Welcome back. We have been discussing about the various aspects of existence, uniqueness and stability of initial value problems. Today, in this lecture, we will see the possibility of continuing the solution. So, what we have discussed so far is, given an initial value problems, say d by d x is equal to f of x y and initial condition y at x 0 is y 0 and the existence and uniqueness theorem that gives sufficient conditions on f, say f is f x y is continuous on some domain d in R 2 and f is lipchitz continuous with respect to y on d. Then the existence and uniqueness theorem guarantees that there exist a solution. So, there exist a unique solution y in some interval x minus x 0 is less than or equal to h, where h is a small quantity is a quantity defined by x, h is equal to minimum of a and b by f. What are these a and b? So, here a is defined a and b are the parameters, which we used to define a rectangle inside the domain d. So, rectangle inside the domain d is defined by set of whole x y such that x is less than or equal to say x minus a, x minus a initial point is less than or equal to a, y minus y 0 is less than or equal to b. So, these are the parameters a and b. They are chosen in such a way that this rectangle is inside the domain d and m, where m is a constant, which is the maximum of the modulus of the function value when x y in d or in r. So, the existence and uniqueness theorem guarantees that there exist a solution that solution is defined on an interval x minus x 0 is less than h. If h is a very small quantity, then the solution, which we obtain is very that is defined only on a small, very small interval. If we visualize it, say this is your x 0 point and this is y 0, you are looking for a solution and the solution is now defined some small interval x 0 plus h and x 0 minus h. So, the question, natural question, what about the solution outside this interval to the right side of x 0 plus h and to the left hand side of x 0 minus h. Can we continue? Can we extend the solution towards the right and towards the left? If it is possible, we say the solution can be continued and if it can be continued indefinitely that is for all x, then we say the solution exists for or a solution is defined for all x on the x axis. But if the system is non-linear, then the existence of solution on the all real axis, on the all x axis may not be possible always. But whereas, if the system is linear, then we may be able to extend or continue the solution to the entire x axis. So, in this lecture, we are going to discuss about the possibility of continuing the solution outside the domain of interval which is also the interval which was guaranteed by the existence theorem. So, to get a feel of it, let us consider an example. So, take an example that is a well-known example, which we have already solved. See the example. So, consider a differential equation d x d y by d x is y square is a non-linear differential equation and the initial condition given is y at 1 is minus 1. So, this x y plane, the solution the initial point y at 1, this is point 1, it is minus 1, this is the initial point 1 minus 1. Now, the existence theorem guarantees that there exists an interval on which this equation has a unique solution. So, let us verify these things. So, first of all our f f of x y in this example is y square, which is lipschitz on any bounded rectangle. So, let us define a rectangle r, r is given by set of all x y point in the x y plane such that x minus the initial point x minus 1 is less than equal to a and y minus 1, which is y plus 1, which is less than equal to b. So, obviously, f is lipschitz, lipschitz continuous on this rectangle. If it is lipschitz continuous on this rectangle and obviously, if it is continuous on r, so therefore, the existence and uniqueness theorem applies here and it says there exists a unique solution in a neighborhood x minus x 0, which is x minus 1 is less than equal to h. We are going to try to find what is h compute h such that x minus x is less than equal to h is a domain on which the solution is defined. So, in our case x 0 is x 0 is 1 that is x minus 1 is less than equal to h. So, domain in which solution is guaranteed by existence and uniqueness theorem that is right. So, what is h? h is defined as h is minimum of a and b by m. a and b are as given in the definition of r and m is maximum value of the function f of x y in the rectangle. So, x y belongs to the rectangle and since f is just y square, f x y is just y square. We know this f is y square and that will have maximum value or this point. So, let us load this one.  So, maximum value of y square is on this side when y is equal to minus 1 minus b. So, m is minus 1 minus b square which is same as b plus 1 square. So, we are looking for h which is minimum of a and b by m. m we got as b plus 1 to the whole square. So, we want to know which is minimum. So, what is the minimum and maximum? Let us compute what is the value of this. The maximum value of f b if I define f of b is equal to b by b plus 1 square, then f prime b with respect to b is 1 minus b by b plus 1 cube. So, maximum value for f b for b greater than 0 is b is equal to 1. So, maximum is obtained at when b is equal to 1.  