Hey everyone in this video I'm gonna be talking about Backroom's level 456 or the Midnight Glacier. This one is a really cryptic and dark mysterious level that I think you're really gonna enjoy. Without further ado let's get into the explanation. So level 456 or the Midnight Glacier is classified as a class 4G which stands for Gravitational and is unsafe, unsecure and is gravitationally unstable. That is probably one of the most unique classifications that I've seen so far at least. The level physically takes place on a massive glacier and the environment in and around this glacier is very strange and toxic like literally the air and the ground is toxic. The level is always at night time and the temperature is freezing cold. The average is negative 68 Celsius or negative 90 Fahrenheit and on top of this there are random blizzards that pop up all the time so that's that's cool. So during a blizzard or any other type of storm huge hailstones fall out of the sky and this hail itself is very very toxic and is made up of really hazardous chemicals and these chemicals are actually inside of the hail's core and they have really weird properties that allow them to change the gravity around the area where they land. So if a hailstone falls from the sky hits the ground the gravity in that area will be different. It either will be harder and it'll pull you down to the earth or you'll be able to float it just depends. But in any case the liquid is very dangerous inside of the hailstones because there are small amounts of methane in them and that's a dangerous chemical obviously. So the chemicals with methane and other dangerous stuff inside of them fall to the ground at fast speeds and explode all over the place spewing the chemical juice everywhere and this juice can affect gravity and it'll make the air toxic and the ground toxic as well. As you can imagine the entirety of this level has a very strange gravitational area I guess you could call it. It's always changing. Sometimes things can fall really fast and sometimes things can float. There's even been someone that saw ice flying sideways instead of straight down so that just goes to show you how weird it is. The entirety of the level is just a barren frozen wasteland with these chemical lakes and ponds dotted around but there's also some evidence that shows that there used to be buildings here or there still are. The buildings are fallout type shelters and we're at one time fully built up but now they're kind of crumbly and dilapidated and just decomposing. Some of the walls inside of the underground bases are fully destroyed or they're just on their way to be fully destroyed but almost every piece of the sticks out of the ground is destroyed. It's rubble. Inside of these rooms there are leftovers of the people who used to live here. Small supplies and canned food pretty much. The underground chambers that I mentioned are actually the most dangerous place to be in this level because of the gravity that can switch on or off and you can fall down long hallways or fall really far into holes. The rooms down there are mostly still intact but there is one room that should be avoided at all costs. It's called the frostbite chamber and the temperature inside of it was measured to be negative 146 degrees Fahrenheit or negative 98.8 Celsius which could unlie the human within a few minutes of being exposed to it just because of how cold it is. And as I mentioned even though some of the rooms of the shelters can seem safe you probably should not stay in them because of the gravitational properties here. Occasionally on the surface and inside of the shelters there are signs of an entity called the groaned and the groans are these lizard-like entities that run around in packs. They eat whatever they can find. They're kind of like wolves because they run in packs but they're big lizards. They have a really really thick skin that keeps all the cold out and they typically burrow directly into the ice in this level but sometimes they do like to live in the fallout shelters. Their skin also leaks a very weird liquid and this liquid is pretty similar to the stuff inside of the hailstones so it's toxic. Not only is it toxic it also gives the groans the ability to not be able to be affected by gravity which is pretty cool. Back on the surface of this level even the ice itself that you could stand on is dangerous because the layer of ice directly under the surface is made out of a special type of ice called profundus or subterra ice which makes anyone who steps on it get infections. Any kind of infection. It's made up of liquid methane, carbon monoxide and other unknown chemicals so it's pretty much just a toxic slurry directly under that ice on top. If you see anywhere the top layer of ice chipped away or broken off don't step under it because you could be in a world of hurt after that. So now I'm going to explain some of those gravitational anomalies that I've been talking about. The thing that's causing the gravity to change is actually the level itself. The levity sends a gravity pattern called the fluctus pulsar. Now this fluctus pulsar shifts and morphs and changes the actual field of gravity itself and changes its strengths. You can't physically see the shifts with your eyes of course but it was noticed that when someone looked through a thermal camera that they had they could see the morphine changing as pictured here and these changes in gravity are dangerous especially if you're jumping around or you're high up somewhere or if you're down in a hallway somewhere. You could just come crashing down at any second and there's no way to track it. To enter this frozen tundra you can jump into any cold or frozen body of water in the back rooms randomly and you'll end up here. This won't happen every time you jump into water which is scary and makes it even rarer. To exit you can risk going into the frost bite chamber in the fallout shelters to go to a trap door in the corner of the room and by going through that door you'll be sent to the level you came from but as I said earlier when I mentioned the frost bite room those are extremely dangerous to go in and you have to be ready and you have to know what you're doing or you'll become a human popsicle. But yeah this level is a massive frozen toxic glacier that has abandoned fallout shelters and packs of ice lizards that run around. Oh and the gravity can be turned off and on at any time. Good stuff! Thank you so much for watching the video I hope you enjoyed it and I hope you watched to the end of it and if you did thank you so much I really appreciate you comment frozen brookly if you're still watching to this point also make sure to tell me what levels do you want me to go over I'm interested in what you all want to see thank you so much for the support of the channels recently on all my channels I'm so appreciative of you the brookly channel is still on the way to 500,000 subscribers guys so if you go ahead and drop a sub when I get to 500k I'm gonna get the full back rooms outfit and it's gonna be awesome we're on the way we're almost to 400k so just hit that sub button if you want to you'll need a lot of me also I just uploaded a video over on Tugli where I hop into some rec rooms back rooms maps which is a VR type thing and I got six of you guys six fans to join with me and we went over several back rooms levels in that game it was a blast to play go check it out if you want more of that and also I'm uploading another video on spooly tomorrow so check it out when that goes up make sure you have the post notice turned on it's over siren head so yeah bunch of stuff going up on all my channels I hope you're ready thank you for watching and supporting me I appreciate it also I just want to thank you all so much because the channel just hit 62 million channel views 62 million so we are well in the way to 100 million channel views which is that is literally so that's a third of the entire US population people that is insane and I owe it all to you thank you so much for that from the bottom of my heart


What's up guys, Mike the Coder here. Today we're going to go over the problem of gray code. I'm going to skip coin piles and problem reorder. I'll come back to that later. But for now, let's just do great. So a gray code is a list of all two to the end bit strings of length and any two successful strings differs exactly one bit. Your task is to create a gray code for a given length and so if you look at here what they mean right now I'm actually in California and I don't have my I did not bring my microphone so I'm just gonna have to do whatever I can. Okay, so we're given the length to and we want to write the gray code. So in this case what they're doing is they're just listing all the different binary values of two. So it just be like 0000 and 01 right and then if you plus one again you get 10. So each of these values could be each of these places could be either one or zero right so this 00 let's make this into one and then here let's make the second one into one and let's make the last one into a one also. So those are those are all the values you have you have 00001 10. Okay, that's essentially what they're doing and then let's say we have the value three you're gonna have you 0000 right and we have to flip each of them into one or zero so let's flip this last place first so then we have 001. Okay, and then let's let's flip this one now let's flip the center one so we have 010. Let's flip this last one 011. Let's flip this one the third one here and one let's flip all these back to zero so 00. Okay, I hope you guys understand what I'm doing here. Then we have this one we'll flip this one let's with the last one 101 and let's flip this one 110 and then we have 11. Okay, so essentially what we're doing is we're going to go to each of the bits and flip them. Okay, so yeah and we just print them out. So here we have a total of two to three here for this one it's two to the three so 12345678 so two to three which is eight and then for this one it's two to the two because there's two to two and that'll give two to four so yeah. Okay, so how do you do this in code? One way you could do it is that you go through every single bit so since there are n bits here right there's n choices here we go through all two to the three bits right and then for each of them we're just going to shift it right for each of these bits we're going to shift to right and then flip that one bit at the end towards that so what I mean is like how do I explain this? I think so I'll show you guys why I'm just looking at my code real quick to see so you could shift it right and then you could XOR because XORing would flip the last values again let's just see what you see right yeah yeah so he's right it okay so so what we're going to do is we're going to go through each of these values each of the bits so let's say I'm on the first bit so the first bit so what I'm going to do is I'm going to loop from one to two right and then what I'm going to do is I'm going to convert this one into like a binary number right so let's convert this one into a binary number so let's say let's see what is one's binary zero zero zero one okay and what I'm going to do is I'm going to XOR this so XOR is basically just like flipping all the other bits I'm going to shift this binary value of zero zero one to the right so when you shift everything to the right essentially is that you're just adding more zeros in the front so this one becomes a zero so then we have zero zero zero and then if you XOR them essentially is that you're going to get the you're going to get you're going to flip those values back flip