a book that made you happy, Michelle Obama's Becoming. This is one of those, and I actually got some comments on my Top 5 Hopeful and Top 5 Hopeless video. Why isn't Becoming on there? And I actually, I explained at the beginning of the video that I didn't feel like non-fiction should be on there. I don't know why, but I didn't feel that that was right because I wanted to keep it novels, keep it fictional. But, yeah, probably the only book that really made me happy, happy this year was Becoming, and I specifically went and looked for that book for that reason because I wanted to be uplifted and it was that time of my life that I needed something positive and that book fit the bill. So, next up, sorry, my nose is killing me all. I snorted too much meth before. I'm kidding. I'm kidding. Susan Burgess, calm down. It's just a joke. So, at number 12, a most beautiful book you bought so far this year or received, Kari Mora by Thomas Harris is an absolutely gorgeous book. I don't know if I have it around. Yes, I do. I'm actually going to show this one off because it fits, I mean, it's the most beautiful book. All this gold that you see on here, it's all raised and whatnot. It is so nice. It is a beautiful book and I don't care if it's bad. I don't care if y'all hated it. I don't care. It's just actually gorgeous. But then you open it up. Oh my God. Oh my God. No, Elder Duckie. Elder Duckie. This is Elder Duckie, by the way. He's sitting back here. I got names for all of my stuffed animals. No, Gregor Zane. We about to have a catastrophe over here so I'm going to stop messing with that stuff because we got one more left. Oh, unlucky number 13. Okay, number 13. What books do you need to read by the end of the year? I just realized that this says books and not book. So I'm going to throw Kari Mora on there. It actually wasn't one of my picks. I actually, what I had on here was the goldfinch because it's really cool. So I'm going to throw Kari Mora on there. It actually wasn't one of my picks. I actually what I had on here was the goldfinch because it's probably going to take me about a month or two to read this book. I'm loving it. It's fantastic, by the way. Pierce, if you're reading it, man, I'm on page, as of recording this, I'm on page 180 something. 181 maybe. I know I'm reading it with him. I'm reading it with my buddy Richard Gerlach and my buddy Scott Kemper. And I'm loving it. The writing's fantastic. That one done. I need to get Kari Mora done. I also need, there's a couple of books I have for review that I got to get through. Especially one by Brian Detzner and then another one by T.F. Allen. Several different books I need to get through. But the ones that I'm looking forward to the most are probably the goldfinch and Kari Mora. And of course, Stephen King's The Institute. We got so many books coming out. Wanderers got to read that one too. So many great books. Mora's tagging people. I'm not sure who all's done this one. So I'm just going to go ahead and throw this stuff out there because they tagged me recently. So Jason's Weird Reads I'm tagging you Mr. Beardy Man. I'm tagging Regina from Regina's Haunted Library. I'm tagging you. I'm tagging JB Taylor I'm tagging you son. I'm tagging Erica. Sorry, no, Ryan. Ryan I'm tagging one more person. I know Steph already did this. So Cammie's Corner. I'm going to tag those five people. So if any of you guys want to do it go ahead and do it. If not, if you don't feel obligated it's all in good fun. But if you do decide to do it then definitely give me a shout on Twitter or in the comments section. Let me know when your video is up. I'd love to go watch it. But until next time, I have an E. You have an U. This has been the book tag video. I'll talk to you guys later. Bye-bye!


Oče, zato sem izgleda, da je vsak zelo izgleda, tako če malo kursi, spaski, 3 zelo, kaj pošliš, kaj se vse prejšel, hodnje, vzelo in vse bizan, taj je odpusten, kaj je zelo odpusten, taj naprav je odpusten vzelo v 3 zelo za vsi, težko vse zelo se kaj je 3 zelo, in we have to imagine that they move around in space, as time goes on. So, the way they move, they should remember the geometry of the underlying curve, which was giving birth to them. So, now the question is, somehow have we finished the study, I mean we have introduced two functions and three vectors, tangent normal and binormal, and two functions, curvature and torsion. Is that anything else we should discover about the geometry of curves? Well, the way to say no, actually, that's it, that's the end of the story, is to prove that if you give me two functions, k that I would like to call k and tau, there is a unique curve having k and tau as curvature and torsion. If I prove this, that means these two functions, it's all there is. There is nothing else to be discovered. This is the topic of this lecture. How do we prove it? Remember, we always start with a differentiable curve and we always assume it's parametrized by arc length because if it's not, we can always do it. This is not an assumption. The only assumption really we make is this is a curve which has positive curvature everywhere at every time, so it's a regular curve. And now there is a little trick because we have learned how to associate to each time, and actually time, since it's the arc length, I will call it s. So to each parameter, I know how to associate three vectors, this famous orthonormal basis, the Frene 3a. And instead of look, so I have three vectors in R3. So just as a convention, I look at as a map from the same interval, so to each time s, I associate a vector, a column vector, t of s, n of s, b of s. So I put the components of the three vectors in column, so we get 3 plus 3 plus 3, so this is a point in R9, 3, 3, 3. And a nice way to write down the Frene formula in this matrix form is to say that the Frene formula say like t prime, n prime, b prime as a vector is equal to what? 2 k n minus k t minus tau b and tau n. So this is component by component, I just put the three equations in vector form, but I want to write it as a matrix representation in this form. So let me write it and then I comment the notation. So this big matrix 9 by 9 times the column vector t, n, b. So what does it mean, this notation? This notation means what I call 0, 3, or o, 3 if you want, it doesn't matter. This is the 3 by 3 matrix whose all components are 0. So 0, 0, 0, 0, 0, 0, 0, 0, 0. So this is a block representation. So if I want to write a 9 by 9 matrix, I can tell you 3 by 3, 3 by 3, 3 by 3, 3 by 3, and so on. And what is ID3? Well, this is just the identity matrix of rank 3. So 1, 0, 0, 0, 1, 0, 0, 0, 1. Now, in this form, this is just a notation. There is nothing new. You see, if I do the row by column multiplication, you see that here I get 0 times t. So 0 plus kn plus 0, so I get kn, which is exactly what appears here, and so on. So it's just a convenient way. We are not learning anything. But it will become very useful. So now let me state what is called the fundamental theorem of the local theory of curves. Long name. So this is the theorem, which answers the problem I was mentioning a few minutes ago. So give me two functions. So given two functions, k0 and tau0, from some interval to r, is a real value functions. The only requirement that these are smooth, because in general they will have to be smooth, and the only requirement is that k, what at the end should be the curvature, has to be a positive function. So given such two functions, there exists a curve from the same interval into space, r3, parameterized with arc length, such that k of s is equal k0 of s. So its curvature is equal to the