We're here to help Delaney Walker retire as a Titan and to speak first, let me introduce our General Manager, John Robinson, with a few opening remarks. John. Good afternoon. So, Delaney, it was fall of 2005 before iPhones and GPSs. I broke out the Rand McNally Atlas. I was in my fourth year as a scout with the Patriots and I made my way to Wernsburg, Missouri, to see the Central Missouri Mules and a hybrid Titan receiver named Delaney Walker. And I happened to find a picture of Delaney in action. He was obviously the best athlete on the field as evidenced by the guy chasing him. And the ball security has improved, but we're a little loose there with the ball. If you'd told me that 17 years later I'd be standing here today. One, as a General Manager and two, talking about that Division II player who went on to have a remarkable NFL career, I'd probably called you crazy. But I was extremely fortunate in 2016 when I came here to the Titans that Delaney was on the football team. He was such a pivotal player for us offensively. He was a difference maker, a huge matchup problem for opposing defenses in that if you put a safety on him, he was going to be too physical for that guy to probably stay with him. If you put a linebacker on him, he was going to be too quick and too fast for him to cover him. And if you played zone, he was so smart and instinctive, he was going to find the void there and get open. All of the accolades that he had on the field, there are numerous to name, but there's four things that impressed me the most about Delaney. One was his work ethic. Two was his toughness. Three was his leadership. And four was his commitment and service to the community around here. All of his on-the-field and off-the-field accomplishments really made him a great example for all football players to look up to and to try to emulate. I'm proud to have worked with you Delaney. We as an organization are extremely excited that you are choosing to retire as a Tennessee Titan. And congrats on every single thing that you've been able to accomplish, man. Proud of you. I just want to make a couple comments about Delaney before we bring him up. Nearly 10 years ago, March 13, 2013, that was the day Delaney Walker became a Titan. And at that moment, almost 29 years old, wasn't always a tight end when playing seven seasons in the Bay Area. He caught an average of one pass per game for San Francisco. He was known more for his blocking and special teams play than his receiving. But he was well known for his toughness. And when he signed with the Titans, most of us who are football fans said, yeah, we know that guy. He wears number 46. But once he became a Titan, he became number 82. And it was like the new number transformed Delaney Walker. It's safe to say that he is one of the great signings in this franchise's history. Over the next five seasons, he averaged five catches per game. 71 catches per season, scored 26 touchdowns, three straight pro bowls. You know what he did off the field? His fight against drunk driving was his number one mission. We could always count on him in good times and bad for the media, for community events. He meant more than just being the great tight end in the number 82 jersey. He stood for excellence and he became a face of the franchise. When you talk about the very best Tennessee Titans, Delaney Walker is at the top of the list. So to all of us, it's only fitting that he is retiring here today in Nashville at Nissan Stadium, where he became regarded as one of the NFL's very best tight ends. Ladies and gentlemen, Tennessee Titan, Delaney Walker. In words, I've been trying not to cry. I'm not the one to cry. And I'm always the guy to tell what's on my mind.  And I want to start off by thanking the Adams family, the Titans organization for giving me that opportunity to come here in 2013. When I was in San Francisco, I knew no one knew who I was when I came here. And they probably thought, why did we get this guy? But the guys that were here, the coaches, the staff, they believed in me. They said, it's all up to you. You have the chance to be great. You just got to take it and run with it. And I looked at that as an opportunity. I knew what I can do in this league. I just needed the opportunity to have that chance to show it. And the Titans gave me that opportunity. And that's why I'm here to retire, because I feel like all my best years in football started here, here in Tennessee. And I'm thankful, thankful to have the career that I have, the family around me, my agents, my publicists, my friends. They all supported me. You guys supported me. I know I could be crazy sometimes and say some wild stuff in the media, but I was just trying to be as real as I can be and let you know how I felt and where the team was going at that time. So I'm thankful. I'm thankful to be standing up here, retiring as a Titan. Everything that they said about me is touch. It's touching. I'm sweating because I don't want to cry, but I'm thankful. I am so thankful to have this opportunity to retire as a Titan. And I just want to see the Titans go forward when a Super Bowl and be successful. That's all I care about and being able to do this. Hopefully this motivates them to get this done, gets them coached because we got things to do. And again, like I said, I'm just thankful to be here and thank you guys. It's been a while since you played. What made this the right time to go ahead and sort of make this official now? I started working with the Legends community and I felt like it was time to transition. It took me a while to realize what the transition was, leaving the NFL. There's no other job in the world like the NFL. So it took me a while to realize that I probably wasn't going to be able to play again. And that moment hit. Once I got my new job, I just realized that it was time to hang it up. And I wanted to do it with the Tennessee Titans. This was a case maybe where the league, the game was done with you before you were done with the game? I would say my body was done with the game, but my mind wasn't. And therefore I knew I wasn't going to be able to play. Just the issues I was having with my ankle, that prevented that. Fourteen years long time. How fast did it go by? I would say it went fast. The first seven years went fast because I barely got the ball. I didn't even know them stats. One catch every game, that's terrible. That went fast, but I think playing my last seven years, it fell forever. Because I think I love where I was at. I love the guys that was in that locker room. And I didn't want it to end. So I think that's why it felt longer being here in Tennessee. Years ago, you made that decision to come here. What was it that made you want to come to a city that you probably never even visited and make it home for so long? Opportunity. The 49ers, they offered me to stay, but I didn't want to be the backup. I didn't want to be the number two. I wanted to be the number one. And I remember Dow calling me up and saying, you know, we have Craig Stevenson, but he are a blocker. We need a receiving tight end. And if you got that skill set and you know you can be number one, then the job is yours. So I took that as a challenge and I came here and it happened. And that's what I was looking for. Just that opportunity to be the number one guy. How personally validating was that once you came here and had the kind of career that you did? It was big. That was a goal.  All they see is that I'm a tough guy. I can play special teams and I can catch the ball once again. So I knew my goals was to show them, show the city of Tennessee that they didn't make a bad free agency pick up. I was going to be that guy. I was going to be accountable and I was going to be tough and I was going to play my heart out every game. No matter if we was losing or winning, I was going to go into the last, into the fourth quarter, that last whistle and I did that. So it fulfilled everything that I thought it was going to. What did it mean to help elevate this franchise to the point where you did get recognition and now this team is winning and competing to win division titles and go deep in the playoffs? That's what it's all about. Recognizing that we have talent. The city of Tennessee, Tennessee Titans, we are a great football team. When I first got here, when you lose games, you don't get recognized a lot. Even though we had the talent, guys like Gerald Casey and myself that was snout from Pro Bowls year after year because they, we wasn't recognized. And I remember sitting there and Gerald Casey can probably remember this as well. And I'm like, for us to be recognized, we just got to go out there and woo people. If we don't woo people, they're never going to recognize us. And then that momentum started to shift. We started winning. We started going to the playoffs and then we started getting recognized. Pro Bow after Pro Bow. And then the guys now, the team that we have now and what they're doing and how they're talked about, how they're getting all the big time games and Monday night games. That's where you get recognized at. When you hurt the ankle, did you know immediately like, hey, this is worse than just a regular injury or what point did you know this? This is really a problem. I realized it was bad when I didn't feel it. So I knew something was up. I couldn't feel no pain. And I don't know if John was out there, but with the guys that was out there, I didn't cry. I didn't make a face. I didn't do anything. I couldn't feel it. I literally didn't feel anything. It severed my nerves. And at that point, I kind of felt like it's going to be a tough one to come back from. But knowing me, I was that guy knowing that I wanted to come back early. I wanted to show the team that I worked my butt off to get back on this field. And, you know, it just didn't happen the way I wanted it to. I took an injury. I think I took a hit in week five against Chicago, and it just never came back to where I needed to be to be able to play. How long do you think you would have played if not for that injury? I feel like I still would have been playing right now if I didn't break my leg. And as far as when you first came in the league, who or maybe some of the guys you watched and learned from, and then as your career went on, you got here, were you aware that some of the younger guys coming in were watching you? So I'm going to start off by some of the guys I was watching was Larry Allen. When I came in to the 49th, I had Brian Young, Larry Allen, Jonas Jenning. I got to play with Isaac Bruce. I got to, you know, I saw true legends go to work and do it every day and do it with a smile on their face. And I got to see that. And I remember just watching them playing Madden, and then I got to step in their rooms and one thing I took from Brian Young is he came to me and was like, that cold tub should be your friend. If that cold tub ain't your friend, you won't last in this league long. And everyone who knows me, I'm in the cold tub 24-7. So I took advice from these older guys that played the game very well and very long. And I hope these guys that's coming into the league now, you know, recognize that from a guy like myself, or Jarell Casey or Brian Rekpo, who was in that locker room, that showed them how to play the game at a high level and take care of everybody at the same time.  