Right. So we are back for our lovely coffee chat. I've got my ginger kombucha here. It's absolutely delicious and Yeah, it's a beautiful day over here. How is it you Bryce? It's well spring is always an interesting time of year down here in Georgia We get a lot of tornadoes and all that kind of stuff this time of year But you know the junctions of the seasons are interesting. It's always a very you know We think we I talk a lot about friction and when the nature is is taking its junction If there's always friction in the air, but it's beautiful outside today. Happy st. Patrick's Day to all of our Irish Friends out there funnily enough they say they're more Irish people in America than there are in Ireland and according to my DNA That I did before and it was bad. I have absolutely zero Irish in me none whatsoever Which I was actually surprised about but happy st. Patrick's Day to all of our Irish friends out there Yeah, happy Patrick's Day. They'll be celebrating that install. It's a beautiful day in spring The cats are all on the go. The wildlife's all on the go. It's really really lovely day to day So I'm feeling tip-topper and we're going to be discussing some interest and stuff because you and I We've been talking about so many different things for months and months now and about really feeling ready to sort of move off Um, not that it hasn't been a great experience But take the focus of what's wrong and put it on what we can do positively And certainly I've been really looking at where I'm going with my channel and moving forward a lot of my focus I'm still going to be having interesting conversations with all sorts of different people But a lot of my focus is going to be how people can practically at a practical level Set their lives up for success. So that's their physical body Their emotional body their spiritual body because obviously, you know, I know when everyone knows they all link together And one of the interesting things came up about when we were just chatting was about self-integrity, wasn't it? It's a starting point. Yeah, absolutely being integral to yourself You know, and we um, I was actually when we first started recording I was thinking about someone said once and I thought it was brilliant I'm going to paraphrase, you know, we all have these dreams these things that we want to do in our life and um, and so we have these fantasies about What we love and I think we have these dreams for a reason that's we're all different We all have something we want to do, but we don't get from point a to point b Like that we have to take steps to get in between where we are now and where that dream is And so every day if there if you like we were talking about if you want to own an animal sanctuary if you want to You know have a rehabilitation center for humans You're not going to go from being just an you know an average person with a dream to then all of a sudden having that There has to be steps taken in between to get you to that point And so every day making a conscious decision to do something It doesn't have to be the big thing that changes everything But something little to help you get too closer to that point. I heard someone say once um Do something today that yourself tomorrow will thank you for That's such a good saying and it's so important because we all Go through different stages of our lives and we're all going to have ups and downs and periods where for example on a physical level You know, I love the fact that louise haze sort of says if you're going to spring queen your house You know, you've got to get around every room But it doesn't matter what room you started Unless you're having people a food dinner that night and then you might want to start in the dining room And that's a bit like you know, stir fast So we've got house our physical body in a physical body You can break down into lots of different exercise to keep it simple Water food and nutrition and exercise and then you've got your mental body So what are you doing to keep yourself positive there? What are you doing to control your thoughts emotions? And then you've got your spiritual side There's so many different areas to this And all of us will have a different starting point because we'll all have something that's a priority in life So like for me at the moment I'm I'm really good. I love my flasker energetic water bottles And I'm really into I have been for a long while obviously my herbs my supplements my really good food I love cooking water quality, etc But what I've really let slip Is my stretching so I do a lot of walking a movement because that's absolutely crucial to me I just really really need that and I've set my life up to that every day includes a lot of that But what I haven't done much my daughters in audience Is the stretching so now so everyone's got something once I'm assuming stretching isn't an issue for you You're going to have different priorities Well, it's funny though because when you do ashtanga yoga, you'll you'll you realize how sore you get from stretching I've been sore for like 15 years. That's how That's how intense that can be but it's so it is so important It's so funny because when we talk about doing things every day to get you to a certain point I actually just had a conversation with someone for 15 years now I've been getting up at the crack of dawn and and doing this crazy practice And I and I was on the phone with my friend. We were talking about this group. We're going to be working through I'm like Not once in those 15 years.  I might not once have I ever thought that because that's what that's what a discipline is You do it because it serves you and even though you four o'clock in the morning for me I don't want to necessarily you're tight In the early morning hours your body is so tight like it's not there's more of a vulnerability and for 15 years It hasn't been actually it hasn't been pleasurable. I mean I've enjoyed it at times But but it's because it's what sets me up for my day like any time And I think that's kind of the first step regardless of whether it's getting up in the morning and taking a walk or meditating or Even something simple as making up your bed the first thing you get up It will set your mind into a productive routine And I think one of the things that I've noticed and I think this is really big in the western world I know it's probably just a human trait anyway, but I see it more in the western world. Oh look at it Sorry, I love it. Um is we have this idea that being uncomfortable is wrong And being uncomfortable is where magic happens Yeah And so part of life, isn't it rice? It's part of life And I think you said something so important there about do something today that your tomorrow will thank you for and that is so important because A lot of us a lot of us and I know every single person's um situation is different this little mitzy um, a lot of us uh, are lucky enough to have a lot of choices In the people, you know, just anyone who's got a chance to sit down and watch videos like this Is normally in a pretty good place in their life in terms of compared to a lot of people globally where they're very much in survival mode And consistency is really key and and there's a lot of talk about self love But I find it really fascinating and my dad always used to say this to me You know when he was growing up they didn't give their kid, you know, they didn't have Chris and sweets and they had a few but you know, it was everything was rationed and if you were good You've got an orange or an apple and now we've got it into a culture that we give our children a really sugary sweet or drink as a treat and it's like Again, anyone who's watching this knows that the whole world is upside down. We've been tricked into Really doing all sorts of things that are really bad for us physically and mentally But when you think just about that, why do we give our most precious precious beings in the whole world our children? Something that's really bad for their health and call it a treat Right, right. That actually drives me crazy. I and maybe just being you know, being born in the early 80s Like I thought I was laugh and say I was born into the jazzercise low fat diet age I remember my mother doing Richard Simmons like the, you know, jazzercise stuff and and we've got and as I've gotten older It's like We treat food. We treat these things as treats or punishment treats or punishment and before we were filming Catherine You said something that I actually think the as well like every day in my life is a good day I've set myself up not just look, you know, that song everybody's working through the weekend. Well, that's a pretty sad life If Monday through Friday, you're miserable and you got two days a week that you're actually Looking forward to then that's kind of a shit life in my opinion And and so you have that power though That's the plot twist is that you have the power to