first given function, and its torsion, and tau of s is equal tau0 of s. So this answers the first part of the problem. So give me any two functions, such that the first one is positive, such that these two functions are curvature and torsion. But I want to know more how many curves are there with this property. Moreover, so that's the second answer that this theorem is giving us, alpha is unique, and as we commented last time, unique, what is the best uniqueness theorem you can hope, up to rigid motions of r3, up to direct isometries. Remember, we just commented quickly over r3. Isometries are all two types. Basically, they are translations plus an orthogonal transformation. The orthogonal transformation could have determinant 1 or minus 1. If it's positive, so plus 1, we call it direct. So, well, that's the best you can hope. This is telling us that the problem is solvable and it's solvable in the unique way, which is meaningful. OK, let's prove it. Unfortunately, the blackboard is quite small, so this notation is useful, but let me start here, and then we have to erase proof. Let's look at the following ordinary differential equation. Look at the following. So, x prime of s is equal a0 of sx of s. Let me call this equation star, where a0 of s is formally the matrix that I constructed here. You see, this 9 by 9 matrix, but where I use, of course, my starting data are these two functions k0 and tau0. I still don't have a k and tau. OK, so formally I just define it to be 0,3 k0 of s. I write of s only here, then I drop it, because these are functions, 3 or 3 minus k0 identity or 3 minus tau0, or 3 or 3 tau0 identity or 3. OK, so I use these two functions to construct this matrix, and now what do I do? So, of course, x will be a vector in R9, because this is an equation in R9. OK, choose. Now we have to make some choice, and then at the end we will comment the effect of this choice on the final output, but choose some fixed vector a in R9. You see, if you want to solve an ordinary differential equation, you have to restore the equation, so how we have to give an initial data, and this will be the thing. And, sorry, choose a vector in R9, but of course we are interested, so such that we have to split it in the first three components, the second three components, and the third three components. These are the geometrically interesting bits, so such that if I call t0, as a vector, the first three components, a1, a2, a3, and not a4, a5, a6, and b0, b equal a7, a8, a9, OK, sorry, of course, you're right, OK. So the requirement I make on the initial data, a, is that if I take the first, I split into three vectors, t and b, formally, they are still not a frenetriadron of anything, but t and b, I would like them to form a positively oriented, so such that these three vectors form an oriented orthonormal basis of R3. That's a very natural thing to ask because at the end I would like this to be true at every time. So this is kind, I want to start from a configuration which looks like an orthonormal basis. Then I want to evolve following this differential equation, and I want to prove that it stays an orthonormal basis. OK. So now, formally, how do we do, how do we do, set f to be a function from i to R9 solution of star? OK. Solution exists because this is a linear ordinary differential equation. OK. But then if we take a solution in R9, again we split it in the first three components, second three components and third three components. OK. We define t, sorry, t, which now is a function, a vector valued function. OK. To be f1, f2, f3, n will be f4, f5, f6, and b will be f7, f9. OK. And now these are functions of s. Sorry, of course I didn't write it, but it goes without saying. So set f to be a solution of star with initial data a. OK. The unique solution with initial data a. OK. So what do we want to prove? We want to prove, first, that actually these three vectors are presented orthonormal basis for any s. OK. We know it for s equal to zero. We know it at the beginning. And we want to know that this property is preserved. So we want to prove that if I put now t and b as three distinct vectors, this is and orthonormal positive orthonormal basis of r3 for any s. So this is the point. How do we do it? Simple trick. Look at this matrix here. M of s. How do I know if something forms an orthonormal basis? I can consider the matrix of all possible scalar products. So I take the 3 by 3 matrix given by tn, tb and so on. tn, it will be symmetric, of course, nn, nb and then tb, nb, bb. So let's look at this matrix here. Another way to say to state our claim is that this matrix is constantly equal to the identity. So the point is that this matrix automatically satisfies a nice differential equation because x was satisfying star. It's a simple computation to prove the following. If I take twice the derivative I get exactly this. A of s M of s minus M of s A of s where now this is a 3 by 3 matrix. This is a 3 by 3, 3 by 3 and A will be a 3 by 3 matrix. A of s is the matrix constructed. Formally, you see, this form here but instead of imagining this of b 3 by 3 blocks I just put them a number. So 0, 1, 0, so this is just a matrix. 0, k0, 0, minus k0, 0, k0, tau 0, 0. Of course, of s. The function. k Now this is very simple. I'm not cheating you. In three lines you prove that star implies this equation here. And the fact that we started from an initial data with the property that if I split it I get an orthonormal basis I also know that M of 0 you see, at time 0 matrix is the identity because of the property of t0 and not b0. But now again this equation here has a unique solution given an initial datum. So the only thing I need to observe is that M of s constantly equal to the identity is actually a solution. Put M equal to the identity of course the derivative of the identity is 0 because it's all made of constants. So you get 0 is equal a minus a, 0. So it's a solution. But the system has a unique solution given the initial datum and this satisfies the initial datum of course. So this must be the solution. But that's exactly the claim. That's exactly the claim. This matrix here is constantly the identity but that means that this is constantly equal to 1 this is constantly equal to 0 this is constantly equal to 0 and so on. So exactly the claim. This is an orthonormal basis. There is actually a little comment to be made here. It was a positive basis at time 0. It stays orthonormal for every time and that should be a positive orthonormal for every time. Please speak much louder because of properties of the determinant. What does it mean positive? It means that if I write the matrix transformation which takes one basis to the other for two different times positive means it has determinant 1. But now how is it possible? Suppose that for some s this has become negative. This is positive or negative because it's a basis. But by continuity of the determinant it means in between there has to be a time where it was 0. The transformation between the two basis had to have determinant 0. But this is impossible because it has to be an isomorphin for every time. So if it starts positive it stays positive for all time. So also this property is easily checked. Ok. Up to now what have we done? Given two functions k0 and tau0 we have constructed the only and now we will comment why it's the only frene basis t and b which a curve, a possible curve could have if it had curvature k0 but So now the problem is where is the curve? So now we have t and b how do I construct alpha? But that's not the problem. Now define alpha alpha from the same interval to r3 to be what? Alpha over s