Run it up, do run it back. Run it up, do run it back. Run it up, do run it back. Run it up, do run it back. I don't know what you're saying. Good morning. It's Monday. It's early. It's the West Coast. And we are running back. And look who's here. Danny, all week. All week, all week. Danny Green is here all week. I appreciate you guys having me. We love this. Lou Will, as always, moves over a seat. You get real wordy in this seat, and we love this for you. No, you did. I like it. I'm here for it. And Sean Shirania joining us from his palace in Chicago, Illinois. And you've got some info for us today, and I'm excited about it, because the first story of the morning, it took place on Saturday. But man, did it produce some laughter for me anyways. Eme Adoka ejected in the fourth. After joining with LeBron James, LeBron also got teed up for this one. According to Adoka, quote, we had some conversation, and they, the refs, didn't like what they heard. And so, of course, the speculation began immediately. What did they hear, guys? Your best guess is what? Well, the audio's been leaked now. Well, now it's been. But when you first saw it, what are you thinking? What are the words, the magic words that you can't? It's about three. Yeah. It's a couple. It's about three words that are off limits, that are fighting words. And two of them were used last night. So kudos to LeBron for keeping this cool. I think that was the one time I would have enjoyed to kind of see LeBron lose it a little bit and show that side of his personality with the things that were being said. But that was interesting. I mean, they were beating them pretty good. They were up 15, 20 at the time. So it was no reason for him to lose this cool. Fair. I think they both, just the monotone, the mannerisms, it didn't seem very aggressive. No, it was smiling. The talk was aggressive. Aggressive enough. But me and Lou, we played partially in some of the old school type of basketball. I think the texts are giving out too quickly. I like to see that. I think the fans want to see that. I think tossing a guy for talking a little trash, even though they are words that you shouldn't be saying, I still think talking trash should be allowed or OK in our league amongst grown men. I mean, OK. So let's just, OK. First of all, you know what? Let's get to Sean's, because I do have questions, thoughts when it comes to certain words that seem to trigger people more than others. I love the fact that they're very calm. It's almost terrifying when someone's calm and talking smack at the same time. But we did see a coach get ejected to Sean's. It was very bizarre to watch. What's the impact of what happened on Saturday? Well, I think terrifying is the right word. When someone is that animated without having any real, like you didn't see any real tension with them. You didn't see them go chest to chest. You didn't see them go at it. You didn't think it would escalate physically. So that does make it a little terrifying that they were able to say what they were able to say in that way. But I think for Yume Udoka, this is a guy that has called his team out for their physicality. They've smashed mouth basketball. Like that's something that he's brought to that organization. When you think about the last few years in Houston, it has not gone well. They've been the bottom dwelling team in the NBA. So you bring in Yume Udoka to bring in a culture. And what he's brought is physicality, defense. And I think even though they're 8 and 9 right now, they're playing much better. They're playing harder than they have in the past seasons. And I think everyone in Houston is crediting Yume Udoka for their start. And I do believe he moves the needle that much. When you talk to people around the Celtics in that locker room, they really believe they would have won the championship last year with Yume Udoka as their head coach. But obviously, he departed. And now he's in Houston. Now we've got to call a spade a spade. This is a team that's ranked 10th in the West. So listen, it got to just match up. The words, the attitude, the physicality, all of those things that Shamsa is saying he's credited for. The record has to match up. They're trying. How hard. So look, again, we're talking about the Houston Rockets again, based on things that have nothing to do with basketball once again. So the games, and they all talk, and the tough stuff, it got to start matching up for me. Do you think they're doing better than last year? Yes. So I think that's something to be by pinch of salt. OK. It's still early, but I think they're doing better last year. I think the culture is changing a little bit, bringing Fred, bringing Dylan, and Yume. And you have a lot of young guys with potential, a lot of talent. It's not going to happen. Even San Antonio, I thought they would be a heap better. They're still struggling at the bottom. Things can change in a year. So much can happen. Even Memphis, I thought they would still be better, even with the injuries and certain guys being out.  Yeah, we don't want this team to be known for the wrong type of things. Getting better, putting more pieces to that puzzle, where they can progressively get better and better under his leadership. But again, we're talking about this team for the wrong reasons. And I would like for it to be basketball related or something. I mean, we are talking about the coach, though. That's a little different. Stars at the top. Getting thrown out for chirping. I'm a former teammate of E-May. You know, I know him. E-May's a former player. So sometimes he goes back into that mode. I think that's why he started talking a little bit. I kind of loved it, though. Have you had one of the coaches? Is that a thing? Not me personally. I don't think we personally have ever had. I mean, you might have in practice with your own coach. Yeah. Yeah. But I've seen it. I've seen it with other coaches. I thought it was kind of funny. I played in the D-League before. Yeah, before the G-League, I was in the D-League. And I had the coach of the name of Eric Musselman. Oh, sure.  He's a little guy that will get after you. And I've seen him talk some good trash to some opponents. I think it was, E-May was light compared to what Eric was talking about. Really? But yes, some of the things he would say to certain guys. Is it just that, did he get thrown out because coaches aren't allowed to? I felt like it was pretty calm in my, I mean, granted, with the worker. I just think the referees were trying to, because the situation had lingered. There was some other tension going on. I think they were just trying to control the situation. They felt they needed to toss somebody. Because there was a lot of other bickering going on in the game at that point. And again, like we mentioned, it's a handful of words. They aren't acceptable in their fighting words. And he used a couple of them. So I think it was just probably a little overboard. Is everybody sensitive to these same words? And why? Not everybody, no. Yeah, a majority, so. But certain words, some guys are not going to take certain things.  You're not going to be able to touch. And they're going to let you know about it. But some guys.  Yeah, it is going to get checked. Is that a man thing? That is, yes. Interesting. How ironic. It's not a term. We are the actual bitches. It's not just a men thing. For women, women do not like it as well. I do not. I just know, it's funny to me that there are no words put it this way.  I said it's certain people. Yeah. Braun kept his cool pretty well. It's not the first time he's been called it. I'm sure it won't be the last time. For sure.  