It means a lot because, you know, John is one of the best at what he does. And you can see over the years on how this team has changed and what he's brought this team into and where he put us at. So it means a lot to hear that from John because he's one of the best to do this. And I just, to hear them kind of words him saying, him come to Central Missouri, small town, word, word, Missouri. You probably wouldn't, you know, I probably didn't even know that and to hear him say that story and it means a lot because I know what kind of guy John is and I know how hard he worked to be where he at today. What about younger guys like John Smith? Oh, John Smith, I thought you said all. Impact on a guy like John. Well, John knew, you know, I took John who under under my wing and because I seen something in them. I knew he was the type of player I was. He had that ability to be a breakout guy and be great in his league. And I just try to give him all my knowledge. Anyone who was ever in that tight end room, I never held back. I wasn't the veteran to be like, they brung him in to take my job. I looked at as they brung him in to make us better. And if I can help that to make him better, that's going to make overall make the team better. So I did everything in my power to make sure every guy that was in my room knew what I knew and had to try to give them the ability to do what I did. I just remember you, when I hear your name, I think of quadruple coverage in Indianapolis and Marcus dropping it in the buck. That's my lasting memory of you. What's your lasting memory? What's the play you remember? The play I remember. It was Kota had to probably be against the Patriots. I just remember coming in that week and, you know, they wasn't talking about us at all, you know, just grunk, grunk, grunk. And this is just me. You know, I ain't tell the team. I was like, I'm going to outplay grunk today. And that's all I talked about. And I remember we were down and they came to me like, we need to play. And then Zach Mittenberger was the quarterback at the time. He threw me like a five-yard pass and I think at that point I was just angry. I was running out of anger. And I ran over like two people, ran down the sideline, jumped over somebody, stiff-thorn somebody, and then ran into it for a touchdown. And I always remember that. That's one play I will never forget. I felt like that was probably one of my better plays in NFL. You've stayed through several different coaching changes. When that happened, how nerve-wracking is that for a guy like you? And did you go to new coaches and say, look, you just give me the ball, you'll be fine? Or how did you approach that? So I've been used to having different coaches. When I was in San Francisco, we wasn't good at first neither. So we started off with like three different coaches. So I had knew pretty much every offense that you can probably run in NFL. So when we was having coaches changes, every time a different offense came in, I knew it. It wasn't that give me the ball. I let the coaches say, we're going to rely on you. I never was the guy like, throw me the ball, throw me the ball. I need the ball.  So I just let it come to me. I let them, I show them by doing. If I made plays on the field, I knew that they would come to me because they trusted me. So that was my mindset. What would people say to the people they see in the streets today, Titans fans? What do they say?  You should sign up, call John. I'm like, it ain't that easy. They mostly, and then they just tell me, you know, I'm one of the greats. But most of them will be shocked because I literally sit there and talk to them and shake their hands, hang out with them, invite them on the boat. If they dirt bike, I'll go dirt bike with them. I feel like ever since I stopped playing, I'm more genuine out with the people because it's almost when you play football, you kind of hide away a little bit because you're doing a season you don't really want to be out there. But it's like when I stopped playing, it's like I got to see more love. I was out more and I got to see people actually know who I am. And sometimes I wear a hat, I wear a mask and they still recognize me. Like, you Delaney Walker, just the other day we was in Target and this guy came up to me like, Delaney. I'm like, how you know it's me? He said the hair. So I'm like, I get that all the time. It's the hair. Everyone recognized me through the hair. So it just shows me the love that I have out here in the city when I do step out. What do you think Delaney, your legacy is with this team in this town? My legacy, that's a good question. I don't know. I feel like my legacy here would probably be my grit if that would be it because I never held back. I think I was too honest at some times with the media and I know that's not good. But I think, I know y'all do. I don't know. That's a good one. I'm going to have to tweet that when I realize what it is. So you're going to have to do it off the field stuff as well, do you think? I think a lot of the stuff that I did off the field was just because you know how much I care for the city too. And I grew up in a single parent household so I had the means to try to get back and show kids that they can be whoever they want to be. You don't have to feel like you trapped in a box. So I try to do as much as I could to show that message. So that could be my legacy too. I mean I got Man of the Year award twice, I think, yeah twice. Is there a reason why you love Nashville? So obviously you talked about how good the playing time was here but why did you follow up with the city side? You know it's coming from California to Nashville. The people here were way more nicer.  They didn't care that I play football. They may take a picture but they're not coming up hounding you and then cussing you out when you be like I don't want to take a picture. You know it's that different feel but then just the love of the city. I would have to say in my neighborhood I've never been in a neighborhood where everyone waved. I remember when I first moved to my neighborhood they waved at me. They looked like, do y'all know them? Why are they waving at us? And it just shows the love that people have in the city with each other. And I think that's what grounded me here. And I just, like I said, I just love being in the city. It's a lot to do and I've been here so long I feel like this is just home for me. There's a lot of fans who would say your legacy is the best tie down your team's ever had. Oh, uh, I don't know. I Frank, why check, you know, I watch Frank and some of the stuff Frank did. We two different tight ends. You know, I can't say that I am the best because what Frank has done for this organization is great too. So I always put Frank in front of me. I will say I'm the second best. What do you think when you watch this current Titans team? And maybe the players are one of some of them used to be your teammates and how much are you a fan now? I'm probably the biggest fan. I can't go to the games because I'm so much of a fan. I don't want to offend nobody because I'm yelling worse than Rable. I promise you. So, you know, I watch every game. I can tell you how to every player. I just want to see them do good. It's tough being when playing for a team and not watching them win. It hurts. I feel the same way and every time they win, I feel like I was in that locker room. I'm jumping around screaming when they lose. I'm on the same way. I'm like, John, can we cut him? Can we bring him in? Let me get my stats right. So I just, you know, I try to watch as much football Titans football as possible because I want to, I want to feel like I'm there. When they do win a Super Bowl. What do you think of the next young athletic titan and chigacombo with some of the fights that you would give him? I think for where he at now, he's doing really well. Obviously, every player can get better and he will get better as time go. He will learn the game a lot more, understand the concepts of what the coaches want him to do. The last game they played, he had that touchdown.   So I'm excited. Hopefully I can, when I come to the game, I may say a few things to him. I haven't talked to him this year, but I like what he's doing. I see him getting on the field more and that just shows that he's building his confidence. So I'm excited to see how far it goes. You played a long time. What do you miss the most about not being a part of the game anymore? I miss being in the locker room. That's one thing I miss. I don't miss getting hit. I don't miss practicing. I don't miss any of that. I actually miss being in that locker room with them guys. It's not like any other job to go in a locker room. You can joke, play, laugh, just to have that love with your brotherhoods. It was hard. That's the one thing that I miss the most and it's hard to swallow is just not being in that locker room with them guys.


So this time around we're going to be covering trees and ultimately heaps since heaps are just a specialized tree Some of the concepts behind trees this is Going to go a bit more in-depth than lists. They are a rather sophisticated data structure. So It'll be a lot of explaining ad goes fairly simple We want to add a one you add a one at the top add a two the two gets added as a branch So unlike a list they're not chained together They do branch off With the most typical type of tree being a binary tree. So that is each node branches off into two other nodes There are others there are trinaries as Like two two three four trees and they're I've even seen Only once an unbounded tree one that could accept any number of child nodes Given what trees are normally used for you usually just see binary trees But then we want to go out of three three gets added to the other side Now one important thing with trees is generally you try to limit the number of levels And that's to help Improve on what they were created for but if you were to just continuously chain on to the To one node you you just wind up with a list anyways So the you generally try to limit the number of levels When out of four on since the first node is already filled You have to go down to the second level and find the first empty spot And then similarly to add on a five we can add that onto two since the two still has an empty node Oh, yeah, no, no, I'm getting ahead of myself. Okay. Yeah, we're fine as for deleting this one Mostly works as you'd think Until you start deleting nodes that have children So for example if you want to delete a five it's very straightforward. You just clear out that node On the other hand if you want to delete say the two You actually have to you know Store the four delete the two Move the four over and then relink now If you're just the one using the tree, you don't actually have to Mentally consider all this stuff. You just delete two and Did that's what happens? But there's also an operation called prune. Let's say you want to delete two but also delete everything that is a child of two That's what pruning is you go through remove the child nodes of it and then remove two similarly you have graphed where you can take a another tree or part of another tree and graphed it on to the existing tree Now as for different types of trees Similarly to the list there's just a lot of them and it has to deal with why Trees were really created in the first place. I will get into that bit in the use cases but there's a lot of different optimizations for trees which creates just Dozens literally dozens of different types of trees There is one I want to mention here because it behaves a little bit uniquely to the other Trees and that's a heap Heaps are a tree that Really bad definition Enforce the heat policy that is the data In the heap But it'll be easier to just show it That's kind of why these are here. So if we're adding to the heap Let's say we have a 10 You want to add on an 8 that can be added as a child just fine Add on a 5 again that can be added as a child just fine Add on a 2 that's fine add on a 6. That's fine But if we want to add a 7 to what is otherwise a max heap you May notice that each parent is A larger value than its children and each child here is Smaller than 7 so you cannot add 7 as a child Instead what has to be done is Breaking off the 5 Moving the 7 up to be the child of 10 and then making 5 the child of 7 Otherwise all the operations are the same as long as the end result still satisfies the heap principle So as for uses of trees It's a lot just like lists. They are very sophisticated data structures Which makes them useful for a lot of different purposes But you do see them very common for sorting data and that's sort of how they originated especially the heap the heap was created to implement the heap sort algorithm But they're very good for that But they are also useful for the random access of data It's quicker to get to any random spot in a tree than it is in a list and that has to do with Trees different types of trees having different Organizational schemes and you can use that organizational scheme to quickly get to any location Next up I think we're gonna do buffers I'm not sure on that one there though