the last bit all those last bits are going to get flipped and then you're going to have the next value to print out so here if we flip if we shifted one to the right and we flipped it um one XOR zero is still going to be one right because the bits of XOR is like that um zero zero zero zero zero zero okay so then this would just print out one okay now um when we get to like as we get higher and higher bits um so let's say it was at like two and then three and then four so let's say it was like um I don't know so let's say we're at two so I'm going to erase this actually so we already did one so since I'm moving from zero two to three so that would have displayed zero zero one now let's say we're at we were at two so what's two's binary so two's binary is uh zero one zero so two is zero two the one yeah zero one zero and then I'm going to shift this right uh bits to the right so if I shift it to the right um so shifting one bit to the right would be this one would go to the right side and then all the rest would be zero so this zero is gone right this zero is gone and then it would be one zero okay so I'll just write the next bit shift here one zero zero so then after I bit shift it to right and then I XOR it zero one becomes one one zero becomes one zero zero becomes zero and this would be the next bit of adding one to the to the right side of this so essentially what we're doing is that we're gonna we're basically flipping the last bit into one okay and then uh for each of the values from two to the two to n two to n so because if we shift it right shift the last bit to the right by one and XOR um all the values if it was one all the values get added by one okay in order to to display it so if you look at the pattern in tier of three you'll realize that like the pattern of these sides basically what they're doing is they're just flipping the last bit into one and if it's one it flips to zero and then it goes to the next one and flips last one and one into zero so on so forth so essentially what we're doing is that if we shift it right by one shift the number right by one and then we XOR it we're gonna we're basically changing each of the bits the last bit to turning it on or off for each of values okay so then if we loop from one uh loop from zero to two to the n zero to two to the n and we do it for all these values all the values from i from zero to two to the n um what we're doing is that we're basically flipping each of the last bits over and over again and then in the end we're gonna have all the actual bits there that are correct okay so yeah if you essentially shifting right by one and XORing it um you're gonna get whoops you're gonna get uh each of the bits are gonna be uh the last bit is gonna get flipped so as you can see here right to this last bit the zero got flipped into one here so yeah once we do that for all the numbers from zero to two to the end it'll display all the last bits that are flipped so here's the code um we loop from i equals zero and go up to two to the n and do i plus plus then um our value what i do is i just take the current value of i i XOR it by i shifting right by one and then what i'm going to do is i'm actually gonna you know because i don't want to like go through every bits and print out if it's on or off right the last bit is on or off i just put this this uh this number this value for the bits um if you just set equal to it like a number of variable what it does is actually it actually converts it back to base 10 so this is now an actual number and then what i can do is i could put this number back into like a bit set so then i could convert it back into binary i know it's kind of crazy but like what this is doing is that this gets you your bits right after you shift it right and then XOR you get your new bits of zero one one right so now what i'm doing is i'm converting this back into like a number so it would be like two to the zero one times two to the zero plus one times two to the one plus um yeah so it would be zero times zero one two right so the zero times two to the two plus one times two to the one plus one times two to the zero okay plus one times two to the zero right so what i'm doing is when you set it equal to a variable long long value is equal to this it converts it back to a number right so this would become like a number it would be like equal to two plus one which is three this converts back to number three and then what i could do is i could put into this uh bit set whoops my bad i could put into a bit set and then what i could do is i could call two strings so then i could just print out all the bits okay so i don't have to like check if like each of the number of bits is like one or zero and they're printed out right so this is like like an easier way cover into a number put into a bit set and then cover into a string okay then here um i'm going to loop from i is equal to backwards i'm looping backwards essentially because bit sets are weird in that the bits like if you wrote to loop um in order to print it out in the proper way um you have if you like it's weird in that this one one is actually opposite it's like kind of flipped right so what i did was i loop backwards from 32 to uh 32 minus n and i is less than 32 and i plus plus right and the reason why i did this is because uh yeah it's because for some reason it's backwards so yeah i just printed it out um print out the bits backwards okay um yeah and then i just printed a new line here um the reason why it's 32 is because there's 32 bits in an integer i believe yeah so one integer is four bytes and there's eight bits in one byte so there's 32 bits okay so yeah that's essentially the gist of this problem i hope you guys enjoyed this video right come subscribe i'll check you guys later peace


Freedom! How's it going? My name's Adam Maripos-Vox and I'm back with another video to tell you about a minor update that YouTube has actually introduced that I just noticed this morning. And that is that they've added visualization for your different monetization formats.  And for some this was very, you know, kind of difficult to understand. And that's pretty understandable because they never directly in this section told you what those ads meant. Now with the non-skippable ads, they told you that, hey, if you do long non-skippable ads, people may not watch your video. But now they have visualization for this to help you figure out what you want to do. So they have a box to show where the display ads are, where the overlay ads are. They have a skip button for the skippable ads, and then they show something different for the non-skippable ones. Which is pretty cool. This makes it so much easier to understand which ad formats you're using. Not only that, but then for your pre and post-roll ads, which means your ads that are shown before and after your video, and then your mid-roll ads, which for longer videos are shown in the middle of your videos at certain points. They actually have a whole new player for this. It's actually like a timeline. And you can check whether or not you want an ad before or after your video. And then it actually has an entire timeline of your video and a preview. And you can play your video and choose where you want your ads to go. This is so much easier. In the past you had to just put in time codes.  You never really had a way of knowing where that was unless you had another copy of your video pulled up and you were watching that and putting in the numbers. With this you have an actual preview where you can skip to where you want an ad.  Makes it a lot easier. Over on the advanced tab, they actually have a couple changes as well to the comments. Used to you just had to allow comments or allow people to see your ratings. Well, now you can allow comments and you can actually tell it whether or not you want it to automatically sort by the top comments, which are the ones that got the most attention, had the most likes on it, etc., or by newest first. So if you don't want the top comments to be ruling your video, you can actually tell it to put newest first. That way everybody always just sees the newest comments at the top. Pretty cool. You didn't have control over this before. That was completely up to the person and the person, you know, the viewer may not ever actually change that drop down box. So it's really cool to see. Hopefully they'll be adding some other more useful things like this as the visualization of the other of the ad types is actually very nice. Just wanted to let you know about this quick update to YouTube. If there's anything else, I'm sure you'll be seeing other videos on this channel about it as well. Just wanted to get this information out to you guys. Thank you so much for watching. Be sure to smash that like button. If you liked it, dislike the video. If you want to see me cry at night over on my channel, subscribe to Freedom Central. If you're somehow not already, come check out my channel over at YouTube slash epos box. And I'll catch you in the next one. Hopefully we got some other cool content coming up here on Freedom Central for you as well. Also, if you didn't notice George is back. He was actually in a video again recently for the first time in forever. So go check out that video in the YouTube card or the end card. Something on the screen here. Do the Macarena. Okay, bye.


Yeah, I was so excited. That's awesome. I love all the wiki tree swag we have now. So we're counting down to wiki tree day and if somebody's new to this, these live casts, here's the help page on wiki tree day and pinned at the top of the live chat is the registration link. It's free. You're entered to win for door prizes so it's kind of a no-brainer to register. Of course. Oh look, we have people coming in. Loving the shirts. Oh, so we have a winner from yesterday. Go ahead and bring that up. Okay. Who is it? And I think Greg should be the one that says the name because I know you have a pronunciation in here. I'm not completely sure on how to pronounce it. Okay, looking forward to this. This is where it is. Lisa McQueen's a bit. Hey, Lisa. Congratulations. I didn't know how to say it. Yeah, Lisa's from Canada. She's just just outside of Ottawa. And as I've been saying, Aowyn's our four-star. She helps us with all the prizes. So go ahead just email her aowyn at wiki tree dot com and she'll get you taken care of. Congratulations. Awesome. The favorite part of the day is the giveaway. That's great. That's excellent. Ed, here's today's question that everybody can respond to. Do you have Italian roots? Well, I personally don't have Italian roots, but I'm married to a first-generation Italian. So I claim that I'm an Italian in law. Right. Yeah. So my wife and all our children have Italian roots. Nice. Yeah. So yeah, even if your answer is no, it's still counts. Definitely. Yeah, comment on this video. Reply to the Twitter that's going out live right now. It'll be up on Facebook and Instagram and TikTok and master it on soon after this live air. So nice. Yeah. Azure, we have a question in the chat from Jen Lawrence. And I think it's regarding the prizes during the symposium and wiki tree. So if you're registered, you're entered, right? Yeah. The door prizes are pulled from the registrant. Yeah. But not with today's prize. Right. Not today. Yeah, that's separate. Yeah. Jen, if I misunderstood your question, let us. Well, it looks like no one in the chat has got Italian roots either. Well, they can just answer that. I wish I had Italian roots. That would be a good answer. Yeah, there you go. All right. Well, thank you guys for joining me for the broadcast today. And we'll see everybody tomorrow.