if I know the tangent vector it's enough to know t because if I know t alpha of s will be just the integral between s0 and s of t of u in the u. What is t? T is the first derivative vector. So if I integrate I get alpha. There is only one alpha who could have t as a tangent vector. So the first part of the theorem is proved. Because now we got alpha. What is the tree addron associated to alpha? By construction t so what is the tangent vector to this alpha is precisely this t by construction. What is the normal vector to this alpha? Well it's the derivative of t times k but this is exactly the derivative of t has been constructed in a way that it is exactly n k normal of alpha again I take the derivative of the normal and so on. So it's all constructed in the way that the tree addron of this is exactly t and b and the curvature and the torsion of alpha are exactly k0 and tau0. There is nothing to be proved. So one comment about uniqueness because we said this curve now we have a curve with the desired properties in which sense it is unique. Well I had one degree of freedom here because nobody has told me where to start to integrate passing from the tangent vector to the curve itself. What is the effect of changing this base point? It's just a translation in our tree. It means I'm just starting the curve from another point translation. And then what else?  So let's go back to see if I had picked another vector a of course the properties I wanted so another vector if you want a prime whose first three components second three components third components formed basis. And then repeat the argument. Of course f would be different because it's a different initial data. But then m would be m is always the identity so f will be different and the three vectors t and b will be different because are the three components again splitting of this function. But how do this change? Well, if a and a prime they have this property they are related by an orthogonal transformation of r3 and then pick this orthogonal positive with determinant 1 pick this orthogonal transformation of r3 and that means that t if you want you have t and b and t prime and prime v prime everything is related by this transformation. The final output is related by the same transformation because t and t prime are related by an orthogonal transformation so also alpha and alpha prime would be related by an orthogonal transformation. So there is really nothing to write except identifying the places where you are making choices and see that the output is translation plus orthogonal transformation of r3 of positive determinant. Ok, so that sends the proof of the theorem. Well as of course the name of the theorem says that's really the end of the story for curves in r3. It means we have discovered everything that was to be discovered so a curve is completely determined by curvature and torsion and so that's it. So besides making some nice exercises there is this is really the end of the first part of the course. This kind of differential geometry in dimension one it's over. But I would like to use this last part of this lecture to tell you about a classical problem in the theory of curves and how it's inspired so much research that I think you should be aware of it. So the problem I would like to describe you in the solution is about planar curve. Simple closed planar curves. What does that mean? Well clearly it means we have a function our curve now goes in r2 automatically because it's planar. What does it mean it's closed? Well suppose we give names to this interval so suppose that this interval is given by some a, b I'm slightly stretching our definition because usually the interval is open that doesn't really matter now suppose it's defined on a closed set and differentiable means the obvious extension to the probability so it means you have a limit of the derivative going to the left extreme coming from the right and the limit of the derivative coming to the right extreme from the left. So closed means that alpha of a is equal to alpha of b so it's really a loop. Simple means no self-intersection if you want alpha is relative. And when I say differentiability I also mean that the tangent vector coincides also when you take the limit on the two extremes. So really we are talking about the simplest thing. So it doesn't really matter where I put alpha of a is equal to alpha of b. So you start from here you go around, you go back here at the other extreme and the two tangent vector coming from this way and this way it must coincide. It has to be smooth also in this direction. So there is a beautiful problem coming at least from the third century before Christ so this is the first time at least we have a written record and actually you have to apologize your lecturer now because I'm full of western civilization and of course we tend to think that Greeks invented everything and all our mathematical culture come from Greece from ancient Greece. It's very likely that in India or in China or somewhere in Africa similar problems were studied couple of thousands years before but at least that's the way we came to know it. What the problem I would like to describe you is called the isoperimetric problem. So for what we know it appeared in a mathematical treaty about that time so what does this problem say? Question. Among among all planner simple closed curves of given length of length l suppose you give me a positive number so among all planner curves of that length which one bounds the region of largest area May I ask you how many of you have seen this problem? Please raise your hand. One one Good enough to repeat it. You will be a bit bored. You understand the problem. So for example suppose this curve as length, I don't know one meter more or less so here is another one with probably the same length and so on. So actually this question is hiding a very delicate problem. So a simple closed curve in R2 separates the plane in two parts. One which is bounded and another one which is unbounded. This is very intuitive but it's actually not easy to prove. It's called the Jordan separation theorem. It was one of the early success of modern topology. But of course everybody assumed it was true. You see, things can get very, very complicated because this is a simple closed curve and so on. Now, if I tell you which is the interior of this curve, is this point interior or exterior? So of course it's a matter of enlarging. Of course, there are topological techniques which are actually quite easy. A little bit what is called degree theory gives you a simple answer to this problem. But nevertheless it's true. So let's assume I'm not going to make any topological consideration up to now. So this question is about of course the area of the bounded, so every curve splits the plane and of course you can measure the area only of the bounded part because the other one will have infinite area, whatever the curve is. Actually the first Greek contribution, the place where this problem was born, the only contribution it was made to this question was to prove that if you give me a number, a positive number, the area enclosed by the regular polygon of that perimeter grows as the number of edges grows. See what I mean? So the theorem that was proved here, for example if you take an equilateral triangle of a given perimeter the area inside is less than the square of the area inside the square of the same perimeter and the area of the square is less of the area of the pentagon and the hexagon and so on. Actually this is a guessing the solution but the solution escaped the author of the problem. The solution, not much