Good evening viewers and welcome to this evening's monthly edition of Commissioner's Corner. My name is Lucia Campriolo and I am your elected school commissioner representing Ward 5, which is in Burlington's south end community. And this evening I am absolutely thrilled to be joined by my colleague and friend, Commissioner Martine Gulick, who represents Burlington's Ward 4 community, which is home to Flynn Elementary School, which incidentally I had the chance to visit for the very first time last week in person, which was awesome. I was attending the third of the workshop series of three workshops about gender and pronouns. And it was awesome. It was a student-led conversation. Not surprisingly I was wildly impressed with the young students who led the conversation and it was just great to be in community with students, parents, educators and everything. So great fun to be able to visit in person. But in addition to Martine's role as school commissioner where she co-chairs the Finance and Facilities Committee and is a regional representative on the Vermont School Board Association, Martine recently added a new title to her resume thanks to voters of Chittenden Central District who elected her to serve as state senator this past November. And so Martine has just begun her term. Congratulations and welcome. Thank you so much, Lucia. I really appreciate it. It's great to be here. It's great to say hello to everyone who's watching out there. And you know, I guess I want to say thank you again to the voters for giving me this wonderful opportunity. It's been incredible. It's been like what, eight weeks, eight, nine weeks or so. And it's been really wonderful. Thanks. Awesome. Well, I am in awe of your service. Obviously we've gotten to know one another and work together for the past year, but it is taking public service to the next level for sure to throw your hat in the ring for state senators. So thank you so much. And also so exciting because this evening we have the pleasure of speaking together about some of the education policies that are swirling in conversation under the golden dome as we say. And also because Martine is vice chair of the Senate Education Committee. And so just especially fortunate to have your expertise both in your role as commissioner and also your experience as an educator in that space. So really truly a service to all of our mentors. And I guess I'm curious, what maybe about your role as commissioner prepared you for your role as state senator, if at all? Thank you so much for that question, Lucia. And before I start, let me say thank you to you for all that you do being on the school board. And for those who don't know, Lucia very graciously took over the clerk role when I decided that I had to step down from that role. So thank you for doing that. And thank you for keeping this show going live at 525 or commissioners corner as we like to call it. You've just slipped into these positions so nicely and seamlessly. And I really appreciate it. So thank you. Thanks. So what prepared me for this role being a commissioner? Well, one of the big challenges that you have to take on when you decide to run for office is you have to campaign, obviously. And I did campaign for school board. My first two races were not contested, so that wasn't too, too challenging. But my third race was contested. So obviously campaigning is its own beast. And you have to kind of figure out how to do it, how to get out there and meet with people, how to knock on doors, how to send letters, ask for money a lot of times. So I was prepared because I had done that before. And I had also taken an emerged class, which prepares women to run for office. So that was fabulous. And then in terms of the legislature itself, it's a combination of having worked on a school board. Having been at that governance level of policy making, where honestly a lot of time spent listening. A lot of time spent waiting for your time. And again, figuring out where you fit in the picture. Governance is very different from advocacy, which is very different from working on the ground. So, yeah. Thank you. I can relate to that obviously on a smaller scale having joined the school board and really also navigating the difference between advocacy and policy making. And so often advocacy is what drives us to serve. And policy making is quite different. Well thank you. So before we move into the meat of the conversation, which is really to examine some of the policies that are underway in Montpelier that relate directly to public education, I do want to first open with gratitude to Burlington voters. Thank you all so much for passing with a healthy margin the proposed school budget for the coming school year last week on Town Meeting Day. We take your support seriously, and so we are very grateful to you for it. It's also a huge responsibility and a core component of our job to shepherd and be held accountable for the school's budget. And so it is a very serious vote. And again, thank you. For that, other school district related outcomes of Town Meeting Day include the successful re-election of three district commissioners, Kendra Sowers, Jeannie Walts, and Jeff Wick, along with newcomer Gary Golden, who was elected last week and will be sworn in in April, actually will all be sworn in again at the first Tuesday of the month meeting next month. So congratulations to all four volunteers, and congratulations and huge gratitude to outgoing district commissioner Kathy Allwell for her many, many years of service to Burlington School District wearing a variety of hats, including two separate stints, I believe, as school commissioner and just all around advocate for children and for public education. And I think, for me, in the short time that I've gotten to know Kathy and enjoy working with her, her commitment to equity, to transparency, to real excellence in education are just some of the qualities that stand out to me about her leadership, and I will continue to channel her wisdom as I continue my own service. And so just huge thanks to Kathy for your years of service. Can I just add to that? Please. She's been on the board the whole time that I've been on the board, so I've watched her in action and I've learned a lot from her. And one of the things that makes Kathy kind of a hero to me is that she was always willing to be the voice for folks who might not have a voice otherwise, and always, as you said, just fighting for equity and fighting to make sure that folks got treated fairly and got what they needed to thrive, and that especially our students got what they needed to be successful. And that's not always easy. You know, we're in a system that is built on systemic racism and inequities, and Kathy was just always there for folks, and I admired that greatly, and she's a fierce, as you know, fierce, impassionate advocate. Yeah. Thank you. You're absolutely right. Finally, worth noting as well, voters also last week approved expanding rank choice voting in Burlington to include the mayoral election as well as school commissioner elections. So that will go into effect this time next year. Mm-hmm. Yeah. That's exciting. Yeah. It is, especially because next year we will elect eight district commissioners. Right. Thank you for that nudge. So next March, I will be up for reelection, and there will be seven other seats that will be open, and I just want to take a moment to really ask folks to consider stepping up to run for school board and to get engaged. If there's one thing we're all learning right now as we look at our country and the political landscape and what's happening with public schools, which are under threat in ways that I never thought imaginable, this public school success takes all hands on deck. It really takes everyone getting involved, supporting each other, running for school board. It's just a multifaceted community project, and so I do want to encourage folks to run. That doesn't mean you have to secretly put your name on a ballot. You can go to someone and say, hey, are you running this year? And if not, I'm thinking of running. Maybe we can work together to make this a success. So it doesn't have to be a me versus you kind of scenario. It can be a very collaborative scenario. Some of us have been on the board now for six years, and it might be time for some new blood on the board. So anyway, I want folks to keep that in mind. I think you can reach out. I know you can reach out to any of us any time to ask questions. But I can say, and I'm not saying that I'm not running or that I am running, but I'm just putting it out there that I hope folks engage. And a lot of people say, oh, Martine, being on the school board is so onerous. It must be really terrible. It's not. I've enjoyed it so much. I've been at it for almost six years. And I can say it's great work. I really, I don't agree that this is horrible and difficult all the time. It is difficult sometimes, but it's great. It's great stuff. Yeah, thank you so much. I'm rambling. No, not at all. I'm so glad you mentioned it, because I totally agree with you. Participation is essential. I think on the one hand, certainly the fact that our three incumbent district commissioners were ran uncontested obviously speaks to their success and the way that they have successfully engaged their immediate communities in the work over the past several years. And participation is important. And so I'm with you 100% on just encouraging folks to