Well, it's good to be here with you and We have a variety of ages here, but I do see a number of younger people here and Grateful for that, but I'm also grateful that there are some older people here I might feel a little insecure if it was only young people here. Welcome to all of you I would like to just begin at this session by Telling you that addressing educational considerations and options for church planting especially urban ones Would seem like a very unlikely thing for me to address I was a rural Kansas farm boy and loved animals loved You know, I wonder if maybe we should The two mics too close together see whether this would help us out a little I loved animals. I loved nature and considered myself a Farm boy so Thinking of ever in my life being in the city just didn't even occur to me I remember as a third grader we had from our school teacher this little sheet where we were supposed to dream about what we would be when we grow up Well, my dream at that point would be that I'd be a cowboy when I grow up. I Think most of my students in Brooklyn, New York could hardly imagine me as a cowboy today But that was my perception as a little child my initial experiences in school were not so easy and in fact I would have perceived myself as basically an academic failure as a young child I remember as my first year of school felt like the longest year of my entire life, which of course was only seven years at that point But it seemed like almost like an eternity it just would go and on and on and on it was not an easy experience It was a very hard experience. I would consider myself a late bloomer and in almost every regard but certainly academically and I remember as a third grader reading an autographed book one of my classmates and One of my first grade teacher had written in it a poem about all of my classmates And of course I knew that would include me so Of course my eyes quickly went to what she would have to say about me and to this day That's the only piece of that entire poem that I can remember But my line went like this and Dwight who was so slow that came from my first teacher and Honestly, it didn't necessarily knock me out because it wasn't a new idea to me. I realized I was slow I didn't see myself as an academic giant and That didn't really shock me. It just kind of confirmed in my mind that school was not for me I remember when I was in the fourth grade that The state of Kansas decided that the Amish could stop school at eighth grade And I thought you know, I will claim my Amish roots and stop my suffering as quickly as possible And so that was some of my early journey into academics and education but when I was in the seventh grade I had my first male teacher a godly man and The first teacher whoever apologized to me and the thing that he apologized to me about was something that He wouldn't have had to but it meant the world to me and School wasn't it wasn't that I was opposed to the children. I love children I've always loved children children have been just something really special to me from the time I was can remember from as far back as I can think of but it was it felt like School brought the cross to everything. It just was the thing that was so difficult And suddenly I realized if teaching meant that I could work with children the rest of my life maybe it was a cross worth bearing and For the first time I started thinking about teaching But then I yeah, it was it was quite a little journey and at one point I asked I prayed this this question to the Lord said God Where do you want me to teach? I've grown up in this community. You want me to teach here? Where do you want me to teach? It seemed like God responded that question more clearly than about any prayer. I prayed it wasn't audible, but it was so distinct It went like this I've given you many things. I've given you loving parents I've given you a loving church, and I've given you a loving community And if you really want to say thanks for that kind of a gift Give that gift to children who don't have it Wow, okay so my next question was so God where's that and I Didn't get as clear an answer to that but the answer that's just I never could feel at peace with any possibility besides a Major inner city or overseas and from then on That was just so clearly in my heart what God meant for my life, and it was so powerful that I From then on Considered nothing else Well that prayer eventually took me to New York City And I've been there ever since that was in 1997 and this is 24 years later And in that period of time the Lord blessed me with a wonderful wife three wonderful children and We have lived there ever since Brooklyn, New York is The home of our children and I've heard it said that when you go to a new place The point at which you can really call it home is when you've got children who call it home When you've been transplanted especially to something very foreign and very different and so I would say there's a lot of truth to that This journey could could raise a lot of questions and honestly it did in me it's one thing to can I would consider myself an intense idealist and It's one thing to live out your ideals as a single it's a whole nother thing to live out that ideal as a Couple but it takes it even a step further when God blesses you with children and Then it takes you even a step further When you consider being in that setting that most might consider dangerous and Would they feel like at a certain point you need to bring your children back into the home community? because Well, they need to experience I guess there's a number of reasons I won't even explain all of those But as a father that that weighs heavily on a father's mind and it feels like an entirely different consideration than being an idealist as a single and It raises questions questions such as how safe is the city? How wise is it for a single visionary man to ask his new wife to live in a city like New York City for perhaps the rest of their productive life how advisable is it to raise children in this potentially dangerous setting especially through their teenage years and I Do have teenagers in the audience here, and I just felt like maybe at the end of this session It could be useful for them to answer some of these questions They might offer it from a more completely Child's perspective than as a father. I might be able to present it So at the very end I might if it's okay take the freedom to have them help me out in my in my presentation today and so this morning as we take a look at How do? Kingdom followers plant kingdom schools within a Church plant and I would propose that we should increasingly be thinking of church plants being where the majority of people are The cities and so I would take that to that level as at least a consideration. I Would just say You might say so so in talking about this. Why would we bring in? Children well, I would just say that families are probably in a church planning team Families are some of the most powerful Parts of a church planning team in presenting the gospel people may watch your children more than they watch you and they may deduct what Christianity means through what they see in your children as Much or maybe more than what you might have to say and so Children are an incredibly Significant part of a church plant and so if they are then how do we nurture them? How do we take care of the educational needs of our children if that's where God has called us to? minister How do we adequately care for the children that are in our care? Just Earlier this summer as I was doing a little painting project With some of our children and it was actually the same day that I got the phone call that my father had died But we were in the front porch. We're doing stuff together. We often do stuff together We usually eat our meals on the front porch together For several reasons. We don't have an air conditioner in our house. So it's in the summer.  I've been watching the kinds of play that they have so different from how most children in the neighborhood play and When I walk past your place, I feel a peace and I've recently discovered that I have leukemia and He ended up just talking a little bit about his own life journey but the thing that's shocked me was People are watching beyond what we have any idea and they notice children and I could give you another story, but I think I think I'd better leave that story But children are such a critical part of church planting and if they are how Do we continue that church planting effort in a setting that seems very dangerous? In a way that rightly and sufficiently really does protect and care for our children and And addresses their academic needs well Well, if you're going to start a church plant, there's probably just so many options that are available for education There's the option of homeschooling there's the possibility of developing a church school in that new church plant In the past often a boarding school was an option. I'm so thankful that that's increasingly Not an option feels like there's some really sad stories that come out of the boarding school option I just personally couldn't do that to my children. I don't think at least Not unless it was a very unique. I don't know. I haven't come up with it a Scenario bad enough that I would want to do that for my children yet. There may be that exception I don't know and then the public school and in some places around the world That is the only option that is legally allowed is the public school. So those are options that that Educational options that we can look at if we're we're developing a church plant and and we're thinking how do we Academically nurture our children. I think there's economic considerations If you're living on a shoestring budget as many missionaries are The most economical option is public school because it's free If you're looking purely at economics The next most economical, I would say would be homeschooling. I'd say the church school is the most expensive one And so how big a role should economics play in this journey of Education for your children, but maybe there's issues even bigger than economics. I suggest there are Another question to take a look at and I'm not going to be answering some of this immediately because I want to kind of stir our thoughts as to What's there before we? Zero in on what might be the best options What priorities should a church school have the first year of a church plant? Or the second year or the 10th year for our Church plant in Brooklyn, New York the church school option didn't happen until about the 10th year of the church's Existence The vision there was that whole families within the church plant team Would provide homeschooling for their children that to at the same time you start this big adventure that this big venture of church plant if you have Besided also the the huge venture of starting a church school those are two pretty huge ventures and it's pretty hard to give them both the level of Focus and development that are needed and so in my personal journey in Brooklyn, New York I came at a 10 years after the church plant had started and I came not to primarily support the church planters children, but instead the church was seeing that as they were reaching out to the community they had Community families that were broken the community families of single parenting and just the sense how fair is it to? be Offering what we are to our children while a single parent isn't able to do that And the only option that is left is to place them in the public school where the Faith is already a very difficult thing to nurture and develop And so there was just a sense that this is not fair to our single parents within our church to not provide that for them and so for us The initial target audience was the single parent families within the church And I think that is a critical question for us to take a little look at as We consider the schooling options who? Who is our target audience? Is it the church plants team? Is it the church or is it the community or is it all three of those? What is the target audience? But I think a similar question could also be asked. What is your target audience for the church? Is your target audience for the church? your Church planning team is that your the extent of your target audience or it does your target audience extend To the people you're ministering to in the community and If that is the case that it extends to the people in your community Should your school also put perhaps extend to that? If it doesn't I think I think it's important to ask Why does it in the one case and not in the other something to think about at least? An additional question might be what is or who is your church for? What is the extent of its? Purpose is it is is it for your team your church your community in your neighborhood? in Considering our target audience for school in a church plant consideration Here are a few questions that I think are at least important to consider They may not answer every question, but I think they're important to think about What does it mean to as Jesus said suffer the little children to come on?  