W-E-A-F, New York. Scurrets, please. Yes, sir. Oh, just a moment, sir. Don't forget your change. You'd never guess, but Avalon's cost you less. Being welcome to Avalon's time with Red Foley, Jeanette, Edna Stillwell, the Avalon chorus, Bob Strong and his orchestra, and Red Skeleton. The orchestra opens the program with step-up and shake my head. Distinct advantage that makes it superior to all others. You'll gladly give it a trial, won't you? Well, Avalon cigarettes have two all-important advantages. Highest quality, exceptional economy. Points of marked superiority that have made them the outstanding cigarette buy of today. Now, Avalons are union-made from an unsurpassed blend of the world's finest Turkish and domestic tobaccos. Millions of smokers say you couldn't get finer quality cigarettes regardless of price, regardless of brand. That's why you'd never guess that Avalon's cost you less. Three to five cents less per pack than other popular price brands. Highest quality cigarettes at a worthwhile saving. Avalon certainly deserve a trial. Why not get a pack tonight? Social security. I went to New York and saw Nova in the Bears Den. What a fight. The first-round bear looked like he was born with gloves on. The 11th-rounder looked like he was gonna die the same way. I wanted Edna Stillwell, my secretary, to go to the fight with me, but she was so modest she refused. Just because the newspaper headline said, Tonight, Nova will fight bear. I love fights. When I was a kid, I was the problem child of the neighborhood. Every time I'd show my face, all the other kids would start running. And they never caught me. I'll ever forget the first time I fought in the ring. I walked to the center of the ring and I took off my robe to show my chest, and I got a mash note from a washboard. Mmm. I only lost one fight my entire career, though. I misunderstood the referee's instructions. I knocked my opponent down. The referee yelled, Run to a neutral corner. The only one I could think of was Randolph and State. My next big fight was in the Madison Square Garden. In the second round, I said to the guy, She says, You're yellow. He was yellow. I was black and blue. I drew back the theme and I see a terrific right coming. I was pulling up my trunks, both hands being busy. I blocked it with my eyes. The, uh... Mmm. The next round, I drew back the hit. And I heard a bong. I was nervous at first. It was the bell, but I thought it was the horseshoe that fell out of my glove. I carried a horseshoe in my glove that night. It didn't do much good, though. I think the other guy had the whole horse in his. Okay, and that guy knocked me so cold they had to carry me out with a pair of ice tongs. But I was a big favorite in the fight ring. Every time I'd step to the ring, the people start yelling, screaming and stomping their feet. But not once did they ever get their money back. Well, I think I've been out here punching long enough. So I'll step out of the ring and let Red Foley come in with building a sailboat of dreams. Hit it, fella. It's about the hands. Did someone call me? Well, I wasn't, but I feel all right now. My blood pressure's normal, my heart action is normal, and my pulse is normal. I wish you weren't. Who is that, anyhow? Oh, that. That's my new fiddle player, Roger Donaldson. I'm making some improvements in the band, and he's worn out. Yeah, some improvement. But, confidentially, Bob, the boys do play a lot better now since they learn how to read music. Yes, and with the six men I've added, the band will be a lot better now. Six men, eh? Well, who are they? Well, there's Joe Strongin, Felix Strongman, Carl Strongdale, and Pete High Strongpin. That only makes fine with this Roger guy. Who's the sixth man? Well, that's Jack Warren, the drummer. Warren, how'd he get in here with a name like that? Well, he married my sister. Connection somewhere would say this Roger guy. Tell him to keep still, will you? Well, I have to be kind of careful with him, Red. Careful with a fiddle player? Why? Well, he knows these onions. What are you all into? I mean... Hey, let me show him, Bob.  Roger boy? Add the last three letters of Jersey. Hello, Pumpkin. Hey, what's going on around here? I thought I was your steady fella, isn't it? Steady? Yeah. If you were any steady, or you'd be motionless. I want a real boyfriend. I need a gable type.  Help! She's on fire! I'm your man. Yes, Bob, but will you love me when I'm old? Love you? I'll idolize you. I'll worship the ground under your little feet. I'll... I'll... See, you're not going to look like your mother, are you? Now what? If a loaf of bread was as old as these jokes, what a marvelous, tanky dressing it would make. That, Red. I don't pay any attention to that droop. Oh, yeah? Hey, it's Kevin. Hey, let me hear you pronounce your vowels. My vowels? A-E-I-O-U. How's that? Your A-E is all right, but your I-O-U is no good. Who's going around here anyhow? Hi-O, hi-F. Oh, hi-U-O. Foley's getting high-clad, saying U-O. Used to say Ewan's. Ah, gone with the dawn. But, honey lamb, you sugar pie. I was mad about y'all. What's the matter with you, Foley? A guy'd have to be crazy to know what you're talking about. Thanks, Red. I'm glad we understand each other. Yeah. I don't think I'm crazy, because if I was, Mr. Selznick wouldn't have sent for me to play a part in that picture going with the wind. Ah, now go on. Oh, start bragging about you're going to be in going with the wind. Why not? Isn't that something to blow about? Yeah, but...  You mean Scarlet O'Hara? Hey, that's a woman's part. Can you play a woman? Can I? Boy, show me the woman. Well, I got to go now. So long, Edna, honey. Honey, hey, where does he get that honey stuff? He knows you're my girl.  Yeah, it's my girl. Why don't even talk to me, you dope. Dope? I'm a dope? I'm a dope? Stop bragging, Scouting. Listen, don't interrupt me when I'm speaking. Don't speak while I'm interrupting. Yeah. Hey, Bob, Edna's my girl, and that settles it. You can't talk to me like that.  Okay, I... what glasses? Those are circles under my eye. Well, take them off. Now, wait a minute, boys. No fighting over me. I'll give each of you a test.  Well, you make love to me. Then Bob will make love to me, and the best man will win. Oh, gee, at the cinch for me. Well, go ahead. All right. Oh, Edna... Oh, gee. Edna, dearest, look through yarn window. Look at the moon. Look at the stars. What a combination. Is that thing showing again? Hit the back wall and bounce back through now. Well, put your arm around me. Now, hold me closer. I can still breathe. Yeah. Now, put the other arm around me. You've been eating potatoes, haven't you? Now, what do I do? Oh, send for Bob Strong. Yeah. The title, I never knew heaven could speak. The picture rolls of Washington Square and the songstress our own lovely Jeanette. Switch to Avalon cigarettes in preference to all other brands. And the reason? Well, Avalons have more to offer. Yes, they give you highest quality. They're made from a superb blend of the choices Turkish and domestic tobaccos and still cost three to five cents less per pack than other popular price brands.  Now, remember this, friends. You can pay more, but you can't get finer quality cigarettes than Avalons. Try a pack tonight. You'd never guess they cost you less. Hey, that was very nicely said there, Dale. Well, thank you, Red. Are we going to do a sketch tonight? Yeah, I've written a play this week called The Case of the Stolen Plan or Who's Got Hands in the Plan. Now, I'll play the modest role of Ace Skelton, a crack reporter, and the sob sister will be played by Edna Stillwell. The scene opens, I'm sitting in my office planning big things. Hello. Yeah. For you, Skelton. Thanks a lot. Deal me out this hand, boys. Hello, Skelton talking. Skelton? Yes. This is Greta, the FBI speaking. Sit out the waterfront and see whether you can dig up any data on the international spy ring. International spy ring? Thanks a lot, chief. I'll go right down. My car's downstairs, so come on, Edna. We'll bust up this spy ring or my name is Mud. Can I go any faster? Well, we get it started, may go a little bit faster. Master, well, I'm too tired to get out and push. Say, where do you expect to find this spy ring? Oh, I don't know. Somewhere along the waterfront. Snap on that radio. Calling all cops. That's right near the dock. Okay, we're out of gas. There's a cab over there. I'll go over. Hey, taxi, are you engaged? Engaged? Why, say, I don't even have a girl. Countless and awful out of fun driving a taxi. Yes, you're running to a lot of nice people. You mean you hit pedestrians? Oh, good heavens, no. Why, this cute little old cab wouldn't hit anybody. It's yellow. Well, take me down to the corner of Hickory and Dickory. Yes, sir, Hickory. Oh, say, that's the toughest part of town.  What?  They wouldn't dare. I'm looking for spies. The spies. They forgot the answer. Well, do you have to go down there to look for them? Goodness, why, that place down there was so tough when a kitten wants a bowl of milk. He hijacked the cow. Well, come on, get going, Herky. Skelton never flinches. I hope.   I'm very nervous.   Why, I know every ash can and telephone pole along here. Look out! I guess I wasn't introduced to that one.  Here we are. That'll be 50 cents, please. I'll give it to you, just as soon as I get up off the floor. Here's 25 cents on account. On account of what? On account of having gotten the other 25 cents. By my goodness, Mr. Skelton, no tip or anything. Nope.  I'll see you. Hey, wait for us, Herky. Somebody's got to get his stuff. Gee, this is a creepy-looking place, isn't it? What was that password again, Edna? Tomatoes are cheaper. And don't look so scared. Who's scared? Surely I'm not scared. I'll knock on the door and see if anybody's here. Nobody's here. Let's go. What's the matter? Are you getting chicken-hearted? Who, me, Skelton, the ace reporter getting chicken-hearted? I should say not. I always been that way. Someone's coming to the door. Well, what do you want? Tomatoes are cheaper. Oh, I can that stuff. Hey, you wouldn't be a detective for a newspaper man. Not live. I mean, uh... Maybe we spies would better get down to business, huh? Very well. Come on in. Say, I think all the spies are here. I'll call the roll. Uh, Sammy the spider? Yeah. Homer the hornet? Well, why didn't you answer? I didn't hear you the voice two times. Let's say, who are you, stranger? I'm Mickey the rat. And I'm Minnie the mouse. Okay, now for some sinister business. Sammy the spider, have you got that secret code message figured out? I'll finish, chief, and it's just what we thought. Okay, read it. Cubs 10, Brooklyn 5. Now, men, we have a very important job coming up. Now, what is it? The Ukrainian government will pay $10,000 to find out... what happened to Buy-Mere-Bistushane. Say, I better phone the newspaper right away and get my story out. Hey, you mean you're not a spy either? No. What do you mean, spy either? Well, I'm from Scotland Yard. Yeah, I'm a G, man. I'm a secret service man. Well, I'm a monkey's uncle. This is Red Foley and the Avalon chorus create the musical image... in the chapel in the moonlight. Little old church, that's covered with mull, the chapel. But Avalon's cost only $0.10 plus city or state tax. It looks like it winds up everything now, huh?  What did you say? I said your role was waiting for you. Yeah, it shows as coffee. Yeah, oh, watch the youth. Good night, folks. PM B-U-L-O-V-A, Boulevard Watchtime.