reach out to those of us who are serving, ask if we plan to continue serving, and also just let folks know that you're interested in running. There is space. So thank you for that plug, for sure. All right, so let's see. We have been very ambitious, Martine, in our agenda. And I'll transition us to kind of the meat of the policy conversation, which really is kind of a feature of some of the pieces of policy that are under consideration and that really are moving their way through Senate Education Committee now. And to give folks kind of preview of what we'll talk about, we'll name school construction and PCBs, obviously on the minds of many Berlingtonians and others statewide. This is a statewide conversation, not a Burlington-centric conversation, but certainly fresh on our minds here in Burlington. Public funding for private education or Vermont's voucher system, preserving safety in our schools, and also a ban to or a bill to ban the retail sale of flavored cigarettes, e-cigarettes, e-liquids, I think a bunch of different things. So those are just a handful of things that I know we're interested in covering tonight and also scratches the surface of all that is in your portfolio. So I'm going to turn the mic over to you and invite you to kind of walk us through what you think folks should know about these conversations. Thank you, thank you, yes. So PCBs, a hot topic at the state house, as you can imagine, mainly because of what has happened in Burlington, but also because we are now in the phase of testing schools. So there is a testing process that is going on. Some schools have been tested. Some have had levels that are above the actionable threshold. So they've had to either close or pivot quickly to figure out what to do. And I have to mention there have also been some school closures that have not been PCB related. For example, Randolph had to close because of an aging HVAC system that just decided to stop working. So our construction, school construction needs are vast and they're complex. And I'm going to talk about that in a minute. But around PCBs, I have to say that recently in Senate education, we had a representative from the AOE, the Agency of Education and ANR, Agency of Natural Resources in talking about PCBs. And I did have kind of a difficult conversation with them because they kind of don't want to acknowledge that Burlington was the first school in the state to have this PCB discovery. They always refer to Cabot as the first. Cabot was the first to discover PCBs once there was a system in place. We were before the system. But I always feel as though it's the elephant in the room. We need to be mentioned. We need to be named. So I did bring that up and I also asked, there was a lot of controversy around the way it went down in our city with that 15 nanograms per cubic meter level, which was the lowest in the world as far as I can tell, that we had to move out so quickly given that threshold and that later on these numbers were adjusted unbeknownst to us. So I did ask, when will the harm that was inflicted on our community be named? And there was no good answer to that question sadly. So I'm still asking questions. I'm still trying to do some advocating for Burlington. But it's a heavy lift because there are needs in other parts of the state and there probably will be more. So that conversation is ongoing. We'll see what happens there. But one of the conflicts that I should mention is that there are schools now who are being tested for PCBs. And an issue is that some of these schools have massive construction issues. They don't want to be sinking millions of dollars into any kind of PCB remediation if they're going to need a new roof a year from now. So there is a little bit of a conflict going on there. Does that make sense? Yeah, absolutely. And so you're adding a layer of how these programs, one of which no longer exists. We had a school construction fund previously. We don't now. But the concern around sinking taxpayer dollars, which is how in Vermont, we currently fund school construction into a project that you might discover down the road or we might already know there is more significant need beyond the PCB remediation. Exactly, exactly. So that is something that is being talked about. So a brief primer on school construction, which is that there is a bill that I've worked on with Senate education that it doesn't have a number yet, but it will. But it's something that we've been working on. I've talked to the new treasurer, Mike Petschek, a few times, and he seems to be fully on board and excited about this. But a little context is that our state did have a PCB process and aid at the state level that was suspended in 2007. It was right around the time of the Great Recession, which we think of as 2008, but had started in 2007. So they decided that they had to make some cuts in the budget. And that is what was cut, sadly. So since 2007, so we're talking well over a decade, our schools have not had any kind of state aid for HVAC renewal, for roofs, for any kind of structural assistance. So unfortunately, they are in bad shape, really bad shape. We've been listening to superintendents tell us their stories and it is shocking what we've heard. So we have taken a lot of testimony from folks in Rhode Island and Maine who have very strong structures around how they dole out and how they identify needs, how they dole out money and identify needs to various districts and schools. So one thing that Rhode Island does is they have a minimum of 35 percent that the state chips into a district to help with the school maintenance and construction. And then they ask the district to make sure that they earmark 3 percent of their budget a year to maintain, because that's really important. And one thing that we heard from superintendents in the state is that a lot of times it's going to come down to trying to get the voters to vote for your budget, which is not easy in a lot of parts of our state. And if it comes down to having to choose between programming for children and putting on a new roof over the gymnasium, it's always going to go to the programming for the kids or staffing, for example. So, you know, hopefully with some state aid, we won't be able to make those hard choices. There will be money that will help us with the construction piece. So I'm excited about that. What how it will help Burlington remains to be seen, but it is going to be not, you know, here's some money. We're going to throw it out haphazardly. There will be a structure in place. And this particular bill calls for a group to convene the summer and work over the summer to put in place what kind of governance structure this is going to have, how we're going to identify needs and prioritize needs and things like that so that when the big assessment comes out in October, which will be which will be fairly all-encompassing, we hope it's October anyway, we'll be able to hit the ground running and really get things going. So that's that's the hope. Yeah, thank you for initiating that conversation. As you mentioned, it's been a need. We've got schools contending with deferred maintenance for years. And we know simply, you know, the aging infrastructure is facing districts around the state, really. And so the the the costs are there and they're significant. Yeah, so thank you for initiating this. And let me just also mention this if you don't mind that one of the things we talked about is this is also like a workforce development piece. If you are a young family looking to maybe make a move to Vermont, are you going to want to move to Vermont and put your kids in schools that are old, that are often can be dangerous, as we know, depressing, that are not conducive to a healthy learning environment? Or are you going to stay in Massachusetts where they have got so many new schools? It's just absolutely astounding. So, you know, we think about it in bigger terms. It's very important. Yeah, absolutely. Well, thanks for your leadership on that one. You bet. We've got about 10 minutes left. So I will leave it to you to decide where to take us next with each of the next three topics, all of which are equally important. Yes, yes, they are. So I'll talk a little bit about S 66, which has a house companion bill called H 258. And this is a bill that talks about funding to to schools. And there are some great resources online for folks that they want to explore this issue more. They could reach out to me or you and we could send them some great resources. But basically this bill came about because of the Supreme Court decision. Carson v. Macon, which some folks may have heard about. Carson v. Macon, which came down to the Supreme Court from the state of Maine, basically says that a state does not need to subsidize private education. But once a state decides to do so, it cannot disqualify schools solely based on the fact that they are religious. So why this is important in the state of Vermont is that we do have independent schools, private schools that receive money from from the public that receive public dollars. So suddenly, you know, Carson v. Macon says, well, then you're going to have to send those public dollars to religious schools as well. And for a lot of people, the separation of church and state is important and it's real and it's one of the values that they hold dear in our country and they are not comfortable with this. So the question is, well, then what do you do? The simplest