You just not allow people to disrespect. And you see Russ, when the fans come to him. That's true. Certain things they talk about, you're just going to stop it right there. Look, you're not going to talk about this. You're not going to call me this. It's not going to happen today. I said something, I'm going to have to nip in the bud before it gets out of hand. So he gets double teed up, coach does, thrown out. We have Dillon Brooks, obviously, on record numerous times trying to get under LeBron skin. Lou, it feels like a lot of time and energy is spent from this Houston Rocket Squad to get under LeBron skin. And that's the energy I want this team to get away from. I don't want them to be known for just being the guys that want to get under LeBron James skin. This isn't a rivalry. They're not fighting for any playoff positions at this point. They're not in direct competition with the Lakers. And so for this to be part of their calling card and part of their MO, it got to get nipped in the bud. It got to stop. And I think that's where Fred comes into play. I think Fred Van Flee is going to be the guy that keeps a steady locker room or keep guys level headed and not doing so much talk, but more play, more action. So that's the big reason why they signed him. So I think they just need another one or two more guys like Fred to keep it more balanced. They have a lot of young guys right now. It's going to be hard to establish that this early. And like Danny said, look, they got they got pieces, right? They got Jalen, Jabari. They have some young guys, the other kid. Sengoon. Yes, Sengoon. Sengoon, he's another piece and you have and you have your coach of the future. You have a lot of great things in place that can go your way. So the foolishness and all of the talk just make it make sense. But it was fun, though. Definitely fun. OK, good. Well, we also have some some Shams scoops time. Some news coming out of Philly, Shams. What's the latest? I'm told Kelly will return to the lineup likely this week as soon as Wednesday, they play against the Wizards in Washington, D.C. Or he'll come back Friday when the Sixers host the Atlanta Hawks in Philadelphia. But this guy that's been out since November 11th with that fracture and rib injury that he allegedly suffered in a hit and run accident. But Ubrey, guys, before he went out, he was averaging over 16 points a game, 50 percent from the field, 38 percent from three. He became a key member of this of this rotation key cog of this lineup. And it's like getting a trade acquisition right now. We've been talking about what is Philadelphia going to do? They have assets. What can they do in trade? I think they do like this group that they've assembled. They've got a ton of role players and getting Ubrey back in your 20 point per game score. They feel like we'll be a good acquisition for them. Could happen as soon as Wednesday. That's good news or 12 and 7 right now, obviously, without him. You were there. You've got intimate knowledge of this organization, this team. So what is his importance to the squad? Well, I think with the trade, they've gained a lot of depth. He was the depth off the bench for them. He became a starter once the trade happened. They've been playing really well, even without him, even without some of their guys. They had a game the other night in Boston. They were in a game that they weren't supposed to be in with Tyrese, Maxi and Joel and Bede being out. You get Nicholas Batum back and you get Kelly Ubrey back.  So he gives you another scoring option. Of course, another spark off the bench, if not starting. But he's a guy that you're going to need, especially when things get dry. You also shams in the Oh my God, I forgot about him. You had a tweet as well about Ben Simmons. It's crazy how much we talked about him and now it feels like we don't. But there's an injury update. Yeah, Ben Simmons had an epidural injection in his lower back. And the hope is over the next two to three weeks, he's able to feel better and work toward a return. He's going to be re-evaluated in two more weeks. But that's going to be shelving him for a month in total since this injury first popped up. And since he initially was sidelined, there's got to be concern with that lower back. It's a nerve issue in his back. He's missed time over the last couple of years with this nerve impingement, this nerve irritation in his back. He had to have surgery in the off season for herniated disc. So it's multiple back issues that's popping up for Ben Simmons. We know what he's done over his career, multiple all star appearances, all defensive runner up for defensive player of the year. I know Danny played with him there. But listen, if this epidural shot injection doesn't work, I don't know, you know, where this goes. And you have to have a level of concern. Danny played with him. So I'm very curious what his reaction is to this. And just overall, what we've seen from Ben Simmons. I have a question first. I mean, I know you're not a doctor. I'm no doctor. But an epidural for the fans that have no idea what they are, what it is, what does that actually do for the lower back? Do you have any idea, Sean? Oh, God. It's supposed to provide numbness.  I don't know anything else. When they have pregnancy. So it's not a fix. It's a pain relief. It's a pain reliever. But it's something that clearly if there's whatever, inflammation, if there's irritation, you have this type of shot. This isn't the first time I think an NBA player has had a shot, especially with a back injury. But clearly this is this is designed to relieve some level of pain and allow him to put himself in a position where he can rehab it. I will say that Ben looked really good early on in the season. I seen him in preseason. I saw him early in the season. He was moving well and it's a shame that he's having to set back physically, which can affect him mentally.  So will he ever get back to being at all start level? I don't know. It's going to be tough to have these injuries, especially back injury. And hopefully his mental doesn't take a hit, but he looked like he was moving well early on. I would like to see him get back there. But it's going to be tough and they have a lot of good players in Brooklyn that are playing really well without him. So hopefully he gets back healthy and hopefully he gets back in rotation and playing some good rotational minutes. But right now they're doing pretty good without him. Danny, I'm curious, playing with Ben Simmons when he was at his peak and you saw the other side as well, like what were your conversations like with him? Like, could you could you guys tell him that locker room? Like, this is a guy that's clearly dealing with something not only physically, but mentally at the time? No, it came later in the season, probably during playoff time. During the season, there was some increments of it. But during during the year, he was he was confident. He was who we was. We had a lot of fun. And I love playing with him. You know, he made me look at I shot 40 from three. I had a career high in attempts from the perimeter and playing with him. I hoped he came back the following year. He didn't. I signed back with Philly and he didn't play. So we had to play without him. So we didn't have many conversations about it until the time of you know, the playoff time in the following year where he didn't want to come back. We tried to talk to him to coming back. So we did talk about it then, but we didn't have many, you know, we didn't converse with him about it much. But you can just tell in his his demeanor, his mannerisms that he had lost a little bit of confidence in the mental side of the game. But I said earlier this year, he looked pretty good. Guys, we have it. It's here tonight. The end season tournament. It's back. We move forward and it's Celtics. Pacers, we're going to do a little preview for you right here. So Celtics are sitting at 15 and four. Pacers are 10 and eight. This is the first game of the night. Pacers finished the end season tournament four and oh, Celtics three and one. Here's where we have like a head butting situation. So Tyrese Halliburton's averaging just under 35 points a game over his last five. Meanwhile, the Celtics have only allowed one player to score more than 30 points in a non OT game, I think once. Yeah, one one player's done it. Something has to give here. What's it going to be, Lou? I think Celtics, they've been known to be a great defensive team. This year, they're a top three rated defensive group. Halliburton is doing everything he can to keep this Indiana Pacers team competitive, standing in the mix of everything. But I just I just like the Celtics and how they've presented themselves on a defensive end year after year. They have a balanced attack of guys that can guard. Halliburton, keep fresh bodies on him and just make it hard for him. And and alone, it's hard to average 35 points right over the course of a season. And so for him to do that for five games straight, really, really impressive. But going against a top three rated defense with something on the line, I think it's going to be hard for him to do that tonight. I like I like Indiana still scoring a lot of points. I mean, Tyrese may not get 35, but they're putting up 130 a clip as a team. Yeah, Rick Carlisle and these guys, you know, letting them lose. They're playing with great confidence, great energy and getting up and down. So I still think Boston wins the game. If everybody's healthy, I think they hold the whole Tyrese under 30 points. But I still think, you know, Indiana is going to put up a high clip is at least 125 points, but Boston's going to have to outscore them. Now, if they don't, if they have drew, if they don't have drew, how that dictates a lot of their defensive rating and how they, you know, keep Indiana within that that scoring range. But I think it's going to be a game. It's going to be a really good game. I'm looking forward to watching. Weirdly, do we get those courts? I guess we'll find out. We get the courts back, right? Me, well, my favorite courts. They probably get worse. We've got to be given.  