So, hello students. Good afternoon. So, today we will take the exercise six of sequence and very chapter. So, in this exercise, we will be particularly dealing with the questions on series. Like questions based on method of submission, whether it be a Sigma method of submission or method of difference, including VN method. And also, we will see the questions based on arithmetic or geometric progressions, like we what we used to call it as a GP. So, without wasting any time, let's start our working on exercise number six. So, here's the first question. We're saying the sum of first in terms of the series, one series is given here 1 by 2 plus 3 by 4 plus 7 by 8 plus 15 by 16. And we have to find the sum of first in terms of this series. So, let's try to write the Rth term of this series. Okay, we will write the Rth term of this series. So, what will be the Rth term, if you observe it will in denominator, it's a simple right in denominator, it's a two raised to power R. Two raised to power R. Okay. And in numerator, it is two raised to power R minus one, if you can observe, it is two raised to power R minus one upon two raised to power R. So, this is our Rth term for this particular series. Anyway, anytime we, if we have any doubt we can put the value of R and we can check whether our Rth term what we have written is correct or not. So, for time being let's I'm putting it as R is equal to three. So, our third term will be two raised to power three minus one upon two raised to power three. So, it will be eight minus one that is seven by eight. So, here also our third term is seven by eight, hence our Rth term what we have written is correct. Okay. Now, we have to find the sum of first in terms of this series. So, it will be sigma TR R going from one to N. Okay. So, we write it as sigma R is equal to one to N. What is our Rth term? It is two raised to two raised to power R minus one upon two R. We can further rewrite our Rth term as one minus one upon two raised to power R. Right. So, this will be summation R going from one to N. So, now I will distribute this sigma over both the terms and it will become one R raised to power one. Sorry, R going from one to N minus one upon two raised to power R, R is going from one to N. So, this thing will become N one plus two plus three. Okay. This will become N because one, it is not having any R component in it. So, it will be one plus one plus one, how many times? N times. So, it will be basically N and what will be this? This will two raised to power one put R equal to one. It will be one by two plus one by two square plus one by two cube up to one upon two raised to power N. So, it is basically a GP. This is a GP where the first term is, where the first term is one by two and common ratio R is also one by two. So, we can write the sum of N terms of a GP. It will be a R raised to power N or we can say one minus R raised to power N upon one minus R, one minus R. Right? So, further we can rewrite it as N minus this one by two and this one by two, this will become one by two in the denominator. So, it will be cancelled out. So, it will become N minus one plus one upon two raised to power N. Further, we can write this as plus two raised to power minus one. So, two raised to power minus N plus N minus one will be our answer. Two raised to power minus N plus N minus plus N minus one. So, option C. Option C is correct here. So, this question is done. Let's move to the question number two. So, here one product is given two raised to power one by four into four raised to power one by eight into eight raised to power one by 16 into 16 raised to power one by 32. So, this product we can write it as two raised to power one upon two square, right? One by four can be written as one upon two raised to power two. Then we can write it as two square four can be written as four, we can write four as two square and in power it is one by eight. So, we can write it as one upon two cube. Similarly, this eight we can write as two raised to power three or two cube. Power may two raised to power four. Then two raised to power four. Escape power may a jagat two raised to power five. And this product will go up to infinity, right? Sorry. So, if you see, okay, we will go one step further and we will write it as two, nothing is there. So, it is power one only and power will be multiplied by this. So, it will be one by two square as it was earlier. But look at this term. It will be two raised to power two upon two raised to power three, right? And it will become two raised to power three upon two raised to power four. Similarly, this term will become two raised to power four upon two raised to power five. Okay, this will continue up to infinity. Now, the target behind this is now you can see in this the base term is same like the base term is two only. So, we can write it as two and this power will be summed up. Like we can sum the power of this. So, it will become two raised to power two one upon two square plus two upon two cube plus three upon two raised to power four plus four upon two raised to power five. And this will go up to infinity. So, now what we will do, let's assume this as a series. What's written in the power of two. We will take it as a series s. So, we can write s as one upon two one upon two square plus two upon two cube plus three upon two raised to power four plus four upon two raised to power five dot dot dot dot up to infinity. Okay. Now, if you observe, sorry, if you observe this is the terms written in numerator is in EP 1234 with a common difference of one and that is multiplied by a GP with the common ratio one by two. So, for this what we do we use to we use to multiply this sum by the common ratio that is one by two s and we use to write the terms by shifting one side, like by shifting by right hand side. So, we can write it as it will become one upon two cube. Then it will become two upon. So, two upon two raised to power four, then three upon two raised to power five, and it will go up to infinity. Now, we will subtract this. We will subtract. So, subtracting this, this minus this we will have s by two, right. s minus one by two s will be s by two is equal to one by two squared plus one by two cube plus one by two raised to power four plus one upon two raised to power five and up to this will continue up to infinity. So, again, this is this. This thing is forming a GP, right. This is a GP with a common ratio of one by two and the first term is one by two squared or one by four we can say. So, we can write it as and this is going up to infinity. So, this is a infinite geometric progression series. So, it's a sum can be written as a upon one minus sum of infinite series of a GP, right. So, what is a? A is one upon four and one minus r, r is half. So, one by four upon one by two. So, it will become one by two. So, from here, our s becomes one, right. So, what's written in the power of two, this whole thing becomes one, this whole thing becomes one. Sorry, right. So, this s is becoming one. So, our product will be finally our product will be two raised to power s, what we have considered this two raised to power s. So, it will be two raised to power s, what we got s is equal to one. So, two raised to power one is equal to two. So, our product will be two. This will be our answer. So, option C is correct. Option C is correct for this question. Now, going ahead, let's move to question number three. One series is written here 1 plus 3 plus 7 plus 15 plus 31 plus dot dot dot up to n terms. So, we have to find the value of the series up to n terms. Okay, let's do it. So, let's assume this is some series as h, this summation as s. So, it will be 1 plus 3 plus 7 plus 15 plus 31 plus dot dot dot up to n terms. So, we have to go up to n terms, right. Now, if you observe the difference of the terms, the difference of the terms is will attain one progression. How? See, 3 minus 1 is 2, 7 minus 3 is 4, 15 minus 7 is 8, 31 minus 15 is 16, right. So, the difference of the term, the first difference of the terms, this we are getting a GP. We are getting a GP. What is the common ratio here? Common ratio is 2, okay. So, for such type of series, we can write the nth term as, sorry. So, we can write the nth term for such type of series as a r raise to power n minus 1 plus bn plus c, right. What is r here? The r is the common ratio, common ratio which is obtained after taking the difference. So, r here is 2, okay. So, our nth term, we can write the nth term of this original series as a 2 raise to power n minus 1 plus bn plus c. And what is a, b, c here? a, b, c look, a, b, c are constants here whose value we can identify, like whose value we can calculate, how to calculate, we will see it. So, we can write the nth term. Now, we have written, since we have written the nth term, now let's find the value of a, b and c. So, put n is equal to 1 here. So, we will get t1, t1 will be equal to a into 2 raise to power 0, 2 raise to power 0, that will become a anyhow, plus b plus c. So, I am deleting it and writing a. So, it will become a plus b plus c when we have taken n as 1. So, a plus b plus c is equal to, now what is the first term? First term is 1. So, we will equate it to 1. Now, let's write the second term, putting n equal to 2. So, it will become 2 raise to power 1 means 2a, 2a plus 2b plus c is equal to, what is the second term? Second term is 3. And similarly, let's write the third term as 2 raise to power 2, that will be 4a plus n was 3. So, 2 raise to power 2, 4a plus 3b plus c is equal to 7. Now, let's assume it as equation 1, this equation 2, this equation 3. So, subtracting equation 1 from equation 2, we will get a plus b is equal to 2. Similarly, subtracting 2 from 3, we will have 2a plus b is equal to 4. Now, again subtract it, again subtract it, we will have a is equal to 2. If a is equal to 2, put it its value here. So, if a is equal to 2, b will become 0. So, a equal to 2, b equal to 0, then put the value of a and b in equation 1, you will get 2 plus 0, 2 plus 0 plus c is equal to 1. So, c will become minus 2 plus 1, that will be minus 1. So, we got the value of a, b and c. So, we got the value of nth term also, right? So, we can, now we will write the nth term of the series as a was a is 2. So, 2 into 2 raise to power n minus 1 plus the value of b is 0. So, it will eventually become 0 and what is c? c is minus 1. So, the nth term of the series becomes 2 raise to power n minus 1 plus 1, that will be n and minus 1. So, this is our nth term. Now, we have to find the sum of n terms. So, simple you put sigma t r. If nth term is this, then our rth term will be replaced n by r, 2 raise to power r minus 1. So, sigma t r, where r is going from 1 to n. So, it will become sigma 2 raise to power r minus 1. r is going from 1 to n. So, distribute this sigma over both the terms. It will become 2 raise to power 1 plus 2 raise to power 2 up to 2 raise to power n and this will become minus n. So, this is a GP with first term as 2. So, we will write it as 2 r.  