control your To set up your life in the way that you want to move forward with your life And um, and so and that's how my life is like I enjoy every single day like every single day I enjoy it and and it's because it's Every day i'm happy, you know, because it's i've set it up that way and it's taken a long time It's taken many years to get to that point. Um You know getting up at two o'clock in the morning in india was not fun But i'm at that point now where i've had all this experience is to bring me here and so When we have to be uncomfortable we have to embrace being uncomfortable in order to change And um a lot of people, you know, they want to have the specific life but they're not willing to take those steps to get there and That's but that's your superpower is when you can actually put yourself through those steps to create that life that you want to live I hope that makes sense Yeah, it makes massive sense and i'm in exactly the sense of my whole life I'm just hold on to things because my internet connection cables so dodgy here. Oh, no mitzi darling We'll be cut off again for us and i've been cut off for many a video I need to get a better plug in connection for my computer. That's not so fragile But so classic example my whole life i've had a lot of criticism for everyone saying Oh because you've got so many animals you can't be spontaneous and just disappear off whenever you want to And i'm like no i can't but the gift of what the animals give me it's such brilliant physical health Rain or shine snow wind All of the family members i mean my children are the fittest children ever because right since they've been born They've been had movement and being out of nature has been a huge part of their life Um, so don't get me wrong again. There are times i'm not It's really cold and windy and wet and i don't want to get up and do them But the benefits there's always a sort of payoff the benefits of what i get from sharing my life with the animals but equally What i think is really important the message i want to get across today when we're talking about self integrity The first step to me is recognizing What you're happy with and what you want to change not judging yourself because you know The whole point as we learned by our mistakes as you and i said, you know 20 years ago We weren't in the situation we're in now I have now got two grown up children that that can get around themselves and can drive and are working and Or studying and whatever so i'm not in the same place as i was when i had two toddlers When my life had different pros and cons to it So i think being really gentle to yourself a bit having targets of Or golds or whatever you want to call it is so important. So okay, this is what i'm at now And recognizing it's like if you've got a drink problem There's no point in your family trying to send you along to get help You've got to accept that you've got a drink problem and if you accept that so being really honest with ourselves and accepting What areas of my life do i want to improve on? And then having funds setting in place things because we're not going to be able to do it all at once But wouldn't it be boring if we could? Yeah, it would be it would be and i will i mean So like i i'm the only female in the state of georgia that's authorized to teach what i teach And um to me that's a really big accomplishment that i made for myself And i remember when the possibility of that coming it overwhelmed me when i realized that when the possibility of going back and forth and and um, of course when we think about the big Picture of what we're we're working towards and if we just cling to that it can be so that self being self gentle And i remember thinking okay I just need to take this one day at a time while i'm here in india one practice at a time if it happens it happens And then it happened and i think if i had focused on that that um It i would have self sabotaged in a sense where it wouldn't have happened And i do think that that being gentle with yourself and really breathing through things and allowing things to come that you worked for You know it's not that that things just fall in your lap because they do no you usually have worked your life You worked for something and therefore you need to be gentle with yourself instead of like self-sab which something I think a lot of people do is self. I know i'm guilty of that from time to time to self-sabotage And um and yeah in different phases of your life are going to offer you different Different different things. I mean i never i think we've talked about this katherin.  I went to the vibrum almost every night. I had a lot of fun But i'm those days are over and i don't and that was a different time And and um and so yeah, it is going to so you I also heard someone say this too Don't ever compare your chapter one to somebody else's chapter 10 yes That's really important because you know i i have been quite a competitive person and it's really great when you then Have fun doing something that you've got no expectation You're going to be good at so i think i've mentioned before my neighbor and i who's hysterical We decided we were going to do this thing called couch to 5k Which is building yourself up to running 5k now to most people most people come on 5k But i've just never been a runner. I just don't enjoy running But i thought i thought i thought to do myself a challenge so i'll do that but i never it was such fun doing it Because i i never was trying to be a good runner, you know, i can walk for miles.  Just so they were having as much fun with it laughing with me not at me And that's that is such an important lesson the dropping of expectation Because we will always put more expectation on ourselves than anybody else will and it's i you know, i uh I was telling a class on sunday I was talking about soreness in the body and how even if you're sore you still have to practice And I told the story there was this one time I was in philadelphia used to fight to philadelphia to practice with my teacher david greek and in philadelphia Of course all the buildings are really old So his studio was like shawla was way up on like the third floor And these old buildings have very steep narrow stairs And it was the last day that i was there with him for this time period before i flew back to atlanta And I remember standing at the bottom of the stairs and my body was so effing sore I didn't know if I was going to be able to get up the stairs Like it was literally like I don't know and I got up there and I started Ended up being one of the best practices I ever had because I didn't have any expectations I had no expectations of what was going to happen that day on the mat because I was sore And so that is such a good lesson because when you drop those expectations when you take the ego out of it Magic happens joy happens and another another thing people say is comparison is the thief of joy Yeah, it really is it so is And everyone can do something so you know, I'd like to set up on a challenge and we're we're gonna be talking about this Lots lots more because the great thing is Isn't it brilliant that there's not a single person that's watching this I I can't imagine it this would ever happen that hasn't got something they'd like to change or improve or You know try something new and we're all going to have different things but all of us will have similar but You know benefits of example when we were speaking to shanty about the meditation Literally you can start with three minutes You can literally start with three minutes and even if you've got a newborn baby Or you've got whatever your situation is everyone can find three minutes even if it's when you're sitting on the toilet Well, that's what I said like if you're if you're looking for something to like Jump start a new change and you don't you're not someone who makes your bed up Just start making your bed up for a week and see see what it does to you You know get an hour early and just go walk around the block You don't have to do something super crazy that you know Just just to try drinking if you're not a water drinker try drinking a liter of water a day. See what happens yeah There's so many little things you can do and They add up, you know, it's it's like uh Back before cell phones. We had our telephone books, you know And the papers and telephone books were like bible paper. They were really thin You know and if one paper alone looks like nothing But if every day or every week you added another little little thing you did by the end of the year Look how big of a change that is that you should see you like that whole telephone book adds up You know and so and this is this is the true. This is the world. I believe this is the world We're walking into we can't sit around and wait for something to somebody do something for us You know, you can't you feel frustrated and all that wasted energy.  