Oh, God, I didn't think about they're going to add to it. Look, the Pacers lost the game to the heat recently.   So the mindset's there. He was also worried, though, that that was going to turn into a meme and come back to haunt him. But if your leader, if the guy on the team that's doing the best has these types of words out loud, how is that a bad thing? I see it as a positive. Yeah, I think he doesn't. He's not satisfied with what he's done himself, even though he's done all he can. And they're playing well. They're playing. They have a pretty good record. I see them being a top six, seven team in the East and being in the playoffs. So then playing this well and him still thinking that they're not doing enough. I think it says a lot in a positive way. So I enjoy watching him play. And I enjoy how he humbly carries himself within the media and his teammates in the locker room. Yeah, and we just had this conversation with LeBron and a big loss that they had last week.  And he's a young leader. He's trying to turn that corner to become, you know, a cornerstone guy for their organization. And so I don't I don't mind him saying this, you know, this is this is motivational for everybody around. Is he a top five point guard? Absolutely. This year he's having a coming out party. Absolutely. Yeah, 100%. Am I supposed to ask you who the other four are? You could. Every tough. But this is where it always ends up being seven or eight people long. And we're getting there. We're going to figure this out. Shoms, I'm I'm weirdly excited about tonight and tomorrow's games. What's the one thing you're looking for in this match up? Well, I think for sure how the Celtics play without Porzingis. He's going to be out tonight. So Danny, to your point, Drew, how are they supposed to be available tonight to play? Chris, I was posing is still out with that calf strain. This is really a week to week injury for them. But Chris, I was posing is their third best player. Anytime you get a guy like that, who can come in as your third, fourth option on any given night. That's that's a great get for the Celtics. And so he's going to be out tonight. But to me, this is clearly setting up to be you have the final four. You know, you have this final eight grouping right now. Like how much March Madness energy are we going to get? Like, are we going to get an upset? I think if the Pacers win tonight, I think a lot of people will be surprised. I think there's a lot of expectation. The Celtics, when you go into the season, this is a team that can be a, you know, dual champion, you win the end season tournament, then you win the NBA championship. So what what happens with the Celtics tonight and the Pacers? There's a legitimate, I think, upset chance, especially with this game being on the road for the cell. Well, with that new information, I got I got the Pacers winning tonight. OK, we just changed it. We're back. I got the Pacers because I just don't see Boston outscoring Indiana without Porzingis. Why? What are they missing now? We're missing rim protection and a 20 point score. 20 points. And we're missing 20 points in rim protection and Indiana, the way they're playing at that pace, they're going to still put up 100. I don't see Boston. Are we disrespecting Al Horford or what are we doing? I respect Al Horford. I just don't think I don't think he's enough to stop Indiana from scoring 126 points per game, which they average, I think. I'm going to go against the grain and say I still like Boston. I like any Jason Tatum lead team. And listen, you just we just said it.  So mentally, they are motivated, but they're also going through their they're going through their struggles. They're going through their ups and downs and of a season. And I feel like Boston is pretty much where they always been top four team. And so I still like Boston there. Got another game tonight, the West Coast game. It's Pelicans at the Kings. Kings, of course, won their spot for no Pelicans were three and one in their in season tournament play. But the Kings are 0 and 2 against this Pelicans team. But those were both games in New Orleans. They get to actually host tonight where they are six and two. Well, the beam be lit tonight, Lou. The beam will be lit tonight. This is this is a group that plays really well at home. And Sacramento has a great fan base. Don't be mad at me, guys. Here we go. Listen to great fan base. I love Sacramento, great fan base. And so this is a team that feeds off the energy of their crowd a lot. Play what it feels like they play faster when they're home. They play more relaxed, more comfortable in that building. And so I feel like this is a great opportunity for them to get a win at the crib. I agree a month ago. The beam is going to be lit tonight. They're playing extremely well at home. They they they also they fight for longer at home. You know, I feel like on the road, a team like that, I'm going to say they're really young, but they are younger aside. And if a team goes up with a 10 or 15 point lead, they'll probably, you know, shut it down. But you see Mother Night, they have a down 22, 24 to Golden State. They still fought back. I can see them regardless of any situation of what they get down against any team in that building. They have a fighting chance. And I don't see them going down 22, 24 to New Orleans by half time. But, you know, they play and they're playing extremely well. And Darren Fox is leading it. So bonus is playing well. A Malik Monk off the bench has been unbelievable. So it's going to be a fun game. But I think the beam will be lit tonight. I like Malik for six man a year. Yeah, I'm going to say it now. OK, we're saying it's December coming from the six man. I like that. Yeah, that holds a lot of weight. As a fan, I like to think that we play a part in some of these moments, these big playoff atmosphere type situations. But do they? Is there a big difference? Like, what do you hear? What does it feel like? It's just energy. It's just energy. It's a feeling when you come out of that tunnel and, you know, every the majority of everybody that's there, they're there in support of you. Your family is there. The crowd is there. You probably have the T shirts. And so it's just it's just a vibe that you can't get on the road. Me personally, I was a guy to enjoy playing on the road because I wanted to play the role of the villain. I wanted to keep everybody quiet. But home court advantage is definitely a real thing, especially when you have an excited crowd that's itching for some success. And this Sacramento team has been getting them what they need. You know, having that playoff run last year and now building on that. This is an excited fan base. And so that definitely makes a difference. It's weird to be this excited about a game on Monday. It is Tuesdays and Thursdays, random days during the week. I know, but you know, the league has done a great job of making these these games, you know, special and a lot of fun. Yeah.  You know, the court seems warmer. You guys are just, you know, feeling it. And it feels like that type of atmosphere. So it's fun. You're competing for something. And a lot of these guys, some of the younger guys that can change their lives or change their year. So yeah, something to look forward to the bonuses and they get to go to Vegas and enjoy a different city. They don't tax you there as much. So yeah, they collect a lot more of their check doing that. And you have some fun playing some good basketball or, you know, people can the gamblers can kind of try to predict the point differential. This this is going to be good. The Pelicans have won some games over some pretty good teams this season. So far, the Zion Ingram of it all shams. What have you seen growth wise from the two of them playing together? You're starting to see them play cohesively. I think this is the best as I understand we've seen since he's got in the NBA. That's just not from a statistical perspective. I think the way he's playmaking, embracing, playing point guard. He's spending a lot of time on the ball, facilitating and serving as the lead playmaker. When you look at and you compare it to how the Pelicans started the year, he spent the majority of his minutes playing in the mid post, in the high post, setting screens, playing a lot more inside. But this is a guy as I Winston, who can dominate with the ball in his hands, can get to the paint when he when you need to. But he's very dynamic in the way he