We demystify what goes on behind the therapy room door. Join us on this voyage of discovery and co-creative conversations. This is The Therapy Show behind closed doors podcast with Bob Cook and Jackie Jones. Welcome back to the next episode of The Therapy Show with Bob Cook and Jackie Jones and we're following on looking a little bit more around personality traits and the one that we're doing in this week's episode is the passive-aggressive personality trait. That's right and I think, off camera you're talking about that book you like, but I personally had adaptations by Ian Stewart and Paul Wern and they talk about different styles of character. I think they call this person if I'm like, is it the playful resistor? Yeah. Am I right? Yeah. Yeah. Yeah. Yeah, I'm right. Good. Which is a really clue into how to work with these styles, if you like, and these are the people who present quite passive and in their passivity quite aggressive or may appear like that.  Go away. Quite regularly in the therapy room as well. In their family of origin, it might have been a different story.  Yeah. And that's the way they've survived. That's the way they've attempted to get recognition. Unfortunately, usually negative recognition from their parents of origin. Yeah. But any recognition is better than nor recognition for human beings. Well, that's certainly true because otherwise they're shriveled up and die. So in this character, it's an attempt to get their needs met, a desperate attempt to be seen, a desperate attempt to be understood, a desperate attempt to really explain this. I suppose I've explained it quite well, to get their needs there to be understood. And for the parents just to turn around and say, well, you did a really good job. So in other words, to get validation. But the way they choose it, the way they attempt to get their needs met, the way they attempt to make connection, the way they attempt to be intimate, if you like, actually may result in pushing them, pushing other people away. Yeah. Because it's they, their attempts to get connection are often quite aggressive or can be seen as aggressive. Yeah. Yeah. And leaving the other person not wanting to make that connection. Yeah. That pushing all again type of thing. Yeah, leaves them not wanting to initiate. Yeah. Now the levels of passivity are high. Now, again, if we talk about traits, rather than personality disorders again, they're still high. So procrastination, for example, not doing anything, expecting to other people to think for them, and then they disagree with them. Yeah. Possibly. Often seen as oppositional characters to the most one of the most main features is the attempt by the client to get the therapist to do the thinking for them. And then when they do the thinking for them to disagree with them aggressively. Yeah. Does that make sense? It does. It does. In a way, I was just wondering. Is that identification again? Yeah, well, this, I don't have the passive aggressive thing, but it doesn't. Your clients, you think. Oh, yeah, understand that completely. This kind of like that learned helplessness, but then they come out on the attack. Yeah. That's the phase. Come out on the attack. Yeah. You know, it's a way, it's a desperate attempt, though, to make connection and to let the other person know I'm here. You know, I am here. I want you to meet me. But actually what they do pushes people away in most cases. Again, you know, in touching on what you said in the last episode, I think it's really important as the therapist to not take it personally. That's the bit. Not to take it personally. Yeah. Yeah. They're going to, you see, you know, for most clients, the therapist will represent the authority figure. Yes. Yeah. Now, the passive aggressive client will go into battle with the projected authority figure. And if the projected authority figure then goes into battle with them, it's the same as going to battle with a paranoid that we talked about in the other podcast that will go nowhere. In fact, they'll be repeat of history. Yeah. Yeah. And it's interesting. So, you know, I've always spoke about it quite early on about the pacing of the therapy sessions and things. And I think sometimes you can tell by the response or the atmosphere in the room, whether the pace needs to slow down a little bit, whether they're feeling under attack or I don't know that you can see straight through them. You need to just tread water for a while in the therapy room. Sometimes I think. Yeah. Because they will seek out what is called in TA negative strokes with recognition because that's been their diet as a childhood. Yeah. So, they will scorn authority. They will be resentful authority. They will go into sulky behavior. They will induce the parent, i.e. the therapist, in some way to push them away by this so-called inadvertent commerce bad behavior. Yeah. Which again is a protection mechanism. Yeah. And you're right. Passive aggressive clients who have grown up with that way of an attempt to get strokes or recognition are very good at promoting these battles with their therapists. Because if you trace it back to their history, that's exactly what they did with their parents. Because they didn't get the validation, they weren't met, they weren't understood.   Yeah. Because I don't want them. Because I don't want them. Yeah. So you go around in this sort of, you know. That's a wonderful example of it, what you just did then, Bob, is literally that the arms crossed, whatever it is, that is literally what I think you would see in a therapy room. It's, yeah, I don't want it anywhere. Don't want it anywhere. That's exactly it. And that's their frame of reference. So they play these battles to get validation, etc., etc. And when they get it, they push it away. Because they don't need it and they don't want it. And then you've got the whole process goes around again. So you've got these repetitive behaviours, which we call games and transaction analysis, which, you know, is an attempt maladaptively to get their needs right. It doesn't actually work. But it actually works to a certain level in their childhood, where they got some levels of recognition. Yeah. And they attempt to enact the same process out in life. And of course in relationships, then the problems really start. Do you find that sometimes there's a fine line in the therapy room of buying into it, into the adaptation and playing that part, and not buying into it? Is there a point where we need to play the game up to a certain stand so that the client stays in the room and keeps coming back? Well, it's interesting about this, because if you talk about games and behaviours, repetitive behaviours, there's many ways we can do that. One is what you've just talked about, where you may stay in the game and play the game out and then see what's the script, the payoff that they actually take, and then actually do a bit of educative therapy and take it back to their early history. You can do that. You can actually do some educative therapy before the games actually begin. But what you're talking about is staying in the behavioural. It is a fine dance, because the problem without moving to some educative therapy is that you may reenact its history. Yeah, but it is a fine line in playing it out so that it's familiar to them and they feel comfortable in the situation somehow, and refusing to do it, and them up in the ante, playing an even bigger game somehow. You can do that, because it's a bit of a trap though, because there'll be better at it than you. So I'll tell you a good way to work, I think, clinically with people with this type of ways of defending is through humour. Because if you can get to their playful child, this is why I think Ian Stewart and Van Joys nicknamed this type of character playful resistance, is because if you can use your own humour to bypass those defences of resistance and get to the child which has been not validated or not met, then I've always found that a really good channel. Now, I've naturally got good humour, but I don't think of using it as a technique, but I do think, interestingly enough, clinically, that with this type of client, using my humour as a way to, or a channel if you like, to get to the energy which is often quite blocked in the child part of the person, is a useful and a technique that is effective. I can see that, yeah. If you go the other way and get caught up in that sort of battle you were talking about earlier, you've lost. Yeah. If you can get to the part of the child, in other words, the part underneath the coping mechanisms or defences, in a way they'll allow you in and a way they'll engage with you, you're more likely to get to the part of them which is being so hurt. In a safe way, yeah. Yeah, he's in quite a safe way. Yeah. You know, the paranoid might feel tricked by humour, which isn't, I didn't say that in the last podcast, but I think the style of character comes from this sort of passive-aggressive process often feels engaged by humour. They don't go quite to the same levels that the paranoid person does. Yeah. I've always found that a good way to work with these people in a safe way to reach what often is called in the books the inner child. Yeah. Which really means the vulnerable, the younger part of the self. Yeah. Yeah. No, I can see that working. I can also see you doing that in a therapy room as well. Yeah. Yeah, because humour, I like humour. Yeah. It's an interesting one, humour. Just sort of touching on that this moment, because you know, you're on a fine line again because you're after engaging with the child that's been so hurt. That's why they pull these defences up in a safe way, quite correct. But if they feel in some way that you're laughing at them, rather than being with them. Yeah. You'll reenact history. Yeah. If they feel like they've been ridiculed or made fun of or anything. Yeah. So humour is okay, I think, from a thought out place, if that makes sense. Yeah. People call that technique, maybe. But I think with these types of people, using humour, I've always found very effective to engage their child, because that's where the trapped energy often is. If you can come alongside the vulnerable child, you're more likely to move towards a more power to process therapeutically than moving to some sort of battle with them. Yeah. Yeah. It's interesting. You know, just looking at where all this stuff comes from, you know, often what is played out in the therapy room is reenacting exactly like you say, something from the child and something that's happened that made perfect sense at the time. It's just in the therapy room, adult-to-adult interactions, it's not helpful. No. They're level procrastination. They're level sullenness, they're level of resistance, they're level of aggressiveness. Often...  