I'm gonna think about me and my family and my life and now What do I want to do? Should we set everyone just like your love challenge, which is going around to everyone? I really love that. Should we set everyone who's listening anyone who is drawn to To have to set yourself One change that you're gonna implement and you're gonna stick to for the next 30 days Oh, I love that in the comments below and we do not mind at all and I hope you don't mind at all How big or small that change is it literally can be the first thing I'm gonna do when I get up in the morning Is have a glass of water instead of coffee or it could be Something really amazing like you're going to train for marathon or something. It doesn't matter what it is I'll give you one something. I started this week that I just started that's oil pulling I've um, I did a show with shanti about the are you vatic and I've always done tongue scraping But I've never done oil pulling even though my best friend's an oil puller and after I did that show with shanti I was like I'm gonna try this and so I've been oil pulling every morning It's just an extra 10 minutes out of my morning But it's actually made me feel a lot better because it pulls the oil from the digestive system I don't know if you guys are familiar with oil pulling, but It's something I've wanted to do for ages.  Don't swallow it for I think you can start at 10 minutes You can build up to 20 minutes and then you spit the oil out then you brush your teeth What it does but the oil does when you sleep at night all of the bacteria and your body comes up through your mouth And so But the oil does especially fatty oil like coconut oil is it will pull toxins out of your mouth and then you spit it out and so it starts And I've noticed a huge difference in the way that my whole over my not just your oral health because I was always very very Very clean, but just the way that my whole it whitens your teeth. It's supposed to help with headaches If you drink a lot at night, it's supposed to allegedly help with not this is alleged help with uh hangovers Because it This is gonna be mine as well a tablespoon is basically what you um What you hold on one second guys, I'll get I ordered it specifically from an Ayurvedic shop. Let me get a hold on one second And while she's doing that This is a really good idea because this is something I've been thinking about doing for ages because I absolutely love I I'm gonna tell you in a minute the other things they use coconut oil for But I'm going to try this because this is something I've wanted for ages and I say and I'm not being vain here saying it But all everyone who says I'm 54 And everyone says I've got quite good skin for 54 year old Um considering I'm out in the winter in the rain all day, but all I cleanse my face with is coconut oil Yeah, so I just use normal coconut oil So rub it in even when I make up remover and wipe it off with a hot flan and then everything and I'll tell you what one There's no nasty chemicals in it. It's way cheaper than buying some expensive face cream and it makes your skin feel amazing part of the cast Do like licking you afterwards so Well, I ordered this it's called guru nanda and you can find um that likes let me actually turn my law for a second You can see um, this is from an Ayurvedic shop here in the United States Now you can find Ayurvedic shops anywhere if you just uh google oil pulling Um any country your end just google oil pulling and I got this specifically now you can get you don't have to get something fancy You can just use coconut oil or avocado oil Whatever because it does it is a very weird sensation because you don't want to swallow it because if you swallow it You're swallowing all of your toxins. You want to keep it in your mouth? But this so I fill it out that it comes with a little cap Uh to 10 milliliters which is just right here So it's a very little bit it will get bigger in your mouth as it starts to pull all those back all that bacteria Um, but yeah, it's it's a see natural teeth white it whitens your teeth um It just it's so it's and it's it's literally guys like this is something that I just started started doing this this week um I'm gonna start I've got the solid coconut oil But that's great because the solid coconut oil isn't fractured and it was soon mailed to my mouth anyway And you can put coconut I put coconut oil in my hair from time to time It makes it stop and um, and it's literally like I would if I were you guys I didn't do this I probably should have done this take a picture of your teeth and then 30 days later take a picture of your teeth so yes difference and I'm gonna do that So that's mine As well because I I had a couple things one, but that's really really good Um, I am actually going to be starting next week I'm I'm taking quite a few days off actually and got some tricks with my daughter and some stuff with you mitzvah She's sitting here right here everyone. She's so cute She's doing really well And um, and then when I get back the following week I'm going to be starting my sort of series of you know talking about a lot of these things and morning routines is So important isn't it wise morning routine? Yeah the mornings. I don't do my full morning routine I feel like I'm lost all day. I feel yeah me and you know, it's it's um the morning I was telling Catherine And I got I cleaned my bathroom at five o'clock this morning before I started That was what was so funny so to die It was hysterical That morning comes the best time It's the quiet time and and that might be something for someone too if you're if you're not used to getting up early In um in the are you vatic system from 2 a.m. To 6 a.m. Is the vata time of day It's actually easier to wake up between two and six than after six is us cop a time of day And it's so quiet they call the time of god It's brahma mortis the time of god. It's so quiet in the world That it's amazing the peace you have when you're doing something at that time because everything else is just so I know runners of course here in georgia people in the summertime Especially people have to get up super early to run because it's too hot otherwise And they talk about that here that at 4 4 35 o'clock in the morning running down the streets of Atlanta And it's just quiet It's just so it No one's up and it's just you and god and your breath and your heart beating And it's just such a very special magical time. And so that might be a challenge for people watching to get up an hour earlier Or go to bed an hour earlier, which is another brilliant habit to get in so I mean, there's so many different things have a celery juice um gratitude journal meditation go back some from meditation videos Manifesting start to do some manifesting on doing my things. There's so many things it can be at the end thing it can be Groom your dog or your cat Consistently every day for a month or something like that. Okay. It doesn't matter what it is But can you anyone who's happy to share please share below because you'll inspire other people as well And you can let us know how you're getting on and then we will because we can just remind everyone how it's going With with us and asking everyone else from the next few weeks I'm really excited about that that's great Exactly. Oh, that's so funny. Yeah. Oh my goodness bullion. So anything else that you want to leave us with Uh, I well, you know and we've talked about exercising and your animals with the veterinarian in uh, India that helps us with our dog rescue He has a sign in his clinic that says if you're overweight it means your dog isn't getting enough exercise So that I love that sign. So if that is one of your changes might just be extra spend time with your dog or You know out walking in and uh, you know, make that a real big thing your dog will appreciate it You'll you'll you'll love that time and that fresh air with your animals that could be something too. So Yeah, whatever you want to do It's it's so so true and um, you know So pick something today Don't wait till tomorrow because that we us humans are very good at that One thing today write it down somewhere really important to write it down somewhere Whether it's a post-it note a note on your phone You know, whatever it is because when you write it down, you're making a commitment to yourself And you'll remember what it is And have fun doing it because each time you're doing it Remind yourself that your tomorrow's body or mind or person will thank you for it. Absolutely Absolutely. Thank you so much for watching everyone and I will be seeing twice again soon because we're just about to chat to the amazing Turn the page which you need. Yep. Absolutely Bye guys