plays. And I think one thing we can overlook, Trey Murphy, the third got back in the lineup on Friday. He had 18 points, four threes. They're very high on him in New Orleans. I think this guy has a chance to be possibly the third best player by the end of the year behind Zion and Brandon Ingram. And then the CJ McCollum, I know things are heading in the right direction, looking much, much better than they were. What's his availability for this team? CJ McCollum is a full go. He's been playing back in their lineup. He obviously for for him, it's a different role that he's coming back into. He started the year as a point guard for the Pelicans. I think now that he's back in the lineup, he's been playing off the ball. And this is similar to his role that he played in Portland, playing next to Dame Lillard, playing off the ball a lot more. Spot up shooter and the Pelicans need his shooting, getting his shooting. Trey Murphy shooting. Those are two big time shooters back in the Pelicans lineup that can only give Ingram and Zion Winston more support. We like that role for him. I do. Yeah, I do. I like points, Zion. I think it was a time where Zion did play point a little bit. So weird. But I think it's just I think he's playing his best basketball because he's just more available. He looks healthier. He looks in better shape and he's still getting in better shape. But the chemistry, it looks pretty good. He's taking on, I guess, the role or what they're asking him to do. I didn't want to say it, but he looks good because we're watching him play. Yes, he's always been a talented basketball player, but he's available. So I always feel like I'm walking on eggshells when we talk about Zion, because I don't want to jinx anything.   So I'm just sort of like, shh. Well, we're going to talk too much. We're a quarter of a way there. I know, bro. We've got some good basketball out of it. It's good. All right, we're going to take a quick break here. When we come back from the Cleveland Cavaliers, it's George Yang. Bright and early on, run it back. Run it back. There he goes. George, you found your corner, didn't you? Run it back. Run it back. All right, there he is in the corner that he found. George Yang, eight-year NBA vet from Cleveland. He is here and we are going to start the show. George, first of all, thank you for the early time, nicknames. Minivan. Well, so that's a Donovan Mitchell creation. Why? What is that? No, I mean, so when I was fighting my way to make it in this league, as we all know, I was I wasn't in the rotation. I had an opportunity to get in at the end of the game. And I had like a wide open dunk and I went up there and, you know, kind of like laid it in. You know, I got to the locker room and I think it was like Joe Angles, Donovan Mitchell. We're like, well, what the heck was that? And I was like, listen, I know you guys are like Ferrari engines. Wow. I'm like a minivan. I need a couple laps around the block to get the top speed.  I hate to say it, George. It's started. It fits. Do you like it? It's fitting. It's fitting. Has it turned into any sort of moneymaking opportunity? I mean, there are a lot of minivan companies, I guess. Right. Let me let me tell you this. You put something, anything on a sweatshirt or a T-shirt and sell it. You can make some money these days. It's a great point. A minivan company would love to get an NBA player. Yes. We got it. We got to get you a minivan. We could cook something up right now. We got to get you a minivan, brother. OK, I love the idea of nicknames. Lemonpepper Lou, which forever will follow you. Icy Hot down there on the end. These are these are just I think they're fun. Is there a best nickname and a worst nickname that you can remember? I definitely have the worst. OK, fine. I don't care for mine either. No, I don't. Yeah, mine isn't great at all. Really, you guys, nobody likes their nicknames? No. I've had a couple that were decent. OK, give me the ones you do like. Icy Hot one when I was I definitely hated that one. OK, we hate Icy Hot. We're not going to call you that ever again. Which one do you like? When I was in the Lakers, Deadshot was one. I mean, Green Ranger, everybody goes by like your Instagram tag. Yeah. We talked about Kelly Ubrea earlier. You had the tsunami poppy situation. So most people go by the Instagram tag, which aren't, which isn't bad. Villain, obviously Dylan Brooks. That one's good, self-pointed.  Yeah. It doesn't represent a great thing. Yeah, you know, it represents a time in the bubble where things didn't go well. I think it's legendary, quite frankly. It's legendary. All right. Well, who is somebody who has a nickname out there? It could be an old one, too, that really stands out. I like the Slim Reaper for Kevin Durant. I thought that was, I really like Slim Reaper. Yeah, Reaper's good. Yeah, very fitting. There's one that comes to mind, the best one I like. But people don't know about it. I used to call this play Dylan, right? I used to call him Frozone. Frozone? Yeah. Good. All right, I like that. If you see him and look at him and how he used to play. That's hilarious. He kind of, like I skate on the court, like he always. That's hilarious. I like that, actually. Strides is why he had strides. We're shams, because I feel like we need a good one for shams, too. Although the internet has given him some shams. Gee, to follow up on easy, you guys went three-in-one. You guys went three-in-one in group play. You guys didn't advance in the end-season tournament, but I'm sure you won that 500K. So how disappointing was that? And how bad did you guys want that money? Yeah, it was frustrating. When you saw how we were playing the last game against Atlanta, trying to get to beat the points spread, it makes you wish you could go back into games one or two when you had its team down 20 in the coach subs in, and you give up a lead. Don't get in any trouble, George. I mean, it's just a whole different, yeah, yeah. I mean, I'm just being completely honest.  That's making me trouble. You're just trying to get to the point where you could play in Vegas for a lot of money, and the point differential thing kind of makes it hard to adjust, right? You're so used to preserving your superstars and not trying to overwork them. But at the end of the day, you need to get to a certain point amount, especially if you've lost games early in group play. So if there's one thing you could change about the tournament, sorry, Shams, to cut you off. What would you change, George? I mean, I think through group play and everything like that, it's actually been pretty smooth. There wouldn't really be anything that I would change it. Maybe, you know, give six teams in each. So we can get it to you for this money. But other than that, I thought it was pretty smooth. I think they did a great job, especially for just, I don't want to say coming out of nowhere because we've heard about it for a couple of years now, but I thought it was pretty, you know, well run. Some of the courts were pretty hilarious. So I thought it was a good job. That's a good way to describe it. Yeah, G, in that Hawks game, the Hawks pulled their starters down 20. You guys left your guys in trying to get that point differential. Was that awkward for you? Were you guys uncomfortable? Heck, no, it wasn't awkward. I thought that if someone's going to give you an opportunity to continue to beat them, you want to take that opportunity, especially, you know, with the point differential, it made you think back, you know, to whether, like I said, whether it was Detroit or whether, you know, you know, we could have had a better ending to the Indiana game where do you not foul and just play it out and only if you're going to lose by four rather than fouling and lose by six, it just adds a whole different dynamic and excitement. And I can't wait to see what this week does, you know, definitely with the games tonight and then in Vegas.  It can't help it. Well, as the viewer, that's all we see. But as a player, I mean, does it bother you guys at all? Has it been just sort of something to laugh about? The Indiana one, I thought we were playing the Indiana Cookie Monsters because that was the craziest court I've ever seen. And that was our first look at it. But some of them, I don't even know who's, like usually when I turn on the TV, I can see who's playing. But some of the courts, I have no idea who's playing. Ooh, that one. But I think it was a good switch up. And at least, you know, the fans know that, you know, the game is meaningful when that court is on and it's an in season game. And I think the NBA did a really good job and obviously there's room to grow, but I think this was a great, you know, head start on this. G, you played two scenes in Philly. What was your favorite part about playing for the Sixers?  