So, it will become 2 raise to power n plus 1 minus 2 minus n. So, this is our summation of n terms. 2 raise to power n plus 1 minus 2 minus n. So, option b is correct. So, option b is correct for this question. Hope this is clear to all. Now, let's take the next question, question number 4. So, 99th term of the series, this series is given as 2 plus 7 plus 14 plus 23 plus 34 plus dot, dot, dot it and it is asking the 99th term, the value of 99th term. Okay.  So, if you see, now let's take the difference. So, 7 minus 2 is 5, 14 minus 7 is 7, 23 minus 14 is 9, 34 minus 23 is 11. Okay. So, we are getting AP here after taking the first difference of the terms. So, this is actually AP, right? This is actually AP with the common difference of 2, with the common difference of 2. So, for such types of series, we write the nth term as, we write the nth term as a n square plus b n plus c, right? Where a, b, c are some constants, which we can anyhow calculate like we did in our last question. So, but the important thing is the nth term for such type of series can be given as a n square plus b n plus c means it will be a quadratic in n. So, let's try to find the value of a, b and c. For that, we will put n equal to 1 and we will find the value of t1. So, it will become a plus b plus c and what is t1 here? t1 is 2. Similarly, find t2. t2 will be 4a, 4a plus 2b plus c equal to 7. Second term is 7 here. The third term will be 9a, 9a plus 3b plus c is equal to 14. Third term is 14. Now, let's take as equation 1, equation 2 and equation 3. Subtract equation 1 from equation 2. We get 3a plus b is equal to 5. Same way, subtract the equation 2 from 3. It will become 5a plus b is equal to 5a plus b. c will be cancelled out. 14 minus 7 will be 7. Now, again subtracted, you will get 2a, b will be cancelled. 2a is equal to 2. From here we get a is equal to 1. Now, put value of a here. We will get if 3 means b will be 2. Now, put the value of a and b in equation 1. 1 plus 2, 3. 1 plus b is 2 plus c is equal to 2. So, c will become minus 1. c will become minus 1. So, we got the value of a, b and c means we got the nth term. What will be the nth term? nth term will be n square plus b and b and a was 1, no? And b was 2, okay. So, nth term will be n square plus 2n and c is minus 1. So, this will be the nth term of the given series, right? The nth term of this series. So, question is asking to find the 99th term, right? T99th. So, we have to put the value of ns99. So, let's do one thing. Let's make it a perfect square. So, it will be n square plus 2n plus 1 and minus 2, right? Now, the benefit of this will be it will become n plus 1 whole square minus 2. So, put, now put n as a 99 here. So, it will be 100 squared minus 2. That will be 10,000 minus 2. That will be nothing but 9,998. So, this will be our 99th term. So, option a. Option a is the correct one for this question. Okay. So, this question is done. Let's take our fifth question. So, this one is 6, this one is 5th. Okay. So, let's take our fifth term. The sum of the series 1 into 2 into 3 plus 2 into 3 into 4 plus 3 into 4 into 5 plus up to n terms is. Okay. So, first write the rth term for this series. First write the rth term of this series. So, rth term we can write it as r into r plus 1 into r plus 2, right? This will be the rth term put r is equal to 3 to cross verify. So, t3 will be 3 into 4 into 5 and here also t3 is 3 into 4 into 5 means rth term we have written correctly. Okay. So, we have to find the sum of this series. So, I will do one thing. I will do like we will solve this question by VN method. So, what I will do? I will try to break this rth term. I will try to break this rth term in terms of like in difference of two such functions which will be consecutive in r, right? I will break this rth term in such type of functions which will be consecutive in r. So, let's try to figure it out. So, I am defining one function VR as I am defining one function VR as where I will be taking one like r, r plus 1, r plus 2 into r plus 3. Like I have taken this extra term here, right? And I will also define VR minus 1, right? So, what will be VR minus 1?  Now, take the difference of these two functions. Taking the difference of these two functions, we will eventually see our the rth term. How? Let's do it first. Let's first do it. So, VR minus, VR minus 1, so VR minus VR minus 1 will become, so if you observe these three terms are common. These three terms are common in both the functions. So, I am taking that common that will be r into r plus 1 into r plus 2 and what is left out? Left out is r plus 3 minus r minus 1, right?  Like it will become 4. Now, you observe what is written here.  So, we can write it as 4 times of dr. This is what our target was. We had to break, like we were trying to break this rth term as a difference of two functions which are consecutive in r. So, we defined one function VR. We also defined one function putting r less than 1. So, VR minus VR minus 1 is equal to our 4 times rth term, right? So, this will be very much useful. How? We will see now. From here we can say our rth term will be 1 by 4 times VR minus VR minus 1, ok? Now, let's write our first term. So, our first term will be 1 by 4 put r is equal to 1 here. It will be v1 minus v0. What will be our second term? Second term will be 1 by 4 v2 minus v1. Similarly, third term will be 1 by 4 v3 minus v2 dot, dot, dot. If we take the nth term, nth term will become 1 by 4 vn minus vn minus 1, right? Now, submit, add all. Adding all, we will get t1 plus t2 plus t3 up to tn. This is nothing but our sum to the nth term is equal to 1 by 4. Now, observe this thing. This v1 is getting cancelled out with this minus v1. This v2 thing is going out with this minus v2. Similarly, this v3 will go with minus v3 and this vn minus 1 will also go from its preceding term. So, we are left with 1 by 4 into vn minus of v0. So, here we are left with vn and here we are having minus v0. So, our sum to n terms becomes 1 by 4 vn minus v0. Now, what is vn and v0? We have defined the function vr here. So, put n in place of r. So, we will get vn and put 0 in place of r in vr. We will get v0. So, it will become 1 by 4 and n into n plus 1 into n plus 2 into n plus 3 and minus v v0. v0 will be nothing but 0 only. So, write 0. So, finally, we are left with n into n plus 1 into n plus 2 into n plus 3 upon 4. So, this will be the sum to n terms. So, option c is correct. Option c is correct for this question. So, let's take the next question, question number 6. 1 upon 1 into 2 plus 1 upon 2 into 3 plus 1 upon 3 into 4 dot dot dot dot plus 1 upon n into n plus 1. So, here already the nth term is given as 1 upon n plus 1. So, we can write the rth term as 1 upon r into r plus 1. Here also we will apply the vr method or vn method. How? We will again break this tr in 2 such functions will be which will be consecutive in r. How? Let me define one function vr as 1 upon r plus 1. So, what will be our vr minus 1? vr minus 1 will be 1 by r. Replace r by r minus 1.  No. So, replace it. No. r minus 1 let me replace. Okay. We have defined this as vr. So, replacing r by r minus 1 here we will get 1 by r only. Okay. So, now this vr minus 1 minus vr. Let's observe it.  Okay. So, it will become r into r plus 1. Then this will r plus 1 minus of r. So, it will be 1 upon r into r plus 1. Right. So, this is our vr minus 1 minus of vr.  So, this is our tr or the rth term. Right. So, our rth term becomes vr minus 1 minus of vr. Now, let's identify. Let's find out the first term. So, our first term will be v0 minus v1. Our second term t2 will be v1 minus v2. Similarly, third term will be v2 v2 minus v3. Okay. Similarly, it will go up to nth term. So, nth term will be vn minus 1 minus of vn. Now add all this. Adding all this it will become sum 2 n terms. Now observe here. It will minus v1 plus v1 will be cancelled. Minus v2 plus v2 will be cancelled. Then minus v3 this thing will be cancelled out. So, we will be left out with v0 minus of vn. Okay. So, this will be our sum 2 n terms. Now sum 2, what is v0? v0 is put n equal to 0 here in this function. So, n equal to 0 will be v0 will be 1 and vn will be replace r by n. It will be n plus 1. So, our sum of n terms will become v0 is 1, vn is 1 upon n plus 1. So, n plus 1, n plus 1 minus 1 it will become n upon n plus 1. So, sum 2 n terms will be n upon n plus 1. This is our answer. So, option b is correct. Now let's take this seventh question. Sum of n terms of the series 3 upon 1 square plus 5 upon 1 square plus 2 square plus 7 upon 1 square plus 2 square plus 3 cube, 3 cube. Okay. There is one correction in this question. It will be 3 squared basically. So, let me correct. This will be 3 squared. Okay. So, we have to find the sum of n terms of this series. Okay. So, let me write, we can proceed with writing rth term and we will use sigma method of summation.  Okay.  Like I am finding the rth term of the ap written in the numerator. And in denominator if you see denominator it says 1 square plus 2 square plus 3 square dot dot dot up to r square. Okay. So, what is a here is 3 plus r minus 1 d is 2. And this thing 1 square plus 2 square plus 3 square up to r square we can write it as like sum of first n squares of first n natural numbers we write it as r into r plus 1 that 2 r 2 r plus 1 upon 6 right. So, this numerator will become 2 r plus 1.  So, t r means rth term in the simplest form we can write it as 6 upon r into r plus 1. Okay. Now, this question now seems to be easy because here once again we can apply that we in method what we did in last I think fifth or sixth question. So, this tier is basically 6 upon r into r plus 1. So, now let me define one function vr I am defining one function vr h 1 upon r plus 1. So, what will be vr minus 1 or vr minus 1 will be 1 upon r. Okay.   So, we can write it as 1 upon 6 into tier right. So, this vr minus 1 minus vr we can write this as 1 upon 6 into tier because if we put tier the value of tier 6 upon r into r plus 1. So, 6 and 6 will be cancelled out. So, it's okay. We can write our, so from here we can write our rth term as we can write our rth term as 6 times vr minus 1 minus vr. Okay. So, let's write the first term first term will be v0 minus v1 t2 will be 6 times v1 minus v2 t3 will be 6 into v2 minus v3. Similarly, nth term will be 6 times vn minus 1 minus vm. Okay. So, adding all these we will get sum to n terms as this v1 minus v1 plus v1 will be cancelled minus v2 plus v2 minus v3 plus v3. And so finally, we will get sns 6 times v0 minus vn. Okay. Now, what will be our v0? Our v0 will be put n equal to r equal to 0 here. We will get v0 as 1 upon 1 and our vn will be 1 upon n plus 1. So, our sum to n terms will become 6 times v0 is 1 minus vn is 1 upon n plus 1. So, 6 times n plus 1 this will be n plus 1 minus 1, 6n upon n plus 1. So, this will be the sum to n terms sn will be 6n upon n plus 1. Option C. So, option C is correct. So, we are done with this. Now, let's move to the next question. Question number 8. Question number 8. Right. So, one series is, okay, the value of nth term is given here as 1 by 4 into n plus 2 into n plus 3 for n equal to 1, 2, 3, dot, dot, dot. Then we have to find the value of 1 upon t1 plus 1 upon t2 plus 1 upon 3 t3 plus dot, dot, dot 1 upon. 2003 term. Okay. And nth term, the value of nth term, they have provided it. Okay. So, nth term is given as 1 upon 4 into n plus 2 into n plus 3. Okay. So, we can write 1 upon tns, we can write 1 upon tns, 4 upon n plus 2 into n plus 3, right. 