So, therefore, h is minimum of a and the maximum value for b is 1 by 4. Therefore, if a is greater than or equal to 1 by 4, if a is greater than or equal to 1 by 4, b by b plus 1 the whole square is less than or equal to a for all b positive. So, this implies that h is equal to b by b plus 1 the whole square which is less than or equal to 1 by 4. So, does not matter what value of a is. So, regardless the value of a of a. On the other hand, if a is strictly less than 1 by 4, if a is strictly less than 1 by 4, then by definition naturally h is strictly less than 4. Thus in any case the a is greater than 1 by 4 or a is less than 1 by 4 in any case the value of h we obtained is 1 by 4. So, there is now for b is equal to 1, a greater than or equal to 1 by 4 gives h is equal to minimum of a comma b by b plus 1 the whole square. So, which is minimum of a 1 by 4 which is equal to 1 by 4. So, thus the best. So, this tells us the best possible value of h value 4 h to have a solution. So, to have a solution is 1 by 4 to have a solution is 1 by 4. So, the tells us by the existence theorem by the existence theorem there exist solution. In fact, unique solution for x minus 1 is less than equal to 1 by 4. So, that the interval is 3 by 4 less than equal to s less than equal to 5 by 4 is the interval on which we have a solution. But this non-linear initial value problem we solved by using analytical method and we found that see if we solve this equation d over d x is equal to y square separating out the variable y square is equal to d x and integrating and this is 1 by minus 1 by y is equal to x plus c or y is equal to minus 1 by x plus c putting the initial condition y at 1 is minus 1 gives us c is equal to 0. So, therefore, the solution general solution which we get by analytical method is y x is equal to minus 1 by x is a solution. But this solution we know that this solution is defined solution is defined for all x between 0 and infinity. We look at the graph of it the solution. So, the given point is 1 this is minus 1 and the interval in which we got the solution is only this. So, 3 by 4 and this is 5 by 4. So, existence theorem guarantees that there is a solution only on this region that the solution is given by this portion. But look at the solution 1 minus 1 by x says the solution is defined between 0 and infinity. So, therefore, the question natural question is can we continue the solution the existence theorem guarantees that there is a solution in the interval 3 by 4 5 by 4 can we extend the solution to the right and also to the left to get a solution in a more large interval. The solution of the initial value problem we want to continue to the right and to the left this continuation this process is known as a continuation of the solution. So, we deal with this one. So, continuation of solution. So, consider the differential equation d y by d x is f of x y and y at x 0 is the initial condition y 0 and existence theorem implies that there exist a unique solution existence and uniqueness theorem implies that there exist a unique solution y on x minus x 0 less than equal to h. So, therefore, the solution exist for all x in the interval x 0 minus h to x 0 plus h. Now, the idea is to continue the solution to right and to left. So, we will deal with the continuation of solution to the right. The similar argument holds for continuation to the left. So, graphically we have the domain d and inside the domain we have a rectangle r and the initial point is inside the rectangle and existence theorem says that the solution exist to right and to left this is x 0 plus h. So, solution exist the point is x 0 and we have a solution. So, this is x 0 y 0. So, existence theorem says there exist a unique solution y let me just call it instead of y it is a solution say phi 0 phi 0 on this interval. So, phi 0 is defined phi 0 x is defined on x 0 minus h and x 0 plus h even at the n point x 0 plus h and if I call. So, let x 1 is equal to x 0 plus h that is this point and the value of phi 0 at x 1 the n point if you call us y 1. So, this point is x 1 y 1. So, x 1 is x 0 plus h and y 1 is the value of the solution at x 1. So, the point x 1 y 1 is a point inside the rectangle and the rectangle is inside the given domain d and the function satisfies all nice properties like continuity and a Lipschitz continuity on the all domain d. So, therefore, the question is now can we start the solution can we take the differential equation with a new initial point. So, consider the initial value problem with new initial condition y at x 1 is y 1. So, therefore, we are trying to start a solution we are going to start a solution from the new point x 1 y 1. Now, again apply the existence theorem that theorem says that we can find we can find another rectangle find another rectangle another rectangle such that x 1 y 1 is a point inside the rectangle and continue the solution or get a solution to a new point. So, this point is now solution on the first interval is we denote by phi 0 with the new point with the new initial point let phi 1 be a solution that is defined which is defined on x 1 less than equal to x less than equal to x 1 plus some h 1 h 1 is a similarly defined a constant for the new rectangle. So, now, because of the existence theorem we could find another solution phi 1 which starts from x 1 y 1 which was n point of the previous solution and it is extended up to x 1 plus h 1 that is a maximum interval guaranteed by the existence theorem. So, we got two solutions phi 0 and phi 1. So, therefore, we have two solutions and if I combine these two solutions into one solution that phi x I defined phi x is a solution which is phi 0 x for x varies from x 0 minus h and its upper limit is x 0 plus h which we denoted by x 1 and the second solution is phi 1 x. So, phi 1 x is defined from x 1 is less than equal to x which is going to x 1 plus some h 1. Now, this combined solution this is now phi is a solution phi is a solution defined on the interval x 0 minus h to x 1 plus h. If we write down the formula for phi 0 phi 0 x is equal to by the basic lemma y 0 plus that was the initial condition plus integral x 0 to x f of t phi 0 t d t and phi 1 x is equal to starts from y 1 plus integral x 1 to x f of t phi 1 t d t. And phi t if you combine these two this is phi x is equal to the solution starting from y 0 and y 0 plus integral x 0 to x f of t phi t d t. So, this phi this phi t is defined by phi x here. So, therefore, we have extended the solution to. So, we thus continued the solution from x 0 minus h to x 0 plus h to a larger interval x 0 minus h to the x 1 plus h. Now, what we can do is we can repeat this process. Now, take