Yeah. If you think about where all this comes from, to me, it's the battle with the parent in the individuation stage. So in other words, they are attempting to be seen, to be loved, to be validated from the significant other people, person. Now, if that doesn't happen, then what they could withdraw and shut down, like the withdrawn clients we talked about in the podcast, they could go into a tap, blame, and control that we talked about in another podcast. In this style, what they do is they attempt to get the validations, the strokes, and the love by actually acting out negatively. And then interestingly enough, when perhaps the therapist, sorry, the client could put the therapist later on, sorry, the parent rather than the, you know, the parent in their earlier history has, does then attempt to meet them, they then push them away because it's like it's too late in the framework. Yeah. Yeah, you've had your chance and you missed it. Yeah. They don't allow the parent to even go anywhere near their places because it's too late. Yeah. And then they go around in a circle, talked about earlier. Yeah. So it's, it's a very sad tragic tale, I think, because it's an attempt to get a different type of parenting. However, when that different type of parenting came along in their early history, it was too late for them. And they pushed them away from a very heard place. Yeah. So for the therapist to get to that child and, and engage with them and validate them, so they got a different imperative experience has to be done with patience, gentleness, and in a safe place. Yeah. Not straightforward therapy, this isn't, because if the problem is, if you buy into their attacks or their control mechanisms, or their procrastinations, or their passive behaviors, or their aggressiveness, and move into that sort of control battle, you'll lose out, you'll repeat history, you have to, and that's like, this is why humans, I think, quite a safe option. Find a way to engage with her child. And, and that's, that's, that's easier said than done. Yeah.  That's how I see that connecting with the humour bit, it's a distraction, let's get away from the heavy stuff and let's, let's look at something less deep. Let's engage, yeah, let's engage that hurt part somehow. Yeah, yeah. So it's, it's, it's, if you see the therapy as the client's vain attempt to get a different type of, you could even look it like this, a different type of permitting, which attunes to them, counts to them, counts for them, and attempts to understand them, then I think you're on to more of a winner. The problem is what we said earlier on the podcast is that if you get, if you combine to their negative threats, their intimidation, their passive resentment, their solidness, you'll reenact history for that. Yeah. Which again, is why it's really important, a lot of the time, for, for therapists to have supervision, to, to talk about the impact of seeing certain clients on them. Again, I talk a lot about fine lines. There's a fine line in not taking it personally and not being invested in the therapy. If we're invested in the therapy with the client, then sometimes we do take things personally. Well actually, that is true because we're all human, however, or stroke and if we have enough therapy and supervision ourselves, I hope the investment isn't exactly the opposite. In other words, the investment is staying out of these power battles. Yeah. But of course, I think we often need our therapy to do that. Yeah. Yeah. And when I say the investment, I meant, you know, the investment in the therapy session and wanting the best for the client. I am invested in each and every one of my clients in one form or another. And in doing that, I open up the potential for taking things personally. Yeah.  Yeah. So, you know, one thing, when we talk about passive, the passive part of this type of the character we talk about, I want to go back to something which is really fundamental and that is they will want to manipulate you or hypnotically manipulate you to do the thinking for them. So they then can reject it. Yeah. Now that's a really interesting one because it's very important in the end that they do empower themselves and grow up and don't stay infantilized and caught in this passive aggressive battle they often are. So how does the therapist do that? How does the therapist go to a place where they're encouraging the person to think in a safe way? In other words, they encourage them to think without the crowd being so afraid that the work is going to be taken away from them or they can enact out this aggressive place because in the end of the day, you do need to get to a place where they start thinking for themselves and not manipulating you to think for them because if you go down that line, they'll just throw back in your face again. Yeah. So it's an interesting, I think the way through it is to get to the child, like I've said before, and help the child's scare about thinking. Yeah. Do you think particularly with passive aggressive clients that the way maybe to do that is through activities? Yes, yes, yes, yes. That's often a very good way to do it. Yeah. Rather than the thinking and the feeling business to get them doing something. Yeah, because if you think about it, they're invested in in passivity. Yeah. So they can induce the parent in and then they can of course then spit them out again. Yeah, yeah. So if you can move to behavioural activities or that is a safer way, I think, to go and certainly through the behaviours you might get to their feelings and then their thinking. Yeah, without, I don't know, hitting the trip wire that can get the defence mechanism up. It's, yeah. I think that's where I feel less challenged in a room when we're doing something activity based behavioural stuff. Rather than trying to outwit each other. Yeah, yeah, yeah, because it also therapeutically confronts the passivity. Yeah, yeah. They need to move and get unstuck or something. But you know, if you think of this, as I said before earlier in the podcast, it's a tragedy their history because they're attempting to get connectedness, nurture, intimacy. And when it comes, they throw it back again. And that's the whole game. Yeah. Somehow you need to cut across that. And I, again, I think playing with them is a really good way. Yeah. Gaze the child. Yeah. Which, again, you know, the humour side of things can be used as, you know, behavioural and making that connection that way. Yeah. Fascinating. Fascinating. It's a wonder any of us come out of there alive sometimes, Bob. Well, of course, with the passive aggressiveness, and I think with many of these characters, especially the passive aggressive part, I don't really like, I much prefer playful resistance. I like that. I much prefer that. It's often seen as a battle to the death. Yeah. And of course, we need to find a way where they can honour life and we have a different reparative process. And as I said, I've probably said the fourth time this podcast, I think engaging humour and playfulness to connect with their inner child is the way forward. Yeah. So they can learn to connect in a different way. Safe way. Yeah. Yeah. So, what we're doing next episode, Bob, do we know? Well, you've got your list off. I've got my list. We're going to do the histrionic. Let's move on to histrionic. Let's do the histrionic and the narcissistic client. Okay. Because they sort of go together in many ways. But quite often the features of the histrionic client is similar to the features of the narcissistic client. And often the narcissistic client and the histrionic client get mixed up. Interesting. So I think that'll be interesting. Right. We're grouping them together then. Right. So until the next one, where we'll be doing histrionic and narcissistic. Yeah. That's, as you said earlier on, you know, narcissism often is the flavour of the day. But there's a great call for healthy narcissism, which is a genesis, of course, for self-esteem. It'll be a great podcast. And again, it's a sliding scale. We all have narcissistic tendencies. We're human. We are. Yeah. I can think of many well-known figures for next week we can talk about, but I'll have to be careful. But I can think of many of them. And they are on the right side of this spectrum. But I do think we can put them together, histrionic and narcissism to certain extent. And they often get diagnosed the wrong way round. Maybe that's something we could do in future, Bob, with these personality traits is pick somebody in the public eye that we can say that's what they are. That's that. Well, obviously in a lot of social media, you know, Trump is often seen as an arch narcissist. You know, I think one of the ways that I got to grips with these when I was doing my training was to look at EastEnders and Coronation Street and Emmerdale and look for characters that were displaying certain behavior types. Yeah. I mean, it's a very, very good one. Unfortunately, they're full of narcissists. But we're not talking about the actors or the characters. So we can't get done for libel or anything. I meant the characters. Yeah. Yeah. Right. So I shall see you on the next episode, Bob. You will see on the next episode. Take care. Bye. You've been listening to The Therapy Show behind closed doors podcast. We hope you enjoyed the show. Don't forget to subscribe and leave us a review. We'll be back next week with another episode.