mystery is this one. So if you give me a length of course you can construct the circle of that perimeter and the area inside the circle is maximal among all simple close curves with that length as perimeter. Actually this has been popularized at the beginning of, I mean around in mathematical language it was really formulated precisely about I think 200 after Christ by a mathematician called Papus in a very intriguing treaty about the life of bees so why somebody studying bees should come up with this problem that's a curiosity of course. If you look at what is called the hive then of course you would like to give us an explanation why bees live in hexagon and inside they form circular tunnels and somehow this is related exactly to this question they want to maximize the space where to live of course building their home costs energy because it costs wax so you want to make the biggest space out of the least possible wax so in some sense bees know the answer to this solution ok and the other historical comment before putting our hands in the proof is that this was actually became a very famous problem in mathematics because it's part of a famous history by Virgilius so this is about 50 after Christ where he's telling us story of the queen Dido in fact it's always it's often referred to Dido's problem so Dido was a Phoenician queen which was for some reason had to live Middle East and with some people escaped to Cartago which is in modern Tunisia ok when they get to Cartago they asked the king of Cartago in some land where to build a new town of course the local people didn't want to give a land ok but there was they were obliged in ancient times of course hospitality was supposed to be a holy thing so instead of saying no the king said ok you can take all the land that you can put inside a cow of course this seems like a trick ok because you kill a cow you take the skin and it's probably more or less like this ok so what kind of town can you build but of course Dido knew mathematics so what has she done she has taken a cow she killed, she took the skin and she made a little wire with the skin and then with this wire she embraced a huge piece of land and to maximize the land she actually put the wire into a circular configuration so she knew mathematics and she guessed the solution and of course she was able to build a pretty big town by solving this problem and cheating the king who was actually trying to cheat her very noble story ok that's why you will always see it referred in books as Dido's problem but now end of story let's go to mathematics actually the first complete mathematical solution to this problem came by wire stress was given by wire stress in 1870 around 1870 well there was probably another proof but it's not clear whether it was really complete 30 years before so wire stress wrote the complete proof the one I'm going to tell you is given by Schmid about 1914 and since then we now have many solutions many proofs of this of this fact the reason I'm telling you first because I think it's good you know a little bit of history actually if you like I mean this and other problems of this type are beautifully explained in a book that I strongly recommend you is called the parsimonious universe by Anthony Tromba by Tromba and I think also Ildebrand probably there are two authors but I remember this is a set of mathematical problems all coming from the same philosophical point it's that nature minimize effort in doing whatever it wants to do and this is one place where we can see it now so the proof I'm going to give you heavily relies on Green's theorem so let me remind you the version of Green's theorem of Green's formula actually it's a classical theorem in calculus it's a corollary of stocks theorem for what it comes so suppose you take two functions of two real variables f and g at least of class c1 over rt and suppose r is the interior region or the bounded region given boundary sorry bounded region inside a curve c in r2 ok now by a curve I really mean the image not just a parameterized curve so Green's formula tells me this so then if I take the integral over r of the function dg dx minus df minus df dy in dx dy this is equal to the integral over the curve of f dx dt plus g dy dt in dt this is a linear integral so it depends on one parameter t ok so this is a general theorem actually the way I'm going to use it f is equal to minus y and g is equal to x if I substitute there what do I get well if f is equal to minus y of course here I get minus 1 with a minus it's a plus and dg dx is another plus ok so here I get 2 the integral of 2 but that's exactly twice the area of r twice the area of r is equal exactly to well if c is our simple closed curve parameterized by alpha from ab so this is the integral between a and b and then f well let me first write g which comes with a plus so g is x d dy dt then plus f so minus y dx dt in dt ok so this is actually the corollary of the Green's theorem that I'm going to use ok and so now I can state the theorem which goes under the name of isoperimetric inequality because actually so under all the notations that we are using I'm not going to repeat it l squared is greater than or equal 4 pi area of r and moreover equality l squared equal to 4 pi area of r if and only if c is a circle or if you want alpha parameterizes so this is the complete solution to the ancient problem in mathematical language give you the proof I need to make a little picture so so the picture I want to something like this so suppose I have my simple closed curve ok this is my c in some I take I decide to bound it by two vertical lines so the first one tangent will be this one the second tangent will be something like this and then of course my picture won't fit but I mean now here so this gives me a possible a candidate diameter for a circle so below here I try to draw somehow the corresponding circle with this diameter ok but more or less ok so here there will be more or less the center of this and this I call x and this I call y so this is my curve alpha of s suppose I am going in this direction this is alpha of s and suppose I choose time and suppose this is alpha of zero after all changing names of the point doesn't matter and suppose that this is alpha of another point and now I am not free to choose another name I cannot say this is one so suppose this is alpha of s1 so these are the two points where there is a vertical tangent which is bounding the curve itself ok so this is the region inside r and this is our curve ok so this is kind of a background background picture to understand what's going on now so in my picture these are called l and l prime so referring to this picture I call this the center the center of this it's clear how it's constructed so these are some lines which are the first one on both sides which intersect the curve c so this gives me some kind of an amplitude and below my curve I draw a circle with this diameter I am not going to write in language the explanation so if alpha if c is parameterized by arc length as alpha of s so this is a planar problem so it has two x of s y of s it has two components again I choose the interval in such a way that these points corresponds to alpha of zero and these points correspond to an unknown number s1 ok if such under this condition we can choose a parameterization of the circle we can choose a parameterization of the circle below in fact let me call it c prime ok of c prime as again beta of s so it will be another curve beta but I can fix this first coordinate to be x of s but now of course the second component will be another function that I call y