x 1 plus h 1 as a new point if I call this point as x 2 x 1 plus h 1 as a new point x 2 and the value of the function phi 1 at x 2 if I call as y 2. So, I got a new initial condition x 2 y 2. Again, if x 2 y 2 is inside the domain and f of x 2 y 2 is defined it has got all properties since f is defined on d and the conditions of the existence theorem are satisfied. So, therefore, you can find an h. So, continue further to get the interval of definition enlarged. So, we continue this process. So, continue this process further. So, to get larger intervals like the end point is x 0 minus h, the right end point is x n plus h n where x n and h n is obtained at each step. So, repeating this indefinitely thus repeating the process indefinitely. So, this repeating this process indefinitely on both sides. So, what I have shown is only on the right hand side the same process can be done on the left hand side on both left and right. We continue to get we continue the solution to successively longer intervals. So, if I call those intervals are a n and b n where x 0 minus h x 0 plus h is the one which we started which we denote by a 0 b 0 and the newer one a 1 b 1 continued on both sides a 1 b 1 then which is a subset of the next one a 2 b 2 and so on to a n b n. And if take the limit of this a n let a is equal to limit a n n goes to infinity and b is equal to limit n goes to infinity b n then we obtain a largest open interval a less than x less than b over which the solution phi d y by d x is equal to f of x y such that the initial condition phi at x 0 is y 0 is defined. So, if you can find such a larger interval a less than x less than b on which the solution of this initial value problem is defined. Now, in this process there are two possibilities. So, two possibilities. So, one is this a is minus infinity and b is plus infinity. So, and in this case we say case solution is defined solution is defined for x is between minus infinity plus infinity. So, this is one of the possibilities that solution can be extended both to right and to left. So, that the solution is defined on the n r x axis. Now, the second possibility is either a is finite b is finite so or both are finite or both are finite. So, a is finite number or b is a finite number or both are finite or one is infinite the other one is finite. So, we remark that even if f is even if f is continuous and this lipschitz continuous on every bounded domain d if f is continuous and lipschitz continuous on every bounded domain d we cannot conclude the case one above. So, f could be continuous and lipschitz continuous on every bounded domain d still we may not be able to conclude that the solution is defined for the n r x axis. Taking an example the same example of d y by d x is y square the same example if we if we choose with an initial condition say y at 1 is minus 1. So, we have seen that the solution exists y x which is minus 1 by x the existence theorem says that the solution exists only in the interval 3 by 5 and 3 by 4 and 5 by 4. But we can now further extend to left and right that the solution is defined between 0 and infinity. So, what we have here is in the above two possibilities a is equal to 0 and b is infinity. So, remember f of x y which is equal to y square is lipschitz every bounded domain every bounded domain. But note that f is not lipschitz on an unbounded domain if f is globally lipschitz then there is a possibility of extending it to the entire the solution can be extended to the entire x axis. But here the non-linear function is not globally lipschitz solely lipschitz on bounded domains. So, if we lipschitz on an unbounded domain then we can expect larger opening interval over which the solution of the initial value problem is defined. So, we state this in the form of a theorem and which we will not prove it the proof follows if we use a successive approximation method theorem. So, let f x y be continuous. Let f x y be continuous in the unbounded domain denote this by d which is equal to set of 4 x y in R 2 such that a is less than x less than b x is bounded between a and b and minus infinity less than y less than infinity. It is an infinite strip where x is varying between a and b and y is varying in the entire y axis on the entire y axis. So, let f of x y satisfy lipschitz continuity lipschitz continuity on d then a solution call it phi solution phi of d y by d x is equal to f of x y with the phi at x 0 is y 0 the initial condition is defined on the entire open interval defined on the entire open interval a less than x less than b. So, if this is the case when the function f is continuous and lipschitz continuous on a given bounded domain is not bounded with respect to x and is lipschitz continuous on an unbounded domain of y axis then the initial value problem has a solution on the entire open interval x between a and b and in particular if a is minus infinity and b is infinity then the solution phi is defined or x that is x is varying between minus infinity plus infinity. So, here the solution exists globally. So, if therefore, if f is lipschitz on an unbounded domain then one can expect a solution on the entire real x axis. So, what we have discussed in this lecture so far is the existence and uniqueness result guarantees a small interval on which a solution exists and the solution is unique and we have seen that the solution can be extended towards the right and also towards the left provided the function f is good smooth. So, if the function is lipschitz continuous on an unbounded so globally lipschitz continuous then the solution can be extended further on an opening interval on which the function is assumed to be continuous on lipschitz otherwise still we have to have a small interval x minus x 0 is less than h. Now, let us look at one example consider an example. So, d over d x is equal to y square the same example at this time the initial condition is y at minus 1 is 1. So, the initial