solution for us just to say, OK, no more public dollars to private schools, period. That is problematic for a lot of folks in the state. We have four historic academies that have been around a long time that are loved in their communities. And then from those four academies over the years have have grown a host of other public private schools. You know, they're sharing Academy for an example, but there are many, many private schools in the state that sometimes fill a gap because there's no public school nearby. And some, you know, for whatever reason just decided to take root in Vermont and have been quite successful. So it's it's a touchy subject for a lot of people, but this Carson Fee making decision has really given us an opportunity to look at our educational landscape and make some decisions about how we want to go forward. And it's been it's been interesting. We've had a lot of interesting conversations, but some of the issues around independent schools are, for examples, that they don't require their teachers to have licenses. They don't publish their state assessments. Their accountability is not clear. A lot of times they don't have to make public what their finances are. They don't have school boards. So even though their school might be made up of eighty five percent of their students might be tuitioned in, for example, they don't have a school board. So the local taxpayers aren't really having a say in the operations of the school or the governance of the school, I should say. So these are all issues that are being talked about. And we'll see what happens, but stay tuned. It's a big topic of conversation. There have been some articles out there already and we'll see what happens. I was just going to name there have been a handful of articles in the digger and in a variety of sources that have highlighted this conversation. And I think it would be fair to assume that we will see continued litigation around this conversation, probably for the foreseeable future until we arrive at, you know, until this work that you are in the midst of right now kind of moves through various processes, because, as you noted, it is near and dear to many people. And so it will be an ongoing conversation likely for the near term. Yeah, it's it's a lot of often it's not on the radar of folks in Chittenden County, just because we do have such strong public schools that it's we we're not really thinking about these independent schools as much. But it is important for us to be aware of because somewhere between 50 and 100 million dollars a year go to these private and independent schools. So it is money. It's resources that are not being placed in the public schools, but are being funneled out to other schools. So that's important for folks to know. I also just wanted to say that there are some provisions in the bill that say, you know, if you independent school, you have a choice, ultimately, if this bill were to pass, you could become a completely private school and sort of, you know, give up your your public dollars, or you could go to your local voters and decide to become a public school. So we'll see again, we'll see what happens. But early stage. Yeah, early stages. Thank you. Thank you. We are close to wrapping up. Would you like to say just a couple of words on both the ban to flavored tobacco? Sure. And yeah, great. What do we have for time? We have about five minutes. All right. Five minutes. Very quickly, there is another bill that's working its way through our committee around school safety. This bill would ask for biannual options based drills, which are around school safety as well as fire drills. But one of the pieces of the bill that has been a little bit contentious is this idea of a behavioral threat assessment team that the schools will be required to have that would be made up of a variety of folks, nurses, teacher, special educator, but also usually a member of law enforcement from the local municipality. So we did hear some testimony from folks that said this is great. You can really identify some kids who are struggling and help them out. But we also heard from some folks who are concerned that students who might be on an IEP or a 504 could be targeted in a different kind of way than other kids. So, you know, it's something that I'm concerned about. We also heard that this particular these behavioral threat assessment teams aren't designed to be punitive. They're designed to really help students who might be struggling, but they often sadly end up being punitive. So it's something for us to keep an eye out. I have asked for there to be some bias training in the annual training that this team gets. So we'll see where that goes. I just thought that that could be helpful to, you know, sort of center folks around equity and inclusion. Absolutely. Well, you're making me think a lot about the equity tool that we use in Burlington School District as we to help us make policy and really ask the opening question of who benefits and who's harmed by this policy. So I'm pleased to see that you're taking that approach and not surprised, of course. Well, thank you. Lastly, I just want to mention S-18, which is a flavored tobacco ban. And the reason that I'm bringing this up in the context of schools is that those of us who have worked in schools know this is a huge problem. Tobacco companies have predatory advertising practices that really prey on young kids, middle school age, as well as high school age. Some of these flavors are, for example, dragon breath, spiced apple, you know, crunchy caramel, really enticing flavors that kids want to try. And they are loaded with nicotine. Kids get hooked very quickly. And then they, you know, these tobacco companies now have a customer for life. And unfortunately, what we heard, we heard a lot of testimony from educators who say kids have to leave class so they are missing class time to go and vape or, you know, get a hit of nicotine. And they're agitated, they are anxious. Sometimes it can lead to depression. I mean, these are all things that I'm very concerned about. I know other folks are as well. So I hope this bill passes. I think it's going to be on the floor of the Senate this week. Great. Well, we will we will look forward to seeing that progress, which sounds like it will be swift. So that's fantastic. Well, I also related to education. I want to also acknowledge your good work in the other committee that you are a huge part of, which is the Senate Health and Welfare Committee, where you all are working so hard on S 56, which is a child care bill that would really go a long way in strengthening Vermont's early childhood education system, which currently serves kids ages zero to five. And what excites me most with my school commissioner hat on about this bill is there is no better time than birth to five to prepare kids for lifelong success, but most immediately for success when they enter elementary schools. And so I think so much about the impact on our K 12 system when I think about the readiness of the youngest Vermont citizens who have no voice and yet are our future. And so a just huge shout out to you and to your colleagues on Senate Health and Welfare as well for taking such a broad look at all of the ways in which we can support young people. And you've been an important voice in this conversation, too. So thank you. But we know the first couple of years of life are absolutely critical to long term success in education and in so many other areas of life that this is really important. I agree. It's awesome. Well, goodness, in such a short amount of time, Martin has obviously taken the state house by storm. Thank you so much for your leadership and for really for just even raising your hand for the role. It is such a huge undertaking. And we're also fortunate to have you in that space. We are over time, a couple of very, very quick announcements just for folks to have on the radar. We are celebrating this week and have been celebrating for the past week. BHS Girls Nordic Ski Team 2023 State Champs for the third year in a row, I think. I loved Superintendent Flanagan said go ski horses, which was so sweet and fitting. And congrats also to the Burlington Tech Center Health Science Academy students who won first place at the Brain Bee Neuroscience Competition at UVM School of Medicine last month. Huge deal. BTC won first place as a school, first place as a team and a student Schuyler Foster, I'm sorry, won first place as an individual. And she will go on to the National Competition, which is huge. Lastly, kindergarten, I'll turn it to you in just a second. Kindergarten registration is open through April 1st. And our 2022 annual report is published. It is live on the website. You can find it at BSDVT.org. And there are a couple of hard copies here and there, but the electronic version is great. And the hard copy versions are translated into a variety of languages as well. All I was going to say is groundbreaking tomorrow. Yes. Yeah. Oh my goodness. What a perfect way to close the conversation. How could I have missed that? Thank you. Groundbreaking tomorrow for our new high school and tech center. Yes. Three o'clock, 345. I think so. At the current, at the old, do we call it the old, the current, the campus on North Ave. North Avenue, yeah. Yeah. 345, I think, right? 345, yeah. Check the website. 345, groundbreaking. Be there or look for coverage on the news. We're so excited to celebrate that. Thank you.