Now we will begin with our study of first class of optimization problems which is optimization of a function over an open set. So what this means is that the feasible region is an open set and the function objective function or precisely objective function, we will assume this to be a differentiable function. Now since we are going to talk about differentiable functions, I need to tell you a little bit about my notation for derivatives, second derivatives and so on. So now for that let f be a function from Rn to R. So any x in Rn, I will write its, I will denote it in this sort of way, x will be denoted with its coordinates as x1 till xn. So this is, so every vector x in Rn, this way it will be interpreted as a column vector. When I write something like fx evaluated at xat, what this means is this is the derivative of f at xat. So the small x here, the small x in this notation just simply says that derivative is with respect to x. So this will be important when we are talking about functions that are functions of more than one variable. So we may want to take derivative only with respect to one of the variables. So this just stands for derivative with respect to x. Another notation for the same thing is evaluated at xat or now the important thing to note is that this quantity f sub f x at xat, this is actually a row vector and it is defined in this way. You consider the partial derivatives of f with respect to each of the components of x. So you evaluate them into a row vector and evaluate all of these at xat. So f sub x evaluated at xat is this row vector of this thing. There is a related quantity which is denoted in this sort of way or to be more explicit about what we are differentiating with respect to that is denoted this way and that is simply the transpose of this derivative. This thing is called the gradient of f at xat. And once again the small x here simply denotes that the gradient is with respect to the variable x. Suppose if I have a function f which is a function from rn cross rm to r. So my variable x, the x variable lives in rn and the y variable lives in rm. Then if I write something like this f sub x, if I write something like this f sub x at xat, yat, this here is, can someone tell me is this a row vector or a column vector? It is a row vector with how many components? n component, because that is the number of components. I am taking derivative with respect to x here and x has n component. So this is a row vector of this particular thing also denoted by. Now if f is, so in both of these cases here in this case as well as in the earlier case, in both of these cases f was a function that mapped to r. So f itself did not have multiple components, it has just one component. So f is a scalar valued function. So then now if f is vector valued, let me just write this for your reference here. So this is the case of a scalar valued function. If f is a vector valued function then say we have, suppose f is a function from rn to some rm and what we will do is we will think of this every output of this vector, every point in the image of this of f is itself a column vector. So f should be thought of like this, f at a point x is equal to this kind of column vector f1 of x, f2 of x, dot, dot, dot, fm of x, it has m columns. Now if I want to, if I take the derivative of f with respect to x, what I need to do is take the derivative of each of these components with respect to it. So this evaluated at x hat now becomes, so every row, every component of f will have a derivative and will, its derivative would be a row vector like this. And so what you are going to get now is row vectors of that one below the other, so the whole thing would become a matrix. So this would now, this would become, so that is your, this is also, there are multiple names for this, you can call, this is called the derivative of f at x hat, that is one of the names. Another name for it is that is called the Jacobian at x hat. Now we can also write another higher order derivative, so this is what is called the Hessian. So the Hessian is simply this. So if I take the derivative of the derivative, but the derivative of the derivative, I need to take, when I am taking the derivative of the derivative, the inner thing has, so let me put it like this, I am taking the derivative of the gradient and evaluating that at x hat. So this is simply another term for the same thing, another way of writing the same thing would be, this is the whole thing evaluated at x hat. So this will again, because the gradient is a column vector, I can now take the derivative of that and that then will give me a, again a matrix, matrix that looks like this, all of these evaluated at x hat. Another notation for the same thing is simply del square evaluated at x hat, alright. So along with derivatives, we also need an important theorem that pertains to derivatives, of different derivatives and approximations of differentiable functions. So this theorem is, it could be known to you in some or the other form probably before this, this is Taylor's theorem. Taylor's theorem basically says that if you have a differentiable function and if you look at the value of the function close to, take a reference point and look at the value of the function very close to that reference point. So what Taylor's theorem is basically saying is that close to that reference point, the value of the function is very well approximated by a linear function that you can construct using the value of the function at the point and the derivative of the function. So what does it mean by well approximated and what is the sense of the approximation, that is what is made precise by Taylor's theorem, okay. And the main idea is basically that when you are close, if your function is differentiable, then and you want to look at how the function behaves near a point, you have some reference point and you want to know, well near it, how does the function behave, well it tells you that a linear approximation is, it can be obtained and it tells you what that approximation is, it tells you in a very precise sense. So the theorem is the following, so let f form Rn to R be a differentiable, let A be a point in Rn, so this is my reference point, this here, this you can, this is my reference point. And what I want to know is how does the function behave at another point x, okay. Let it say, then the theorem says there exists, there exists this sort of function h such that if you take f of x, then that value of the function at x that other point x is given by this, given as f of A plus f of A plus just change my notation, I want to instead of using the point, instead of denoting this by x, let me denote this by a y, okay. So my reference point is A and the other point at which I want to evaluate the function, let us call that y, so f of y is equal to f of A plus what is this vector now, this is a row vector, row vector which is the derivative of f with respect to x evaluated at A, okay. So that transpose y minus A plus another function h of y times y minus A where and this is the important part where h of y tends to 0 as y tends to A, okay. So now I want you to appreciate what this sort, what this theorem is actually saying and it will become evident as we go into the next main result also. But remember just for clarity, I want you to see what this is saying. See as y tends to A, of course it is true that f of y and f of A will come close to each other. As y tends to A, f of y will approach f of A, so that is not saying anything here, okay. What this theorem is saying is that as y tends to A, okay, if you look at f of y minus f of A, f of y minus f of A divide that whole thing by y minus A, then that starts behaving more and more like fx of A. So what this theorem is effectively saying is that if you look at the, it is of course true that f as y tends to A, as y tends to A, f of y tends to f of A. So what this theorem is actually telling you is how fast does f of y tend to f of A as y tends to A. So what this is saying is it is telling you, telling you somehow a measure on this difference, it is telling you that this difference f of y minus f of A divided by y minus A, this is something, this is equal to fx of A plus h of y, where h of y is a quantity that will become smaller and smaller, this will become small as y tends to A, it will become close to 0 as y tends to A, is this clear? So this is what the theorem is actually telling you. So it is not only telling you that the function values near A are close to f of A, that we already know, but it is also telling you how fast they approach f of A, okay. They approach f of A at a rate that is linear in y minus A, okay and the constant of linearity there is roughly equal to fx of A, which is fx of A plus this h of y, where h of y becomes smaller and smaller as you come close to. So all of optimization is about these, about how fast different quantities converge, okay. The relative rates at which different quantities converge is something that we keep exploiting all the time in optimization. So that is why an estimate like this one which comes from Taylor's theorem is you can say cornerstone of optimization, okay.