What does it mean as Jesus said to love your neighbor as yourself? What does it mean to snuff out the smoldering flax What about Jesus's words in Matthew when he said in as much as you have not done it to one of the least of these You have not done it unto me Children especially broken children Hold a special place in the heart of God and think about the passage where Jesus said that is Really serious when you offend a little one It would be better if there was actually a rope put around your neck and you were thrown into the midst of the sea Jesus takes personal offense when We offend a little one and then Jesus said in as much as you've done it onto the least of these You've done it unto me and so who are the least? I think there's a lot of ways in which children could qualify as the least They might be the least heard they might be the least Able to advance their interests they might be the least have the least experience They have the least options and resources Both their voice and their abilities are pretty limited Jesus also said He that would save his life will lose it But he who loses his life for my sake and the Gospels the same will find it In what ways does our school policy? In what ways is it driven out of a desire to save my life and to what extent do we see a willingness to risk and Our lives for the sake of the little ones Who very easily could be destroyed without our involvement and then just another Thing to consider what should be the academic Strategy if you are to develop a church school. I would suggest and this is not exactly how we did it We started with being available for grades 1 through 12. That is a pretty wide Feel to start out for the first year. The Lord was gracious. We survived But I think in many cases I I would see wisdom and maybe starting without with say K through 1 or 1 through 2 Whatever your lowest level is and maybe each year add another two grades and then in that way you're not needing to get teachers for the whole spectrum and You can grow the school. You can start seeing some of the Challenges you can start understanding the community on a smaller scale and you can build small and strong I could see wisdom in that kind of an approach I think we should see the church on a broader sense as a place of educational resource Not only just in the traditional educational sense but how do we How can we equip parents to? To care for their children. I know that brother Alan Roth He was the administrator of our school for many years and under whom I began teaching in Brooklyn, New York The challenge he placed on us as teachers was that I really believe you need to be connecting with the parents If you don't have the parents Then on the long haul you don't have the children and he said I would like to see you be in every home maybe once a quarter and every week being one or two homes Does that sound big? It sounded huge to me Especially my first year there trying to get used to a whole new urban setting and I confess We didn't do a very good job of that but I would also say he had an excellent idea and I wish we would have done a better job and I would say that the more that we see parents as a very significant part of the purpose of the school and that the more that we invest in parents The more that we are investing in the children in the long haul and that we don't just see it as a purely separated two entities kind of thing Brother Alan also had the The perspective that while children's ministries are great and they can provide certain levels of Influence and exposure that are good for children. He said I don't think any long-term church plant is going to really happen if that's the primary focus of a church plant and In my years of observing church plants. I see that to be true Investing in the actual families is Where you develop church not through primarily focusing on Kids clubs kid clubs are a lot easier. They're a lot more exciting. I think they may be kind of fill up our emotional tank of Satisfaction more easily and quickly. They're a lot easier to do But I don't think they're quite at the real core of our presence there Advancing the kingdom well if that's our soul Dependence and even when that is an active piece of it unless it's coupled with a fairly active involvement With the parents of those that we are ministering to then I think it's a very limited ministry. I Might just give you a little bit of a background of my own personal journey My first eight years were in a small public school a half mile from our home at that point our church didn't have a church school but Our principal was actually from our church And so it was about as close to a church school as you could have gotten without being a church school probably He hired all of the teachers and they were all professing Christians. We had devotions In every grade I think or at least prayer in every grade from first grade through eighth grade So first through eighth was in a in a small country public school. High school was in our church school I Then later went to junior college and then to a private Christian college In terms of teaching I taught two years in Canada before I went to college and then eight years in a public school in Kansas And in the past 24 years in Brooklyn and so Though I had really wanted to escape school as quickly as I legally could The last nearly 50 out of 60 years of my life have been in school either as a student or as a teacher And in some ways kind of both My wife has home schooled our children through all of their School years though there have been a few classes They've come to school for when they were just little toddlers. They'd come into my class for art class because I taught art and especially when I did ceramics and but I think most of it for several years and Then they also went there in high school for Spanish and for algebra to You those were the main classes that you had taken there so some people look at me and think I'm a really strange Mixture and I probably am but and they ask how could you who have invested in education? Education public and private all these years be homeschooling your children. Isn't that almost a betrayal of? Of what you're doing well it might depend how you defined betrayal or or I'm not sure what all but I will tell you that when I was just a third grader home schooling was first being pioneered in our community in Kansas and During that same time. I saw my little sister going to first grade and crying almost every day and dad who was the school bus driver would often come in to try to comfort her and The teacher didn't really like that. He felt she felt like she should just toughen up But I was just seeing all of that and I was thinking, you know God did design parents to nurture their children and I'm seeing my mom nurture my child and my sister like this teacher isn't and Silently without telling my parents or siblings or anyone else The ideal of homeschooling started to be birthed in my heart and mind and I just always dreamed that if I ever had children regardless what the other options were my wife would be my Teacher of our children just I just felt like that with the ultimate level of nurturing that that is possible on this side of heaven, so Being involved in education isn't because I'm this great Admire of public education or private education and and so to not have my children in those Institutions is a betrayal of my vocation. That's not really where it's at for me for me We are called to nurture children and the ways in which we can do that best. I believe God wants us to do and and I think sometimes it's conservative and Baptist. It's time for us to think a little outside the box on that front and Really think how can that best be done and ask God to show us how to do that? And so I'm kind of a strange mix of Having been involved in public and private Teaching but having my own children in homeschooling. So I don't know how you would Process that one, but I just expose that to you for you to realize that how your speaker has lived his life. I Have found it interesting that before COVID our children were a little bit cautious to tell their neighbors that they were being homeschooled and and even if they did Their neighbors would wonder what's that? COVID has done a wonderful work for the homeschooling front Since then if people ask them What is your educational experience there? Oh we homeschool. Oh, great And suddenly that is an honorable and acceptable option COVID did bring acceptance to that option it seems and so In conclusion before I have my children Talk a little bit about the risks of a church planting family being in a setting like an urban setting How those risks look to them as having personally experienced that? they They have more of an understanding of That world and then the world I did as a child growing up on a farm But I just thought it might be interesting to hear that but before we do that I would just like to to think a little bit about the heart of Jesus when Jesus said Suffer the little children to come to me and forbid them not But he doesn't stop there He makes it into a kingdom issue. He says for of such Is the kingdom of heaven and so I think it's right for us to really seriously think About children when we think about church plans How are we going to take care of them? But perhaps we need to think beyond just our own children How are we going to take care of the single parent families that come into our churches? Hopefully our heart is to care for the brokenhearted and for the the needy within the place He has called us to minister as a church plant and so if that brings Those additional needs, what are we going to do with those needs?  How are we going to do that? What about our neighbors that we are reaching out to? How are we going to are we going to be open to caring for their children and? How do we risk I view the risks that? ministering to the local To our neighbors may bring and even the risks That that may place on our family and on our children. How do we look at risk? I think that is so important that in the last session I had talked about risk and there's an excellent book called reaching America by Gary Miller and Some of you may have read this book already excellent excellent book My daughter saw this this summer and quickly showed it to me and said dad We got to get this book and she says Gary Miller is my hero and I was glad to hear that of course when she said that How could I keep from saying? Yeah, let's get a book. So we got the book and as we were driving to Kansas where I Grew up to visit there. She was reading excerpts out loud, and I was saying boy that that's really good I should have that as a part of my talk, but Gary Miller raises an interesting question he talks about risk and how we Deal with risk and which risks are worth embracing and which risks are wrong to embrace and He suggests that we actually aren't that scared of certain risks and that actually some of the risks We aren't scared about Jesus calls us to be pretty scared about That's a little sobering and Then he goes on to say the risks Jesus calls us to are sometimes the risks that we are least willing to take I Think as we consider church planning with this question about Risk is something we really need to take a look at What are the risks that Jesus considers worth our taking and What are the risks that Jesus does not consider worth our taking and does our life represent that? I'm here to say that if it doesn't then the verse where he said he that would save his life will lose it But he who loses his life for my sake and the gospel the same will find it is very true And so I just challenge you to maybe daily ask God What risks do you want me to take today? And you know We often I guess it's the only way we can do it. We look at risks through our mental Framework our perception And yet our perception of risk and yet our perceptions so often are super faulty and they really need to be confronted with Jesus's perception of What is really the true risk? So I'm going to at this point before opening it up for questions give our two oldest an opportunity to Communicate about Some of the questions that typically are raised about children being raised in an urban setting in a place of What would from our local and rural communities seem like a risky place and maybe too risky a place And so I'm going to just Ask them to to share what they have prepared So yesterday afternoon we were at the buyers conference center where we're sleeping And dad was preparing for his message and I said we're sitting around and we ended up talking About his message and I was like, oh you should share your thoughts and so Here are my thoughts that came to me last night So I was born dad and mom got married in 2000 were there and I was born in 2002 There and have been there all my life. I'm 19 now and I plan to stay there for for Siebel future. I doubt my whole life, but I don't plan to move away too soon And so this topic kind of like raising raising children the city or Because the way has affected me Like when I think about it, it really causes a lot of like deep feelings rise in my heart, I guess the last Year or few years it's for something that as children have been like thinking like thinking through and the way we relate with cousins and friends who are not from the city and The other way it has formed us and made us Have a different perspective on certain areas of life as to those didn't grow up there So there's just so many things you could talk about this probably just a huge range But I'll share with you three effects That growing up in the city has at least has had on my life and I assume on many children have The first one is that living in a city gives children the opportunity to interact with people that are very different in themselves so for me, I grew up and we still live in a community that is Majority Hispanic and so there are very few white people there and It's starting to change a little bit, but especially even now especially when we were younger.  