condition is given y at minus 1 is 1. So, y at minus 1 is 1 and we know that the solution is y of x which is equal to minus 1 by x plus c and putting the initial condition we get c is equal to 0 and the solution is y is equal to minus 1 by x and if you look at the interval see that solution exists. So, this solution exists for if you try to continue the solution further see the solution exists for minus 1 to 0. So, at 0 that blows up. So, therefore, the solution cannot be continued beyond this point. So, up to 0 it cannot be extended solution does not exist it cannot be continued to minus 1 to 1 minus 1 to 0 it cannot even include 0. That is natural because it is not violating the previous theorem previous theorem says if the function is lipschitz continuous on the unbounded domains on globally lipschitz continuous, but here if it is not f of x y which is y square is not globally lipschitz it is not globally lipschitz continuous. So, therefore, we cannot expect that the solution is solution can be continued further. So, we stop the discussion of continuation of a solution at this point and now we come back to system of equation come back to initial value problem which are not scalar, but a vector differential equation. So, we spend some time in dealing with the existence of solution existence and uniqueness of solution of vector differential equation. So, vector differential equations or is a system of differential equation or system of differential equations. So, for example, if you have say d x 1 by d t is equal to f 1 of x 1 x 2 and d t d x 2 by d t is equal to f 2 of x 1 x 2 t with initial conditions x 1 at t 0 is x 1 x 0 0 1 say and x 2 at t 0 is x 0 2. See if you have two equations coupled equations then what can we say about the existence and uniqueness of solution of this equation. So, in general we can have an n equations. So, if you have n equations so d x 1 so we will write in a vector form. So, d y d t of x 1 x 2 up to x n which is equal to f 1 x 1 x 2 up to x n t f 2 x 1 x 2 up to x n t and f n x 1 x 2 x 3 up to x n t you have n equations with the initial conditions x 1 at t 0 x 2 at t 0 and so on x n at t 0 is x 0 1 x 0 2 etcetera x 0 n. So, this is where each f i is a function from r n cross r to r n is a function not necessarily linear and if you denote this vector this x y just x x t and all these components this into say f of x t t then this equation can be written in the form d x by d t is equal to f of x t t with initial condition x at t 0 is x 0 x 0 is this quantity this is x 0 and this is x at t 0. So, the question under what condition this initial value problem has a solution and solution is unique and we have the stability of solution etcetera all these things can be similarly studied along the same line. See here the conditions are so our system is d x by d t is equal to f of let me write this t comma x this also a notation conventionally and x at t 0 is x 0. So, for each time would say t 0 t 1 is a time interval then x of t is in r n and f is from f is now r cross r n to r n and x 0 is in r n and we can show that if this function f is Lipschitz continuous with respect to the second argument f is Lipschitz then this implies that there exist a unique solution. So, if the vector value function the vector function f is Lipschitz with respect to the second argument x then this system has a unique solution and the solution can be continued and the solution is stable with respect to the initial condition x 0 and all these things can be studied and analyzed in a same manner as we have done for scalar case. So, with this we finish the existence uniqueness continuation and continuous dependence of solutions of initial value problem. Thank you.


and we're going to do a little science today. You've probably seen this particular demonstration before, but you may not have realized what it really means and the real science underlying it. So the demonstration is very simple. I've got a balloon with air in it and a source of flame. Now, when I lower the balloon down to the source of flame, guess what? Boom, the balloon pops. Now, I've got the same kind of balloon here, but this one has water in it. Just half an inch, well, a couple inches of water. Same thing, lower it on here. And notice the real difference here. This balloon is not popping. Indeed, I can stand here and hold this flame on the balloon for quite a while and it won't pop. So why is this? What's going on? Why doesn't the balloon pop? What does this tell us about water? And what does it tell us about science in general? The reason the balloon pops in air is because the flame melts the balloon. The air inside the balloon is under pressure. The skin melts and pop. The balloon's gone. When we do it with water in it, however, the water removes the heat from the skin of the balloon faster than the skin can heat up. The skin never reaches a critical temperature and never melts. The water just gets very slightly warmer and the balloon stays intact. And what this tells us is that water has tremendous heat capacity. It can pick up heat from the atmosphere. It can pick up heat from a flame and it holds it and moves it around. The real implication of this is when you think about this on a global scale, think of the flame as the sun, the water balloon here as the ocean. In the tropics right there where the flame is hitting, the water is heating up and moving around the skin of the earth. It's transferring heat all over the surface of the earth and that's why the earth is actually as habitable and temperate as it is. If it weren't for this amazing property of water, the tropics would be very, very hot and the poles would be incredibly cold. The earth would not have very much space for life, only a narrow band between a very hot and a very, very cold region. But as it is because of the heat capacity of water, the earth is habitable virtually around its whole surface. That's it. Real simple. Thank you.