Hello, everyone. Welcome to another capsule of international relations for the Shankar AAS Academy. Today, we will discuss the group of 20 summit, which was held in Rome last two days, 30th and 31st of October. Since Prime Minister Narendra Modi is personally attending this meeting, it attracted more than the usual attention in India. Not only that, this meeting has been held at a very critical time in the history of the world, just as G20 was formed. G20 was formed after 2007-2008 economic crisis, to deal with the very grave situation that arose in the world economy in that particular time. And since then, it has been meeting every year to review the world situation, and they may have applied some correctives to some routine decisions and so on. The difference between G20 and, say, the Security Council is that in G20, everybody is equal, nobody has a veto path. And therefore, G20 is emerging as some kind of an alternative, an economic alternative to the Security Council, because all the important countries are present there, but they are all on equal status. And also, these 20 countries represent 80% of global GDP, 75% of global trade, and 60% of the population. So it virtually represents the whole world in terms of GDP, in terms of trade, and in terms of the population. So the present situation, first, of course, the pandemic, second, the world health, pandemic is a world health crisis, and also world economic crisis following the pandemic. And inability of the United Nations to act on it, because of China's role as a permanent member, who vetoed any suggestion that the Security Council should meet. So in these three circumstances, the meeting of the G20 assumed tremendous amount of importance. And when you look at the result, and of course, I should have mentioned climate change. So this is actually the climate change summit started today. So this took place just before the COP26, Conference of Parties of the Framework Convention on Climate Change, COP26, it is called. And it has a summit segment, two days, the heads of states are meeting. So in that context, G20 actually became, if we look at the outcome, we look like a rehearsal of COP26. Because most of the time of G20 meeting was devoted to the climate change issue. So virtually every shade of opinion in the United Nations was present there. And therefore, the discussion took place basically to prepare for the COP26. And that is the other fact that was the most significant part of G20 meeting. It also dealt with some other issues like global taxation and private public participation, etc. But even though we don't have all the details of what happened with the G20, the most prominent part of the decision making there was on climate change. Because climate change is on the way to changing tracks again. The climate change strategy was developed in 1992 in Rio de Janeiro. Then it changed in 2015 in the Paris Agreement. And now in Glasgow, it is supposed to take another change. We'll come to that later. But Italy, which chaired the summit, Italian Prime Minister, said that he was satisfied with the outcome of G20. But then immediately he added that this is only a start. We must not forget that. We must remember that it is only a start. And taking the decisions or the positions taken by the G20, which of course will go now to the COP26 where everybody will be there. The main effort of the United States and partly China was to abandon the Paris formula. Paris formula, as you know, is to or was to make voluntary reduction in greenhouse gases. So every country says how much they can reduce. And then you put it all together. And the temperature should not go up beyond two degrees Celsius. And that was the objective of the Paris Agreement. Now people say that even two degrees Celsius is too much. It should be 1.5 degrees Celsius. So one decision, technical decisions, I will say that G20 took was that the effort should be to make sure, commit ourselves to making sure that the global warming should not exceed 1.5 degrees Celsius. This is very hard to accomplish. And therefore it is only an objective. That is, all our efforts in future should be to making sure that the global temperature should not go beyond 1.5 degrees Celsius. And that is a wish, whether it can happen. The suspicion is that it may not happen. But the more pressing thing that the suppose 1.5 is already an objective. But what the United States wanted was to forget about voluntary reduction of emissions etc. And go straight forward in net zero carbon situation. When can you do a net carbon situation? And United States already said by 2030 they will be able to do that. China has said that 2060 they will be able to do that. And several others have fixed different years. And India is under tremendous pressure like other developing countries to declare a year because that means by that year our consumption of energy should peak and then start reducing. And that is when it becomes a zero carbon, net zero carbon situation. And so the push in COP26 is to make everybody declare this. And the leadership of the objection to this or a different approach to this is India. And the arguments that India is making are the same old arguments we have been making before Rio de Janeiro. And all through these negotiations we have been taking a fundamental position that developing countries need energy to develop. And therefore it is unfair and just for developing countries to ask to reduce greenhouse gas emissions because their emissions are not very high if you take per capita. An average Indian emission is one fourth of an average American emission. So this is our argument we have been saying is all through. And therefore if we have to to get used environment friendly technology we need the technology and the money. If we don't do that we'll not be able to reduce our greenhouse gas emissions. And nor can we declare a year as net carbon year, net zero. And so this is the argument which India put forward India as usual leading the developing countries of the world in this argument as against the developed countries. And that division has been existing also in Rio we came to some kind of a compromise. But the developed countries walked out of it when they refused to sign Kyoto. And so we got Paris and now they are leaving out Paris also and say now we started a new a Glasgow formula. So what happened in the G20 was since everybody their all our opinions are reflected that's what will probably happen in COP2. They said that we must have a 1.5 degrees Celsius only below that. And secondly we should strive not to they're not willing to designate a year. They're saying they should strive to find a year in the middle of the century. People are saying 2050, 2016. So all countries must strive to accommodate and find a date which is suitable for them and declare themselves a net carbon net zero emission country. And so that is a year as we can go to but I don't know whether in COP26 they will change it any further. So the position of the developing countries which India is championing and so the developing country's viewpoint was put forward by India and that has been registered. So whatever discussion that will take place in COP26. And therefore the position that developing countries particularly India has put forward is that we must concentrate on the climate goals, what these goals are and then try to achieve it through financing and developing of green energy for the developing countries. Because developing countries are bound to use fossil fuels particularly coal. So one of the movements is to avoid using a coal altogether. As you know India has the largest deposits of coal and we are very much dependent on it. So unless we develop alternate strategies for energy in a big way we simply cannot stop using coal. So they are using some techniques like not allowing countries to know the countries which develop industries etc on the basis of coal they discourage it. The developed countries will not invest in coal industry etc and China and India are being accused of using too much of coal. So the obligations of the developed countries have been highlighted, financing for environment friendly technology and the cost of developing green energy. And again the argument that we used was the very same one and I used to be the chief negotiator in Berlin in 1995. The speeches I used to make there were the same speeches that have been made today. Like one of the things that we say is that we have to cut down wasteful consumption. See the whole world has been depleted of many of its resources because nobody bothered about it during the industrial revolution. Everybody was consuming those rich countries were consuming all the energy and now that the world has been deprived of it and there is this great calamity comes. They are saying developing countries should not develop or you should not use coal, you should not use fuels and how can they develop? So this is the dilemma. So the call was for cutting down wasteful consumption, conspicuous consumption. The phrase used is what the developed