the Mossberg Maverick 88 security model. What a great shotgun this is. A lot of people love it. They say it's a working man shotgun. It's priced right 200 bucks, two and a quarter. I think it's a great deal. A 20 inch barrel and a magazine tube to hold seven. Plus one is eight round capacity. A corn comp, four end, flat darker stock and four end. Skeletonized recoil pad, nice trigger, action release, right behind the trigger guard there. Already mentioned cross bolt safety. It has a barrel clamp, right there. Fixed cylinder board choke, a bead front sight. Cause I have run all types of ammo through the Remington Nitro Turk three inch load. Whoa, it's a phenomenal shotgun. A lot of people speak highly of it. That is why they call it the working man shotgun.


There's a lot of observers that I don't know why we have them Okay, because a lot of them. It's just sort of like or this doesn't feel like an event or or this is batched work Or something like that and and the go-to has been to create and Observer for it and really don't need that. We could just you know the three observers right now Mutation mm-hmm resize mm-hmm intersection mm-hmm. I can also come up with three Anyone who's done some work with CSS at some point at using responsive stuff with media queries and such has Kind of had the idea ha this media query stuff is okay But what I really would like is a way to style this element differently to how big this element is and then Go on Twitter and say they have had a bright idea or file a bug about her and I'm basically saying what I did By the way, this is what I did it years ago and we're like yes. Yes. We know yeah many people have had this idea the reason we can't just have element queries is you know because you can end up with a Query which changes based on width and as a result it changes width and you end up in An infinite loop bad idea right that seems pretty bad So there's a web standard called resize observer and it's stable in Chrome and it is yet for an element You just say that element there Observe yeah, let me let me know when it changes size. All right, that's cool And that so that means you can react. It's a JavaScript API so you can react with JavaScript exactly So so we are back at the infinite loop problem. So I was reading your article and you've got a section on on that Well, do I you've got a little bit a little bit of text on it Changes will only be processed in the same frame if the resize element is deeper in the DOM tree than the shallowest element Processed in the previous callback. That's a weird menu. Perfect So, but that's just words That's just some words you like in an order. I think I explained it pretty concisely. It's actually what I wrote Yeah, talk us through it. Okay. I'm just saying I don't understand so I'm okay. So imagine You have an element That has children as you know is common and you call resize observer dot observe on this element on on on the parents Yeah on the big all right. All right. All right. That means whenever this element changes size You will get a callback and you can react to it cool. Excellent. Yep So now let's assume you also call another research observer observe on one of the children Okay, because as a result of the parent changing size the children could change so you want to be notified about both So both research observers would fire Their callbacks and you would get notified right Let's assume and a third thing that in one of the children's callbacks I change the parent's size. It's JavaScript. That's possible, right? I can just change anything in the launcher and it could even be done implicitly by changing the size of the child Which would potentially if it's just text flow or just append some text, right? Okay parent could suddenly grow and then Technically the outer the bigger research observer from the outer element would have to fire again And the smaller one probably as well And then it could say I'm happy again and again and there's usually and how we break this loop is with the rule that Readers observers all the research observer will fire in the same frame before layout and if you change within the same They will also fire within the same frame Unless the change has been made to an element that is of the same level or higher up at the dorm tree So it's like in terms of how we talk about events capturing. It's sort of it's a reverse bubbling. Yeah, we're capturing So that's that's the so that's the direction it goes so I can only you can only have multiple invocations of your callbacks Downwards of the tree, but if you if some of them that are high up in the tree would have to refire That would be delayed until the next frame So what you're saying is that the the change is only processed in the same frame if the the resized element is Deeper in the dump. Yeah, then the shallowest element processed in the previous callback. That's exactly what I'm saying That's also exactly what I wrote Makes sense now. It's perfect. You should You should have put that in the article like you did. I was I think at the end I I think I remember writing this article There were lots of things changing and so I got a bit annoyed because I was I think I was working on an animation And now at the end I was like Just copy and paste that from the spec job done, right? Well, yes, I like it I think we should keep it in the browser and I think other people should implement it That's that's us doing advocacy. Yeah, that's like other people should Please we didn't give that we didn't give that a trendy weightless CSS name. Oh, did I did I did it? Um, Layout enhancer layout enhancer that's I think I get a lot of emails about that to my span folder It's a real cafe. It's a real cafe. Yeah, of course where does math for the podcast could be anywhere? Now when we do the two-minute segments, I want that is the nice


Welcome to Moments with Melinda, my new TV interview show that will focus on sharing with you the stories of interesting Vermonters who have a story to tell. My first guest on my new show is Bernie Lambeck. Hi, Bernie. How are you? Melinda, I'm great. Thank you for inviting me onto this show, especially the first one. I'm honored. Well, I'm so excited to have you with me and I just want to tell our guests that Bernie and I serve on the board of ACLU Vermont together and it's been such a pleasure to serve with you on that board.  So Bernie, let's start by having you tell us a little bit about your early life. My early life, my early life began unfortunately a lot a lot of years ago. So I'm from Montreal, Canadian, although I became a naturalized American citizen in 1980s. My parents were refugees from Hitler's Germany. My father from was from Germany my mother was from Czechoslovakia but both German speaking Jewish families, and they ended up meeting in Montreal, and I'm one of three of their sons. And, and went to Dartmouth College from Montreal that's what brought me to the States and to Vermont, and New Hampshire. I did a few things, including eventually teaching elementary school for a few years then I went to law school. So I lived in the upper valley where Dartmouth is for a few years, ending up in Thetford for several years, and where I was living where I met my wife and was and had two of our kids then we went to New Haven Connecticut where I attended Yale Law School. My third son was born there. And after three years of law school we decided to move to Montpelier in 1988 and we're still here. I'm right now sitting in my office in downtown Montpelier. That's the early part that well that that's and thank you for that. So, I know that you're into social justice and racial justice and you've been involved in that for your entire life.  I don't know, it's hard to choose one person and that but when I lived in the upper valley, especially my last year at Dartmouth and and in the two or three years after that I was very active in the peace movement and and social justice movements. So there were a lot of movement activists that influenced me a lot and that I looked up to. And when I got involved in law, you know, my certain professors at Yale Law School were influential and after law school I clerked was a law clerk first for Justice Jim Morse on the Vermont Supreme Court he was new on the court and had me as a new law clerk and he became a lifelong friend as you know he was also on the ACLU board for many years. So I clerked for Jim Morse for two years and I clerked in the federal court in Vermont with Judge Fred Parker, who was an enormous influence on me. I clerked for him when he was a district court judge and then I went back and clerked for him when he was appointed to the Second Circuit Court of Appeals in New York. And he had chambers in Burlington and so I was in Burlington but we would go to New York regularly for a week at a time to hear arguments. That was 1994 and 1995. Bernie, you went from you went from lawyering to novelist. Tell us about that transition in your life. Yeah well I haven't left lawyering I'm still lawyer you're from your lawyering but you've gone from your lawyering into being also a novelist. Yeah, I just decided. The Civil Liberties. This book here which was published in 2018 I really started work on it a good seven or eight years before it was published so I think it was to 2011 that I began to work on a novel and it was just new for me. I didn't know what I was doing I just decided to give it a try. And I wanted to write about the law both of these novels are very much about the law particularly First Amendment law. And I want and I've always been a reader of mysteries and lover of mystery novels. And so I wanted to create a mystery that was serious