bar ok y bar is just another name for another function ok if you want to call it another name it's ok now remember that s was arc length so actually the interval where the curve c is defined is zero because I'm assuming I'm starting from zero there to L L is my given perimeter in the isoperimetric problem ok arc length measures exactly the length so the final point will be parametrized at time L now let's try to give an estimate about the area the area of r just one second ok remember the formula I just erased let's comment one second on this formula remember we have just observed actually first I put the two here so this is one half so the formula we wrote before was the integral between the two extremes now the extremes are zero and L ok of what of x y prime minus x prime y of t of s in ds ok so this was the formula we took from green's theorem ok but now the point is that these two reintegrals are the same because the curve is closed you see now the only little observation is this one if you take the integral between zero and L of x prime y for example in ds by integration by paths how much is it you see I can imagine this to be x y no between zero and L minus y x y prime x y prime ok but this is zero because it's closed it's a closed curve so if I evaluate the functions x and y at L I have to get the same thing as zero but then if these two things are the same you see these are the two things which come here I can erase one of them and erase the two ok so let me keep it to the positive one so this is zero L x y prime in ds so if I also give if this radius is r how much is the area inside the circle below there but that's a circle of radius r ok but by the same reason it is what so this is by geometric consideration remember in fact we still don't have any estimate on r so this is just an almost useless at the moment consideration but I can use the same trick I was using up here for the curve beta ok so this is equal to minus the integral between zero and L of x prime y bar you see now I choose the other one the same property but I choose the one with the minus ok ds so what do I get out of this the area of r plus pi r squared plus this but this is equal to the integral between zero and L of the sum of these two integrals so this is x y prime minus y bar x prime in ds but now this is less than or equal to the integral between zero and L of the square root of the square is a simple fact x y prime minus y bar x prime squared and then other manipulation this is less than or equal to the integral between zero and L x squared plus y bar squared times x prime squared plus y prime squared in ds ok, I leave you to check this but these are arithmetic nonsense I'm not using anything now now I use something this is the fact that alpha was parameterized by arc length if it's parameterized by arc length that means that it's tangent vector as norm one but what is the norm of the tangent vector to alpha is the square root if you want of x prime squared plus y prime squared if it's that's equal to one also the square of it is equal to one which is exactly this object here is exactly equal to the integral between zero and L of the square root of x squared plus y bar squared in ds but what are the functions x and y bar parameterizing note note that I'm using the fact that s is the arc length for alpha I have no idea if s is the arc length for beta in general it won't but here I'm using its arc length for alpha but now I'm left with this but xy bar is a parameterization of a circle of radius r so x squared plus y bar squared is r squared of course under square root it has to be positive so it's the integral of the constant r between zero and L so this is equal to L r so we are done we are done because well at least we are done improving improving the inequality because now remember I write it down here so the simple of course arithmetic that I'm using is this I actually a little hint to prove this I already used that property here now I use it again it's Cauchy inequality as you want you are free to choose your favorite proof now let me use again this property this simple property here and now I tell you the square root of the area of r times the square root of pi r squared so that tells you what is a and what is b this is less than or equal to 1 half times area of r plus pi r squared by that nonsense but what we have just proved we have just proved that this is less than or equal to L r divided by 2 so this is less than or equal L r over 2 but that's exactly the statement of the inequality because now divide by this and square it and you get exactly the isoperimetric inequality now I leave you with an exercise because the theorem was made of two parts you had the inequality which is here but you had also the characterization of the equality so if in this equality I get equal I have to prove alpha itself was a circle how is it possible that here I get a quality what it means that here I had an equality it means here and here I had a quality so exercise for you if these are a qualities x and y parametra is a circle ok completely trivial I remember when I was a student it took me a bit of time to prove this that's why I keep on giving it as a nice exercise because a little bit of sadism ok now now we are really done but let me tell you so this is all very classical and you can see we have not used very sophisticated mathematics 19th century mathematics and yet this kind of question is still an active area of research once you manipulate the question in a clever way there are two possible clever manipulation of this type of problem first of all well of course Greeks and I think I can be sure also Indians and Chinese and Africans or whatever nobody has thought about geometry on something different than a plane before 200 years ago ok it has been since the birth of the topic that we are going to study starting next lecture I mean differential geometry that people has realized that the same question we have been studying in Euclidean geometry should have been studied on a different ambient space now what does it mean in ambient space instead of taking a simple close curve in the plane what does it happens to this problem if your universe is for example a sphere so draw a simple close curve on a sphere well again this encloses well now you have first you have a problem because you have two regions of bounded area so which one you choose the other one should be the exterior but still is there an isoperimetric inequality so among all curves with a given length on a sphere is there one which maximizes the area inside and if so which one is it and then why the sphere why not asking the same question on any surface that you can think of why you should rule out your universe to be something like this then start drawing simple close curves you can certainly measure length you can measure areas and you can ask the same question this is much more difficult and actually we don't know in general the solution okay in some in the two cases I drew we know because these are surfaces of revolution okay we have this kind of rotational symmetry which makes the problem easier but in general we don't know and again but then there is a more sophisticated upgrade of the problem so what we are really asking is the following think of the question in another form we are fixing a one dimensional I mean we are fixing a length okay and we are trying to maximize the area inside a curve of that length well length is a one dimensional measure curves are one dimensional objects surfaces so the inside it's a two dimensional thing well we should be ready to ask the same question in any dimension meaning what fix a number but then prescribe it to be the volume of an n minus one dimensional object can you feel this n minus one dimensional object in a maximal way with an n dimensional object you see in how many ways you can ask the same question the question is always the same it's just an upgrade up to modern mathematics okay but in all these forms there are open problems and these are kind of fundamental problems because again you can also mix the two problems I was telling you together you can ask the higher dimensional question in a space which is not Euclidean okay this is a fascinating part of active research in basic differential geometry and analysis in some sense okay I mean this is ground zero okay this is the first issue of a series of problems which are open up to now and I wanted you to have a little feeling about this okay so I think for today that's it and this ends our study of curves okay so on Thursday we will start with surfaces