Your weak foot is currently letting you down. I want to show you how to improve shooting when you're weak. Any of my weak foot videos, I've done a few. I always talk about no more weak foot. If you want to be a good player with two strong feet, I need you to eliminate that phrase from your vocabulary. From now on, you have two strong feet. Having that mentality, saying that to yourself, like, ooh, it was on my weak foot, that's why I missed. That's just setting yourself up to fail. From now on, especially if you want to follow my content, and you want to work with me, my players are two footed players. You go both ways, you're good with both feet. So that starts in the mentality. Allow yourself to have two strong feet. In this video, I want to talk about how you can improve your weak foot faster than what you're doing right now. Number one is with that mentality. Next, I want you to think about it. Just think about it. Hey, what's up? I hope you're finding this content helpful. Watch this all the way to the end if you want to find out which subscriber got this video's special shout out. Next, we have to think about how many more shots you've had on your stronger foot compared to your weaker foot.  But if we had to just estimate and put a number on it, maybe this leg's had 100,000 shots on it. In your entire career, maybe this one's only had 5,000, 10,000. It makes sense why this one's so much better than the other one. We don't have to over-publicate this video. It could be very simple. The reason your weak foot isn't as good as your strong foot, because you haven't put in enough repetitions. If we even out the repetitions, we'll even out the skill. Okay, so one thing is practicing. On both feet. When I'm practicing by myself, I'm always shooting with both feet. If I have one on my right, I'll try again. In your team practice, try to do the same, just because other players are watching, but a lot of players have shots. So number one, if you're shying away from shots in your team practice, your teammates, how are you supposed to do it in the game? So think about that. Always trying to shoot on both feet. How many times have you had the opportunity to strike the ball under your side, but because it was under your side, it wouldn't do. So get back on your strong side, and then the opportunity was gone.   The defender was there, and the opportunity was gone. Don't do that anymore. It's so much more valuable for you to have it on your weaker side. It totally shined the shot, but at least you took it. At least you were brave enough to try on your weaker side. So if you ever have an opportunity on your weaker side in the game, hit that shot. Whatever happens, happens, but at least you try. You can learn from that. You cannot learn. You cannot improve. So when it's on your weaker side, practice game by yourself. Hit the ball. Always hit the ball. You'll learn from what happened. Next thing I want you to think about is the analysis and comparison between your stronger and weaker leg. So let's say I'm a right footed player. What does my technique look like on this side? It can be a licensed technique. What does it look like on my strong side compared to my weaker side? If my technique is totally different, then my shot is going to be totally different. So what you need to learn is to try to make that knee the exact same on both sides. Because this is a few things I see a lot. So let's say I'm a right footed player. My technique on this side is very nice. Nice ball through. Good backswing. Making good contact. Then you go to the weak side. There's no backswing. Very little backswing. Contact point is not where you want it. Let's say I'm trying to hit with laces. Maybe I'm hitting it like here. Because I don't know how to flex my foot in that way. And then my ball through is not making strong. So if I want to produce the same type of shot on both sides, I need my technique to be the same. So think about leaning on the strong side. Nice flowing technique. You need to learn how to replicate it on the other side. And if you can do that, over time you'll improve a lot faster. Rather than just getting repetitions. Most players, yeah you want to go and practice your weak foot. That's fantastic. But what are you doing? You're going out there. And you're getting the same shot. The same, the exact same way. 100 times in a row. And then getting upset when you're not improving. You have to change the technique if you want. You have to get outside yourself. And say, okay I need to have a bigger backwing. I need to have a stronger foot. I need to have a better ball. Focus on a few points. Right now for technique that I think will make a difference for you. So number one is the foot flexion.  For you to flex your left foot, point it down and really make it strong. If you want to have a strong shot, you need to have a strong foot. Because if I make contact with a weak foot, I'm just going to have a weak shot with a lot of backspin. If you want it strong, you need to make this foot strong. You need to make this leg strong. Now I'm going to guess, especially if you're really struggling with your weak foot. On this side, when you flex, that's easy. It's natural. When you flex and you try to make it hard on this side, it's hard to do and your foot might even be crappy. Because you don't have the strength in it. And that is the truth. You don't have the strength in it. You don't have the mobility in it. You don't have the muscle memory in it. Think about it like this. Basically what you've been doing is if you have one foot that's really good and the other one's not so good, it's like going to the gym for 10 years and saying, hey, I want to get big arms. I want to get big biceps. But you know what? I'm just going to curl on my right side all the time.  Maybe I should have two big arms. And you start curling on this side. You can't lift the same amount of weight. And you can't even squeeze it. You can't flex it in the same way. When you flex it, it hurts. It's because you don't have the muscle memory in that arm. You don't have the muscle memory in your foot. So in order to develop that over time, just get those repetitions. But focus on making that really strong, really hard foot make better contact. The other thing that I see a lot and I want you to focus on and make a big difference is a bigger backswing and fall through. On your weaker side, your backswing might be here and fall through here. So really try to increase the range of that and the speed of that. But if you can add those two things, you're going to start hitting better shots on your weaker side. This is the featured subscriber for this video. If you'd like to be featured in future videos, hit that like button, drop a comment below, and let me know how my videos have helped you improve and achieve more in this sport.