about some of these legal issues that I care about. Tell us a little bit about on civil liberties. What's it about. Yeah, on civil liberties is well both of these books take place in Montpelier and the issue in on civil liberties the main issue it has to do with the death of a high school girl who she's found dead at the beginning of the novel and it turns out she was the the the victim or the subject of some homophobic writing on Facebook by a schoolmate of hers a friend of hers, but this friend his name is Ricky and he's the main character in the book is is an evangelical Christian and believes that she is wrong that his friend is wrong to be living a as a lesbian and so he calls her out on it. And then she's found dead and so this is a mystery about what caused her death. So the issues that the legal issues involve free speech in the schools whether students have a right to engage in speech of the type that Ricky engaged in, which of course is called hate speech by some people. The issues legal issues, anti discrimination law principle gets fired, and there's a question of whether she was discriminated against. There's another set of legal issues around town meetings that take place and prayer at town meetings whether it's permissible under the Constitution to hold a Christian prayer at town meetings. So I explore all those legal issues. And that's a quick summary. So now I haven't read on civil liberties, but I do understand that Ricky who by the way is a black man. No, no he's not not. He's not. Aha. I had the impression that he was well that's interesting that sort of changes changes my perspective here but anyway, but Ricky and Sarah are both pulled through through that novel and into your new novel, or at least he is an intent to commit. Yes. Yes. So tell us a little bit about about the second novel that we're going to talk about today and intent to commit. It's a sequel of sorts from the first novel and as you're noting it includes some of the main characters from uncivil liberties particularly Ricky and Sarah are there they're sort of the younger generation of characters and uncivil liberties, and they're as the protagonists in an intent to commit, and some of the other characters from uncivil liberties have less central roles in the second novel. The, the focus is that Sarah Jacobson is an activist becomes an activist organizing in the black lives matter movement in Vermont schools. And there are legal questions about schools ability to fly the black lives matter flag and whether students with a different viewpoint or families with a different viewpoint have a First Amendment right to have their own flag. Yes, the school has chosen to fly the BLM flag. So there's some, there's some court action around that. But then the heart of it gets to some hate mail and opposition against Sarah's organizing and other activists organizing around these issues in the schools and ultimately, it's not a secret. They're kidnapped by some right wing zealots, and the plot focuses on the kidnapping and the resolution of that. And the opposition wanted to be able to, to put up a flag to support was it their gun rights, gun rights, yeah. I find this so interesting that through this whole book. Ricky was a black man for me, and I saw him as that isn't that interesting anyway that is interesting. And he always will be to me. He lives in my brain but Sarah has another as a boyfriend from an earlier period in her life and section kind of looking back on that. And he is, he was a black man. Yes, right. Yes, I mean, yeah. Um, so thank you for setting the stage for your book on an intent to commit. And for my the folks that are just just tuning in I am talking to Bernie lamb back who was a lawyer in Montpelier, who's written a wonderful book called an intent to commit, and it is actually being released tonight. Thursday, November 18 at the Lost Nation Theater. So I'm so glad that I got you before you released your book I feel really honored about that. Now Bernie intent to commit is set here in Montpelier. So how much of your novel is is is true to form is. The settings Montpelier and some of the events are based some of the events in the book are based on real events so the flag flying at Montpelier High School. The BLM flag and the BLM flag flying at you 32 middle high school. Those events happened and I drew quite largely from articles in the press, particularly the Times Argus. Those events and some of the quotes I used are quotes from the students that were participating in the flag flying ceremonies. So that part is based on real things that happened in and around Montpelier. And some of the places that I describe in Montpelier are real places sometimes I change the name sometimes I don't. The kidnapping story is entirely fictional. The main characters are entirely fictional. There was there was not a there was not a challenge to flying the Black Lives Matter flag in Montpelier, but you created that and then you leave that incredible legal story that flows through your book are you Ted Surowski. No. No, I'm not. Ted Surowski is this, as you're mentioning it, he's this the school district's lawyer. Yes. No, I mean, the lawyer Sam Jacobson who's the more or less a protagonist of uncivil liberties and appears only in a few places in an attempt to commit. He was originally based a little bit more on me. Okay. I kind of started out that way, you know, you write about what you know and all that stuff but what I needed to really do as I was writing on civil liberties is to separate the character from myself and create him as his own true fictional being. And so he departed from me, but it was never never Ted Surowski. Okay, never Ted Surowski. Okay, well that's good to know. So I would love to have you read from your book for my viewers and we're going to we're going to focus on. So why don't you set the stage for what you're going to read to us on page 35 of your set the stage of what what our folks are going to hear from you. Right. Very good I'll read that and Sarah Jacobson is featured in this section she at this point in 2017 is still living in Providence. Rhode Island. And she hasn't moved back she's from Vermont but hasn't moved back to Vermont yet with Ricky which she does in the book but, in fact this scene here directly preceded and as part of the reason why she chooses to move back to Vermont. So let me begin on a cool day in October 2017. Almost three years after Tyreen's death. That's Tyreen, who we mentioned a moment ago. Sarah was sitting on a bench in the scrappy park next to her workplace on Manton Avenue in Providence.  She faced the busy road with her cell phone in her hand, and an egg salad sandwich on a sheet of wax paper in her lap. She walked through the streets by, and the sun that cleared the buildings on the southern side of the street warmed her body. She scrolled through her emails reading some saving a few discarding most in the human rights network newsletter she noticed a posting for a job at an organization called Green Mountain Black Lives Matter. Looking to her right down the street she saw a family with a stroller on the sidewalk at the end of the block heading slowly in her direction. She watched them briefly. She paid attention to the phone. She followed a link in the job posting to a website for Green Mountain BLM. It was a newly formed Vermont organization that was looking to hire a staff person to be its youth organizing coordinator. Sarah knew there were other BLM organizations active in Vermont. This one appeared to be focused on middle and high school students. There was movement in the hills of Vermont. The family on the sidewalk came closer to her. They were Hispanic looking probably Guatemalan she thought, like many of her clients. The mother was pregnant. At this moment, the man crouched down to fix a wheel on the stroller that had gone kinky. Sarah smiled and waved to the toddler in the stroller but she didn't think the girl saw her. On the sidewalk to her left. Sarah noticed three young men with barrel chests. They had a kind of rolling side to side gate that made her think they were proud of their masculinity. Sarah worked for a nonprofit coordinating campaigns to organize local residents in the Latinx community on issues relating to immigration workplace abuses and foreclosures. But internal divisions embroiled the organization. Meetings had become awful yelling experiences. Some who professed a passion for equity and inclusion engaged in the worst personal attacks. Sarah didn't see much light through the tunnel her workplace had become. On top of that she hadn't been paid for three months as expected funds had not materialized from granting agencies and donors. She was ready to jump. The whole thing made her sad. The wind picked up putting her phone down beside her careful to balance the sandwich on her lap.  