4 upon n plus 2 into n plus 3 is equal to 1 upon nth term, 1 upon tn. Now, let's try to go through a VN method, because I am able to say that we can express this 1 by tns, the difference of two such functions which are consecutive in n or r. So, I am defining one function VN as 1 upon n plus 3. Okay. 1 upon n plus 3. So, what will be VN minus 1? VN minus 1 will be, replace n by n minus 1, it will be n plus 2. 1 upon n plus 2. Now, take the difference of these two. This will be VN minus 1 minus of VN is equal to 1 upon n plus 2 minus 1 upon n plus 3. Okay. So, it will become n plus 2 multiplied by n plus 3. In numerator, it will become n plus 3 minus n minus 2, right. So, this plus n minus n will be cancelled, 3 minus 2 will be 1. So, this will be 1 upon 1 upon n plus 2 into n plus 3, right. This is our VN minus 1 minus VN. And what was our nth term? nth term was 4 divided upon. This was our nth term. Like, I am taking 1 by tn as the like nth term since our question was asked in terms of 1 upon tn. So, we can write it as like 1 upon, let me divide it by 1 by 4. Let me divide it by 1 by 4. So, it will become 4 in the numerator. Okay. Right. No. So, eventually we can say this VN minus 1 minus VN is equal to 1 by 4 times. Now, we will rewrite it as 1 upon tn. Okay. Since 1 upon tn was given as like we have calculated it as 4 upon n plus 2 into n plus 3. So, this equation we will use further. So, our 1 upon tn will become, this becomes equal to 4 into VN minus 1 minus of VN, right. Our 1 upon tn, 1 upon t1 will be 4 into V0 minus V1. 1 upon t2 will be 4 into V1 minus V2. 1 upon t3 will be 4 into V2 minus V3. Similarly, 1 upon tn will be equal to 4 into VN minus 1 minus of VN, right. So, adding all this we will get the required sum what was asked in the question. So, it will be sum of N terms will be equal to 4 into these things will be cancelled out minus V3 plus V3. So, V0 minus of VN, right. And what will be V0? What will be V0? VN is this function. So, V0 will be put N equal to 0 there. So, it will be 1 upon 3 and our VN will be 1 upon n plus 3, right. So, our sum to N terms become 4 into V0 is 1 by 3 minus 1 upon n plus 3, okay. But let's see the question. Question is asking to find the value like 1 upon, it is saying to find the value of 2, 1 upon t2003 only, right. It is going up to, N is going up to 2003. So, let's put N equal to 2003. So, N equal to 2003 if we put our sum to 2003 terms, 2003 terms will become 4 into 1 by 3 minus 1 upon any 2003 plus 3. So, this will be 2006. So, finally it will become, let's take LCM 3 into 2006. So, 2006 minus 3, okay. So, it will be 4 into 2003 upon 4 into 2003 upon 3 into 2006, right. So, let's divide it by 2. It will become 2. It will become 1, 0, 0, 3. Further, I think we will not be able to divide by any number. So, it will become sum of 2003 terms will become 2 into 4003 will be 4006 upon 3 into 1003 will be 3009, right. So, this will be our answer. 4006 upon 3009. So, let's see whether it is there in option or not. 4006 upon 3300 linear. It's there in option D. So, option D is right. So, let's move to the next question, question number 9.  This series is going up to infinity then we have to find the value of this series where A is the any constant, where A is any constant, okay. So, this series, let us write the Rth term first. Let us write the Rth term for this series.  This will be the Rth term. Let's put R equal to 3 here then it will become 1 upon 3 plus A multiplied by 4 plus A 3 plus A plus 4 by A, okay. The third term is going coming correct means the Rth term written is correct. Now, similar process we will approach this question by VN method where we will define VN as 1 upon R plus 1 plus A. So, our V, sorry R since we are writing in terms of R. So, let's write it as VR.  So, it will become R plus A. Now, take the difference of these two functions.     So, eventually we got the Rth term itself. So, VR minus 1 minus VR is equal to Rth term itself, right. This is nothing but TR, no? So, our first term will be V0 minus V1, okay. Second term will be V1 minus V2. Third term will be V2 minus V3 similarly. Our Nth term will be V in minus 1 minus of VN. So, sum it. So, we will get a sum of N terms as V0 minus VN, okay. Sum to N terms will be V0 minus VN and what will be V0? V0 will be put R equal to 0 here. So, it will be 1 upon 1 plus A and what will be VN? Replace R by N, it will be 1 upon N plus 1 plus A, okay. Now, in question the series is going up to infinity. The series is going up to infinity means what? We have to take N as infinity. So, our sum to N terms, let me first write the sum to N terms.  Now, we have to take this sum when N is approaching to infinity. So, we have to take the limiting case where N is approaching to infinity, okay. When this is the case, when N approaches infinity, this thing will go to 0. 1 upon infinity, this will go to 0.  So, option A is correct, okay. So, let's do this 10th question. I think this is the last question of this exercise. So, let's do it. It is saying f of x plus y, okay. fx is a function satisfying f of x plus y is equal to f of x into f of y, right, where x, y belongs to natural number, okay. And f1 is given as 3. f1 is given as 3, okay. f1 is given as 3. And question is asking to find the sum of sigma fx where x is going from 1 to N, okay. This is given actually. This is given as 120. Like a summation of fx where x is going from 1 to N is equal to 120. f of 1 is given as 3. And this is this function f of x plus y is equal to f of x into f of y. So, we have to find the value of N, okay. We have to find the value of N for which this equation holds, okay. So, let's take, let's use this equation. So, f of, we know f of x plus y is equal to f of x into f of y, okay. So, let x is equal to 1 and y is equal to 1. So, it will become f of 1 plus 1 that will be 2 is equal to f of 1 into f of 1. And we know the value of f of 1. What is f of 1? This is 3 into 3. 3 into 3. This is nothing but 3 squared. Now, let's put x is equal to 2 and y is equal to 1. If we put x equal to 2, y equal to 1, it will become f of 3. f of 3 will be equal to f of 2 into f of 1. And we know the value of f of 2 as 3 squared. So, this will be 3 squared into 3. This will become 3q. Similarly, if we put x equal to 3 and y is equal to 1, we will be able to find the value of f of 4.  That will be 3 raised to power 4, okay. So, now we have to find the value of n here. Let's open this sigma first.  It is going up to n. So, plus f of n is given to be 120, okay. So, what is f of 1? f of 1 is 3. So, let's write it as 3. f of 2 is f of 2 is 3 squared. So, it is 3 squared. Similarly, f of 3 will be 3 cubed. So, 3 cubed. So, f of n. What will be the f of n? It will be actually 3 raised to power n. And this is given to be 120, okay. So, what is this? This is a GP. This is a GP with first term S3 and the common ratio. First term S3 and the common ratio is also 3. So, let's write this as sum of this GP as 3 into r raised to power n.  That is 3 minus 1 is equal to 120, okay. So, this will become 3. Let's divide this 120 by 3. It will be 40, right. So, 40 and so 3 raised to power n minus 1. This becomes 2, 2 into 40 or 3 raised to power n minus 1 is equal to 80. That is 3 raised to power n is equal to 81 or 3 raised to power n is equal to 3 raised to power 4. That means n is equal to 4. So, this is our answer. n is equal to 4. So, option a is complete means option a is correct for this question. So, we are done with this exercise. Hope like everyone find this video useful because in this exercise we have done a lot of questions on based on the method of summation vn method. It has, it had a lot of questions on vn method. So, I have seen students struggling with this vn method. So, it's not that much difficult. So, this is all for today. So, we will meet once again. Till then, ta ta goodbye. Take care.


Working on a weekend like usual way off in the deep end like usual Niggas where they passed us they doing too much having done my taxes. I'm too pumped up Virgil got a paddock on my wrist on us niggas call me slipping once I pay, so what? Someone hit the block up.  I think I ended um the last clip at breakfast this morning, but I don't really know if the lighting is really good in here. I don't know But I am outside big lots and the beauty supply store and I just dropped Prince off next door to the petco. So I have Everything that I need over here in this little outlet um Prince is getting groomed right now His appointment is at 1 30. I dropped him off at about like 1 22 ish So he goes to a lady named Melissa.  She's really good pomegranate and she's in there doing a pomegranate right now But I kind of want this to be a spin the day with me. So if you're new here, hey, my name is Akira Jenae Don't forget to subscribe and join the family before you leave So I think first I'm going to go to um I'm going to go to the beauty supply store Just to like get that out of the way because I think I only need like three items out of there and big lots Is the one I'm going to be in for a minute So the beauty supply store I need I want to try like hair glue like actual like boat hold or something So I'm going to no ghost bond. I think ghost bond was the good one So I'm going to get ghost bond. I need some hair pins for when I curl my hair to keep it You know the um curls end longer and then I'm going to get a lace grip holder So like when I do glueless installs like this one, this isn't glued down I want that little lace grip so it doesn't slide, but I got an elastic band in this But anyways only need a few items and then big lots. They actually got like some sales going on So I'm about to go in there and basically like household items is what I need out of here Literally, that's all So yeah, I'm going to get in before everybody get these tie pots They got if you spend over $35 you get a free pack of 15 or 20 k out tie pots So baby we're about to get in there and get the deals. So I'm about to go in I'm going to vlog a little bit while I'm in there. I don't want this video to be too long So it's going to be kind of like Bits and pieces of you know what I'm getting what's in my basket and then when I get home From all these stores I'm going to today. I'm just going to do a whole little like I guess a haul you can say so let me put my glasses back on And go in and someone's looking at me right now. Yes, baby. I am vlogging. So let's go Okay, so I am on the some male goods aisle They like to play music in here. I forgot when I used to work here, you know But yeah, I don't want to get demonetized. So I'm probably just going to be like doing basically like b-rows and Voiceovers possibly but I do need some more wall plugins. So here they are um I thought it was a three pack for $10, but I may be mistaken. I think it is just the two but I need a huge pack of air wig So I'm probably going to have to go To like one Marta Kroger's for the air wig because you can get like Six or seven for like ten dollars a day. So I think I want to go for that And so I'm on my last um Swiffer wet jet little like refill thing So I have this one at the house and I have this one. This one is what I used to mop with and then this one is what I use for Like sweeping up Cheapest poop spray I've ever seen. Usually, you know, like those like poopery or whatever poopery is usually like Five six dollars this right here. It's called poopsie daisy and it's literally only one dollar. So I'm about to get like three of these I'll leave one for someone else But literally one of these is like five dollars it like tj makes one more for the poopery and this smells so good I just smelled it. It's a citrus fragrance. I smell more kind of like lemon though, but definitely getting three of those topper But I don't know where I would put this like It can't fit on my dining room. Maybe under my tv I can move that home thing I don't know. I'm really feeling it though. I think I may get it and then if it don't work I'll like bring it back, but I don't know. I'm just really feeling this It was just so crazy How much stuff they've gotten in because when I was working here We were not carrying all these big name brand items. It is just so crazy Like This is kind of cute. I would get this from my mom 22 dollars. Probably not but This was like 10 dollars I would definitely get that for her I was thinking here In a weekend This is how you make money that too, but it's how you make money A dog channel In here shopping, I literally just bought a bar cart. So I'm gonna need some cups and stuff for the bar really cute These are only 11.99 though. So if I drop this baby, this is breaking. This is like really thin glass But I'm gonna get it. I like it and I vlogged that guy. Well the valet trash man. He literally took my sign It was like a little foldable welcome sign that was in this material from here This is kind of like it.  