countries are using is what is called luxury emissions while what developing countries need is survival emissions. So the same argument which I used to make they are still making. So on energy climate instead of focusing only on climate goals the situations of developing countries in various needs of the developing countries must be focused. So that has been presented. How it will be accepted in Glasgow we don't know. Then G20 identified sustainable and responsible consumption and production. So the developed countries also seem to have agreed to this along with provision of finance and technology as critical enablers of achieving climate goals. So this is the same old point that climate goals mean you must enable developing countries to grow. For that developed countries have to reduce emissions so that there is some more space for developing countries to emit greenhouse gases for their own development. And also it was pointed out and Prime Minister Modi himself spoke about sustainable lifestyles. The amount of machines they use, the amount of energy they consume every day can be reduced. The number of air conditions could be reduced, number of cars could be produced. So he stressed the sustainable lifestyles and they pointed out also that this is one of the sustainable development goals of the United Nations adopted by the entire UN. So this has to be done. But of course developed countries will never listen to that because that means their lifestyles have to change. So this energy intensive lifestyle of the developed countries was questioned. And they should invest in the developing countries where developing countries are improving their livelihoods. In the developing countries it is the livelihoods that have been improved but in the developed countries it is a luxury. And so all these marginal people, marginal farmers etc should be helped so that living livelihoods are not destroyed either by the pandemic or by climate change. So G20 talked about developing, developed countries should not shift the goalposts. Every time they say in 92 they said something, but in 15 they said something and now they are shifting the goalpost an expression relating to football. You play in a ground and then you get accustomed to a legal position and then you suddenly find when you go to the ground the goalposts have been shifted and how do you play there? And so this was said that we should do more for the planet and put the money where their mouths are the developed countries. So meaningful and effective action has been repeated in many places in the declaration of G20 but there is no concrete action. There has been no agreement on concrete action because emission have to be controlled and it cannot be controlled only by the developing countries. So there has been a suggestion that coal should be dispensed with which of course many developing countries will not accept so they are saying that they will not finance coal projects for power generation. You use nuclear or you use wind energy or solar energy etc. So if you ask for investments in coal-fired power generation the developed countries will not cooperate. This is something we know but we have to carry on and so at the end of it they have said that this is the last chance. Glasgow is the last chance for humanity to save itself from damnation and that is the conclusion and then they have said about other things like private public partner should be encouraged and no time bound decision on climate change, no commitment to ending domestic coal consumption. So these are some of the and these were pushed by India for safeguarding the interests of developing countries. So this will be now a traditional role right from the beginning. So in the Paris Agreement there was a commitment to provide $100 billion to the developing countries. It was not realized. So they recommitted themselves to producing this $100 billion nobody knows who will pay it but there is a commitment that that commitment was definitely to be renewed and G20 recommended that. What will happen in COP26 we don't know but this is an old commitment. It has not been delivered so it is natural that they should be accepted and then on COVID-19 they took some good decisions about vaccine production greater vaccine equality because in many countries there are problems even we have a problem about one of our vaccines not being recognized. So the G20 asked WHO to recognize all possible vaccines and of course they cannot do it without trials and so on but they asked WHO to recognize more vaccines and more international public and private funding not only for vaccines but also for green projects. So there was but as I earlier mentioned there is a compromise in the G20 as against people who want countries to be identified I mean years to be identified as net zero. Now what the G20 says is that stress the key relevance of achieving global net zero on carbon emissions around mid-section. You know in the UN always you find a compromise language which is good for everybody. So we have not committed to a day or a year but we have said which is important to find a day and an indication that that could be in the middle of the century which can be 2050, can be 2060, even 2070 you can consider it middle of the century. So that is a big compromise of G20 between developed and developing countries and recognition of all whites etc and India's position has not changed as I said from the beginning. So we are asking for climate justice so we are willing to reduce emissions as well as possible that we are committed to that but any kind of forced fixing of date is not acceptable to us. India does not have adequate techniques in fact another issue this was new that India raised is a clean energy we can produce maybe but it's not enough that you produce clean energy we must have the grit to hold it you know what I mean because they if you provide green energy and if you use it immediately that's not good for the future. So large amounts of clean energy even if you produce it we don't have a grid and therefore more money will have to be spent on the grid stability. So clean energy is not as deep as they think because the creation of grids will cost money and that has also been highlighted. So the United Nations Secretary General at the end of the G20 meeting expressed his disappointment that no decision was taken about a particular year when it will become when the world will become net zero year but then he said my wish has not been buried and I hope that this will be further discussed in COP26 which has just happened today. So these are the basic climate change decisions or recommendations that G20 has made then there are some other subjects which would have been very important to keep climate change was not in the focus and that is about money laundering you know you may know that there is an organization called Financial Action Task Force FATF this was established in 1989 it's a governmental group to combat money laundering and terrorist financing and this has been watching it and reporting to the world. So as you know you might have heard that Pakistan is now there is a white list a gray list and a black list so the black list of countries are fully accountable they are responsible for many of these terrorists financing and but Pakistan is not in the black category because they have been fighting it and so they came into the gray category and then now they are trying to be in the white category means they are not doing counter money laundering or terrorist financing so the G20 decided to strengthen this and also to make sure that the international financial system should not be challenged by these countries and the latest in the list is Turkey has been recently added to the gray list because Turkey is supposed to have that money laundering so that is another thing that they decided that enhanced confidence in the digital environment because there is always this threat of cyber crimes and cyber attacks cyber warfare etc etc and also by sheer default sometimes serious things can happen you know a virus can get into your system and destroy the whole system so it has become it becomes a warfare if you deliberately do it but sometimes it can happen also by mistake and so enhanced confidence in the digital environment because it has several elements I'm not going to all those details this is one of the things that they have supported then zero tolerance for corruption corruption of course is a is a major disease of the whole world economy and in Vienna when I was there in 2003 the United Nations formulated a convention against corruption a UN convention against corruption and that was signed by many countries etc but still corruption is rampant in particularly in developing countries even developed countries are not free from corruption but mostly developing countries but developing countries it's kind of small corruption at the individual level but in the developed countries it is at the highest level huge corporations millions of dollars is what you hear so corruption is only a matter of degree and