And then obviously, you know, the type of fan support, what if I was good, bad or indifferent, you know, they're gonna let you hear about it. Danny can test to that too. And then, you know, just being surrounded by, you know, a solid group.  You know, so just being surrounded by, you know, those guys playing in Philly was great for me. It jolted my career to a new spot and now I'm enjoying my time in Cleveland. That's crazy. Didn't mention me. Didn't mention playing with me, George. That's crazy. I thought you were gonna say one of the best times I had was playing with Danny. I didn't want to do that because then people are gonna be like, this guy's fake and you know, that's not me. That's not real. We appreciate your genuine answer. So honest. But I know Danny can speak to it as well. I pulled up all of you in the corner and it was a three. We had great times together. Dead shot. Yeah. Green range. I'd love to hear both of you guys talk about the Philly fans though. How do those fans compare to Cleveland fans? Danny was just seeing Cleveland. How do they compare to Jazz fans? George, how do Sixus fans really compare to those fans? I'll tell you a story. When I first got to Philly, I think it was a pre-season game and I like humpfaked and dribbled to the side and dribbled off my foot and it went out of bounds. And there was some dude in the stands that was like, what, we're going to shoot the ball. And I was like, wow, this just got real. They are one of a kind. They are, there are no fans like them in the world, but you gotta love them. And they have gotten better over the years. I will say that. My first stint was rough, but over the years they have gotten a lot better and they've become more welcoming to the teams and have chosen different routes instead of booing us at times when they could have booed us. I appreciate the Philly Flint. I'm actually glad that I spent my first eight years in Philly because it taught me tough skin. Tough. Yeah, it gave me an opportunity to learn what the NBA is really like. Very tough fan base, but I tell you what, you do your part, you will forever be legendary in Philadelphia. I've actually been in a restaurant after a loss and they walk over to your table like, why are you, like, what are you doing? Go home. Y'all just got beat, bro. Like, why are you outside? Yeah, like, you shouldn't be human. You should not eat after a loss. That's the type of fan base they are, but if you do your job, man, they will love you forever. So I can attest to the Philly fans. I mean, if you watched the Eagles game yesterday, they're crazy. You and Joel and Bede are close, but when you first got to Philly, he said, I used to think he sucked. Yeah. How did you win him over? Yeah, what is this, a roast? Mine, good. Just good information. Yeah. You know, I think if you know Joel, Joel wants to be surrounded by guys that, you know, know how to play and can keep their defenders out of his way. So after making a couple of threes, I think, you know, I gained his trust. And we had a real good relationship from there. I know, you know, I think Joel puts a lot of pressure on himself to be great. So he expects it, you know, out of everybody else on the court. And I don't want to say I was lucky enough because I work at it. But if you can make enough shots and keep the guys out of his way, you know, he'll trust you. You know, Dave and he can attest to that. He'll even walk up to you. I think after you miss a shot, be like, I need you to make that three. I need you to make. No, I just, I think that's Joel's take on everybody when they first get there. Really? And then if you make a couple of shots, he will start to like you.  The first thing he'll say to you, you make shots, you can stay on the team. No pressure. You also went to his wedding this summer. And I'm sure it was a beautiful ceremony. It was very classy, very nice. But you got to tell me about the after parties, man. What was the wildest thing you experienced at the after party?  Actually at the wedding, I was like, I'm not, I don't really do a bunch of cool stuff like that. So that was probably, you know, the coolest part.  We know how he is as a competitor. What's he like to party with? You know, I don't think he does it often, but when he does, he does it big. He doesn't like the MVP, that's for sure. Gee, this is the second time you're playing with Donovan Mitchell. How has he improved since those Utah days and what have you seen in his growth? You know, I think the biggest thing is when Donovan was in Utah, I think he was just so athletic, he'd get anywhere on the floor and do whatever he wanted. I think now he really realizes where his spots are and has really turned into an elite, you know, three-point maker, whether it's contested, wide open, catch and shoot, he's really turned into an elite, you know, three-point maker. And I think he knows where he wants to get on the court, where Utah was kind of like figuring out where I could get. I think he knows his spots and where he wants to get. And I think he's ultimately, you know, grown in the point guard position, whether it's getting his teammates involved early so that late in the game, he can take over and he does an elite job at that. Was your familiarity with Don, the reason why you chose to go to Cleveland? Was it one of the reasons why you chose to go there? Yeah, I mean, for sure.   And I want to see how long they can drag this thing out and signing a three-year deal knowing that there's a young core here that, you know, we will have a chance to be good for a long time. George, I want to just apologize ahead of time. I feel like I'm getting the bad questions for you today, but here we go. It's all right. Is it true that DeMarcus Cousins once called you a teletubby?  Why am I getting all these awful questions?  I do, I don't know why we got here. We have bad, we have bad reports, but it's cool. It gets better. It gets cool.    I was a, it was like my second or third year in the league. Nobody had heard about me. I'm a, you know, well proportioned. So it's a great way to put it, George. Well proportioned.  And so that's what he was saying. Let me tell you this. I was avoiding that corner by the Warriors bench like the plague though. I was playing like that. So it worked. Yeah, don't go, has anyone ever said anything, called you anything? And this, for all you guys, that made you actually laugh? Ah. Yes, for sure. A hundred percent. Really? There's a lot of things. Oh, Danny, Danny, Danny's a culprit of this too. And now that we're a teammate, he's a snake. When we were in the, when we were in the bubble, he went up and down the court and the whole Lakers bench would be calling me like baby duds, maybe you're a duds. He was calling baby duds, baby Jared Dudley. When I was in Philly, we used to call him, but we were teammates so we didn't ever tell the other team but we would make fun of him, call him some funny names. I won't put it out there because people might start trolling you on the internet. But we had some funny, some good funny names for George. I like to try that. Some from Sesame Street. I mean, that's cute. Oh no. Some characters from Sesame Street. That is bad. Does it, do you do homework? I mean, to try to, in the past there have been some good moments from certain guys that they did a little homework and they dug extra deep. Do you guys do that when you come up with trash? No, I'm not one of those trash targets. We have a couple guys come through the past that done homework, but we weren't when those had to trash. That deep. Yeah, no. All right, fair enough. By the way, George, I am sorry. I really had so many nice questions to ask you about your hobbies and things you like to do. And then I just got the roast questions. Yeah, we put her up to it. Forgive us. Oh no, I'm sure Danny would probably had you do something like that. But next time, next time. Next time. And make sure we get some good ones. We appreciate the time. I want my personality out. By the way, good luck the rest of the way. We appreciate the time. Thank you so much. George, before you go, she had one more for you. I mean, the last one, I'm so glad we didn't get to. So we're out of time. We are out of time. Gilbert Arenas, not this time, buddy. You're not getting us. Thank you so much. Good luck, Brody. Corona back returns. Appreciate you guys.  