So we have we have different people or people from different ethnicities in our church besides Traditional Monday night and so one example is carrying meals. So we'll have like meals of everybody brings food to church to be Like very non-traditional night food. I love the food and one one interesting fact So we had this tradition at church you bring your food and then you don't expect to take it home So I go after we eat You can take any food that's there home with you and so it's great and then already Three years ago.  I love will be pies I just took a week by with me home. I'm like I was I don't take food home. You just eat what's when you're there and Anyways, so I guess it's example of different cultures and then one man I just really want to tell you guys about and Just his story can take a long time to tell but anyways, his name is Marcus and He got to know him when I was just a little toddler and he was a man who was semi-homeless abandoned house and Drunk he would collect cans and bottles a little bit of money Anyways, and he would terrorize The VBS women VBS in the park. Anyway, so we got to know him and he became a family friend over the years and he would stop in any time of the day and Eat food with us if we're eating supper you're offering separate us and so that really That really gives an in-depth view of interacting with someone that's very different than ourselves that he would When he wasn't it when he wasn't drunk He was just the nicest guy and he would gladly help with any projects around the house But when he would come dead drunk He was a very different man and speak very fowly and anyways. Yeah, he he passed away two years almost three years ago now. I Was really hard Yeah, it really gave me an experience of interacting with someone and coming to love someone who's not a Christian And he was a drunk and he was just very different from us And my second point is Living in the city causes children as they grow older to make a deliberate choice as to who they will serve I feel like in the city there's a starker contrast between the way of light following Jesus and the way of darkness and and So it forces you to choose Along this way or that way and there's not as much of a middle grayish area And so we've had to stand alone a lot and sometimes I've gone so tired standing alone but I think in the end it's good for us because It may it forces us to make the choice Who will I serve will I follow the way of light and Yeah, follow the teachings of my parents or will I Do things that are not right to Try to fit in with those around me And kind of going along with that My last point living in the city gives children a Unique perspective that is both valuable and challenging To deal with so it's almost like and this is the same for for Children growing up in like third world or other countries You almost feel caught between two worlds And so like for example, you know, even though we live in the city You kind of did things a little more the country way I'm gonna call it that least from the people who live there they're perspective of us So we were blessed with the rarity of having an empty side lobby inside our house that was owned by the same landlord as the house That we live in and so we fixed up into a backyard have a little backyard there And so when I was about like eight or ten or somewhere in that age range in the summertime I had a weater and I was weeding some of like grass and weeds that were out by the sidewalk And I was barefoot and it was hot summer day Also, this man in a truck comes and he pulls over gets out and yells at me and it's like where's your dad or whatever And that I go and get dad and that comes out and this man is angry because I'm there we eating I'm barefoot and I guess she thinks This is not safe for a child to be doing and so You know those that grew up on farms and ever this is just normal, but for there and it was normal for me But there it's it's just they can't understand That a child you're working like this Then from the other side when I like go visit family in Kansas or wherever They just can't comprehend how I could Love the city or how I could call it home and it is home for me Even though there's things I love about the country now like man out of the country I would love to do this, but that's not my home right now my home's in the city and They just can't get it and so it's kind of like you know Where where do I belong because I live in the city, but I'm not quite like the people who Live there, so even though I was born there. They still don't consider me from the city But yeah, I don't live in the country, so I'm not from the country and so that That can kind of be trying to deal with sometimes but it gives a unique perspective that is different and I Think it's it's really good to have that and I just don't really respond to the common ejection the data was mentioning the city isn't safe to raise a family and So one one thought the guy likes to say is Along these lines wherever God calls you is the safest place to raise your family And so the question has to be asked What is safe safe from evil influences? The country needs Jesus every bit as much as the city does Now the sin might be more a little more obvious in the city That same sin thrives in the country. It might be a little more under the rug, but it's still there Also, I would strongly argue That with the rise of social media Worldly influences are increasingly just as strong in the city or in the country as in the city and almost What you would see in the city and say oh, that's worldly that is being made Nowadays through or is being formed through social media and so the things That once just kind of rise in the city thought that are now being spread worldwide to the same lingo or or whatever Let's only give you an example of this So last month Sarah and I were with the traditional midnight youth group conservative youth group in a rural setting in the country and So we were out in the evening gone some food and then went to a park and we're just hanging out the park and a few of the youth have learned this dance from tick tock and decided they wanted to teach All those that wanted to learn this was something that Sarah and I had never seen before and and as we observed it like yeah, we don't use social media and You know, we we know about it from people who are not who are not anti-baptist But to see actually the anti-baptist youth group acting like this was we'd never it was just we never said before And so we had to think what would our non-annabaptist friends in the city? Think they would be like if we can think of people if they would have seen what went on They'd be utterly shocked like even though they participate in those behaviors themselves They don't expect us to be that way or live that way act that way They might even want us to they might wish like this less if they would see us Live or act like that the conclusion am I saying that the city is the only good place to raise a family? No, I'm not saying that but it is a good place to raise a family if that's where God is calling you to and So I just challenge you all Go where God is calling you. Was that being a city on the country? And if you follow his what if you walk in his will Not only will he guide your path? But he'll also guide the paths of your children So I'm just gonna make this really quick But one story that I thought of when we were talking about this last night When we were in eighth grade and we're studying New York State history And then we were also doing New York City history And I remember one day mom said here to me and Isaac look at this paper And it was a map of the boroughs and the communities of New York City and it had Places with green yellow and red areas with the green being the safest and the red being the most dangerous Guess what? Cypress Hills is very very dangerous to live in and we thought I was where we live in we thought it was so funny because we're like It's not even dangerous. What are they talking about? Of course, you have to lock your car doors You have to do that everywhere in the city. So it just reminded me of that. I think Last night I was thinking I think often what Satan does is he makes what's really risky look harmless Like it's not a big deal But the actual worthwhile risks they might be risk, but they're worthwhile. He makes them look irresponsible With the whole thing of bad influence I've actually found that having a much closer look at sin has been an example of what you don't want because you don't only see just the glamorous side of sin you see the results of sin and Yeah, with even a lot of immorality you see what comes out of it You see the broken families and you realize there's no way when I'm the age of these people do I want to be dealing with What they're dealing with? Yeah, like Isaac said standing alone has definitely been a big thing but I think since we started it from young up it has strengthened us and also like Isaac was saying There might be that our friends from the city who haven't Embrace the way of life that we have they don't actually expect us to participate in the activities that they participate in and so it might be lonely, but it's not um the level of temptation that it might seem like it would be and um as I was visiting our family who's in a more traditional Mennonite setting and Through different experiences one including the night at the park. I was realizing that you know in the smaller issues the issues were Personal or people or were families land in different areas I think for me it's actually easier to stick to those choices that maybe dad has made for us or that I personally feel In the city because I'm already different and they don't actually expect me to whereas in a traditional community They um would think Well, we're kind of we're all Christians anyway, and we're all like really the same So it's kind of awkward if I'm telling someone who's just like me. Well, I'm not going to do that But we're already different in the city. So it's not really a big deal and um like Isaac was saying I think social media You know some of the things that friends in the country participate in Like he was saying my friends in the city They would like make fun of me if I would do that because they do it but they think it's really weird if I would do it and Sometimes it's annoying, but it's like, you know, it actually keeps me, you know, not being a part of social media And not being a part of that culture. They don't really expect me To participate in those things and so we're still friends. We still relate But in certain areas of life They don't want me to and I think one thing that I've really appreciated about the city is that Worldly versus non-worldly the contrast is much More vivid whereas in the country Some things might seem now this is generalization, of course but you know sometimes things that I would see as worldly I see my friends participating in in the country because I don't think they see the people that are doing that in the city like if Everyone who's participating in a certain say dance or use of slang is like you it doesn't seem like a problem But if you see someone who's doing it that you don't want to be like It gives you more of an