it's all over the place and therefore G20 demanded that there should be zero tolerance on corruption and one of the points that is always discussed in the cost corruption is you commit a corrupt practice somewhere and take the money and put it in a in a bank in Switzerland so does Switzerland have an irresponsibility for this because Switzerland can say this money came legally to our bank they cannot ask where you got this money from but the governments have been the concerned governments have been asking for them to return the money and the most famous cases of the Philippine president Marcos the billions of dollars he has stacked up in Geneva banks and it was all government's money and the government fought very hard and finally the Swiss banks returned the money to Philippines government there have been other cases also like that but the responsibility is of that government to prove that it was illegal money it's not enough that you say that he took away this money without the permission of the government but how did you earn it in the first instance suppose he earned it in a legitimate manner then can he be punished should that money be given you want to state it's a long discussion I participated in it in Vienna and so this was also very important decision then the taxation system you may have heard when G7 met one of the decisions they took was to make it uniform the taxation system of big corporates and they had come to an agreement that it should be only 15% or at least 15% taxation could be made of international investors and this has also been reiterated in the sense that G20 has approved this decision further strengthened in the economic regime so in the first instance pandemic was dealt with international cooperation was stressed that all organizations must cooperate to fight this and vaccine justice all human beings or anywhere in the world should have the same access to vaccines therefore international cooperation as you know in the quad there is already an agreement that you know some countries will have a innovation some countries have money and some countries are manufacturing capability the vaccine did not succeed because each one was trying to do things that they don't have you have innovation but no money you have money but you have no manufacturing capability so in the new quad Israel India UAE United States part which has just been formed they have said that Israel has innovation UAE has money India has capability and the US will give the kind of umbrella to operate this and that is the situation as well as quad is concerned that's in other words international cooperation that has been stressed the only problem there was China was not allowing United Nations to take any action because they were afraid that the accusation will come to them even the investigation as to where the virus came from has not been completed but China is not giving the right answers or the right data so in other words virtually G20 meeting because of its such close proximity to the COP26 was hijacked by the climate change issue that is what happened because everybody was preoccupied with what to say it's COP26 and so they decided to shape some compromises otherwise again this whole thing so my feeling is that COP26 the discussion will start on the basis of some of the agreements reached in G20 and then each country will try to push its position and finally some kind of a compromise was made in the COP26 and then we will see that is inadequate so we'll have to then go for another another climate change plan so 92 climate change plan Rio you can say 1.0 1.0 then Paris would be 2.0 and now after Glasgow 3.0 but in the meantime ice is melting sea level is rising floods are taking place all over the place droughts and seasonal rains so it's quite true that we have ruined the earth and the earth is striking back and so this is the time if you waste the time today our succeeding generations will have no air to breathe or food to eat and that is a dangerous situation so we owe to our next generations to do something when we still are capable of breathing and of course pandemic it is obvious then there is the terrorist threat another thing that they dealt with before they didn't talk about Chinese threat since the China is part of the G20 but I'm sure on the sidelines they must have discussed China they must have discussed Afghanistan another hot issue but no formally they may be simply talked about terrorism which is actually Afghanistan so on the whole the discussions have helped to understand the issues as far as climate change is concerned the conference of parties will decide and on other things G20's recommendations will definitely be respected and implemented by the G20 nations which as I said the big chunk of the world the whole world is not there but all the important countries are there and therefore what they decide and what they do will have an impact on the whole world so thank you very much well that is you know when you talk about climate change you cannot say temperature should be brought down full stop right because that kind of capability every country does not and the developing countries have a need to increase so and that was what was accepted in Rio de Janeiro they said common but differentiated responsibilities I've heard that word originally we kept saying main responsibility of developed countries and they kept saying common responsibility of all countries okay so the final compromise I still remember in Geneva at three o'clock in the morning somebody said why not common but differentiated responsibility that became the mantra or the bible of the negotiations and that is what helped in the Rio de Janeiro meeting but the western countries have been gradually moving out of that and they have been saying your emissions are bigger than our emission see 250 million people emitting and one million people emitting cannot be equated because you have to take it per capita so there are several elements like that the fact that developing countries need energy and resources to move forward is one thing and secondly the developed countries have to reduce their emissions so there is some space you know there is only enough space so much space for carbon dioxide in the earth and that space has to be given to the developing countries so there are several elements in this and so climate justice has been used but Mr. Modi is the one who has given it great currency and he has talked about climate justice you know in the Mahabharata and you know he has been saying that it depends to be that remains to be seen because the quad of 2000 it was started in 2007 you know how many years it took for us to reach here and basically because India's reluctance to join in a military pact because Americans have clearly seen it as anti-Chinese pact and US Japan and Australia they're already in a pact against the Chinese you know they have a military pact so India was the only one which was not in a military pact so we played it down and the other reason is we have a land border with China you know these others can dance around in the ocean and say China has threat Chinese threat but here they are sitting on our borders so the first attack will be on us as we have seen before and therefore we were not wanting to provoke China but when the situation happened in 2020 we could help it and therefore we moved in the direction of that and then when the AUKUS was formed as a real military machinery then Quad became independent little bomb and so they will now deal with climate change with the vaccines and so on so economically also and supply chains so Quad is becoming a more so people say that the creation of AUKUS or people say AUKUS was a real betrayal you know they made another group and all that that's one view but the other view is now that the military element has been shifted to somewhere else Quad will find a role for itself as well as the the so-called Middle East Quad is concerned that is Israel, India, UAE and the US and certainly they have also created another Quad I don't know you people seem to have forgotten they have a America Afghanistan Pakistan Uzbekistan Quad also so I don't know what that logic was anyway that's also there so this is the third Quad so you can have a Quad of Quad if you're one more there'll be four Quads anyway first point is India does not want to be in a in any military alliance and so we have been dragging our feet even now we are possibly that AUKUS will take care of that but in definitely India will need that support if there is a crisis suppose China invades India totally and then we will certainly turn to Quad and ask for help and it happened during Trump's time Trump was in fact willing to take on the Chinese on the Indian border so now the president is not so keen and it depends but so OECD is a rich man's Quad and they don't have any military aspects for it except that of course they support the NATO and that and that can reach their objectives more more easily because it's a developed country's Quad and they also assist so that kind of homogeneity