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Hello, and welcome to the Grand Line Review, your source for everything One Piece. All of a sudden you've made this channel sound so much more refined than I ever could. No, I'm a terrible actor. You don't need to be good at acting, you're English, you have the accent to you, you don't understand what you were born with. I just talk and people think I'm good at things. Exactly, you sound refined, hurrah. Alright, hello and welcome to World of One Piece, the series where you all get to take a break from my opinions and look at somebody else's experience with the series. Today we are featuring someone with an absurdly charming accent by the name of Oscar. Welcome to the channel, Oscar. Hello there. Now, tell us a bit about yourself. Where are you from? How old are you? What do you do for a living? Get down to it. Who is the real Oscar? I am 19 from England and I'm a student studying engineering, a bit of a nerd really, at university in Southampton. Sorry, I'm just looking up where that is on a map. In the south, centre of the south. Yeah, you definitely are down south, my friend. I'm from the posh south. Very good, not too far out of London. So, Oscar, how did you first become aware of One Piece?  Very good, just curiously, what didn't you like about Naruto and Bleach? Well, I thought Bleach was just a bit not really much going on other than just they fought a bit and somebody got hurt. And Naruto, they just stayed in the same village doing nothing really the whole time, whereas One Piece, they travel around the world and have an end goal and there's a big adventure. Yeah, Naruto has an interesting formula about it. They start in the village, they go on a mission into the forest, then they come back to the village, go into the forest again, then back to the village, and yeah, it gets a bit boring. Yeah, that's about what it seemed like. So how old were you when you became aware of One Piece? I think I was 16, about three years ago. Very, very cool. And what is it that initially kept you invested in the series? I like the fact that it sort of had a long-term plan, like felt like they had a very specific end goal. It was all about the kind of adventure of getting there along the way. I just thought it was good fun. It is indeed good fun, and where are you up to in the series currently? I'm completely caught up in both the anime and the manga. Completely caught up, good man. What do you think about current events in the older Huano? I'm really looking forward to Huano. I thought Whole Cake Island was probably the best post-time skip arc. I just didn't really like Big Mum very much. Some look forward to Huano because it looks like an infinitely cooler place. And can I just say thank you for calling her Big Mum. I have a lot of trouble saying Big Mum because I want to say it as Big Mum, you know, in the American sort of way, but it's so nice to hear someone who says it as Mum. I will never say Big Mum. No, your posh accent does not allow for it. I should never say it again, really. Absolutely not. You've already tarnished your voice by saying it once. I avoid American accents at all costs. I would, but I grew up watching too much American television, so I just say some things in an American way without really knowing. It's very annoying. You've infected yourself. Yeah, I'm infected with America. Aren't we all? I want to go back to something. You said our Whole Cake Island was the best post-time skip arc in your opinion. That's a very interesting opinion. I don't know many people who would say that. I think it was pretty fantastic, but a lot of people got very tired of it, I think. What did you really love about it? I think I really liked Luffy Against Category. That was just an awesome fight all round. I liked the whole story with Sanji and his backstory, and sort of leading up to the wedding was interesting as well. A lot of cool stuff happened, basically, that I didn't think had really happened in the previous few arcs. Yeah, I agree with you completely there, especially with Luffy vs. Karakuri. It's bizarre to think that a series that had almost reached 900 chapters could keep topping itself in terms of fights, but that's probably my favorite fight in the series. Yeah, and that was where I'd co-opt the anime for the second time, and had to read ahead on the manga, so I got it in the manga rather than the shitty anime. That's fantastic. And speaking of, you're all caught up in the anime. I am almost all caught up. What do you think of the state of the anime so far? What can I say? There are cool bits, and I like bits of it, but it's so slow. I think I only keep watching it for nostalgia's sake, because that's how I started watching the series. Yeah, that's pretty much exactly how I feel about it as well. It is painfully slow. It makes 20 minutes feel like about an hour. Yeah, and it's not even 20 minutes of new content, rather it's probably about five minutes. Maybe five? Yeah, I'm glad we agree. But let's put the shitty anime to the side. Who is your favorite character in the series? I think it has to be Zoro, although I'm a big lore fan as well. Interesting. So what is it about Zoro that gets to you, or is he just that cool in the same way that he gets me? I like the fact he uses swords, and he's like the second member of the crew, but also he just looks so cool. Can't not love him. I completely agree. Would you like lore for the same reason, because he uses a sword and just looks cool? Pretty much, it's hard to deny that. Certainly is. Not counting Whole Cake Island, what would be your favorite post timeskip arc? It would have to be Dressrosa, although I was on the anime only really at the time, so that sort of made it slightly shitter. Yeah, that sounds absolutely abysmal. Like it was difficult in the manga reading that week to week for two years, but watching it, I can't even fathom it. And I caught up midway through, so I went from binge watching everything in a matter of weeks for each arc, and then suddenly it was having to wait a week for each new episode, so I just said screw it and went on to the manga. Good, good, yeah. I wish more anime watchers would do exactly that. It's the way forward. It is, and it's the way to discover the true amazingness of One Piece. It is. I've actually just recently bought about half of the manga series, and I'm on water seven rereading all the way through it, and it's so much better. Oh, wonderful. Yeah, I do that at least once a year.  