What has Ritter shown you as to where, you know, you're going to give him an opportunity to compete for that starting job? Right, absolutely. Well, really, when we drafted Desmond, you know, he sat behind Marcus, and certainly if we had, we thought going into week one, if he was ready to go and he had played better at Marcus, we would have played him. But it allowed him to, us to bring him along, we didn't feel like we had to rush him, or we wouldn't have certainly adapted to give us the best chance to win. Times, you know, timing and luck, you know, they help you a little bit, and we had an unique opportunity to end the season, and we felt Desmond was ready. We thought that was the best thing for the team, and it certainly, I thought he improved week after week. He was very, very effective on third and fourth down, and you saw those last two weeks, the growth he made from this first start to really his third and fourth. We're excited about it, and we know Taylor coming in as the guy that gives you a chance to win. He understands his role with the plan to go into the season with Desmond as our starter, so we're very excited.


Here's the penalty that sets sharks coach off. You got number 62, LeBank chasing the puck. Iorio's coming around, his teammates setting up a little pick. They're gonna collide, his leg gets taken out from under him and the ref says that's a penalty and then they fight a little bit about it. But watch, he's kinda blindsided.  So on the other side, you see that his left leg, Iorio's kinda just out. I don't think he really went to clip them, but matter of fact, he did clip them. But my opinion doesn't matter at all.  You've gotta fucking, now I don't know what he says. There's the easiest lip reading I've ever done, but also there's three lines that are really hard and that's why I'm late on this one. I've been trying to open it up every day and just see if I can get it.   It looks like he says, you've gotta fucking, let's see, I'll show ya.   And then the rep says you're out of here.  Now I know that because later on he's gonna say the same sentence that I'm not positive he says for your whole career, for your whole life. But I've been coming back to this and looking at it.  But he also, he pointed the rep and then he points at him right here which makes me think maybe he's saying like you've had it out for me my whole career. The rest of it is really easy lip reading as you see.     Again, that's what I don't know. He says the same lines.      I am so angry.  And he's gonna go back to it again here.    So I don't know what he's saying there. Help me out. But it's something along the lines. Finally the rep's like go, go.      And then he leaves and he has to go and the rep's like all right, that was more than it needed to be. He's out of here. He said he was embarrassed after the game. Ref wipes his nose at him. And then right on the face off now after the penalty, the cap has taken one timer and get the rebound and score. And now it's a three goal game in the third and that's a different story. And coach, maybe he was right. She's happy though.


So if we can please come and welcome our first testimony. Can you please tell us your name and where you're from? My name is Michelle Burt and I'm from Pasco, Washington. Michelle, can you please tell us your testimony? What brought you here today? Well, I was pregnant four months ago. I recently had a baby, but I hurt my hip very severely.  It was very hard for me to walk, lift my leg, bend over. I was just in a lot of severe pain. Where did you go in for solution for your back problems during your pain? I just really spoke to my gynecologist about it mostly. He just said it was something I had to deal with and be in pain because there's no really options during pregnancy because there could be complications. So with this this hip pain, how I received healing was I was supposed to go out of town this weekend. I was supposed to go camping with my family, but I knew God had kept me in town for a reason and I just had that feeling. I had to stay in town to sing at my church and so after that me and my friends went to go to roasters and have some coffee and I was looking through my news feed on Facebook, social media and I noticed Haley. Haley Taylor is my cousin and she was on my news feed. I noticed you guys had an event going on at Howard Amon Park, so I went and you guys had great worship and it was awesome and I stayed. Then a man approached the stage and he just talked about how he ran into this man at the store. He was having a lot of severe back pain. That man received healing that day and so that really spoke to me and what was crazy is the man that went on the stage had a piece of paper of people that had pain and illnesses that day while mine was on there. So shortly after everything ended I went to go speak with him and I was healed that day of my hip pain. God is so amazing. He just works in such amazing ways. I really wanted to go camping that weekend with my family but he kept me there because I was supposed to go through that experience because not only was I healed that day but my faith grew immensely. I saw Lay's leg grow in front of my eyes so after I saw that the man that healed me had me lay my hands on one of my friends' mothers and she was healed through the blood of Jesus. So now that you've received your healing you said you had many complications. Is there something that you couldn't do then that you can do now and can you show us walking hurt really bad but I was not able to lift my leg at all. It was very painful, extreme pain. So the fact that I can do that I can run, I can exercise so thank you Jesus. Now for anybody that may be watching or here in this place right now who is struggling through a sickness, some pain in their bodies, do you have a word of advice? What would you suggest or share with them? Believe you receive. Through the blood of Jesus all things are possible. You already have that healing. Take it. Just believe it. Thank you.