The other one I had was like a I don't know. I'll insert it. I'll let you guys remember it But I think I'm gonna get this one because I really want this to go outside my door I like having a plant outside the door and just outside regardless, but I also found This cute Son This one is 18 dollars and it says welcome. Like this is so cute I think I should have both of these at my door Like it should be one of the other I feel like Or I can have one on one side I don't know I'm just going to get this for now and go buy me a plant and they had like six or seven of these So I'm going to wait on this and then I may come back for it Yeah So I just picked up me some mech Donald's Mech Donald's because you uh was on my ass last time I said that and I get the orange Fanta now. Why is the My camera not white balance right now. It's it's it's come on now Okay, anyways, I got This instead of the sprite. I've been on the Fanta orange for a minute now, but I'm in my parent's house um I'm still waiting on prints to get out the groomers. So I dropped him off at 1 30 He probably won't be done until Like 3 34 they was like give them a lot of time today because they said it was a um A big dog in there like was going crazy.  She said I don't I don't really remember But I'm gonna have to bring him like every four to five weeks. She said we missed a month. So that's why So on his next appointment, I'm going to um schedule out Exactly four weeks from today And have him come or I actually may schedule in like two weeks of bath so he can like Remember what's going on and then Schedule baths in between his appointments In between his haircut appointment. So I think that'll probably help so about two and a half weeks from now I'm gonna schedule a bath in a trim And I'm driving again I'm on my way to take him home And then I'm going to the outlets to do a little bit more shopping just a little bit And then I'll go back to the house and give y'all hall What's up? All they do have the refills in store. I did not know that that was my favorite one I had hit my belly button. I think I recorded Whenever the last time I cleaned up my car So not this past vlog, but the other one and I hit it really hard And it like started gushing blood. So I feel like It basically has to heal all over again But it was healing up really really well And now I feel like it's back in that healing process, but it's like 10 times worse and I cannot find that belly button ring But luckily I had this other This is the one that they gave me when they thought I was going to swell up And I did it so I got really lucky with that one but Luckily I have this very very long one. So Make sure I put this whole on tight I got a long one and This one I feel like let me here I feel like this one Is the one I need right now While it's still in its weird healing process since it want to be really stupid So I'm like tighten this whole So I feel like it's on it tight. It's like bleeding to me I want to show you but here's the cute tip if you got blood on it But girl, I like that one What's up, man? I was just thinking about you I get done All right, so I had to get off because Nikki had called me but I'm not to close my Lines or shades whatever It's not really blind I usually keep This one got right there Because I like for my plant to get like some light and stuff and done my body like I'm on the second floor. So that doesn't matter but This side over here I need to put these down because I usually leave all my shades up during the day mostly Because can't nobody see in but at night time, you know People can see in so usually bring it down to about right there fireplace on um I laid out everything. Oh, I just got done eating. Sorry. I didn't show you all but I'll just put my mouth on your bow and then this is the aftermath. I'm actually I'm actually not done with my steak, but I'm going to set it aside so I can Put all this stuff up and then I'm gonna Come back and finish eating And then I gotta clean up my mess print this up at a parking lot. I don't know what I don't like this. I don't matter Okay, so this is the stuff I got I think I already showed everything but I just wanted to Talk about a few things like these. I got three of these. I think I showed y'all this in the store This is going to be for milk Juice and cranberry juice I'm probably going to set all that up tomorrow because I was so tired y'all I didn't get so much today Um, I didn't even want to go grocery shopping I did actually go to Walmart though and bought this steak and stuff, but I'm gonna finish everything tomorrow Um, y'all so I got this warmer This is going to go in my bathroom to replace the um Fabrice plug-in because I don't really have nothing to go in that corner Because of it's like a weird anyways. This is one in the bathroom And then I got a lot of cleaning stuff. Um Tonight I was going to try to put up my shower curtain, but I'm honestly like really tired Especially since I just ate I'm kind of like Just ready to shower and lay down and I also need to do a shower. I'm going to record a shower routine.  But yeah, I finally found one that I like that's very affordable um Yeah, the only thing I have to do is just put this random stuff up My bar card. I think I told y'all ordered that that's not going to be here until Either sunday or monday today is thursday so Yeah After I take a shower, I'm probably going to do a load of clothes. My battery is dying. So I'm probably going to switch out my battery Um, show you guys my laundry and stuff like that and then I'm going to get back with y'all Tomorrow and then we're going to like really put everything up and I'm going to finish going grocery shopping So this day in my life turned into two days in my life, but I feel very accomplished today. I got a lot done Um, prince is looking good. I got him on a little sweater right now And I also went to with lush in sephora It's night cut off on me, but you will see this in my um shower routine I'm going to talk about a little more over there And then from sephora, I got the fenty scrub if you guys saw me looking at that Earlier and then from back in body works. I just got a hand sanitizer Um, like refiller. I got the one that's because I work at the hospital. So I got this one So cute So, yeah That's all for today and I'll talk to you. Love these tomorrow Earlier today, but it is the next day. It's friday now 2 12. Um, I went to go get my car um, my oil change and tires rotated and stuff like that so Yeah, they did everything only paid a hundred and two dollars for tire rotation and Oil change and you know, all that stuff. So I'm about to go into big lights now. I'm over here Um, I'm about to go in and return My shower curtain rod and these disinfectant wipes that I got that doesn't smell too good So I don't even want them anymore. Okay. So these are the hooks that I got I think I showed you guys I should have showed you all these already But the ones I wanted on amazon were black and they were like 26 dollars and these were only I want to say like 11 So if I wanted to I really could have like spray painted these white But I got a white curtain so I don't want that or I could have spray painted them black But I'm just going to keep them silver because my Accents and stuff are silver. So I think it'll tie in pretty good So I'm just going to put these on my shower curtain and then I'm going to put up the shower curtain And then like put the command strip on the end of and then just like stick and screw it But I'm going to start putting up the curtain now. I have one little hook on I'm gonna put a few more hooks on I'm gonna put a hook on each end And then I'm going to start hooking it in the middle to make it easier Nikki on the phone y'all Let me put the camera down so y'all can see what I'm talking about. The bottle's completely She said she thought I was going to get a half rod. This is the top of it I don't like that you can still see that I want the rail up above the glass So then I would need a shower curtain that's long enough to do that But I do like the shower curtain I just wish it was longer If so, this is the shower curtain one is just pulled to the open part So that's not going to have it anyway because I do like the actual clear part So I'm just going to leave it like that But Y'all know I can't deal with this like that So I'm just gotta use But the shower curtain is not Okay, so I'm gonna leave it up for now because I can't make up my mind because I'm Overthinker and decisive, but I just posted on my instagram story for y'all to vote. So I have For the ones who want me to get a longer shower curtain It's at 47 percent and then all y'all who said it looks fine. Is it 53 percent? So We'll see. Um, I already did order a longer one off amazon Sorry, um, but I think I want to actually like in this vlog today I kind of just wanted to be a two-day vlog I don't want to drag it out through the weekend because they just supposed to only be like a day So I'm gonna um wash a little bit and you know, clean up the house and stuff like that and end that vlog off here today But I'm not going to get the shower curtain until sunday So I'm gonna probably be vlogging again And do another like type of vlog or something and then we'll I'll update y'all when I get it but Um, I also put in my community tab to follow me on instagram, but I will put it on the screen It's at underscore akira with three a's and Yeah, a lay y'all are voting. I'm super excited. Y'all help me out a lot because I normally do these A few times so 53% says no one looks fine, but We'll be the judge of that when I actually get the longer one. So a lot of y'all have been voting if you see yourself Shots out to you little mini promo for you guys Um, I didn't click on everybody, but a lot of y'all are voting So I do thank you guys and then this is for no, it looks fine so Yeah, I'm about to do some laundry and then I'll probably shower and stuff the thing is with the fabric ones I put them inside the shower Um, I was watching I was looking at some reviews on amazon from the shower curtain I just bought and it is fabric and some people actually use fabric shower curtains as like To block the water and they're mad that it's modding. What did you expect? Especially if you're not washing your shower curtain Constantly if you're using it actually for that purpose. This is literally just I'm going to get a shower liner But for right now, I just want just to cover so I don't get cold in the shower, but I'm just like Duh, it's modding. What do you get a shower liner and not a freaking girl anyways I can run about that for a minute, but I'm about to um Go put these clothes in this washer and the rest of this will probably be like Span up Put a cute video or whatever If you've been following me since my last apartment or last two apartments Um, this is