Her scarf was Guatemalan given to her by a member of her organization. Sarah had grown up in Montpelier Vermont small capital city and she wondered about returning home and whether Ricky would want to make the move. Sarah was the only daughter of Donna and Sam Jacobson parents whom she loved and fought with and had needed space away from Ricky had grown up in Montpelier to Ricky's parents Clara and Carver still well were conservative Baptists a rarity in Montpelier. That was complicated for Ricky. Now there's an understatement she thought smiling. All three young men on the sidewalk to her left or a t shirt that said white motherfucker words that she could read as they approached but embroiled in her own thoughts she couldn't understand their meaning at first. All three men wore baseball type hats they were read. Sarah now saw, they were emblazoned with the MAGA letters make America great again. The Guatemalan man if that is what he was stood up from the his stroller repair, looking at the three white men who were still walking toward the family, about 30 or 40 feet away. Sarah could see him then glance down at the girl in the stroller who is probably his daughter. The street was busy with traffic. The father looked for a break in the traffic. The woman squinted into the sun's glare and watched the little family her egg salad sandwich still on her lap as she clutched her phone. If not for the sandwich on her lap, she would later think she might have gotten up to do something. She didn't know what it was she might have done. An opening appeared in the traffic and the family stepped onto the road. The stroller wheel was still not functioning well and veered to the side so the father picked up the little girl with his right arm and lifted the stroller off the pavement in his left hand, the woman held on to his arm and they tried to cross. It all took too long. By the time they reached the middle of the road cars were coming fast in the opposite lane. Five cars sped close by them as they huddled in the middle of the street horns blaring on all sides. Over the traffic noise, Sarah could hear the toddler, who had begun crying. Sarah felt rooted to the bench watching gasping as a moment later a gap in the traffic appeared in the far lane and the family rushed across to the other side. They were dragging the stroller behind them as he held the girl and the mother's arm. Before they made it clear to the far sidewalk, a delivery truck with its horn peeling slammed the stroller, which flew from the man's hand. The truck didn't stop. The stroller airborne clattered to the gutter on the road's edge. One of the wheels was knocked free and kept rolling down the street. The MAGA had guys had reached the pavement in front of Sarah and she could hear their deep male chuckling across the street, the family on the far sidewalk apparently uninjured, reassembled themselves. Both parties continued on their separate ways as Sarah sat still on the bench and watched the traffic on Manton hummed. Sarah let her breath slow down. She ate her egg salad sandwich carefully so nothing would fall into her lap. She turned back to her phone and finished reading about Green Mountain Black Lives Matter and the new job. She decided she would talk with Ricky that evening. And so she did. And so she did. And she did the Ricky that evening. You have a beautiful style of writing, Bernie. It flows. It's narrative, it's visual.  I really enjoyed your style of writing because some of it is very tough to understand I mean the legal part that gets into the minutiae of the law but do you explain it beautifully and you do it with color and you do it. It's very easy so that the so that the reader can understand it. So I want to try very kind. Thank you. Well, and I want to, and I want to recommend to everybody who's watching this show to order an intent to commit by author Bernie Landbeck and Bernie, where can folks get your book. There are bear upon books and Montpelier is carrying it. But it should be available from any independent bookstore and they can order it if it's not on their shelves already. It's at Amazon as well, and can be ordered through Amazon it can be ordered directly from my publisher which is called root stock publishing in Vermont and one can find their website easily enough root stock publishing. Thanks Bernie. So it focuses on the period I under the Trump presidency and it focused the reader on racial injustice and white supremacy. And it's just, it was a really important book to read after all we've gone through and what we're about to face heading into the future so I wanted to ask you and I don't want to give you anything, anything away at the end of the book. I love the end of the book but I do want to know what happens to Sarah and Ricky so I expect that you're going to write a third novel, right, and hopefully you'll carry on these characters because I, I am so intrigued with them and they're such beautiful young, brilliant, kind hearted and loving human beings and I would love to see them in your next novel. And Bernie, how do you see the state of our union. Over the next five years. Where do you think we're going to go with with where we are and where we're going I'd love to get your perspective. Oh my. I was, I was enormously pleased that we had a change of administrations and really hopeful about the Joe Biden presidency and the administration. And I am still hopeful I'm hopefully is going to get the second huge bill passed. But the, the intractability of the Republican Party and the direction they've gone in is to me just so overwhelmingly awful that it's hard to maintain, maintain that hope in the face of that. I don't know where we're going. I wish I could say something more positive about that. Yeah, I hear you, I hear you my friend. I, and, and there's hope there's hope. But I agree with you that it's, and we don't need to get into it because you and I talk about all this stuff in the work that we do. But at the end of the day, your book shines a light on an issue that's really, really important. And that is the first amendment. And where do you stand when you want to fly when a school district wants to fly the black lives matters flag, and then you have another group that wants to put their flag up. Talking about gun rights, and at the end of the day you spell out the legal, the legal, the legal story, and the legal reality and the legal truth of how this, this would play out. And I think you did that beautifully. Do you want to share a little bit about that I know you don't want to give the give up the, you know, the context of the book but share a little bit about how that was resolved and you as a lawyer must have researched it and put out your, your best vision of how that would have been resolved how it happened right. Yeah, yeah, no I'm happy to do that I mean it's interesting to say the legal truth of it. So keep in mind these are contested issues, and I guess we rarely have a legal truth. Until this US Supreme Court spoken on something and even then we don't necessarily have the truth that's lost. I should have said your legal truth. All right, Bernie. I'm not being, I'm not being critical I'm just just trying to thank you when you're a lawyer and thank you for correcting you've corrected me on a couple of things tonight today and I appreciate it. But certainly, I could you share a little bit. Yeah, so that the resolution I and I think it's the correct resolution is that it's the school as a, as an institution of government that is doing the speaking when it flies a flag on a school flagpole. It's a student group that might have urged the board to fly the flag it's really the board, making that decision and once it's government that's doing the speaking then it's not creating an open forum, or a public forum for speech on that flagpole. And so other groups don't have a First Amendment right if it were a public forum, then groups that are want to use that forum do have First Amendment rights to use the forum. Dr. and called public forum analysis that First Amendment lawyers are familiar with. And the question really is is whether the flagpole becomes a public forum in the relevant sense and I don't think it does. But, you know, these are arguments. That's right. And this and have you seen a situation where this has popped up in your in your career or not.  So when when the Washington Central School District, which includes you 32 was considering a policy on use of the flagpole. The board emphasized that it was the school board's decision whether to fly a any particular flag onto that policy. I mean, all there's always there's the US flag and there's a Vermont flag and then the question is, can they fly a third flag and they have a policy that says they will accept requests to fly a different flag and it has to specify certain things and certain content is prohibited. But once the request is submitted and the school board considers it and votes on it then it's, it's deemed to be speech by the school district by the school board. So the policy is actually written to to further the argument that I was just making about it being government speech and not a public forum. Right. And I want to say because we're coming to the end of our show here Bernie but I want to also say that this is a mystery, because Sarah gets kidnapped. I also love the relationship between the parents and Sarah, and, and, and the other folks that were in her life that surrounded her in her life and how they came together is this beautiful group of human beings that it sought to find her, because no one knew where she was or whether she was alive. And it was certainly horrifying for her as well and I'm not going to tell the end of the book but it was a mystery as well and you weave that together so beautifully, Bernie, to make it a read that I literally, I, I'm going to just admit it I read this book in like two days. I would get home from work and I would just sit and read this book, your beautiful book and get through it so thank you for writing it I'm going to go back and read your first novel, and I'm going to wait, wait, deliciously for your third. And so to my viewers, and to you Bernie I want to thank you for being here, and for being the first guest on my new show moments with Melinda. And to my viewers out there I want to wish you all well, and wish you a happy Thanksgiving, and I will see you soon. Thank you so much, Melinda I really appreciate it. Thank you Bernie. Thank you.