this group does not have and that is a reason why is it that the non-aligned group is not able to accomplish as much as OECD this is a lack of resources when the economic crisis came in 2007 and that time the only body there was was G7 G7 were the only powerful countries that are just countries in the world so they realize that unless you carry the less rich countries but more powerful in terms of resources in terms of population in terms of size must also be taken into confidence and that is how it was formed and it played a very big role and Dr. Manmohan Singh as a eminent economist played a big role in G20 and everybody conceded that G20 can accomplish more things than what the security council can do as I said because everybody is equal in that and that is how G20 was formed but its activities of course depends on as much as the members want you know the usual thing that we say when you ask about UN you see UN cannot have the power that people don't give it to them you know every member is a sovereign country unless you give power to the UN UN will have no power and similarly in G20 also so on many occasions you didn't take any action in the in 2020 at the instance of India G20 called the meeting so the Arabia was the chairman and but nothing came out of it about the about the pandemic some pledges were made but no concrete help but now G20 is focused on it what is focused on it now the United Nations will also focus on it and therefore international cooperation and that was the whole purpose of creating G20 okay thank you very much


All right, it's official. Freddy and friends is bi-weekly. We're gonna get an episode every two weeks, which in my opinion is a bit too long, but I'm just excited that we finally got episode two. If you don't know what I'm talking about, Security Breach TV got another episode of the cartoon installment, teasing the release date and more secrets of Security Breach. The website also got a few other secret changes, like I believe there's a new nose honk and there's also a Monty Security Breach logo and some wires that we gotta talk about. But first, let's have a look at the cartoon because I've not seen it yet. It literally just got updated right as I got home. All right, here we are, Freddy and friends, episode two, if you guys are as excited as I am. Make sure you hit the like button, subscribe to the channel and let's hit it. More static. I'm so happy we got another one. I'm so happy. What secrets are we gonna get? A house? Or a restaurant, I don't know. Chica, Freddy, Bonnie, as usual. Where's Foxy? Okay, it's about the same. Chica. Ah, Chica spoke. That's cool. So it's the same setup, which is interesting. Yeah, it's the same thing. There's that secret, I bet that's the secret. Dude, what is up with Bonnie in these episodes, man? They caught him. What is he now? He's still an endoskeleton. I love this. Bonnie's got that new guitar, I see that. Forever and ever. Oh my frickin' god. No way, dude, no way. Wait, what's the number this time? It's one. It's one. So, oh my god, that's still all. I frickin' love you so much, man. Please, please. This is probably the best thing I've ever seen in this goddamn franchise. Like, dude, that's just frickin' insane and they have a voice too, and I feel like does this confirm that they're the same character? Cause you can see the sunburst go out? Yeah, yeah, yeah, look at this. And they're Sunrise, the speculated name for the character, and then they turn or they swivel or whatever, and they change. Or, either that or it's a glitching effect. Yeah, yeah, yeah, it might be glitching, so they might not be the same. Or maybe they are. All right, it's hard to tell. What do you guys think? Do you think they're the same character? Cause I'm still kind of split. I don't really know just yet. Dude, they look so good. They look so good. This is our first like up close shot at Sunrise. Besides them like jumping up in the gameplay trailer. They look so good. I know you guys have been working on this game for a long time, but honestly, truly, it's paying off. It looks so good. It looks so good. And look at that shot. You're like, oh, I love it. Let's get a one. So this is gonna be the month, this is the day, and this is the year, because Steawall is American. Therefore, they put the month before the day. So it's gonna come out on the 10th of some month, you know, of some year. I'm still hoping it's 2021. I still do think it's gonna be 2021. Also, I gotta find the glitch. I gotta find the glitch. It was around here.  That's Monty. You can see his mohawk and his eye. This is his mouth. He's like looking out this way for you guys. Oh my God. Dude, I fricking am so excited for security breach. This looks absolutely insane. This is insane. I don't think there's really much to speculate about. It does look like he has his normal eyes. He doesn't have his glasses. He doesn't have his sunglasses, which is weird, but yeah, it just looks like normal Monty. So now I wanna talk about now that we've gotten episode two out of the way, which, oh my God, is so much better than episode one. Steawall, please, please, please let the last, I'm guessing it's gonna be a total of six. Please let them be bangers. Okay, yeah, so since we've gotten episode two out of the way, let's take a look at what we got for an update on the website about a few days ago. So the first thing I wanna talk about is this monitor over here. Again, this happened a few days ago. It's not really too big, so I didn't wanna make a dedicated video on this just in case we did get episode two today, which we did, but as you can see, if you hover over this monitor now, you get a crocodile or an alligator emoji, and that's because if you double click, it changes to a Monty Security Preach logo. That's funny. Nothing really interesting to talk about with this. I don't think it really means anything, but it is there. Also, you can no longer, what is this? I don't think this was here earlier. I can't tell what it is. Anyways, you can't click this nose anymore. Instead, the plushie has a honkable nose, and it sounds like the honk from Candies. I'm not saying it's from Candies, but it sounds similar. I don't think that was intentional. I think it's just a coincidence. Also, probably the most interesting thing. I don't know if they've taken it out of the website now, but there used to be tentacles that would slither across this screen, and it was tentacles that looked awfully similar to these tentacles, which at first I didn't think those were tentacles. I thought it was part of the static, but now I definitely do think that this is some new creature, some new enemy in the new game. I don't think it's that glitch trap or Afton Amalgamation, whatever he is, the big claw at the end of the gameplay trailer. I don't think that their designs would fit well together, so I do think they're separate. Huh, that's interesting. They bring up the Fazbearer Entertainment Archives again, which if you guys don't know, is mentioned in the ultimate edition of the Freddy Files, and also we're gonna get a whole Security Breach book. I haven't talked about that because I haven't made a FNAF news video in a long time, but that is happening, and I will be talking about that soon. Also, this image in episode one, I didn't mention it in my reaction video because I just kinda wanted to get that video out as quick as I could, but now that it's been a long time, I can safely say that I think that these are the staff robots that we see in one of the, I think it was the NVIDIA showcase video, the trailer back in like last year, I think. Cause you can see, you know, the splits on the face, their eyes and oops, they're like their heads match up really well. I think that these are the staff robots. And I think these are too, a lot of people for some reason on Reddit think that these are the withereds. I don't think that's the case. I only see the withereds making an appearance if they're in like the museum type area. Also, I don't know what this is. I never commented on it in the video. I still don't know what it means. And it looks like there's another secret message up there. I can't make it out. It looks like it's rev five, three or two, one. Still don't know what that means. But yeah, episode two, Freddy and friends, absolutely insane. Can we watch sun and moon one more time? Let's do it. Surrender. Surrender. Surrender. Surrender. Dude, I can't wait. If there's any secrets I've missed, I'll hopefully bring it up in a future video. I have a few FNAF news videos that I got to pump out on Darko's charity stream and also news I've missed out over the past month. So I'll make sure to bring it up in there. So thank you guys so much for watching. I guess I'll see you guys in another two weeks for episode three. I still think it's a bit too long because that means in November we're gonna get the final release date, which means it's gonna be cutting it close if they released in December. But we're just gonna have to wait and see again. Thanks for watching and I'll see you all on the flip side. Goodbye.