what I used to keep my like tissue and paper towels and stuff here So I'm going to put all of my extra Um, comforters and throw blankets and stuff for so when he's gonna take up the whole day That down as good as I can I don't know if I should roll them or just Do them like this and just stack them down because I feel like this one rolled is like really big These are extra pillowcases. These are actually king pillowcases, but I don't have any more king pillows So I can't use them. So till I buy some more pillows. I'm just going to save these This one, I think I may throw away because I don't even need that But these other ones I will save I need to actually iron or steam them, but whatever that one in here Okay, they fit They all fit So all of my throw blankets and Comforters and stuff is in here and I'm going to put this inside my closet Anything I'll get my other stool So I'm about to put that bear that bae got me up here And kind of move some of this other stuff around This is all of like my batteries nails They're basically like my hardware type of drawer And basically my tool drawer, I guess you can say and I've always kept it in this, but I do have a spare um drawer In my kitchen that I was thinking of maybe putting this stuff in and kind of have it organized because I literally just throw everything in there And I'm like girl, you can organize this a little better So I think I may do majority of everything that I can organize like the batteries and the um Nails and screws because I have this one just empty And this one basically needs to be empty too, but it's like just papers and instructions So this is empty um These two I have stuff in though So I think I'm going to try to organize like the batteries and most of that stuff in this one No time and it won't play today make me wonder who you might be playing with makes me wonder who you think playing with Okay, so this is the drawer where we were these are the extra little organizers that I have left over so basically what I have to organize is Batteries and tools and command strips and stuff like that And yeah So I think I'm going to And maybe another long one Since this one isn't really acrylic. This is just flimsy um, I would rather put the Hard tools in there instead of something like this because this can crack really easily So I'm thinking just want to drop these heavier tools up in here Derv these are old or not but I think I may just throw these out honestly And throw these out these are probably old and then I'm going to put these new ones in Okay, so my closet is cleaned out um Has a lot more walk space And I did some rearranging up there And up there as you can see I'm going to color coordinate tomorrow But I just want to everything off the floor, which I did that I'm going to get a hamper where I can do two things like it's put together so I can do Towels and then just like regular clothes. I'm going to get rid of that brown one in this pink one probably Um, that blue bag I think I already told y'all that's going to be goodwill donations Um, that is basically office stuff I'm trying to find a table That I can make an office out of to go over there in that corner by my vanity and then Basically, I'm going to like organize these drawers and stuff like that in another vlog But yeah, basically I got a lot of walk space. I got space to grow which we love So I got that shelf empty that shelf empty um basically that I can actually probably put That foot thingy under my bed Honestly, and then that steamer I can put under my bed But like the other two things I probably just stay there. Um, I'm going to go through those weeks and stuff tomorrow That thing is full of wigs. I put my shoes up Oops, that's more over there And yeah stuff back there, but basically everything is in order these wigs on the bed Are wigs that I'm going to sell so I got this one from svt that I'm going to sell This one that I reviewed I think about a year and a half ago This one and then this is a headband wig. So I got four weeks to put on sale And then tomorrow since I don't have anything to do but sell my tv Um, selling my tv because I need a bigger one. Um, I can't see at night So yeah selling this one tomorrow by some book. Um Can I talk y'all dang? It's um one of my friends that I went to nursing school with she's getting that one And then this one is still on sale. This one is going to be for 150 So yeah, that's all for this vlog So that's all for this vlog. I hope you guys enjoy spending Two days with me instead of just one. Um, I'm going to probably do another one of these videos probably Either like sunday or monday um sunday. I may do like a Sunday reset or something. I don't know Maybe I'll do that like the next sunday because I kind of already I'm cleaning everything and washing stuff. Anyways I'll see y'all in my next vlog or day in a life with me. So bye guys


Hello, today on Typical Books we're going to have a little bit of a May catch up. It seems like I just did a catch up in April and I'm not really susceptible to this time as a big blur thing during the virus because I have a pretty set schedule every day and if I don't then I make a set schedule when I wake up in the morning and figure out tasks to do. So I'm not really that like out of sorts but it does feel like I just did one of these but there have been a lot of really cool new releases so I wanted to go over those and talk a little bit about what I'm reading right now. While going through some of my books and deciding what to read next I was going to read this but I was timing and hiring and going over like the first pages of things and saw what caught me the most and I realized much to the delight of Andrew from Grumpy Andrews Horror House. This is a signed copy. I never looked to this past the frontispiece like it is signed so I count myself pretty lucky because I would have never met James Herbert and I don't have a lot of signed copies. When we go into some more of the upstairs stuff there's a lot of cool collectible stuff that has maybe signature plates and signature pages but those aren't like signed and I have some things like Nancy Kilpatrick signed and things that I've met authors in person but I don't get out much right so this is gold to me. Pure gold considering I paid 7.99. That was my runner-up read over The Pet by Charles L Grant and I am totally digging this. This is such a throwback to the horror that I grew up on and the quiet horror that really spoke to me and it's a little more dastardly than I would have expected from Charles L Grant so I'm very excited to become a new Charles L Grant fan and yeah I'm really enjoying The Pet. I think the thing that I'm enjoying the most about The Pet right now is that the main character reminds me of a super young Jeff Dahmer and not like the Jeff Dahmer that we know from the giant FBI file that maybe I'll do a booktube show on that someday. My husband has everything that you would ever have in a file on Jeffery Dahmer but it reminds me of the Jeff Dahmer from My Friend Dahmer by Dirk Bakter that you may remember from a previous typical book. So as far as what I've been reading I mean I've been slow to read lately. I finished playing The Witcher and it's DLC components and I played a little bit of Diablo but I'm not really into gaming right now. I think The Witcher kind of sucked a lot of that out on me and I haven't watched the series before anyone asks either but I really liked the game a lot and I want to just chew on that for a while so I'm not going to play any other games for a bit. What I have been doing though is writing a lot. I've submitted a couple works. I've submitted work that I had finished writing a while ago and I'm working on two other stories right now that I really need to buckle down on so I've been spending quality time writing those. I've got two novels one on the go one done so I'm pecking away at those for sure but of course aside from all of that I'd rather be making videos because it's a lot more fun than actually sitting on my bum in a chair all day and luckily a lot of other authors have sat with their bums in chairs and brought us some really cool new releases. So to catch up a little bit we had left off with The Finders by Jeffrey A. B. Burton. This is from Saint Martin's Press their imprint minotaur and this will be coming out in a month or two. Mason, Mace Reed, lives on the outskirts of Chicago and specializes in human remains detection. That is he trains dogs to hunt for the dead. My dream job. He adopts a rescue dog with a mysterious past. A golden retriever named Vera. And I love the cover of this book for this reason. I am a big old yeller, homeward bound, used to own a golden lab. And when Reed begins training Vera as a cadaver dog he comes to realize just how special the newest addition to his family truly is. Well that sounds fun. The Shadow of a Shadow by R. H. Dixon. I really like the cover of this too. It reminds me it's sort of like this Ms. Pergwens look to it. Like Les Mis, like I don't know what it is about this picture. It's probably stock but I mean who knows I just really like the design. The typography I think is what gets me. Dracula obsessed Catherine Hall must piece together the disturbing truth of what happened to her runaway cousin Calanth in the summer of 2003. Calanthi? Calanthi? Calanth? I'm not sure how to pronounce his name. Because when she visits her aunts B&B and Whitby something dark and terrifying is growing in the shadows, something that breathes, something that bites. This is from Corvus Carone Press by R. H. Dixon, nice. And his Scream Queen by Brooklyn Ann from Burroughs Publishing. And when Lucio Argento's girlfriend dumps him because she wants to be prom queen and thinks he'll hinder her. He decides to play Pygmalion without cast Jamie Blair and make a rival for the crown. This sounds a little bit like Carrie. However, when other condenders are brutally murdered, Lucio's quest for revenge is abandoned to protect Jamie and stop the killer. Angel's Rose by Lauren Rhodes from Automatism Press. And this book is already out. After they escape from the ashes of Lost Angels, the succubus Lorelai and the angel Azizel want nothing more than to enjoy each other's company. Unfortunately, Asmodeus, the prince demon of LA, has threatened to devour Lorelai's new grown soul if she doesn't bring about Azizel's downfall. I have a hard time with demon names, as you can tell. But yeah, this I thought from the cover and from the name of it was a YA novel. Considering all the demonology, I don't think so. It could be YA demonology, like what not? Jurassic War by John Dennehy. This comes from Severed Press and is already out. US Marines land on a remote atoll to carry out a seek and destroy mission. They encounter Japanese infantrymen and the raiders must also overcome deadly indigenous wildlife. Dinosaurs have not become extinct in all parts of the uncharted world. Turok, too, coming to theaters near you. There was another game trailer for something I can't remember the name of right now, but I was like, is this Turok, too? Is this Turok, too? Every time there's a dinosaur on screen, I'm like, Turok, too. So this might be my Turok. Yeah, I just a big hold out geek for Turok. Turok's rising. The Turok cometh. Turok's in the mist. So there you have it. Those are some new releases coming out. I've got some stuff on the go. I have a horror review for The Haunting of Glatsby House, which is long overdue, and it'll be posted either today or tomorrow. And coming soon will be the Pet from Charles L. Grant. If you have anything that you think I should be reading, just let me know. And always let me know what you are reading, too, because that fuels my toppling to be red pile. Thank you very much for watching and have an oaky spooky day.