incentive to not do that yourself So, um, yeah, I guess those are just my thoughts Living in the city has definitely had challenges But I wouldn't trade it for anything because of the perspective it has given me And because of the person that I think it has helped me to become There's definitely been challenges, but I'm thankful for it as well All right. Well, I'm just going to open it up for any responses either to what they had to say Or what I had to say as just a quick little wrap up and so, um Just open it up if this discussion has raised any questions in your mind that you just welcome a little bit of conversation on Raise your hand and see what we can do and interacting with that Forgive me if I'm overlapping. It's what you already shared But what do you say about friendship evangelism? You see this approach is used a lot in city ministry You spend a lot of time with people maybe aren't real real prepared for the gospel um Pros and cons anything real quick on that. Yeah Excellent question and honestly I think there is an array of tools that The believer has in his Toolbox and As a carpenter we I'm not a avid carpenter, but I love woodworking There are times when one tool really does work better than another tool. There's um and I don't see jesus for instance Dealing with every person in exactly the same way. There are times when it seems like jesus Very compassionately um Interacted with a person and other times when he was rather forceful Um, and I see some who are total Friendship evangelism advocates and there's nothing else but that I feel really uncomfortable with that And I think it can actually be a cop-out when that's the case And then I see others who would be kind of like a great comfort kind of Pitch in the face kind of Approach and if you don't do that Exclusively for every interaction you really don't understand how to share the gospel and I feel uncomfortable with that one too um and It feels to me like there were times when jesus used both um, I Rather than offer one or the other as the exclusive answer I think if we can ask god to show us in each interaction what he would have us to say That might be the the safer road um, maybe two questions here um One on the school um, so you just mentioned the school being started as a Primarily an outreach to The single single parent families and that type of thing Was that something then that most of the people of the church and the outreach there sent their children to as well? or the focus remained on on um single parent families and that type of thing or not and then secondly, um Relating more to your children and their interactions um was Maybe a question on how much interaction did your children have as far as playing with other neighbor children and that type of thing? um Maybe especially even at an early age um Are the things you did to limit that? Obviously children are very impressionable, especially at young ages and the influences they are around shape them a lot Yeah, you have several really good questions and your last one I might just start with and then I may have to get you to Refresh me on the other questions, but the whole question of how do you deal with? Neighborhood children in a way that Really cares for them and yet doesn't put your children at unnecessary risk We never we never had our children go into neighbors homes But our our home and our backyard was always open to neighbors uh, it felt to me like If it's on our turf then it can have our expectations and our observation and our protection If it goes into a neighbor's home Who knows what could happen there? That's worked well for us um we At one point we had a big rope swing in the backyard and that really Caught the fascination of the neighborhood children and they all wanted to come But I with that said you know what I'd love to have you in the backyard And you're welcome there as soon as you bring your your parents one of your parents To us and we can meet and I can show them the risks that are back here And I can make sure that they're comfortable with risk because the rope swing does present some risks and looking back Sometimes I wonder I was totally sane in some of those risks, but uh, I'd grown up loving dangerous big rope swings in the barn and And I thought our children should have that joy and and the neighborhood children just wanted that joy also But I felt like I need to do that and that ended up that was so foreign to the to the city culture that adults talk with each other But when one person finally got their parent to come and talk with us Suddenly there were all sorts of other parents and they came to my child just dragging me here What you got here that show them and they said oh, yeah, that's no problem They gave me any trouble just let us know and it developed a relationship then with the parents that wouldn't have happened otherwise And that worked really well What were the other questions On the school and the um the emphasis of the school did it remain as uh for single parents or was that uh That's a really good question and honestly My heart has remained there, but the reality is that as more people join the church That wasn't necessarily a vision that everyone else embraced and But here is one of the dilemmas that can come out of if it if it's more than that The more that traditional anabaptist families send their children there the more they want curriculum that really tailors to their children's needs and Often that's not necessarily What would tailor best to a broken child's needs and so which are you going to tater to And since my heart was there for the broken ones and I felt that we had another option for the other families My sympathies went deepest With the broken and yet there came a point where I realized maybe that was too strong in me Where somebody said so do you consider my child is less valuable than the neighborhood And yeah, that's a good question to you So there's some tensions that go with the school journey. Um, there came a point to where Another administrator we've had a kind of a different view as to as to the homeschool option and And the purpose statement at the beginning of our handbook shifted some with that Um, and so it's been a journey in its process and the bigger your your church the more you wrestle with Which ideal to place at the top Great question


Welcome to Toffy TV, it is the start of 11 show Brentford versus Everton. A tough trip down to the GTEC stadium as it is now known. It will be a tough game for Everton, but let's get into the start of 11. Jordan Pickford retains in goal for the Toffys. Obviously didn't take part in the game against Fleet within the week. So back in there. Going for a back three again. Same back three for me with Connor Cody, Hallgate and James Tarkowski in there. Tarkowski a little bit dodgy last week against Nottingham Forest. Let's hope he improves in this game. It will be a tough game this for the centre backs with Brentford having a lot of power and pace, but that's the three for me. A lot of talk about maybe going back to a back four and stuff at the moment I think. I think at the moment this is probably the best system for us till we get all our players in that we are looking to bring in day the three I'd go for. Right wing back Nathan Patterson. I think he's been improving every single game. I think he looked good last week against Forest and I think he looked against Fleet. Obviously he was miles above that level, which he should, but players don't always look above their level. So hopefully he keeps going. He's got Seamus Coleman pushing him now, which is good. Seeing last week at the game, Seamus Coleman was actually talking to him while he was warming up, you know, telling them where to be positionally and those kind of things, which is brilliant. Couching whilst the players on the pitch from someone who's been doing it for a very long time. So no issues with him at all and hopefully he keeps getting better and better. The wing backs really after start offering the width. I think I've said this every week, but I think it's a trust thing. It's known the midfield are going to do their job and get back and the centre backs are going to cover. Hopefully that grows more and more as we go forward. On the other side, I'd bring Michalenko back in. I don't think he's had a great start of the season. We've seen Reuben Van Agri play in the week. I don't think he did enough to take that spot away from Michalenko, but again, it's up to him to be a little bit more aggressive and a little bit more positive. As I said, both wing backs need to start getting higher and higher. In this game, that's one of the reasons why I'm going to go for three in midfield. Tom Davis, I'm going to go for him as the holding midfielder. I know he pulled up in the warm-up against Fleetwood, but I expect him to be fit for this game and I would start him and I'd have him just sitting in front of the back three. Filling those spaces in the full-back positions, getting back, overloading when players are being held up by the centre back. I thought he did that well against Forrest. I know he's not everyone's cup of tea, but at the moment, I think, saying he's someone as a defensive midfielder, if you're going to have three, I'd have him. A head of him, I'd have a Wobie and I'd have Onane. A Wobie's been our best player this season by a mile. Let's get it right. But I think if you can take that little bit of defensive responsibility off him and play him a little bit higher and start pulling strings higher, I think he can be even better. I think he's been superb and again on Tuesday night against Fleetwood. He looked miles ahead of the level and was so calm and he concentrated so much on what he had to do, set the goal up as well, so he got the assist. Next to him, I'm going to go for Onane. He's got 90 minutes under his belt now, he's kicked all over the place and listen. Do I think he's ready to start a Premier League game? No, I really don't. But I think starting him in a three, seeing how he gets on for an hour at this moment with what we've got, I don't think it's the worst thing in the world.  Eel of lanes from those games he's played in so far. Don't hold on to the ball as long. Be a little bit more simplistic in your approach. Get the ball and give the ball, certainly around your own box, do the simple thing.  A head of those three, I'm going for Anthony Gordon and I'm going for the Marey Gray. Obviously with Anthony Gordon, lots of talk about him leaving the club, but he's an event player. Put him out there, let's see what he can do in maybe a split role with the Marey Gray. Again, this is not the ideal situation, I appreciate that. And Rondon maybe, Rondon probably will start or another player may start. But I think these two for an hour, certainly, let's see what they can do.  Let's run after them, let's see what they've got. Fulham scored three against them last week. Let's go two against them in the opening game. Let's see what they've got. I know at home it's a different kettle of fish and they're a lot better at home. Let's see what they've got and test them and these two running at them higher up the pitch. And then maybe bring the centre forward on after an hour and change it up. Again, it's not ideal, but you told me I haven't, are you starting Rondon again? Listen, you can see what Rondon offers in terms of being a focal point. But is he a starter? Can he start a third game in the week? I'm not sure. So maybe these two for an hour with the extra man in midfield, we haven't got lots of options at the moment and we're waiting for Evan obviously to bring in players and change that a little bit. So that's the start of Evan I'm going for. I'm not convinced in it myself, but looking at the options, that's what I'm going to go for. And we'll see what happens. It's a tough, tough game. Evan, I've got to make sure the don't go behind. Try and get that first goal and see what happens. We've been making chances. We've made the fourth most chances in the Premier League so far this season, but obviously our goals and our points don't tally up with that. So obviously we've got to start putting the ball in the back of the net. That might mean bringing in players who aren't already at the club. So let's see what happens. It's a big game and then we play Leeds on Tuesday night, don't we? So we followed up with a quick, with a close game. So let me know your thoughts in the comments. As I said, I'm not fully convinced by this, but I don't know what we'd do it otherwise. So let me know your thoughts in the comments on your start at 11. Make sure to give this video a like. Subscribe if you haven't already. If you want more daily exclusive shows, join us over on Toffy TV Premier. The link is in the description and it's come up now on the screen. See you later.