line the five to come up just going praise some on the one it's the same pattern say basically these are the two bass lines they are all infused on the same place okay just fine around it there are lots of bass lines you can create around this chord progression chord changes they are the most commonly used chord progression or yeah progressions on praise songs okay you hear this one five one four five progression always always so basically these are everything I played there what you enjoy if they are just simple bass lines you can add to what you already have so guys like I usually say practice practice practice is a keyboard if you're new to this channel today is the first time of checking into this channel please don't forget to hit that right button and it will get on to you you know please subscribe button please please hit it before you leave you can afford to miss new videos I upload every video okay I entertain and also teach my tutorial and please subscribe like comment and share you guys have been so awesome thank you so much for everything you're doing and if you need private lessons from me every information is in the description below it's on my youtube channel so you don't go and look for it somewhere else it's on this description below you get every of my details my email my whatsapp number is there chat me by whatsapp number and send me email okay and what else on my missing I love you guys keep practicing we'll see you in my next video bye


So, one of the reasons for not one of the reasons, the reason for not including this term in trying to compute delta is of course it would have made the mathematics messier. But the most important thing is that if I had included this term in trying to compute delta, my delta would potentially depend on capital T because this term depends on capital T. So, if I try to compute delta using this term, it could delta would almost certainly depend on capital T ok. And that is just not allowed ok. Because remember first came delta ok, there is no T here when we started talking about delta ok. So, we cannot have dependence on T ok. So, that is sort of critical to remember that is why we got rid of this term just by yeah I mean just by saying that you are always going to go become smaller in some sense ok great. So, now we have been able to choose a delta. The important thing to remember is that there are a few elements here. So, delta does depend on T0 and R because of V is dependence on T0 and of course R is on the right hand side and you can almost never get rid of the dependence on R. But as you can imagine for uniform convergence or uniform attractivity, you will need this dependence to go away ok. For uniform results you will need this guy to go away that is pretty much the key aspect here excellent. Now that we have chosen a delta and we figured out that it depends on T0 and R, but independent of whatever independent of epsilon independent of T which it has to be now we go on to find our capital T. So, we just then we use this small idea ok. What was the idea? We we already know that this is upper bounded by gamma R. The term inside this is upper bounded by gamma of R ok just because of this guy ok that is what we will use ok. So, once you have chosen a delta you have V T0 x0 which is on the left hand side here is smaller than phi epsilon 1 plus gamma of R goes out and the integral is just capital T right integral is just capital T. So, what do I have? I just have V T0 x0 is less than phi epsilon 1 plus capital T times gamma R. Of course, we always already stated by choice of delta norm of x is less than R whenever norm x is less than delta ok. I hope that is clear Q yeah from here ok. All right great. So, once I have this kind of an expression it is pretty straightforward. I need if you just compute T from here you just get this expression T has to be greater than this guy ok and it is it is very natural for you to get a get a expression with T greater than right because any T larger than that is allowed your conditions are not violated for any time greater than this capital T. So, anything beyond this time is ok and you can see this time depends on epsilon right initial time state whatever so on and so forth yeah depends on a lot of things ok. Now, if you want to see dependence on delta directly you can of course use the fact that this is greater than phi norm x0 squared sorry phi of norm x0 not norm x0 square. So, this is greater than phi of norm x0 right just by positive definiteness. So, that will also bring in some kind of delta dependence as you can see yeah because phi of norm x0 so norm x0 is less than delta you will not get an exact result in equality like that but you can see that there is a dependence on delta also just by virtue of this guy just by virtue of this guy because the way we have chosen delta is exactly this yeah. So, there will be some kind of connection with delta here alright ok great anyway so there is epsilon and R alright. So, like I said in order to prove I mean the second exercise of course to prove uniform asymptotic stability yeah. So, for that the first exercise is anyway useful because you proved uniform stability to prove uniform attract sorry asymptotic stability you have to prove uniform attractivity. So, like I said this dependence on t0 has to go ok the delta dependence on t0 has to go. So, therefore, you have to think how you get rid of this dependence ok what is the additional assumption that you use here alright. So, that is the idea ok good. So, these are the only two theorems that we prove ok, but you can see that the other ones will also be very very closely connected to this yeah if I wanted to as you can imagine if I wanted to go to the global version I do not need you know I do not have any ball of radius R ok. So, for all the global versions of the result the ball of radius R business goes away ok. So, for all the uniformity the t0 dependence goes away exponential stability is the only thing that I have not actually even approached ok. That will require a little bit more not this kind of analysis that requires more because you have to like I said you have to use the same order of magnitude ideas and so on and so forth yeah. So, that I am not going into yeah you can check out the proof in textbooks like you know Khalil and Vidya Sagar and so on ok you will have some proof there ok if you are interested alright great. If there is nothing no questions here then I will move on to our next set of lectures which are on Lasal invariance yeah. So, anyway this is again notescribed by some students in the past. So, what we want to do is we want to discuss the Lasal's invariance principle today ok. Now what is the motivation I will simply stated. So, motivation for several asymptotically stable systems v is c1 v positive definite, but v dot comes out to be negative semi definite ok. This happens a lot especially for all the dynamic systems specialists yeah because typically we are I count myself more as a control non-linear controls right. So, for me I put some effort into choosing v which is not necessarily the energy of the system ok. So, a large part of my work is actually choosing good functions to work with yeah. So, we typically do not choose the energy of the system as we may start there, but then we modify it ok. But typical dynamical systems guys they are they want to analyze the system just with the energy ok and when you do that in a lot of cases this will happen that you will have a positive definite and continuous v which is obvious because it is the energy of the system or the Hamiltonian or whatever I mean you can use the Hamiltonian use the energy all of these are energy like quantities. But v dot will invariably come out to be 0 or negative semi definite you will never get a negative definite v dot yeah this happens a lot. And then but you know again like the pendulum case yeah you know I mean I modified the system of course I played with the system. But you know very well that the pendulum the system itself is asymptotically stable just because you use the energy of the system and the v dot turned out to be 0 does not mean that the system is not asymptotically stable it is you can see yeah. So, obviously we need some more mechanism to prove asymptotic stability in such cases this was the first motivation the other motivation was anyway this is the first motivation. The second one is there are systems limit cycle behavior yeah another obvious system is the Van der Waal oscillator we have already seen that in an assignment I hope yeah. So, you the trajectory tend to converge to you know this close bounded set yeah I mean another example is just this oscillator here it is a bit more dull than the Van der Waal oscillator. Because in the Van der Waal oscillator I do not remember it just whatever it has something like this I am making it very badly like this I think yeah. So, trajectory is actually converge to this do this this is a bit more dull because wherever it starts it just continues in that circle it does not converge to it starts converge yeah there is nothing to converge to it just keeps circling like this this is the standard linear oscillator X1 dot to the X2 X2 dot is minus X1. But then the Van der Waal oscillator which is a little bit more nonlinear oscillator tends to do have behavior like this and such systems are very very important I already told you nonlinear oscillators are very critical and are used in a lot of a bio rhythm applications. Okay so obviously we want to study such systems so in for such systems also we want to have a little bit more general definition of convergence okay we want to have a more general definition of convergence not just something as basic as going to a point we may want something more in fact there are more modern problems in controls like you have the say you have the platooning problem do you know what is platooning so it is a very modern you know I would say transportation theory idea in which basic idea there are a lot of these transportation trucks yeah that are carrying a lot of good logistics and it so turns out that if they continue to move in a straight line with uniform distance between each other that is optimal in the sense of fuel efficiency and so on and so forth okay so this is called a platooning problem however you start you maintain this straight line formation with uniform distance between these vehicles very sounds very straightforward but of course here the point is there may be traffic on the street and whatever I mean you may have to change lanes so once you do a lane change maneuver you have to redo the platooning and so on and so so these platooning things are automated in some so this is actually a formation a specific example of a formation control problem okay another formation could be you have a bunch of defense vehicles going to you know carrying whatever supplies arms ammunition whatever yeah and you want to guard them yeah and there is a lot of applications now where you have aerial drones which are circling around them okay and so if they are circling around so you have a bunch of you know bunch of