He started a little series, I hope to do more of this. Here's Lady Aida from high school. A little bit after high school. A little bit after high school, but really close. Because you have the lip ring. I want to say I didn't get that till I was 18.  You look identical. I look the same.    I must, I must, I must. Email Mudge, who's now the CTO of Twitter, and Joe Grant, Kingpin, and see if it's okay to post this story. So Lady Aida, take it away. What is this thing that happened when you were in high school with Joe Grant and Mudge, kind of, well-known people in the hacker scene? Yeah, at the time they were local Boston buddies in the 617 crew. But when I was in high school, I was helping out in the IT department. And they were talking about a bunch of old, like Apple and Coco and T-R-S-A, like really old computer stuff that had been in the cage. Are you saying in high school, you did computer stuff and you were doing stuff with the IT department? It's true. I'm shocked. I know, well at the time it wasn't so cool, but I was just, you know, the IT director, she was really awesome. And I think I was just helping organize and clean up and she was gonna dumpster all this stuff. And I was hanging out with a lot of hacker crews and hacker houses.  And so when I... It tastes better if it's free. It does taste better.  And I said, hey, come out of high school and help me dig through this trash and maybe we can find something cool. We could either sell it at Swatmean or we could recycle it into some projects. So Joe Jogram came by, he does a lot of hardware hacking stuff now and does product design for PowerLax, among others. We dug through some hardware. I think we got a pile of Apple 2Cs and then we had to get it, I think, to the loft. And, you know, me and Joe Grand were like, we weren't, we didn't drive. I think he was like 18 or 19 and maybe he didn't know a car. And I was, I don't think I was 16. I didn't have a driver's license yet or at all. And he's like, okay, let me call Mudge.  This is not the actual car, but I asked Mudge, this is pretty close though. This is, it's the same car, but you know, I don't know if it's, it's a Mustang, it's a Cobra. Yeah, it's a Cobra Mustang. This was the coolest car ever. What's funny is you asked Mudge, like, oh, what was that car? He instantly like knew all the specs and mod. I mean, he loved that car.  Cause it's kind of the outside quad area of the high school.   Why, why do you have a friend with such a cool car? Why were you carrying some Apple II C's?  So I was like, I was kind of cool for like two days. So let me tell you some parts that Lady A does not going to say. Sorry. So, well, first up, let me just do the big thank you.  And I'm kind of tired of it. Like today we got an email, how dare you do retro stuff?  This is mine. It's so terrible what people do to each other. I actually love the people think I'm like 25, like I'm much older than that.  This is a waste of time. Why is this want to be got, I'm not gonna even say the curse words. But like, why is your experience have to be so much different? Like if you were a young boy, it would be like, oh, look how he liked computers. It's so good. But because you were a woman. I don't know. I think we live in a society that's- Yeah, I don't like it. I don't like it. And I'll say this for 2022, I'm sorry everybody. Like we have to call it out. We have to say stop. I mean, we're gonna be positive and we're gonna show good things. But it's a little ridiculous that the day that we're getting this story and you're like, yeah, people made fun of me and I was cool in high school just for like a day because of this. And we're like dealing with people being shitty to you. I don't like it. I don't like it. And here's the other part. And I shrugged up because I think it's not a big deal. I shrugged because it is, you know, I agree. So I have a, let me put it on time travel because I don't want to even have the Apple logo. Look at this. So sorry, Apple logo. Look away. Cover your little rainbow eyes. You're too beautiful. So I remember I was talking to a CEO-like person of a company that's very similar to Adafruit. And I was telling them about something that we had to deal with. We had to basically get a restraining order against someone because of something that they said did sent mail. Just physically. Anyways, it was a messed up thing. It got granted. Yeah. And it was a messed up story.   Have you ever had to deal with having, making sure there was enough people around going to an event so they didn't bother you? Like all these things he's like, no. And I'm like, yeah. So like, please don't say like it can't be that bad.  Well, not only does Lamar have to run a business, but she has to deal with all these things constantly. Like today. It doesn't make the debugger run any faster either. Like I still have all the technical problems too. Yeah. And like Adafruit worked out okay. I would say we're a successful company.  Yeah. So anyways, I'm a little upset because I thought this was a beautiful story, but I also know the other side of the coin. So maybe I'll edit this out later. Oh, we're live, I can't. Okay. So that's our tails from the hack. Okay. Let's.