So, far just to quickly summarize what we have seen it is this, we have learnt how to choose an appropriate basis. So, that any matrix can be block diagonalized like so where each of these aii has what property exactly that it is minimal polynomial will be of the form right and it is characteristic polynomial will be of the form right. So, this is the overall picture for any operator a yeah we have seen that this can be done there after we argued that then it does make sense to take a closer look at these individual blocks because there is nothing more we can do apart from get a simplified structure for the individual blocks themselves. So, here after we decided that we shall look at only operators of this kind that is of the type aii yeah because all of these eventually stemmed from an overall characteristic polynomial that looks something like this right. So, this was the characteristic polynomial of the overall matrix of the operator and this was the minimal polynomial of the same right. So, from this given structure we brought it down to this no further simplification is possible apart from simplifications within these little blocks now. Now these little blocks though I say they are little blocks they can be pretty big which is why it makes sense to dive deeper into structure such as these which satisfy this property. So, that led us to this statement of the theorem for Jordan canonical form how?  So, that is the entire spectrum is set of all eigenvalues distinct eigenvalues possibly is just a singleton repeated multiple times how many times exactly as many times as the size of the matrix or the dimension of the ambient space on which the operator acts right. So, we are only going to look at such operators and it turns out that this aii minus lambda aii is exactly what we defined as ni and we thereafter saw that this is a nilpotent matrix right nilpotent because if you raise it to a certain power sufficiently large power then this entire matrix ni to some power r i let us say will become exactly the 0 matrix yeah what is the justification well it just stems from this right if you substitute aii here and take aii minus lambda aii then that raise to the power fi is exactly going to give you 0. So, it is only obvious so this nilpotent matrix now if we consider what is its minimal polynomial we argued that the minimal polynomial for this ni is going to be nothing but x to the power what fi right that is exactly what we saw. So, I am just recapitulating what we have seen so far quickly please ask if at any point you seem to have forgotten certain things or how the things fit into the place right. So, this is what we saw. So, this is the minimal polynomial. So, based on this nilpotent now I can get rid of this i index because now I am focusing on any individual block irrespective of whether it is 1 1 2 2 I am only going to be focusing on blocks that look like this. So, let me just get rid of this i index here it is well understood at this point that we have only such operators in our mind and not this general operator, but only such operators for which these conditions are true that is these following conditions are going to hold right make sense right. So, this is what we are going to consider and based on this nilpotent matrix we then said that there is a special choice of basis which gives such operators a very special look or appearance when represented as a matrix and that is exactly the Jordan canonical form we of course did not tell you explicitly what that form was we only made the statement of the Jordan canonical form. So, I will repeat the statement of the Jordan canonical form a little less formally I had stated it the other day I am just going to quickly summarize what it said it said that if you have an operator like so all right. So, of course this d I can replace with n when I am considering the entire operator to act on an n dimensional vector space then it is just n no doubts on this right.  So, when I say this a of course you know that you can always choose an n like this.     So, of course from this a simple calculation leads you to conclude that n is equal to summation m v i i is equal to 1 through k plus k the next conclusion about from what can you draw from here look these are more parts of a basis. So, they must be linearly independent so none of these can be 0. However, the moment you hit this with one more n then they must be 0 because there are basis for the kernel of n right.   So, this is what the statement is very loosely speaking I have given a more formal statement the previous day, but this is what more or less it means before we dive into the proof of this let us try and understand the consequence that is what is so special about such a basis assuming that I agree that this is my ordered basis for the vector space v what would this matrix A or rather first let us see what would this matrix n the matrix representation of n look like under this basis. Once we know what n looks like under this basis we can of course just add lambda i subject to a basis and we get the representation of A. In other words before we even invest our time and efforts behind proving this Jordan canonical form we should at least convince ourselves that it is a desirable form to have right and it is short of a diagonal form this is the best you can do apparently. So, let us test that claim out so n subject to this basis but this is the basis.  That is what that is how you understand the representation of an operator as a matrix its action on members of the basis represented in terms of that same basis these are vectors right. So, it goes all the way up to n action on v k is it not what do you think happens here the first column it is all 0s right. So, the first column is entirely 0 what about the second column this turns out to be the first basis does it not because now minus 1 plus 1. So, this turns out to be 1 because the representation of this this becomes the first basis now the representation of the first basis as a coordinate is just 1 0 0 like this agreed let me just complete the first chain.  So, this next fellow becomes 0 1 0 like so until you arrive at this right what is this in that in the order this is the if you if you look at it from this way 1 2 3 4 like this you have eventually gotten to how many the entry previous to this by action of n on v 1 you have obtained n v 1 which is the entry just preceding this so in terms of the ordering of the basis what is the number of this this is the first basis first element in the basis second element in the basis third element in the basis what is what element is this of the basis m v 1 minus 1 right. So, you have 0 0 everywhere until you arrive at the m v 1 minus 1 position and it will have a 1 there yeah everything else is 0 below it next element is you start with n raise to the m v 2 acting on v 2 and let n act on it again that is going to be 0 because each of these fellows each of these fellows belong to the kernel of n do they not. So, again you have another full column of zeros so what is the size of this fellow by the way so if I am allowed to look at it like so would not you agree that this is m v 1 cross m v 1 yeah. So, m v 1 minus 1 is this but if I am considering this I want to square right if I want to square then I would have to take only this but I am also considering one extra column.  Because the diagonal elements of this have to be 0 this has a very special structure in the sense that the super diagonal the first super diagonal is all once yeah the diagonals are all zeros yeah of the counting is clear how this is going see the first one is 0 the second one is the first vector this one the third one is the second vector the fourth one is the third vector so on till this fellow is what there were how many generated here oh there was m v 1 plus 1. So, m v 1 plus 1 right yeah sorry about that so we didn't keep actually keep count of this.     So, the point I am making is that you have these so this block is of size m v 1 plus 1 times m v 1 plus 1 but the same holds for every other block right every time you start letting n act on one of these sequences generated by individual v k's this is exactly what you are going to get you follow the argument I am just showing it for the first one, but in general or rather in a special case for example just because it gets too messy ok. So, we are taking a special example here let us say n is equal to 7 and k is equal to 2 ok. So, there are two such vectors v 1 and v 2 all right now if the numbers have to add up let us just say that one of them generates of a size m v 1 is equal to what 3 and the other generates m v 2 is equal to 2 ok. So, let us say m v 1 is equal to 3 m v 2 is equal to 2 just taking a special case. So, what happens then 1 0 0 0 0 0 0 then 0 1 0 0 0 0 0 and then finally last term will be 0 0 1 0 0 0 0.  So, when you hit let n act on n squared v 2 it just becomes 0. So, this will again be 0 0 0 0 0 0 0 right. Next when you hit it what do you get you get n squared v 2, but n squared v 2 is which element. So, let us just write down the basis here.  So, this is 7 dimensional n squared vector space you need 7 elements in the basis then n squared v 2 n v 2 and v 2. So, by Jordan's theorem judge by the Jordan form this is apparently a basis. So, so far we have not proved, but let us agree that Jordan's theorem is true Jordan form is valid and this is a basis by our claim for such a matrix like this. So, now this is the action this is the result of action of n on this that leads to this. So, this sorry that leads to 0 this is the result of action of n on this which gives me n cubed v 1 that is the first element. So, the representation of this fellow is what 1 0 0 0 0 0 the representation of this fellow is what 0 1 0 0 0 0. Yeah you get the idea right until this last fellow as a representation 0 0 0 0 0 0 1 clear I hope this is clear or no with this example what we are doing. Yeah. So, not such abstract things anymore just giving you a numerical example to illustrate the case you see these numbers you can play around with I am just choosing a specific case. So, what happens this is 0 next what happens this is 1 2 3 4 5. So, now I have to study the effect on the sixth element 1 2 3 4 5 6. So, I am hitting this with n I get this, but what is this fellow's representation in terms of the basis 1 2 3 4 5. So, in the fifth position I must have a 1 and 0 is elsewhere. So, 0 0 0 0 1 0 0 next 1 similarly will be 0 0 0 0 0 1 0 yeah. So, that is it. So, you agree that this is going to be the representation of n under this basis. So, any nil potent matrix has a basis representation like. So, I can split it up now what is the size of this 4 cross 4 4 is mv 1 plus 1.   