drones which are circling this you know arm armor trucks yeah and how do you do that this is also then you are sort of trying to converge to a you know circular pattern in some sense right and this is also convergence to it because obviously you cannot start in the circular pattern and even if you started in the circular pattern and you exactly positioned them you let them off in this very nice circular pattern around them but the vehicles armored vehicles are moving right and they are doing whatever they are doing depending on road conditions especially in India right and and in border areas right there may be no roads yeah so they are doing whatever they are doing so but these guys have to keep you know converging again to another formation right so every time the formation requirement changes the center changes and so on and so forth so obviously they have to reconverse so this is also a sort of limit cycle behavior you are looking at if you want to study it in that sense many people do not most people do not study it in that sense they think of it as a coordination problem but most coordination problems can lead you formation problems can lead you to limit cycle type behaviors okay this is very important set of results actually Lassarian variants all right excellent after this mighty introduction we will look at the systems that we are interested these results work for nonlinear autonomous system going the ones I am stating yeah there are extensions it is a topic of great research of trying to do this for non-autonomous systems also yeah and there are results there and you can look at it but it is still an active topic of research yeah it is not like you know it is not textbook material yet yeah and most of what we do here is textbook material okay so we start with as usual a nice continuous lip sheets locally lip sheets continuous vector field with some initial conditions we succinctly denote the solutions as x of t right we have been doing that okay and we make some definitions okay so remember we start with autonomous systems yeah that is the main thing to remember all right first we define what is an invariant set what is an invariant set a set omega is said to be invariant if you start in this set you remain in this set for all time okay that is what is an invariant set if you start in the set you remain in the set okay great so I mean in this case it is pretty obvious I hope it is obvious that for system like this what is the invariant set it is a circle yeah or whatever radius you started with if you started with a circle of radius square root of c remain in that circle of radius square root of c yeah obviously we are not discussing cases where there are disturbances and errors and sensing and all that stuff yeah this is the precise case yeah this is the ideal case if you may okay great so omega is this okay it is a set of all points in the circle this is how you write yeah omega is exactly this yeah notice it is just the circle not inside the circle not the disc it is just the circle okay so this is what is a typical limit cycle yeah if you are inside a disc that is not a limit cycle that is the stability okay that is what we do if you are within if you are given an epsilon then you start within delta you remain within epsilon that is not nothing to do with limit cycle or anything it is you are in a disc yeah here you have a circle that is a limit cycle okay remember that okay limit point what is a limit point a point p is said to be a limit point of this function x of t again whenever I write x of t it is the solution of this equation okay so a point is said to be a limit point of x of t there exists a time sequence a sequence of time such that as t n goes to infinity such that t n goes to infinity as n goes to infinity and x of t n goes to this point whatever point we are denoting as the limit point okay so basically there is a time sequence such that if you keep keep writing terms x t1 x t2 x t3 x t4 x tk but the important thing is this tk has to go to infinity as k goes to infinity remember whenever I say sequence it is an infinite it is infinite size not finite okay so as k goes to infinity tk has to go to infinity the basic idea is it is limit point I mean infinite we want to look at behavior asymptotically therefore as k goes to infinity tk has to go to infinity and if in that case x tk converges to some point p then it is a limit point okay a very simple example I have constructed just to illustrate how things are different if you look at this series or sequence sorry not series yeah it is half 1 half 1 half 1 and so on and so forth so if I so if I take the time sequence and I have denoted this as 0 1 2 t0 t1 t2 and so on if I take the time sequence t0 t2 t4 okay where what is the limit point correct if I take t1 t3 t5 t7 1 okay so remember any one function or a sequence can have multiple limit points not just one this and this is what constitutes a limit set okay this is what constitutes a limit set okay you can have multiple limit points and the set of all those limit points is the limit set okay just like half the set containing half and one is the limit set in this case and if this limit set is a cycle okay and then the question is how do you define a cycle you can define it mathematically I do not want to get it to the mathematical definition but think like a circle it is somehow closed in some sense closed compact those are the requirements so if the limit set is a cycle then it is a limit cycle then you have a limit cycle behavior again Van der Poel also little okay that weird looking set is a limit set but it is a limit cycle because it has it is a cycle here it is it has a cyclical thing and there is a periodicity here basically it has periodicity okay great I hope those points are clear once those points are clear to us we can state the most general form of the Lasals invariance principle so are these three definitions relatively clear to you yeah invariant set limit point limit set and limit cycle is just an extension of limit set okay okay great let omega subset of D subset of Rn be compact that is closed and bounded in the case of reals compact and closed and bounded are equivalent and invariant what is D in this case D is the domain just like your ball of radius R right D is that ball of radius R type of this is the domain in which you are working so you want the existence of an omega which is compact and invariant inside this domain let V mapping D to R be a C1 function okay such that Vx is greater than equal to 0 yeah look at the interesting things that are already happening we are denoting it as V against scalar valued C1 function looks like a Lyapunov candidate at least but it is not necessarily because you only require semi-definiteness positive definiteness not required so it is not a Lyapunov candidate okay does not have to be and further you want that V dot is negative semi definite in this compact invariant set omega okay then you define E as the set of points in omega such that V dot is exactly 0 yeah it is evident that V dot is 0 somewhere otherwise no need of saying V is only semi definite right so there are points other than the origin inside omega such that V dot is exactly 0 okay and so E essentially captures those points where V dot is exactly 0 yeah of course origin is also there but there are potentially points beyond the origin because V is semi definite V dot is sorry yeah V dot is semi definite and let M be the largest invariant set inside this okay so lot of technical terms coming up now okay we will try to clarify this okay so we have used many sets yeah so we define E as the set of points where V dot is 0 we define M as the largest invariant set inside E then we can claim that if your initial conditions start in this omega then as T goes to infinity your solutions will lie in this largest invariant set M okay and M is obviously a positive limit set okay not necessarily a cycle yeah but it is a positive limit set so the immediate obvious thing is the Lassal invariance principle does not require Lyapunov candidates let us look at the obvious things then we look at the more non-obvious things okay does not require Lyapunov candidates because it is starting with V only greater than equal to 0 second thing it gives a actually seems to give a more general result than Lyapunov theorems right because it talks about convergence to positive limit set yeah it basically at the end of a Lassal invariance analysis you could potentially say that my solutions go to go to say if the limit set contains 10 points or 10 equilibria yeah then you can actually say that the solutions can go to any one of these 10 equilibria okay so that is stronger than not stronger but more general than saying it goes to this one point okay that is a more obviously if it is a limit cycle then Lassal invariance actually gives you a way of saying that you converge to this limit cycle there are hardly any other results which will talk about how you go to limits I mean there is also the Poincaré's theorem but there are very few results which tell you that you will actually converge to a limit cycle or a limit set because or converge to a set for that matter because until now we are only talking about converging to a point yeah we even we have not even said anything about convergence to a set okay in fact if you guys notice this notation is in itself not very obvious if m is a finite set of points suppose m is a finite set of points then this is okay you are just saying that as n time goes to infinity your states go to one of these points so you can analyze any all the points but if m is suppose m is a continuous set like a circle then how do you even I mean this is not a very simple notion to understand okay when I when I use this terminology this terminology is difficult all your it is in a sense what you are saying actually I would put it this way if any of you knows this notation okay this would be the more precise notation that we are used to for what do you know sorry do you understand this norm of xt subscript m what is an m norm mean like L0, L1, L2, m norm no no it is not that although I have used similar subscript notation I agree but it is not that this notation is or maybe I know there is a overloaded operator here but this notation is also used for and if it is not a number and a symbol and or a letter it is definitely used for norm with respect to set or distance from a set okay this is a distance from a set this is defined with a infimum okay this will be defined as inf over all x0 in m norm of x okay it is basically telling you shortest distance from the set yeah so this is actually a set norm because we are until now we are used to measuring so all of this is nice and easy to do in Rn so yeah we can do it in more complicated topological spaces well I will say it is their problem and whoever is working with it they have to figure out all this so this is actually a more special norm it tells you distance not from a point like origin or something it tells you distance from a set so that is rather interesting


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