Those are the best kinds of shelves. What should be angry at? I agree completely, but she hasn't started reading One Piece yet. One day she'll understand, I'm sure. You need to get her to read it. It's disgraceful for you. She's not one of the fans. It is, yeah, but you know, she's busy becoming a doctor and using a musical at the moment, so she has no time. Who needs spare time? She does desperately. Fair point. So, moving on, who would be your least favorite character then? That's a tough one because my least favorite straw hat would be Usopp, but my least favorite current character, the sort of big major character would be Big Mom. Least favorite character of all time, probably Gekko Moria, because he's just hateful. All right, well, let's go through those one by one. What don't you like about Usopp? He's just sort of the least badass out of the straw hats. He's, I don't dislike him. I like him. He's just the least amazing. Has he grown on you since you started the series? He has a bit. He's, he definitely is in water seven where he had the fight against Luffy is where I really started to like him. Before that, he was just a bit sort of a comedy character. Yeah, it helps when you see him get serious and have some driving force about him rather than just, you know, saying I'm too scared for this island illness or being a coward in general. Yeah, it was good to see him actually have some character development. That it was. And Big Mom, what don't you like about her? I'm quite intrigued by this one. See, I think it's because I was watching the anime at the time when I got to Whole Cake Island and her voice in the anime is just horrendous. It's so horrible. And I'd ma ma ma ma ma ma. Exactly. It's I hate it, but I don't really like a character anyway because it's a bit sort of seems a bit too comical and not in the usual one piece way, just in a bad way. Can you give a more specific example of that? I feel like she's she's not kind of serious enough and when she is, it just seems to be her on some mindless kind of rampage. Like she doesn't seem very smart to me either. Like she just seems to either be in her own kind of deluded world or on some kind of rampage. That is correct. Yes. That's what I really like about her though and that she kind of lives within her own world and she just happens to be strong enough to enforce that onto other people. I find her quite fascinating, but yeah, I can see your perspective for sure. Yeah, I can see why you would like it. I just personally it doesn't really ring with me. All right. Well, let's go to something that does ring with me.  Do I need to?  His power could have been amazing, but he just didn't use it.  He just he's Oda could have done so much better with him. In every respect, yeah. I do kind of enjoy the psychology behind what he does because of, you know, his tragedy at the hands of Kaido, but it just could have been done so much better and more aesthetically pleasing. Yeah. And I think even with his kind of bad character design, we saw in Marineford, where I think Doflamingo went after him. We saw, you know, he can be good and can be used well, but in Thriller Bark, he was just so terrible. Let's move on. Let's move swiftly on from him. Swiftly on, very swiftly. What devil fruit would you most like to have and why? Well, that's a good question. I think my answer would probably be the cop-out answer and I like Ace's fruit slash Sabo's fruit because it's just so cool. Sabo and Ace are the same character, so you can just say Ace. They pretty much are, but I think it's just the coolest fruit, I think visually or possibly Marco's fruit because again, that's basically Ace's fruit, but better. Yeah, except Marco's flames can't actually be used for damage, but I think it does look a lot cooler, the old Phoenix fruit. Yeah, I like the kind of the blue aesthetic, which one thing the anime obviously did better because you don't get the color in the manga, but I think it just looked beautiful. There were some really fantastic scenes in Marineford with Marco fighting Kizaru, I think it was, though like when the anime wants to do well, it can do pretty fantastically very much. So, so you seem to enjoy the flames, the aesthetic of the flames, would that be correct? They do, I'm a sucker for a good flame. All right, that's pretty cool. I don't think anyone's chosen Alogia yet in my interviews, so that is a nice first. But they're so cool, why would you not choose one? They're so cool, but in the current state of one piece, they're not that great. They're probably actually the bottom in the rankings because, you know, you can just hit Alogia user with Haki and what are they gonna do? Yeah, that's a good point. I just, I'm thinking more about that they're cooler and they look better, and I can show off with them. I see, I see what your minds are. In which case, which island in the Grand Line would you most like to visit? Uh, that's a good question. Probably not alabaster because it's too hot. I think water seven, actually, because, well, I'm doing engineering at university and it's the land of shipbuilding and building things, so how could I say no? That seems perfect. Yes, would you become a carpenter at Galelar? I think I would, although I am an electronic engineer, so. Oh, it sounds like you've got a leg up on them. I have, I'm just a futuristic version of Galelar. You're kind of like Frankie, really. That's true, actually. I am basically Frankie, Frankie but less American. I'd be Frankie when he fills himself up with tea. Yeah, that was actually one thing I really enjoyed that the anime did because that did not happen in the manga. So, gentlemen Frankie, well done, Toei, well done. Oh, I thought that was in the manga, so I haven't got to that point, but I liked that. It was very funny. There was a whole bunch of stuff that the anime added in to create some filler episodes for the straw hats being separated. That was definitely one of them. Yeah, I liked the separation things. I don't know how much of it was the manga or the anime, but I found them quite enjoyable. An awful lot of it was actually the anime, so that's a very good sign for Toei. Some of it was quite enjoyable. I wasn't maybe 100% convinced with putting Zoro in the kumusi suit. I think, yeah, it was kind of funny, but pointless at the same time. Yeah, which is, I guess, the goal of filler. That's a good point. All right, what would be your most memorable moment in the series, Oscar? Another good question. I think it's between the Silent Goodbye from Alabaster. I thought that was one of the coolest parts. And probably two more. Either Robin saying, I want to live and probably return to Shabandi, because that was pretty cool. All very standard choices, I would say. Yeah, the Silent Goodbye in Alabaster is one of the most iconic images in the series, as is Robin's, I want to live. So let's talk about the one that maybe isn't. Return to Somebody, that's how I pronounce it. I think, I don't know, I think it's, I don't know how they say it in the anime, but... Neither do I, because I don't watch the anime enough, but a lot of people have pointed out on my arc reviews that it's pronounced Shabandi, and I don't see the H. I think it's translated as like Sabaldi or something, but they say it like Shabandi in the anime, but it doesn't really matter. Ah, you make a YouTube video for 15,000 viewers, you'll discover it. That's a good point. The YouTube community aren't very forgiving. No, not at all. Yeah, talk to me about the Return to Somebody. Why does it stick out to you? It was kind of refreshing, because we got to see all the kind of cool character designs, and it showed us, you know, all their work had paid off. I thought it was just a really cool kind of arc that set up what should have been a really good Fishman Island arc, but we all know how that turned out. You know, not terrible in retrospect, but it wasn't exactly what we'd been building up to. Yeah, it felt a tiny bit of forgettable bit of a letdown. Yeah, we had two pretty terrible villains, and not so great side characters either. No, I just didn't like Shirahoshi especially.  