So, this is the typical form now I have gotten a representation of n. So, what how does this help in getting a representation of how does this help in getting a representation for A. In other words what would any operator A look like such that the nil potent matrix was basically A minus lambda I. So, I am only looking at operators which have repeated eigenvalues all repeated eigenvalues right whose algebraic multiplicity is equal to the dimension of the space itself. So, that means I have A minus lambda I because after all this is n right that looks in this special form right. If I could have it multiple here I just have 2, but in general I will have k such blocks right. So, I could have split them up like this you know and only these blocks would matter and each of these blocks has a very special structure with only once in the super diagonals and 0s everywhere else. So, now if I wanted the representation of A in terms of this basis what do you think it is going to be just lambda is added to the diagonals is it not yeah because this is an operator this is an operator you can check that phi 1 plus phi 2 represented under a basis is nothing, but phi 1's representation under that basis plus phi 2's representation under that basis is it not phi 1 and phi 2 are linear operators on a vector space. So, if the sum of the operators under a basis is given by the sums of individual because this is after all the sum of the 2 matrices representing the 2 operators and this is the operators you have taken the sum already in the abstract sense and then you are representing it it does not matter. So, similarly here also A is the representation I want to find out I have A minus lambda is representation. So, let me just add lambda is representation to it, but lambda is representation under any basis it does not matter it is an identity map is just going to be the lambda sitting on the diagonals no right. So, therefore, the Jordan form for A would look something like this what is that lambda is on the diagonals and except for certain ones in super diagonals at some special locations not at every super diagonal by the way necessarily yeah because you see the point at which it branches off from one block to another there is a 0 in this super diagonal yeah. So, you will essentially have maybe a even a single to lambda is like this it is possible right. So, let us say you have 1 like this. So, this is basically a 5 cross 5 representation for instance oh not 5 3 4 5 6. So, the 6 cross 6 representation, but in general it could have any arbitrary shape. So, this is always going to be the best you can do because this is not exactly diagonal, but it is as close to diagonal as it gets right. So, that is the reason why we are investing on this Jordan form because once you have gotten it down to this form it is really good because if you think even in terms of the differential equation at least this this and this equation these 3 are decoupled completely right you think about the differential equation represented by this particular row and this particular row and this particular row they are decoupled and every other row it is only coupled with one other variable which you have already solved. So, it is like a triangular solution right you solve for the first one the one that is completely decoupled know its solution because it is after all the first order differential equation plug it back into the one preceding it get that one and so on and then you have solved for this entire block. So, even within those individual aii's look at the big picture now even within those individual aii's you have managed to break it down into simpler blocks and even each of those simpler blocks have the best possible representation you can think of not just any arbitrary triangular representation, but a very special triangular representation where nothing other than the super diagonal the first super diagonal is allowed to be non-zero that too the only once not just any arbitrary number right it is a fantastic result and so far as decoupling goes of course these days people do not invest too much time in studying this because people are more into the numerical part of it. But it is a very useful result because if you are trying to prove something about Eigen values you cannot assume them to be the matrices to be diagonalizable in general. So, the first assumption you make is ok let us start with the Jordan canonical form of this matrix which looks like so and then you test out your hypothesis if you can prove it for the Jordan canonical form it means you have proved everything there was to prove about it right. I will just summarize quickly a couple more things about this before we get into the proof during the next module first. So, this was this was clear right I will retain the proof of the Jordan canonical form I mean the statement of the Jordan canonical form. You see nilpotent matrices can go to zero in any arbitrary way, but not these fellows you take for instance ok let us why am I making like complicated for myself let me take a small size 1 1 0 0 0 0. So, every nilpotent matrix does not have to look like this it is only when we do it in the Jordan canonical form that a nilpotent matrix will look like this. So, let us say this is n what do you think is n squared going to be if we just try it out you will see it is just shifted once one super diagonal up yeah and if you hit it once more it just goes off. So, it is just knocked off one super diagonal at a time. So, it is very clearly visible what is going on here right and that is another great thing about this particular form of a nilpotent matrix just do well to remember that. Now, if I tell you that this a matrix which has all its eigenvalues identical repeated yeah has a representation like this under the Jordan canonical form that is the Jordan basis. So, I can sort of split it up into let us say 3 it could be 5 10 any number I am just considering 3 suppose this is the largest Jordan block. So, each of these by the way starting with n to the n to the m v 1 v 1 through till v 1 this is the Jordan chain or sorry the Jordan block generated by this v 1 this entire thing is the Jordan chain ok.  So, if you look at the largest of those fellows and you look at a minus lambda i represented in this then what do you think is the minimal polynomial given by of a minus lambda i. So, I am putting it to you it is exactly equal to what the largest block size will govern it because every time you are raising this to higher and higher powers that of diagonal that first super diagonal gets pushed one step at a time. So, the largest one will be 0 last all others are blocks have already been 0 by then. So, in fact, the degree of the minimal polynomial of this which is f is determines it determines the size of the largest Jordan block in the entire Jordan chain for lambda for a given eigenvalue I will repeat it once more. We have plenty of numbers one number is the algebraic multiplicity one number is the geometric multiplicity the other number is the multiplicity of that eigenvalue as it appears or multiplicity of its root as it appears in the minimal polynomial which is f. What I am saying now is that when you have the Jordan canonical form that f is telling you something about the Jordan canonical form it is telling you the largest possible Jordan block for the eigenvalue. So, suppose in the characteristic polynomial x minus 2 appears three times that is it is x minus 2 cubed, but in the in the minimal polynomial suppose you have x minus 2 squared what does that mean? It means that the largest Jordan block for 2 is of size 2. However, the algebraic multiplicity is 3. So, the Jordan chain is of size 3, but the largest Jordan block sitting in it is of size 2. So, in that case you can uniquely specify the Jordan canonical form how it will look just from the characteristic polynomial and the minimal polynomial. However, I leave it to you as a thought exercise is this always possible to determine if I just tell you the characteristic polynomial and the minimal polynomial is it always possible for you to uniquely be able to characterize the Jordan form how it is going to look? It is not just increase the number ramp it up let us say the algebraic multiplicity is 5. So, that it is x minus 2 to the let us say the minimal polynomial is what x minus 2 squared right. That means you have the largest size being 2. So, you could have technically a 2 by 2 block sitting here and you could have had 1 by 1 block 1 by 1 block and 1 by 1 block right. This corresponds to a 5 cross 5 matrix in the Jordan canonical because diagonals are special cases of the Jordan canonical form right. So, you have still have a 5 cross 5 on the other end someone else might come up with 2 cross 2 then 2 cross 2. So, 2 3 4 5 and 1. So, these are both going to satisfy the property what that the minimal polynomial is x minus 2 whole squared the characteristic polynomial is x minus 2 to the power 5. But the Jordan forms of course, permutations are allowed, but even if you allow permutations can you make this one look ever like this. These are completely different Jordan forms even though they share the same characteristic and minimal polynomials. So, be very careful just those two numbers are not enough, but suppose I also tell you the geometric multiplicity then can you fix it up because in this case apparently the geometric multiplicity is what the geometric multiplicity is also hiding somewhere in here can you tell me what the geometric multiplicity is in those number of blocks exactly because number of blocks are exactly telling you the dimension of the kernel and the dimension of the kernel is exactly the geometric multiplicity right. So, this one has a geometric multiplicity of 3 whereas, this one has a geometric multiplicity of 4 right. So, apparently these two share the same minimal polynomial the same characteristic polynomial and therefore, the same algebraic multiplicity, but they do not share the same geometric multiplicity again I will not answer this question, but I urge you to think about it if now I next fix up characteristic polynomial minimal polynomial and geometric multiplicity to be the same then must those two matrices with the same eigenvalues have the same Jordan form permutations are allowed permutations are allowed. So, up to a permutation we consider it to be the same Jordan form someone puts that 3 by 3 block here someone puts a 5 by 5 block here someone else decides to put the 5 by 5 block first and the 3 by 3 that is just a reordering of the basis something that you call as a V 1 your friend calls as a V 2 that is permitted that is just a permutation a reordering of the basis. So, up to a permutation are those Jordan forms identical. So, just think about it I will not answer this question, but it is food for thought right. Now with all of that in place I suppose you understand that this Jordan form does give us some very nice properties and structures. So, it is worth our while therefore to dive into a proof of this which is what we are going to do now in the next module.


We're staying with the Global Education Summit in London, where a cold husband made a government, businesses and philanthropists invest in the future of children. The summit, being co-hosted by the British Prime Minister Boris Johnson and his Kenyan counterpart Uhuru Kenyatta, is aiming to raise more than five billion dollars, being raised to support global education efforts. These comes at a time when charities have criticized the British government's decision to make significant aid cuts around the world. This historic GPE replenishment campaign, together with Prime Minister Boris Johnson, and today, as we have just heard, we not only raise our hands in support to education, but we also walk with our heads held high, confident that we will indeed reach our target of raising five billion US dollars for education by 2025. Congratulations to you all. Well done. Thank you very much. Two few girls in school, and there is a gross disparity, a gross disparity in the education of boys and girls, and if you end that injustice and you give every girl in the world the same education as every boy, 12 years of quality education, then you perform the most fantastic benefits for humanity. You lift life expectancy, you live for capital GDP, you deal with infant mortality, and if you educate people properly in the way that they deserve.