How's it? How's it? We've all been there with our photography that you are trying to take a photograph just willing it to happen and the more that you will it to happen the less it doesn't.  The best example of reversed effort is probably you know trying to fall asleep. We've all been there you're tossing and you're turning just it does not happen and the more that you will yourself to sleep the more it well it doesn't doesn't until you find yourself it's like four o'clock in the morning you're like ah it was Aldous Huxley who came up with this idea of reversed effort when he said that the more that you try with conscious will to do something the less likely you are to succeed and this manifests itself in our photography time and time again in my own case like when I used to take portraits in the studio even though you know I kind of knew more way around a camera and and there was nothing that I had to kind of worry too much about from a technical standpoint often it just wasn't gelling I just it wasn't going but I knew I wanted that photograph and the problem is that I was kind of trying to cling on to it trying to grab the idea too hard when instead I should have just committed myself to the process to surrender myself to photography the way that you can do this is actually remarkably simple and and I owe a debt to a lady called Mel Robbins I think she's her name is who has this audio book a series of books about a process that she calls the five four three two one process and I was listening to this and I thought this is I think what a great idea to use in photography how to get back in touch with that creative spirit that dwells inside us but often that we're sabotaging on the way out because we're putting loads of roadblocks in the way so simply summed up basically what she's suggesting is every time that you want to do something and you dwell on it for too long your mind will say no and in photography's case you will sit there looking at a picture they're quite like to look at that and you will go ah okay well one of my options to photograph this what lenses can I use what exposures can I you know employ will it be colour will it be black and white you know so we've kind of gone from being enthralled about the system or about the about the image or the subject that we see in front of us and have now started dwelling upon the technicalities of things so that created spark is you know split it away so instead of doing all this the next time you're out photographing and I would encourage you to do this as a session that's separate from maybe working on a specific thing or task this is all about the flow of creativity of unclogging that that journey within you to allow you to express yourself you know freely without inhibition is to simply see something that interests you go five four three two one shoot it the committee is in the word shoot as I could say you must take a you know composed photograph and stuff but just that's the whole point throw technicalities throw all the rules or anything like that to the wind go with your instinct just take the camera and shoot don't ask questions of yourself don't allow yourself become mired in what's right or what's wrong just go with your gut instinct now of course you're not going to get amazing photographs every single time I mean that would be foolish to even think that way but what you are going to do is you are going to start learning to trust your gut and of course the more that you are you know kind of comfortable and and sort of untuned with the technical aspect of the compositional aspects all there's other bits the more that that becomes second nature now if you are sort of sitting here thinking oh do you know Alex um I how do I set the exposures but what about this and what about that okay the whole point here is just to go with it so in regards to your exposures you can either set your camera to pee pee for professional right there's nothing wrong with it don't just use it okay in this case we are just kind of worrying more about the visual interpretation of a scene rather than more technical bits right or you if you're feeling daring you could dip your toe into the sunny f16 rule now a short couple of you guys are going out with what is this sunny f60 I've not heard of this thing what is this this is actually one of the it is a hard and fast rule in photography there aren't very many of them but this is one of them so basically on a sunny day that's clear blue sky when the sun is at the highest in the sky at f16 your shutter speed will be the same as the ISO of the film so if your film is 100 ISO then a correct exposure at midday on a clear blue day sky right with proper sun it is going to be f16 at a hundredth of a second if you have 3200 ISO film or you've camera set to that then your shutter speed will be 3200 it's as simple as that and then of course you branch off into the various ideas later on so cloudy day bfa you know etc etc and rather get too much into it here if you want to explore that I'm going to be touching on it in an episode of the five minute photo school soon if anybody in the comments wants to sort of expand on the sunny f16 rule please feel free to I love the exchange of information because don't forget that we are all on different parts in our photography and we you know the more that we can share our knowledge our combined knowledge then the the richer the experience in the community will be for everybody anyway back to the five four three two one right and so yeah when you're out there just photograph just choose a lens you know if you have a prime lens that's cool if you have a zoom lens try and just keep it to one uh you know one focal length don't zoom around I mean tape it and tape up the barrel if you want you know so you can't actually move it uh you know try this right the whole point of this process is to get you creative is to get you to trust that instinct inside of you now first that instinct is going to lead you somewhat astray and that's okay right the point is to go and look through all your resulting images and go okay that didn't work that didn't work that didn't work that that's got some that's got some promise I like this and that's really kind of what we're looking to do here is to to get you reconnected with being relaxed about taking photographs to commit yourself to that process of photography where you are not worrying about all the other things that are contributing to you not having a great image if at this point you're thinking all of this sounds like a bit of gobbledygook kind of mindfulness hui right think about when you either listen to you know great photographers or anybody who's a master of a skill and they tell you that they don't really think about it too much that a great pianist isn't thinking about the individual notes about how they are playing they are relaxed when they are playing you yourself do this without knowing about it you ride a bicycle now you don't think about riding a bicycle you get on it and you just ride it if you were to write an instruction manual on how to ride a bike it would be pages and pages and pages of instructions but you've learned to trust your instincts with us so that's I again if you're thinking that this is maybe not for you give it a whirl you're going to fall off the bike one or two times but eventually you're going to find that this makes your photography so much stronger and will be a skill that will pay dividends for you down the line for years to come so remember when you were out there next time you see a photograph five four three two one and just shoot it you're going to end up with lots of pictures you think of mistakes when you do this exercise but rather than throw them away which would be a huge mistake follow the advice in this video here thank you ever so much for watching and I'll see you again soon


The Gospel of Mark reads like good news for Habakkuk's runner. The vision is made plain from his coming out of the river to his coming out of the stone tomb. And this coming out, this good news, like the prophet's vision, is public. It is not just to individuals and insiders, but to whole communities and outsiders. Through healings, signs, teachings, and exhortations, Jesus goes public with the good news. The time is now. The realm of God is already here. Repent and believe.