Very serious moment right here. Kim Johnson. Ooh. Carolina legs. I like those jerseys. I didn't even know what team there was at first. Ken gets one of these once a year, man. It's crazy. Because back in Carolina, I think his first couple of years, he was still trying to get healthy. And I'd never seen him do that in college. But he's doing it at this level. I feel like those jerseys remind me of the opening credits to Fresh Prince. I can see where you're going with it. Uh-oh. OK. Troy Murphy. Any time, never leave your feet, Troy. Ooh, I like that one. You got your man's dunked on. Oh my goodness, that angle's awesome. He's going to be special. I like his game. I like this kid. He's going to be a really good one. One day. That must be so fun. Trey Murphy. Welcome back. Good lord. All right. Twink, twink. Skipping in the lane. Wow, OK. That was just a, ooh, going through you. That's just man to man right there. Yeah, he barely made moves. He's just like, I'm going to run straight to the lane, get out of the way, excuse me. Excuse me. Oh, it's the same game. They was above the rim in this game. Yeah, this game was fun. Orlando's the point where we worked, too. Orlando won the top defensive league. Orlando was kind of fun. All right, here we go. That's the thing. Damn, Chet. He looked at Chet and said, all right, and you know what? Derek Lively? Yep. He didn't even think twice. He looked at Chet. With a pump, too. Oh, that's good. Oh, Mark Cuban in the back. Yeah, Mark Cuban. Slick, I am one, too. It's always funny to watch you just see different reactions. That's my favorite sometimes, actually. Oh, my God. Oh, my God. That's nasty. It didn't even look like he was about to take. Oh, yeah. Chess in the chest. I like that. Kessa tried to get out of there. Tried to run out. Just tried to take the ball out quick. Exit, look, you tried to run to the bench, you got it. That's pretty fun. Oh, man. It's not, yeah. Last but not least, the kids. Uh-oh. Yeah, this is disrespectful. Let me see this again. It's pretty smart, though. Yeah, it is smart, but it's disrespectful. That's the heads up. Who thinks of that, though? Not one says that cross-smile. What the? What? But you could have a referee that might be a prick and just still say it's off you. Oh, my God, that's awesome. Even though it's perfectly legal. Yeah. And then his smile. Shout out to this young kid, man. That's the heads-up play right there. Who knows, man? Going to Missouri next season. Yeah, maybe they're a better half-court team. They want to slow the ball down. We're going to start a new trend for today's game. Gosh, he's so young. Definitely started a trend. OK, that was, yeah, that was pretty fun. We take a quick break here. We come back a little bit more on it back on a Monday morning.  Time to put on your convincing caps. First up, Danny. Convince me, there should be no fouls called in the final two minutes of a game. So my imagery that I have for the last two minutes of the game is like 21 when a guy has 20 points and you don't want him to score the last basket. So the final two minutes of the game would be like that. There's no fouls called. There's a lot of havoc, kind of like the purge of basketball. Last two minutes are free for all, where you can see real guys get to it and see who's really strong enough to flex on somebody when they get a basket. I'm convinced. Because if you can get a basket while you're getting fouled like that in the last two minutes of the game, you have the right to flex on people. I like the basketball purge idea. All right, Knight and Lou, convince me. When a player fouls out, that team should not be able to replace him. I'm going to convince you guys that this rule should take place only in the fourth quarter. So once you get down to the nitty gritty and teams are not usually subbing anyways, if you foul out, we're playing five on four going down the court. I'm going to say under four minutes, you can't replace a player. OK. I like that. Soccer-esque. I like that. Yeah, I don't hate it. All right, Danny, convince me the NBA should have a four-point shot, but only in the fourth quarter. I mean, I love it. You know, I'm a three-point shooter. The more points, the better. Obviously, make it a little bit further distance. And it makes the game more exciting, more entertaining. So if a team is down eight with a minute to go, they have a really good chance at making it interesting. So I think we've seen something like this in China. And I think we can kind of bring it to our league at some point in the near future. I like it. Lou, you like that one? I'm messing with it. OK, we're doing that. We're doing that. Fair. It would have worked. Convince me, teams would be better off without coaches. It's a free-for-all. Just let everybody do what they want to do, no obstruction or nothing. Let's just see who's really the best of the best. Because coaches really put some players in a position to be successful by their coaches. Let's see who really has an IQ. So let's see who really has an IQ who can really hoot. No coaches. I mean, the leaders would really show themselves as well. For sure. And if you don't have a leader on your team, that's going to get awkward. Danny, convince me, players should call their own foul. This is tough because it's going to be a lot of bickering. It might not get a lot of basketball. You guys are calling their own calls at the end of the game or during the whole game. But I think for entertainment purposes, the fans love it. People love, people argue. People love tussle. People love debates. I love it. So I think this creates a lot more debates on the court. It would be some long-ass games. That's the only thing. Lou, convince me, the Bucks could beat the Pistons with a randomly selected fan from the crowd. I'm going against the grain. The Bucks can absolutely not beat the Pistons with any random. You know, we have this thing. The worst NBA player that you can think of, if he goes to LA Fitness, he's going to run a gym. No random fan can get out there. So no. Could be a ringer in the random fan. We'd have to have it. 0.01% chance. It really is. That's it for us. We'll be back tomorrow. Danny's here all week.


This lecture is part of an online commutative algebra course and will be about some examples of art in rings. So last lecture, we had this rather hairy theorem saying that artinian rings are notarium. And we also showed as a consequence of the proof that any art in ring is a product of local art in rings, which makes them particularly simple to study. A typical example of this might be something like the art in ring Z modulo 60Z. And the Chinese remain the theorem from number theory says that this is just Z modulo 4Z times Z modulo 3Z times Z modulo 5Z. So here we've got an art in ring written as a product of three art in local rings. And this is sort of fairly typical of what happens in general, except it gets more complicated. So now what we're going to do is have a look at some examples of art in rings and we can classify art in rings in terms of their length. So you remember every art in ring has finite length. And let's just do art in local ring. So if you've got an art in local ring, it's got a single maximal ideal M and R over M is going to be some field K. And if R has length N over K, it is in some sense about the same size as an N-dimensional vector space over K. Although as we'll see in a moment, it need not actually be a vector space over K. In fact, you can see it right here. So this is about the same size as a two-dimensional vector space over a field with two elements, but it's not a vector space. Anyway, so if we look at length zero, this is trivial, we just get the zero ring. Length one is equally trivial. We just get one example, which is the field K itself. Length two starts to get a bit more interesting. So one way of doing this is to take a ring, polynomial ring K of X and quotient it out by some polynomial F of X of degree two. So we might take it as to be K of X modulo, say X squared plus AX plus B. And now we get several slightly different cases. We might get KX over X squared. And this is a non-reduced ring. You see that the element X is nil-potent. On the other hand, you might take K of X modulo X minus alpha, X minus beta for some alpha and beta in K. And by the Chinese remainder theorem, this is just isomorphic to the product of K with itself. So here we have an art in ring. That's the product of two art in local rings. Finally, we might have KX over F of X where F of X is an irreducible polynomial. So this will just be a bigger field containing K. So a fairly typical example of this, you might just take the field Q of I, the sort of Gaussian numbers, which is just QX modulo the ideal X squared plus one. So it can be a field or product of two fields or it can be this funny non-reduced ring. So these are examples that are vector spaces over K. We can sometimes find examples that aren't vector spaces over K. So a fairly one we had up there was just the ring Z over P squared Z, which is length two. And here the quotient field K is just Z