Good evening everyone. Happy Saturday everyone. Saturday is usually a time where we get together with friends, spend some time with the kids, with family. Obviously this is another different Saturday as we've had over the past few weeks. We need you to continue to stay home. We need you to continue to do everything we can to flatten the curve. Obviously there are sacrifices we're all making but it's beginning to work. We see promising news out of BC that over the past couple of weeks the measures taken in place by so many Canadians. The choices that Canadians have made have had an impact on the overall numbers but we need to keep it up. We need to continue to do what is necessary to prevent the spread of COVID-19 which means continuing social distancing, continuing to not go out unless you absolutely have to, continuing to think about caring for each other, thinking about protecting each other and thinking about protecting our health care workers and those essential workers who are doing such extraordinary service to keep things going, to keep us safe at the same time. It's a responsibility that we all share to stay at home, to try to do everything we can to prevent this pandemic from spreading or hitting more people. It's going to be extremely important that even on a beautiful Saturday, we stay at home, we stay in isolation and we don't take any measures that will risk our friends, our relatives or our health care workers. But as you know, we encourage people to stay at home, particularly if they have COVID-19 symptoms. We've been telling people particularly if you feel the onset of symptoms of a cold, of COVID-19, you need to stay home, you need to isolate, you need to not travel. People have been following that but I can enhance that we have formalized some of the domestic travel rules. As of Monday at noon, people showing any signs whatsoever of COVID-19 will be denied boarding on all domestic flights and intercity passenger trains. Today, I announce that Transport Canada has brought new rules for travel. Obviously, it has been said for a long time that if you have COVID-19 symptoms, you need to stop traveling, you need to stay at home. But from now on, on Monday at noon, if people are trying to travel by plane, domestically, or by trains between our cities, they won't be able to get any symptoms, no matter what the COVID-19 symptoms are. We need to continue to keep our distances from each other. We need to continue to protect ourselves. We need to continue to take responsible decisions. And I want to once again thank the millions and millions of Canadians who are doing exactly that. It's extremely important to be able to keep in safety, to be able to ensure that when this crisis is over, we will be able to resume normal life and continue to have a prosperous and healthy country. But it demands that everyone do their part today and for the coming days and weeks. Last night, I was lucky enough to do something that I love to do. I was able to spend a little time with the members of my youth council, the Prime Minister. For me, spending time with the young people, even if it's a virtual meeting, it's one of my favorite things, because it energizes me, it makes me understand how young people are interested and involved. I was accompanied by Minister Bardish-Chagger and two parliamentary secretaries, Adam Vancouverden and Darren Fisher. And we had a meeting, an open conversation with the young people of the Council across the country. The conversations I was able to have with the young people on the Prime Minister's Youth Council last night were extraordinary. Obviously, lots of questions and comments around COVID-19 and vulnerable populations from the north to internet access and broadband access for rural communities. Questions about what young people can do, questions around what they can tell their friends who are doing well or not doing well. Talks, conversations about mental health as well, because obviously this is a moment of anxiety and stress for so many people. This was a great conversation, like so many of the great conversations being had amongst Canadians across the country. Our young people specifically, we've been counting on them over the past years to continue to step up in the fight against climate change, in the fight against poverty, in supporting a better world internationally and at home. And we continue to need young people to be that vehicle for building a better future and sharing messages. Obviously, young people like every generation are chafing at the bit in terms of having to be self-isolated. Particularly at a time when we tell our young people at an age where we say now is the time to go out and discover the world, whether it's with a backpack or in a laboratory. Make new discoveries, challenge yourselves, challenge the world. And they're looking at their plans for the spring and their summer jobs and they're realizing that there is a massive anxiety and a massive uncertainty out there. But that doesn't mean we're powerless. Doesn't mean they're powerless. On the contrary, this generation of young people is so committed and engaged to creating a better world that we need you to keep leading the way you are. We need you to share your messages with friends. We need you to lead by example. We need you to be challenging and discovering the world in virtual ways. There are ways that you can continue to shape the future we all live in every single day, not just with your choices but with your leadership. And that's what we need. We need our young people to continue to challenge this world, to continue to push what is possible, to continue to want to be the leaders we need. And during these times of crisis, we still have more needs. So I'm counting on you, but I know that our present and our future is always between very good hands with our young people. We will also be there for you. As young people, there are many of you who are going to qualify for the Canadian Preciation for Urgence. There are others who are going to be supported in your work, in your work at the same time as part of the companies because of the help we give to small companies and small and medium-sized companies. But we will continue to look for ways to ensure that you have confidence, not just in the present but also in the future. We have taken significant measures to help people. Yes, young people who will many of them qualify for the CERB and be helped through the payroll subsidy, the wage subsidy we're creating for businesses and bringing up to 75%. But there's always going to be more to do and we're going to keep listening and looking how we can make sure that Canadians get through this in the best possible way by supporting them now and ensuring that we can roar back stronger once this is