So, this is a definition of the of a game for us to begin with, so a game comprises of the following. You have a finite set here which is called denoted by n which is called the set of players. Now, for each player or each i in n, you have a set let us call this Si is a set of strategies. Now, for the moment I am going to call these strategies and in a few lectures we will produce a more general term for this, but for the moment let us just call these strategies ok. So, for each player i you have a set of strategies, so if I take say X i in Si this is a particular strategy here particular strategy of player i. Now if I put together this collection X 1 till X n, this here you can think of this as some collection or you can think of it as a composite vector with these components whatever you however you want to think of it X 1 to X n here is what is called a strategy profile. So, 1, 2, now 3, so for each i for each player i you have a function let us call this function ui function ui that maps this product right to R, the ui maps the product of Si is to R. What is this is essentially saying that for each profile of each strategy profile that means each composite vector X 1 till X n the ui produces for me a real number and that ui is what is called the player's utility or payoff various names for this sometimes called utility sometimes called payoff. And now ui here is when I when I use the word utility or payoff it effective it connotes that it is something that you that the player gains from. So, this is something that the player is looking to maximize alternatively you can always flip the sign and of this u and say turn it into a cost that he is trying or a loss that he is trying to minimize. So, so utility or payoff or let us say cost say if it is utility or payoff the assumption is that he is looking to maximize this that he is looking for the largest possible value of this and if it is a cost then then he is looking to minimize this. You put together these three things then what you get is a game. So, a game basically comprises of a set of players and a set of strategies for each player and a set of you and a collection of utility functions for one for each player. This here is a game and as I said we are since we are focusing on non-cooperative games are underlying here I need to also alongside all this also specify what is what are the what are the assumptions regarding communication and so on. But so because we are focusing on non-cooperative games the it is in I am going to assume implicitly that there is basically no communication of being allowed between the players. So, this is a non-cooperative game with these specifications with this set of players, this set of strategies and these payoff functions is this clear. Now as since some amount of convex optimization and so on will be involved it is a it is usually convenient to whatever is the function it is convenient to minimize it rather than maximize. So, coming from you know usually in a control or machine learning and so on language we have we have a cost or a loss that we are trying to minimize whereas in the social sciences they tend to look at you something payoff that player is looking to maximize these are just conventions we will stick to the minimize convention alright. So, now this is what this is the formal definition of a game. So, now question is how are we going to solve this? So, what are we and to begin with what are we solving for by now again let us be clear I am not asking you how to compute. So, when I when I say solve I do not mean compute something ok compute comes after you tell me what is it that is to be computed alright. So, when I am asking for solving I am asking what is what should be the solution yeah. So, what is should be now if I just give you this and I tell told you the assumption that this is a non-cooperative game I want to I want something that I should say should be able to say is a solution of this right. So, if there was only one player involved here then the problem would become that well then the problem would be that there is one player who has a set of strategies and a payoff function which is trying to maximize then it is merely an optimization problem right and there is a natural notion of a solution. The natural notion is the optimal value of that of that of that of that particular problem you look for the global optimizer or if you are otherwise look for a local optimizer etcetera these are the natural solution concepts from which we derive our solutions it is a different matter how we go about computing them what algorithms we have and so on. But the logic is that well it is sort of self-evident that is what you are looking for you are looking you are looking for a solution of the optimization problem. Now you do not have one optimization problem but each player has an optimization problem right essentially there are n optimization problem and they are all interlinked the question is how do you solve or solve this and again how do you solve means what should be considered as a solution of this of this of this thing if this particular thing that we just built it is a function of the strategies of each player ok but what properties should that function satisfy without some without help from someone else ok interesting any other yeah so here one second just let me answer that since this point has been brought up a game as formulated does not necessarily have a winner or a loser ok this is all there is to a game which has we ok there could of course you can take certain special cases in which there would you can define such a thing as a winner so for example if you know if the payoff reaches a certain value then you win ok something like that that could be but here this is a far more general setting there is no no you know predefined notion of a winner or anything like that yeah sorry someone else was saying something ok with what distribution ok but the opponent would be doing the same so ok so here this is here is another important point about games and about how we study games ok again once I post this particular thing to you and I say this is the game and we want to be able to solve it when we go about coming up with a logic for solving a game like this we have to first fix a point of view ok point of view meaning that who might be solving this for and whose who is solving this game is it is it a particular player in this situation who is solving the game are we solving say for example for player 1 or for player 2 or for player n are we solving for all of them together so whose I mean this is being solved from whose point of view so this is an important thing right so especially particularly when it comes to applying game theory when you apply game theory say for example you want to apply game theory to a security situation where you want to advise say the security of an airport about how it should be deploying its troops to protect the various you know terminals and so on in the airport are you thinking are you doing this from the point of view of the security company or the security agency or are you doing this from the point of view of the of a potential attacker or are you doing this from a completely different other point of view so this the this is part this is again this is not something that that is there in this problem definition this is again part of the or the approach that we want to take as far as solving a situation like this is concerned so it is it is it is a human choice we are making that we will take the view of not any particular player in the game but but the but the point of view of an observer of the game okay if you remember I I said initially that we are trying to develop something like a law like a bunch of laws so I should be thinking of these players as more like particles that are evolving according to a certain law of motion the law of motion is that they each looks to may have maximize his payoff or minimize his cost whatever and then there is this interaction between them that their costs are interdependent as an observer of this particular system seeing them seeing this particular system play out in the lab I want I would be I would want to know okay how should I be solving this or what should be the final notion of a solution of this so the point of view we take in game theory is not of any one particular player but that of an observer of the game so we do not do things like you know put ourselves in the shoes of the players imagine what the other player would do and so on we we take the neutral point of view of observing what of an observer of the game in which players are equipped with a certain set of assumptions and a certain set of capabilities we ask okay what should have what should they do or what must they do okay so the viewpoint is that so viewpoint taken in game theory is that of an observer of a game so so you will soon see in a few in a few lectures from now there could very well be games in which a player is getting bluffed for instance okay by another player and that if you were in that players position you would play differently from whereas you would reason about the situation very differently if you are an observer if you are an observer you would see that the you could get bluffed but if you are in fact that player you would avoid getting bluffed okay so this point the point of view matters it leads to very different sort of ways of applying game theory and ways of shifting through the the logic of game theory okay so the observe so here here so we are going to stick to the observer viewpoint now if you are observers of this game so okay now again we are we are back back to the same question we are observers of this game seem like we like the prisoners dilemma we are observing that there are these two prisoners with equipped with these options and these these these