modulo PZ. And for higher length, things like this that aren't vector spaces over K become a little bit tricky to classify. In fact, even ones that are vector spaces become tricky to classify. So let's just look at some length three ones. Until nothing terribly new happens, we can get things like K times K times K and analogous to this. We can get things like K of X modulo X squared and then we can take a product of that with K. We can take a field of degree three or the product of a field of degree three and the field of degree two and we can get something that's slightly new. We can take polynomial ring in two variables and quotient it out by the ideal generated by X squared, X, Y and Y squared. So now this is a three-dimensional vector space with basis one, X and Y and any product of two of X and Y is zero. And in dimension four things become even more complicated. So let's just have a quick look at some examples of length four. Well, here for example, we could take our ring R and it might have a maximal ideal and this might have a, has the square and the cube with the maximal ideal and we can take this to be zero and we might take this to be dimension one and we might take this to be dimension three. Now you notice we've got a map from M over M squared to M squared over M cubed and this is dimension one. So we can identify it with the field K and this is dimension two. So and our map could take X to X squared and now what we've got is more or less a quadratic form on a two-dimensional vector space. So there's a sort of quadratic form encoded in this and over various fields K there can be quite a lot of quadratic forms. For instance, if K is the field of rational numbers there are a fairly large number of quadratic forms in two variables. And again, instead of taking this to be this question be two dimension high length this could have dimension higher than two. So the classification of these is going to be more complicated in classifying quadratic forms over the field. For length greater than or equal to five and six the classification becomes starts becoming really rather complicated. In fact, what happens is it becomes so complicated you can't really describe the classification. And this is something whenever you try and classify nil potent objects. So if we've got an art in local ring with maximal ideal m, you know the ideal m is nil potent. So m to the n is equal to nought for some finite n. So we've got a sort of nil potent thing lying around. And nil potent things include art in rings and they include, well, nil potent ly algebras and they include things like finite p groups. And what happens with nil potent objects is if there are any generation by one or two things you can usually classify them. But as soon as they start being generated by too many things and being a sufficiently high dimension, the classification goes completely wild. For example, for finite p groups, I looked up the number of order two to the 10 which doesn't look all that imposing turns out to be<PHONE_NUMBER>2. So the number of nil potent finite groups grows very, very, very rapidly with the dimension and it's sort of hopeless to classify them beyond a rather low point. And what I'm going to do next is to show that for art in rings, the classification again goes a little bit wild. As soon as the length and number of generators becomes a little bit too big. So we can ask what is the dimension of the space of art in rings that are over a field k that have dimension n and have m generators So what we're doing is we've got m generators. So we take the field k of x1, x2, xm and we quotient out by an ideal of co-dimension n and we can think of these ideals as forming some sort of space. And we can ask what is the dimension of this space? Well, one obvious way to get ideas like this is to take n distinct points in affine space a to the m or should just k to the m and then take the ideal i to be all polynomials vanishing on these n points. And we've got n points in m dimensional space. So that sort of gives us an mn dimensional space of art in rings. And in general, you can try and imagine a general art in ring like this to be some sort of limit of n points moving around an m dimensional space. And this would suggest that the dimension of the space of art in rings is mn. And this is a very plausible argument which everybody thinks of when they first start studying this question. And it works for m equals one and two.  And this obviously has dimension n times one. And for m equals two, it's still true. But for m equals three, it just fails totally. In other words, there are more ideals of co-dimension n that you might guess than you might guess by using your geometric intuition about this. And it's not very difficult to see that there are ridiculously large numbers of ideals and dimension m. I'll just write down a few of them. So let's just look at the ring kx one, x two, x three. So we're just taking m equals three. And let's take the ideal m to be the ideal generation by x one, x two, x three. And then we can look at m to the i. And I'm going to take the ideal to lie between m to the i and m to the i plus one, where i is some integer greater than zero. And now you notice that any subspace i like this is in fact an ideal. So we can generate lots and lots and lots of ideals of finite co-dimension by taking any subspace of m to the i over m to the i plus one. And let's just try and estimate very roughly how many of these we're getting. So what's the co-dimension of this? Well, the co-dimension is, I don't really care exactly what it is. Something of order i cubed. I mean, it's roughly bounded above and below by some constant times i cubed. And similarly, this also is co-dimension i cubed up to some constant. This is also a co-dimension that's roughly i cubed times some constant. And then we notice that the dimension, oops, the dimension, let me try again, that worked. The dimension of m i over m i plus one is roughly some constant times i squared. So the dimension of the subspace of subspaces of m i over m i plus one is about order i to the four. So the space of all subspaces of a vector space is called a grass manian. And if a space is dimension n, then the dimension of the space of the grass manian is some constant times n squared very roughly. So we've got enormous numbers of ideals, but the co-dimension, so the number of space of ideals has dimension something times i to the four, whereas the co-dimension of the ideals is something times i cubed. And this number here is going to be approximately the number n, which is the co-dimension, and the number m is going to be three. So the co-dimension of this ideal i is going to be order i cubed. So m n will also be order i cubed, and this is very definitely less than the dimension of the space of ideals, which is order i to the four, order i to the four. So what this is saying is that art in rings with at least three generators tend to be a bit weird and they're rather hard to imagine.  And people study these quite a bit, especially for spaces of dimension one and two, but as soon as you stop looking at spaces of dimension three or more, the Hilbert schemes become kind of wild. The rule of thumb is that anything that possibly can go wrong will go wrong for a Hilbert scheme. So let's have a few more examples of art in rings. One way in which art in rings often come up is as a tensor product of two fields. For example, what happens if I take the tensor product of the complex numbers with the complex numbers over the reals? So this is a algebra of dimension four over the reals. So it's an art in ring and it splits as a product of art in local rings. So in fact, it splits. It turns out to be just a product of C and C. By the way, don't confuse the tensor product here with the ordinary product here. It just happens that the tensor product of C and C happens to be the ordinary product, same dimension as the ordinary product.  