So you didn't like the crying? Yeah, I used to be like that. I appreciate Shirahoshi more in retrospect, but I was definitely on the hate bandwagon at the time. Maybe she's better when you don't have to spend about 40 episodes listening to her crying. Oh yeah, look, I agree with you there. I went through Fishman Island recently, getting screencaps for the channel, and there was an awful lot of that. In fact, I think my entire Shirahoshi folder is her crying. That doesn't surprise me, but it was, I think the whole arc was a little bit forgettable, so I haven't quite remembered how much crying there was. There was a lot, but in Shirahoshi's defense, she did kind of be pretty awesome right at the climax of everything. How do you feel about her being the ancient weapon, Poseidon? Uh, I'm not so sure, because we haven't really found much out about it. I'll probably reserve judgment for when it's actually used as a big part of the story. Very good. That's nice and fair of you. I always give it a chance to see how it goes. All right, now it is time for one piece trivia. You've had a bit of this on the reverie, so I know you're quite good at the old trivia, but this is structured a little bit differently. Are you ready? I was born ready. That's what I thought. Essentially, I have three easy questions for you. They are worth one point each. Then I have two medium questions for you. They are worth two points each. And I have one hard question for you. It is worth three points. All right. Starting with the easy questions. What is Chopper's full name? That would be Tony Tony Chopper. That would be correct for one point. Who was the last of the four emperors to be formally introduced in the story? That's Kaido. That is definitely Kaido. Another point, sir. Why, thank you. What was the first island visited by the Straw Hats in the Grand Line? Uh, hang on. I definitely remember this. Really? It doesn't sound like you do. Just trying to think. Oh, it was Whiskey Peak. Whiskey Peak is indeed correct. So off to a very good start. Three out of three. Let's move to the medium questions. Madame Charlie is the younger sister of which fish man? Oh, this is a question from Fish Man Island. I might not remember this. It is. That arc you didn't pay attention to. That would be, it's going to be my downfall. Um, I'm going to have a wild guess, uh, King Neptune. Is incorrect. Madame Charlie is actually the younger sister of Arlong. Ah, right. How many days did Ace fight against Jinbei before they both collapsed from exhaustion? I think that was five days. And you would think right. Well done. Lovely. Currently you are sitting on five out of a total seven points. We will move on to the hard question. I'm scared. For three points, what is the name of Cavendish's horse? I have no idea. Oh no. It was Farul. Still doesn't ring a bell. That's all right. That's why it's a hard question. So congratulations. You got five out of ten. That is a pass mark. Why thank you. In universities anyway. Yep. P's get degrees. Never have true words been said. And I have one final question for you Oscar. And that is what is the one piece? See it's hard not to say buggy because he is the one piece. So you're saying buggy. Yeah I'm afraid so. Oh this meme is infesting these interviews on. They thought they would. You are not the first person to have said that. And you probably wouldn't have liked it. I didn't think I would be. In any case, yeah. I would quite like an eventuality where buggy ends up being the pirate king. I'm not sure about the one piece though. I think you'll definitely be important in the later stages of one piece. But I can't see him actually being the pirate king. We shall see. At least a yonko right? Oh yeah. Yonko that's guaranteed. Yeah it's pretty much a foregone conclusion. In any case, thank you very very much for sharing your perspective Oscar. It's been an absolute pleasure not talking to myself for a change. That's okay. It was my pleasure too. And if you'd like to be featured on the next world of one piece then all you need to do is become a grand line review patron. Upon becoming a patron of any tier, your name automatically goes into the draw to become my next guest. And very very importantly, your name then stays in the draw for all subsequent episodes throughout your tenure as a patron. With that said I'd like to thank Oscar once more for being an amazing guest and I look forward to interviewing our next lucky individual soon. This has been the Grand Line Review. We'll see you next time.


Hey everybody it's Coach Johnson and we are in lockdown. What does that mean? What do we do with this time? Are we going to binge or are we going to binge on Throws knowledge? So what we're trying to do is put some things together. We want to let you guys in on why are we able to consistently get those big results in just a matter of a handful of workouts over the course of a weekend. It's because of our focus and the details. So we're going to take you inside the training session the last half of what our rotational throwers came in from out of town to work on and you're going to see how they're improving. It's details that make all the difference and that's what you got to make sure you understand. So hopefully you enjoy this video. Check it out. Much better. Much better. That was a nice throw. That was better. We've got to get you used to coming through. Look at that. Look where the shoulder is. Shoulder level, your hips level. So you guys are going to feel this. See how that keeps me stacked. Do you feel the difference? Yeah. There you go. You rewrap the shot. You line the chest forward a little bit. Yep, there we go. Now line that. Keep it long. That was closer. Now here's the key. That was actually pretty close. Open the left arm. Better. Much better. See the difference? Much better. Much better. Look at that. Yeah. There we go. Look at that. I feel it. Yeah, you feel it. Ripping you in. Yeah, exactly. Very nice, dude. I'm pumped. There's a different tension point. This is teaching you to feel this. See this? Tension points there. And then you're going to feel this zing opening. So finish the weekend and we had the Hull's camps, the Kisbees and the Moran's outs. They're all members. They've been to camps and so we were kind of clustered them together to train. So it was a good eight hours of throwing. They were definitely fatigued by the end of the day, end of the weekend.  You kind of see some of the before and after and some of the improvement from when they start to when they finish. And things look very good and that's always the positive. That's why people come out. They'll come in and they'll see a big change over the course of the weekend. One of the big goals, of course, is that we have our system. So we're teaching them the six pillars and we're teaching them how to understand what they've learned over the course of the two days so that they can go continue to apply it and work on it. And that's the major goal. We want to see these guys who take their time and invest their time in their money and stuff and fly out here. And we want to see them continue to improve. And thankfully, we've had really good results with that for going on close to 10 years. So any rate, thanks for watching. We'll see you guys in the next video.