payoffs what must they do and more generally I mean now now that I have written out a general game you should tell me what should be the way to reason about this so the main the so one of the main landmarks in the theory of games is this is the methodology or the logic for reasoning about situations like this situations of with involving non-cooperative games and that and in fact even prior to that the recognition that that how you reason depends on whether the game is cooperative or non-cooperative or whether it is non-cooperative or non-cooperative okay so all of that that observation came from the form from Nash's thesis and so Nash basically said that if you have a non-cooperative game then what you should be doing is basically solving it using this particular concept and that is what I am going to define now. So in the Nash equilibrium is a strategy profile let us call it x1 star to xn star is Nash equilibrium is the following holds if ui of x1 star to xn star so I as I said I have assumed that ui is a player is trying to minimize so this is okay so ui of x1 star to xn star is less than equal to ui of so I will introduce a notation here less than equal to this for I will explain what this means for all xi in psi and and for all i now what does this notation here mean this notation here stands for xi so xi comma x minus i star this notation essentially stands for the following vector so x minus i star is the the the part of the strategy profile which in which I have taken all the other players except for player i so it okay so I have x1 star x2 star dot dot dot x i minus 1 star and now in place of player i i in place of the starred one I am going to insert this xi here so this is xi comma xi plus 1 star dot dot xn star so xi comma x minus i star is essentially this composite vector it fair I have taken the starred values from the first for all players except for player i and in place of player i is strategy I have put in this xi that is chosen for me okay so that is what that is what that is the notation for xi comma that is what this notation means xi comma x minus i star it is a notion notation specialized for game theory because this kind of a thing comes up all the time okay so now let us see what Nash is basically saying so what Nash is saying is that we should be looking at a point x1 star to x10 star is called a Nash equilibrium if the following holds so what what do we have on the left hand side on the left hand side you have the the cost of player i when this strategy profile is played when the players play x1 star to xn star n players all of them played a starred value what I have on the right is the strategy profile is the is the cost of player i when the strategy profile changes to xi comma x minus i star that means all the other players stick to the starred value the starred part of the the continue to play the strategy the starred strategy but player i switches to xi okay so what this is seeing is that the player player i is here this in what this inequality is saying is that a player i is better off playing the starred value than he is by switching to a some other xi provided the other stick to their starred values okay and this holds for every xi and moreover this holds not just for this particular player i that you have chosen this is symmetric it is holds for all player so so every player i refers to stick to his starred value starred strategy provided the others do not switch from do not deviate from their own star value so no player has an incentive to deviate from his from his strategy from the profile provided no one else deviates from their own strategy in the profile okay so this is this is called the Nash equilibrium now why why why is this such a such a big deal why why is this you know I said this is a landmark in the theory of games and why why is that the case the reason is basically this essentially what Nash said gave gave us is a is a essentially the a a watertight way of now reasoning about games what is this situation what is this inequality really saying what this inequality is saying is that if I want to call if I want a point x1 to x if I want a profile x1 star to xn star to be considered a solution then this must hold what should must what must hold well no player should have an incentive to deviate unilaterally from his from that profile so assuming the others stick to the their strategies in the profile I would not want to deviate from my own strategy from the profile now why is this correct or reasonable why is this logical for for a non-cooperative game the reason is logical is because see once a game is non-cooperative okay once a game is non-cooperative only unilateral deviations are feasible there is no way for a pair of players or a group of players to to collective to you know form a unit and then deviate together you know like it happened with the she was saying now for example you know you cannot have that kind of a possibility where a bunch of players deviate come together and deviate together what what is happening here so in a non-cooperative setting when there is no communication is allowed between players only unilateral deviations are feasible if only unilateral deviations are feasible well then what it means is if I if I if any point has to be considered a final solution then it has to be stable against such deviations because if not then the adjustments process is still going on it whatever you are at is not a final is not a solution anymore is not an outcome anymore so this is essentially a necessary condition for any any profile to be considered an outcome if it has to be an outcome it has to it has to be a Nash equilibrium right because otherwise that if it is not if it is not a Nash equilibrium then it means that there is at least one player who under the communication constraints can deviate from it and then if that is the case then whatever you were considering earlier from that point is not an outcome anymore right something else could potentially become an outcome the adjustment process continues you know the whatever the reasoning process continues and and and maybe there is some other outcome so what this basically does is essentially it gives us clarity on how we should be thinking about about non-cooperative situations non-cooperative situations how you are to think of them as something where players if they could unilaterally deviate they they would so if you want a final solution or if you want anything to be considered as an outcome then it has to be of the kind where unilateral deviations are not profitable for the player anyway all right so this this is a this is the this is the Nash equilibrium of a game okay and so this is the solution this is basically the most popularly applied widely applied solution concept in any non- cooperative situation you will you will you know as you go forward you will see how you know the kind of amazing properties it has and so on and how much it is able to explain about about strategic interactions and so on but for the moment let us just go back to the prisoners dilemma and let's see what is the Nash equilibrium for the prisoners dilemma yeah because in a non- cooperative game only unilateral deviations are feasible if you if you allow if you take the same situation in which you have a cooperative game in which a bunch of players could communicate and say well as a group we want to move out move from our from our present form a certain from one sub profile to another sub profile right that would be a different game and that would be a different type of situation and it would really lead to a different type of concept in fact the coalition formation games which is a kind of cooperative game has is there you solve the game using exactly these lines of reason okay the about what kind of coalitions are stable well stable the coalitions that are stable are the ones where in which no subset of players can actually deviate from but here because there is this is a non-cooperative setting only individuals can individual player can deviate yeah so what is the Nash equilibrium of the of the prisoners dilemma to to right testify testify is the Nash equilibrium of the prisoners dilemma and the reason for that is is that if you see what what how are we arguing here we need to argue that assuming the other player plays this his component from this profile I would not want to deviate from my component right so assuming the other player plays testify I would not want to be assuming the place testify a would not want to switch to silent and likewise if assuming if it plays testify be would not want to switch to side now this game is symmetric and that is why this computation is this this is very easy okay and you know but of course in general the number of strategies that players would have could be different for each player and so on alright so let us take another example he has another example this is also symmetric this is okay an example where there are two hunters okay hunter 1 and let us say hunter 2 and they are both poised to hunt down a deer okay they they are both poised to hunt down a deer I mean they let us assume that they are sort of two different two different they there is a deer in some central location and they are both viewing that deer from from two sides they cannot communicate with each other I mean of course there could be visual cues and this and that but let us let us assume that is not possible they cannot communicate with each other they are both seeing this poised to hunter deer ready to hunter deer but then suddenly there is this option that a rabbit runs by okay and then there is the possibility to also hunt a rabbit so and what is the dilemma the dilemma is the following that a deer is much bigger and much takes much more effort to hunt okay so if both go for the deer they will be able to hunt down the deer and