Well, if it splits as a product of two things, these should be generated by idempotence because the unit of this will be an idempotent in this ring here. So what are the idempotence? So in this ring here, we should be able to find two idempotence. You can write them down like this. It's one times one plus i times i over two and one times one minus i times i over two. You can check that both of these square to themselves. So they give this decomposition of this art in ring into a product of art in local rings. We can do another example. Suppose we just take q of root two, tensor over q with q of root three. Then this is actually a field. q of root two, root three. So sometimes a tensor product of rings will be a field and sometimes it splits as a product of fields. So you can see that's the tensor product of r. We join the square root of minus one on both sides and here we join the square root of two and the square root of three. So we can ask, when does a tensor product like this become a product of fields and when is it just a field? Well, that's fairly easy to answer. So let's look at k tensor over k with l with k and l separable finite extensions. I'm gonna say k and l separable. I mean k or l is going to be separable for the moment. So let's suppose that l is separable. So we can write l is equal to k of x, modulo f of x where f has no multiple... So f is a separable polynomial. So it has no multiple roots in the algebraic closure of l. And then k tensor over k with l is easy to figure out. This is just the same as k of x, modulo f of x. And now we notice that f may split in k. So we're assuming f to be irreducible here. So it's an irreducible polynomial in little k of x, but it might not be irreducible in this. So it splits as a product of factors, f equals f one of x, f two of x, and so on. And the key point is these are all co-prime. And the reason they're co-prime is that f has no multiple roots.  And this implies these polynomials are co-prime. And since these polynomials are co-prime, the Chinese remainder theorem implies this is k of x one over f one of x times k of x two over f two of x and so on, which is equal to product of fields. So we see that if l is separable, then this art in ring decomposes a product of art in local rings and all the art in local rings are just fields. Well, I've been emphasizing this separable condition several times. So obviously you can ask what happens if it's not separable. Well, if it's not separable, something a little bit weirder can happen. So let's take k equals k and let's join the pth root of a where k has characteristic p greater than zero and a is not a p's power. So we're assuming that x to the p minus a is irreducible. And let's take l to be k times the pth root of a as well. So l is equal to little k of x and then we're quotient out by x to the p minus a. So k tens of over k with l is just equal to k of x to the p, so k of over x to the p minus a. And let's say big k is equal to little k of b. So b to the p equals a, and I'm calling it b rather than x so we don't get confused. And now you notice this over k, this factors as x minus b to the p. So this is equal to k of x over x minus b to the p. And now you notice this has large numbers of multiple factors and this ring here has nilpotent elements. So it's got this nilpotent element x minus b for example. So in particular, this isn't a field at all. It's some sort of art in local ring with nilpotent elements. So this is still an art in local ring but it's not a field or a product of fields or anything like that. So in characteristic p, if you're working with inseparable extensions some slightly weird things can happen when you look at tensor products. Just to finish off by remarking that in general the tensor product of two art in rings need not be an art in ring. For instance, if you take the tensor product of k of x that's the field of rational functions and x over k with k of y you can check this is not an artinian ring. So these are infinite dimensional over k so perhaps that's not too surprising. Okay, that's enough about artinian rings for the moment and next lecture we will be discussing associated primes of a module.


So it's 9.30am and we're starting to get a wind off the shore. It's just six knots right now, but it's building, it was five knots the last time I looked. So we've got the white sails up right now, but very soon I think I'm going to put the momentum asymmetric spinnaker up. And see if we can milk this for all it's worth for the next several hours. Well, to be honest, this will only last maybe two hours. And then it's going to change like yesterday and come from that direction. So I might, meh, I can easily, well I can't easily tack the momentum in very light airs. It's easier to tack it when you've got 10 knots of breeze than when you've got virtually nothing. Just flaps and flips and flaps. So we'll see. I'm just chilling. I've done all my housework this morning, refilled the fuel tank. I left with the tank the only one quarter full. I was going to go to the fuel pontoon and then I thought, ah, I got 40 litres of diesel on board already. Plus what's in the tank, that's probably about 10 litres. And I'll just restrict myself to that. So that's what I'm doing. I've only run the engine for an hour and a half total so far. And I've now got 30 litres in the tank. About two litres in one gerry can. Why does it matter? Whether it's in a gerry can or not. And 20 litres in another gerry can. I've got about 52 litres of fuel on board. Okay, this is future Dave. I'm just watching the videos as I edit them. And clearly, if I started with 50 litres and I've run the engine for an hour and a half, I don't now have 52 litres on board. That would be quite something. Back to the show. And that's more than enough to be honest. I'm only going to use it to charge the battery when I need to. Yeah, I'm trying a new policy today because yesterday the fridge took too much power. But I was thinking too long term, trying to keep everything in there frozen. And I've now decided actually because this morning I had bacon sandwich but the bacon was frozen. So what I've decided now is to put it on to like zero. Which means that it's not running at all at the moment. And it'll run a little bit later today. And let everything that's frozen in there gently thaw over the next couple of days as I eat it. Like today I'm going to have burgers and I've already had to take them out of the freezer, the freeze box, cool box, whatever it is. I'm rambling on again. There. You don't care about my power management. Look, there's the view. Spain. I've just read on the map where we are but I can't remember.  I even put a little cross on the map downstairs so I'll just poke you inside. You can have a look at the map and work out where we are. We're right there, which is near there. Which is on that chart there. Also on that iPad down there. There you go. We all know where we are. So 11 o'clock and as predicted the unsure breeze has already started. Enough for me to hoist that baby. I've adjusted the, what do you call it? The sulk of the top because previously it was trapping a little bit of the sail, but now it's too long. So I'm going to have to do that again. How much do you think that is? Six inches? That's what you said. I have no idea from this distance but there's a black mark on the rope and I need to be just a bit longer than the black mark on the rope. I think that's from the previous knot. Okay, we'll do that when we take it down eventually. But I think what we're going to do today is a little bit of, what are those sailors called, cutting the pie. Although I'm not really cutting the pie on a low pressure system or even a high pressure system, but I'm going to, this morning and early afternoon, I'm going to be on this tack heading away from shore. I've just forgotten what I'm going to say. So this morning and early afternoon, I'll be on this tack heading away from shore on the best angle I can sail with this sail to get the best VMG. And then it's not really VMG, it's VMG to the waypoint rather than VMG to the wind. And then sometime in the evening, because this wind is supposed to tonight, rather than just disappearing as it normally does, it's supposed to possibly veer a little bit to the south. And if that's the case, then I'll whack over onto the opposite tack and head kind of due north-ish, or as close to that as I can get towards, well, kind of not really Barcelona yet, but back towards the coast. Again, sailing at best angle to the wind downwind with this sail until the wind dies completely, which you will do about, I guess, eight, nine, ten o'clock, I don't know. We'll do the same tonight as we did last night, which is basically just chillax. Anyway, rambling's over. I'm missing the pod chest, should get back. So we're, I think I measured it, six and a half miles off shore, but we've still got plenty of phone signal six and a half miles off shore, but that's going to extend now, so I'm going to lose my phone signal quite soon. So I've done all my text messaging, got the wind, been Facebook, blah, blah, blah, and downloaded a couple of podcasts for me to listen to today, whilst we sail away from Zealand and away from the fish farms and the anchorages for the big tankers and the refueling old-ass boy thing, away from trouble into oblivion. Obviously he lost his job. See you later. And now we're flying. Bang on towards my current waypoint. I mean, we were reading the story. 5.2 knots in 11 knots of wind with the assi flying, just curling the leading edge. Beautiful.