Hi everyone, Joe for Jaspy's casewrakes.com coming at you with the random number block randomizer Featuring this group of teams right here Thunder, Bulls, Nets, Cavs, Raptors, Wizards, and Lakers. Here's how it works Big thanks to this group for making it happen Congrats to people who won those extra spots in those little mini promos that we were doing and there are the numbers right there Let's roll it. Let's randomize names and numbers three into two five times each one two three four and five Jason down to Evan three and a two five times for the numbers one two three four and five Got five down to zero members zero gets any and all redemption for that group of teams Including one-of-one redemptions one still gets live one-of-ones them's the rules All right, so Jason you got five Hans with eight Matt with nine Eugene with two last spot mojo Hans with three Matt with seven Chris K with one Hans with four Evan with six and zero Let's sort these by number We got only have one more random number block to do Four spots left and then we're in breaksville. Let's make it happen. Jasper's casewrakes.com. Bye. Bye


Mae'n gweithio i'r eich llwyddiad o'r ydych chi'n gweithio, boeddech chi'n gweithio eich bod yn blaen o'r llwyddiad o'r ddweud o'r freithfaces ac ychydig i'r arddangos i'r aelodau ar y cwylodau a'r gweithio i'r gwneud o'r concept ffiannig. Mae'n ddweud o'r freithfaces yma, mae'n ddweud o'r freithfaces model. Mae'n olygu yn ddweud o'r freithfaces yw'r ddweud o'r ddweud. On quite knows what to do with this, is an abandoned or an old label facility in southern England. So firstly what do we mean by place? So this is taken from OJ and he talks about the anthropological place. So he sees places as being confined relationally.  And they gain their sort of human element because they're concerned with identity, particular types of place become associated with the formation and the performance of different types of identity. So he defines the anthropological place as a concrete symbolic construction of space. The non-place, he sees as being a product of super-modernity. And that's one of the reasons why I was quite interested in exploring the concept. So it is something which is really hyper-modern, it only relates to the late 21st century or is it another term like the end-propercy which talks about all the 20th and 21st century, but humans have been impacting for much longer than that. He also sees the archetypal form as being a traveller space. So I mentioned earlier he talks about airports, motorway service stations, places which exist out of necessity but are somehow removed from society. And you get that feeling in particular in motorway service stations if you go in from the back entrance where the coaches park because you sort of go through these sort of dark tunnels and things before you go into the big world restaurant. So how can we relate this to the Middle Ages? Because if non-places are explicitly aimed to see from modernity, then of course Middle Ages aren't to see from modernity. And I don't think we should necessarily be trying to create that direct line, but rather see can we use this concept as a tool to think with, to think about how we can address places which are ambiguous or spaces which are ambiguous that we can't necessarily in a defined function on. And more importantly, what can we think, how can we use this concept to think about what these spaces actually do? So how can we look to empty spaces for the first substantial contribution I can find is taken at the 1979 by Wilkin Schiffer who looked at vacant lots in Tucson, Arizona. They took some students out to record what was being found and done on these vacant lots. They found they've been used for travel, so people are using these cut-throughs, refuse disposal, so both things that you cashly throw in your drinks can in there, but also more sort of structured flight in and dumping. Storage of bulk goods, so I think we're using those kind of building yards and just dumping parts of bricks there to be used later. Play and recreation, which was a broad term, so that's a child play and also adult recreational activities. And of course they were being used for camping and as accommodation by famous people as well. So we see that yes, these are spaces in this instance which do seem to be associated with those sort of activities which happen at margins. Jeff already put up a reference to Monica Smith's contribution in 2008, published in Arthological Dialogs, which I think is the most substantive hope to discuss the concept of empty spaces in towns. We did ask Monica to contribute to this session, but unfortunately she's not doing fieldwork in India. So she sees that empty spaces are foci for particular tights of activity which have performed at varying timescales, and I think it's important points that spaces may be empty for shorter or longer periods of time. Some spaces are consciously left empty, so you have buffer zones or you have spaces which need to be used for particular tasks, like drying cloth, for example, or drying nets. And she sees actually these spaces are really important for urban communities because there has to be an agreement that that space will stay empty because if you all want to dry your nets on there and then someone goes and builds them, they aren't ready anymore. So she sees that these empty spaces are shaped by urban authorities and by urban communities and that they are inevitable within urban settlements and critically they are very flexible spaces within the urban landscape and that's something which I'll come back to. I mentioned as well that my awareness and interest in the concept of non-place had come from my reading of contemporary archaeology, so particularly this paper by Shannon Dawdy where she's looking at post-industrial cities and the ruins within them. So she argues that post-industrial cities are characterised by a cycle of ruination, buildings go out of use, fall into ruin, get regenerated. And therefore cities are palimpsest of various forms of city building. Cities built at different times for different reasons by different people with different motivations. And ruined spaces somehow haunt these urban spaces. They have varying forms of longevity whether that's in the way that they force the urban space to be divided up into plots, the way that we see many equal plots continuing in the landscape or the way that we get those sort of problematic ruins which you sort of have a heritage obligation to keep hold of and look after but none quite knows what to do with them and they get used for all sorts of different things and she therefore says that these ruins are kind of generative of particular forms of social life. So can we see urban empty spaces as non-places? I would suggest that in some cases they exist outside of the symbolically organised space of the city which would be OJ's definition of an anthropological place and they are produced by urban life. There are certainly spaces which passed through and in a way are defined by their nothingness. But we've had quite a lot of discussion before the break about whether non-place was an appropriate term and actually the term place and non-place I think needs to be understood in a relative sense. So this is a quote from OJ. Place and non-place are rather like opposed polarities. The first is never completely erased and the second never totally completed. They're like concepts on which is tangled game by identity relations is ceaselessly rewritten. And this is the key point that place is never just a non-place or just a place. It has an element of placeness or non-placeness. And now on to the smooth space because I knew what you really wanted at five o'clock on the muggy afternoon in Barcelona was more French philosophy. So my work is largely influenced at the moment by the writings of Deleuze and Qatari and their assemblage thought or assemblage theory. If you want to know more about it, then please feel free to leave a like or comment book on the subject and to see some of my prisoners. And in very simple terms, they find the world as being formed of flows of energy of matter of people of ideas which pass through time and space and become entangled and they territorialize or coalesce into entities. And historical actions and persistent structures code the way that these flows move around. So you have walls and regulations, for example, which means certain types of behavior can happen and certain types of behavior can't. And therefore this coding striates the space. So you have a smooth space where you have any number of infinite number of entanglements and connections happening and a striated space where historical action, historical structures mean that the outcomes are all limited. So just like a place can't just be a place or just be a non-place that exists on this kind of spectrum, so spaces cannot be entirely smooth or entirely striated because an overly striated space would be too structured. You'd just be stuck on ground all day repeating yourself over and over again and nothing would ever change obviously the world doesn't like that. And similarly a smooth space would be so unstructured that every second would be different from the second that came before it and there would be absolutely no persistence and continuity. So spaces are always going to be somewhat striated but with different degrees of smoothness. And what's critical about these smooth spaces is that they are the spaces that offer opportunities for creativity and for change. And Ian Buchanan has drawn similarities between the idea of smooth space and the idea of non-place particularly seeing smooth spaces and non-places as being these spaces of ambiguity and transience. So I would suggest that empty spaces are kind of an urban smooth space in physical form that is defined by urban activities. They exist because the town and city exist but their role can be somewhat undefined and their places in which new forms of urban experience might emerge those socialities which Dordi talks about. So this is the context in which I'm talking about and we've heard a little bit about it in the previous paper. The late 14th and the early 15th century the period of Black Death and Recession where we get this what historians have identified as this period of urban decline so towns are smaller and poorer and urban decay of urban fabric falling apart. Individual case studies have emerged we've found that this picture is far too simplistic. My aim is looking at archaeological sites from southern England so they're really getting mixed pictures some towns are prospering others aren't doing so well it's clearly a period of adjustment in which what it was to be urban changed and we can see changes to the urban landscape which created new empty spaces. What I'm interested in is what can these new empty spaces tell us about these new forms of a banus? So I've got three very rapid examples which may or may not be considered non places. So the first is a site at Cuckoo Lane in the major port of Southampton which was an area of mercantile housing in the 13th century a very high status area very rich and imported pottery. In the 14th century after the French raid in 1338 when the new defences were built which cut this site off in the waterfront and fire also destroyed buildings in an unrelated event this area reverted to gardens We've heard about gardens already so gardens emerged in this area out of a mixting of coating or straiting and smoothing so this was a land in the town which was possessed by a major institution God's House Hospital it was acted on by all sorts of different processes and actors, royal and urban authorities in the construction of new defences but it wasn't an area which seemingly led to become bait into no groan which would be a non place in the true sense and we're seeing historical tenement boundaries persisting so I think this place shows how empty spaces are created out of the urban processes and that the processes of decline and decay created new opportunities new spaces for urban horticulture changing potentially urban rural relations potentially being really important for understanding the transition now I don't think that this garden is a non place but it's demonstrative of an urban space as a process of smoothing inspiration and that relational construction of space and place which OJ talks about The second site in a way is similar to Jeff's stone public space it's in other ports Shora by sea in Sussex close to Brighton on the south coast of England and this is the road tackle site which is an empty space at the edge of town close to the waterfront as you can see from the side drawings there's not an awful lot going on there there are dumps of 13th to 14th century domestic waste and there's also evidence that this area was used for range activities such as boat building and fish processing so this is a space which existed outside of the formal urban landscape but was essential to the performance of urban life we've got ephemeral evidence here for periodic everyday activities and space which is being made significant through that activities and through the imposition of structure so this is one of those spaces which again is generating it's generating structures generating sociality it appears to be an empty space it's an important mediator in urban life it's one of those spaces which Monica Smith identifies as as a space of consensus building and the third example is the Castle Bay of Guilford Castle in Surrey so this is Guilford Castle keep into Royal Castle in Palace went out of Houston in the 14th century and the Castle Bayly excavations are shown was largely kept clear of weight in a lot of cases the Castle Bayly gets used as a sort of dumping ground so again maybe we've got a bit of that consensus building going on here because what we have is evidence of the use of this area of the drying plot possibly related to the intensification of textile manufacture so here the ruins of the castle the empty space was adopted for particular activities and that lack of royal interest caused this previously heavily regulated space to become smooth it lost that symbolic power it became the transient and ephemeral space in which new forms of urban spatiality could emerge so we've got Cwyddiw Llanewyr striations persisted it's not a non-place as such but empty space emerged after the processes at the road tackle sites in Shorong we've got a peripheral empty space which was engaged with periodically it seems to be smooth but becomes strated it does seem to be ambiguous they made it some time it had that sort of element of non-placeness and then Gilbert Castle was once a symbol of royal power that was lost political and economic change acted upon space it found a new use became more ephemeral and maybe falls somewhere between these two examples so I think that the idea of the non-place is potentially useful to us for understanding the medieval period but the medieval non-places are necessarily different to those of supermodernity which Odria talks about we do see ambiguous and empty spaces that these clearly played an important role in urban life also those models of decay of decline are far too simplistic we rather than just saying spaces became empty in towns we need to understand what the implication of that emptiness was and I guess there's also scope for thinking about this in terms of other context like the decay of the town so we're walking in front row so space I think it's useful to think of as a process this process of smoothing and striating and the idea of the non-place I think it's really helpful for us to think about what persists and why it persists but isn't necessarily a concept which we can just lift straight out of the anthropological theory and drop into the middle ages