they would each get let's say a payoff of 2 but if only one of them goes for the deer and the other goes for the goes for the rabbit the fellow who is going for the deer will not get will not be able to hunt the deer alone okay so the one who is going for the rabbit gets gets the rabbit but the one who is going for the deer doesn't get the deer okay so and if both go for a rabbit the rabbit is much smaller than the deer and so what they will each get is you know whatever half okay so now again what's the reasoning here so one thing you will notice right away is that this is not a situation like the prisoner's dilemma where there is one strategy that is uniformly better than the other one it's not true that regardless of what the other guy does it's better for me to go for the deer right in fact this is more akin to the coordination problems that I was just talking about we we are both better off if we coordinate but coordinating on a better thing is better for both what is the what's the logic here again we don't want to get into the trap of trying to predict what players will do because we again don't know what they will each do because that gets into a whole bunch of other issues like like how hungry each hunter is how selfish they are and so on so forth the amount of trust they have in the other individual and so on that is not our mandate that is not our competence what we are going to do is come up with a bunch of reasoning rules by which we can say what what is the logical outcome not necessarily and the reason is because the whatever the other player does arises you know your distribution of what the other player does for example is is part of the strategic poster of the other player so it is not the point is you may see this is a this is a temptation in games all the time right that instead of trying to say well I can think from the point of view of a player and I say okay maybe the other hunter 30% of the time goes for the deer and 70% of the time goes for the rabbit and then based on that I will try to I will try to decide what I I should do but remember that 30 and 70 is not if you know he is not just some fact of nature it is part of his decision how often he should be going for the rabbit versus deer is part of his strategy all you have done by just bringing in these probabilities is just lifted the same problem to the space of probabilities now each player has to decide not whether to go for rabbit or to go for deer but rather how often he goes for rabbit one or with what probability he goes for rabbit versus what he goes whether as opposed to deer so this this you know trying to model the other player using some probabilistic model basically just gets you to one the same reasoning sort of conundrums that you had even in the strategy space okay you just need but so you have the same issues just in a different space look I mean look at the classic case of the Normandy landings in Normandy right so you could you the during the world war there was this this very epoch making event where where the Allied forces landed in France to liberate France and from Germany from which was occupied by Germany at that time there were they picked two possible locations for landing on the coast on the northern coast of France one was called the name is Normandy the other is Calais the Germans also knew that these were the two potential landing locations alright what they did not know was where they would where they would actually land okay you could say well I do not know where they would land but I think there is I have a certain model based on which I I think that that is where they were likely to come but where they are likely to come depends and how well you will succeed depends also on what you are planning to do just like you are making a model about just like the Germans were making a model about where the Allies would land allies would be making a model about how how the Germans would where the Germans would keep their defense you are effectively just elevated the problem to deciding how should we distribute our troops rather than trying to decide which where we should be keeping our troops so that is all there is the these these things only changes this particular flavor now to be to be fair there is there is another type of class of games called repeated games where things tend to get a little more intricate where where we are where we are playing this game not just once but multiple times okay but with the knowledge that this is being played multiple times and then you can try to sort of bake in some of the issues some of the things that you have in mind but again this is for the first lecture we are that is too complicated for to get into that okay yeah so what's the what's the logic then that's a very different game that's a very different game because there the what there that's part of the assumptions then that you know certain things about the other player yeah so this the assumption here the way I have stated this game you know in this year is that there is no such information all you know is this so in fact in fact the an important thing is okay you which some of you should have asked me before what do players actually know right so these players are choosing their actions without communicating with each other right but what do they know well the only thing that they know is this table okay so in the case of the prisoners dilemma they know this table that this is what has been offered they are being they are choosing their actions without the knowledge of what the other player is doing okay so I as good as simultaneously so they're so they do not know what the other player is doing in the in the Germany in the World War example essentially we do not know where the where the allies are going to land if that is known then that's a very different game or if that is known even with some noise that's a very different game or if the even if I or if I know even that there is a certain probability with which they are likely to land that's also very different game that's not the game that's been discussed no no no it's not see the that so so information changes the character of the of a game so if I know so if I know that you know say for example there is a point of no return after which the allies are going to land in a particular location right then that's a very different game my how I strategize will change very different so let's come back to this then players know this table they know that each player wants to get the maximum payoff they also know that this is how the the payoffs of dear and dear and rabbit and so on are are you know this is what the values are now how do we what's the logic for this so you cannot obviously there is no strategy here which is which dominates the other strategy which means that regardless of what the other guy is doing this is always better that kind of strategy is not doesn't exist we can try to reason about this through the Nash equilibrium so if you see essentially what Nash is saying is whatever is the final you know each guy each player would think think think okay decide okay should I go for dear should I go for rabbit etc etc whatever is the final if I if at all there is a resolution of this as if we were observing these two hunters what they would do is what they ought to do is that either both go for dear or both go for rabbit okay now how why is that the case so if you look at the if you look at let's say dear dear now dear dear is a Nash equilibrium because assuming the other guy is going for dear I would want to continue to play dear okay likewise rabbit rabbit is also a Nash equilibrium because if the other guy is going for the rabbit it doesn't make sense for me to try and get the dear because I won't be able to get the dear alone okay so it's better for me to stick to rabbit and dear rabbit is not a Nash equilibrium or rabbit dear is not a Nash equilibrium so there are two Nash equilibrium in this game okay dear dear is a Nash equilibrium rabbit rabbit is also a Nash equilibrium let's complete with today's lecture conclude today's lecture with one just this global picture so essentially if you want to position position a non-cooperative game theory and you could you could position it in the following way if you here you can think of the single player setting and this is the multiple player players setting single player and multiple player now the first setting and the kind of games that we have seen so far is what is what are called static games static games is when where both where all players where no player has any information about anything else apart from what is the game what he starts off so he does not know what the others have done does not know what else has happened and so on if anything else if any other evolution has happened and so on he does not have any such information those are what are called static games so player just plays once and with the same with a with a sort of a null information except with only the information about the payoffs of the players those are called static games now in the static setting if it's just one player or it just reduces to optimization and if it's if it's multiple players then it leads to static game theory on the other hand if you if there are if if the sitting if the setting is dynamic which means that there is there is a either a time evolution or there is a an aspect of information and so on then in that case the one player case reduces to is what we know as optimal control optimal control with under various names stochastic optimal control or whatever and the in the in the in the case of multiple players it leads to what is called dynamic game theory so my effort is going to be to quickly run through this so that you are you are familiarized with the basics and then then we will spend about 70% of the course on dynamic games.