all done. That's why we put forward big measures to help businesses over the past few days. Increasing the wage subsidy to 75% means businesses across the country are now realizing they're going to be able to keep people on their payroll, keep that relationship going between them and their workers, and even rehire people who they didn't think they'd be able to support over the past two weeks. We know that what we do now to hold things together, to give people the ability to stay home, to isolate, to hold through this difficult time is key to how we will come back stronger afterwards. But we need to stick together and we need to do it. That's why we're helping small and medium-sized businesses and we're also making it easier to access the credit. Liquidity is going to be extremely important for people these days, to be able to borrow, for example, we're going to make $40,000 available through banks, no interest for the first year, and you won't have to pay $10,000 for that if the conditions are complete, if it goes well in the coming years. We're going to work together to ensure that we have the capacity to go through all of that. Our $107 billion plan has been passed to the Parliament. We have been able to really start delivering this aid to Canadians. We know that people are impatient, that it's going to be a big deal, and that we're working hard to deliver to Canadians quickly in these unprecedented situations. But that's exactly what we're going to do together. The Canadian emergency loan will offer you $2,000 every month for the next four months. Therefore, I invite you to sign up for my file on the Canada Revenue Agency so that you can submit a request as soon as the portal will be launched in the coming days. And if you can, sign up for direct deposit so that the money can be invested directly in your account. The Canada Emergency Response Benefit will give people $2,000 every month for the next four months to help get us through this time. I know an awful lot of people have showed interest in it, my recommendation to you is to go on the Canada Revenue Agency site and sign up in advance through my account links. Once you do that, in the coming days, when we're able to start actually opening applications, you'll have a head start. And if you can, please opt for the direct deposit option, which will let you get this money into your bank accounts sooner and is simpler for everyone as well. There are lots of things that we're doing to make sure that we get through this together. But everything we do, we need to do together. Every single individual, every single household has its role to play in making sure that Canada and Canadians do well through this. We also have a role to play in making sure that the world gets through this, both by modeling solutions and demonstrating what can be done when we all work together. This is going to be key, particularly as parts of the world that are much more vulnerable are beginning to get harder hit. We need to be able to get through this so we can help rebuild a world in which people can prosper and everyone has a real and fair chance to succeed. I know Canadians are up to this challenge. I know we're going to do this together. I have a lot of confidence in Canadians and in our ability to get through this because we do what we always do in difficult times. We'll be there, one for the other. Thank you everyone and have a good Saturday.


Hi everyone, this is Alice Gao. This is a short video to explain the answer for the clicker question on slide 8 of lecture 19. For this question, we are given the expected utility of the optimal policy for each state for the grid world, given in the table you can see, and we are asked to determine the optimal action for state 13. And in order to do this, all we need to do is calculate the Q values for each of the four possible actions. Let's take a look at the calculation process. So it is a matter of taking the formula and plug the values into the formulas. Let me go through the first two of the four calculations. So for the first one, our intended direction is going downward. So our intended direction going downward, but with 10% chance we're going to go to our left. And with another 10% chance we're going to go to our right. So I'm labeling these to figure out what are the utilities that I'm going to get in each of the three directions. Then all I need to do is say if I do travel in the intended direction, I will get the utility 0.660. If I travel to my left, I will get the utility 0.388. And if I travel to my right, then I'll get the utility of 0.655. Then we add these together. These give us expected utility of 0.63 something. Okay, let's look at another example where we might bump into a wall. So suppose we want to travel to our left, which means we're looking at the second line. Then if we want to travel to our left, then with 10% chance we are going to end up traveling downward. And with another 10% chance we'll try to travel upward. So if we get to our left, then that's what 80% chance we'll get a utility of 0.655. If we end up traveling downward with 10% chance, then we'll get a utility of 0.660. This is straightforward. Now if we end up traveling upward, we're going to bump into a wall. And if we bump into a wall, then we'll stay in the current state. So with another 10% chance, we will stay in the current state and we'll get an expected utility of 0.611. So in total, our expected utility is 0.6511. So you can use similar approach to plug in the formula for right and up and determine their expected utilities. And then for the optimal policy, we can simply look at the four numbers and choose the action that gives us the largest number. In this case, that's left. So back to the quicker question. The answer is that the optimal action for state 1-3 is going left. By using this approach, if you want some extra practice questions, you can look at the other states and try to figure out the optimal policy and then compare this with what I've given you in the previous videos. That's everything for this video. Thank you very much for watching. I will see you in the next video. Bye for now.


At home, we have a withing scale that continuously tells me I'm too fat and my body a fast percentage. No, I'm kidding. But we also have a withings blood pressure cuff. But I'm here with Paul Buckley who's going to show us yet another withings device that we simply must get. Why don't you tell us about it Paul? Well, I think you're being too hard on yourself with the withings products. I think you're looking great. So every year we introduce a new product at withings at CES and we choose Unveiled as our launch pad. So this year we're announcing BMO. Now BMO is an upgrade from our thermo, which is our thermometer, a temporal thermometer. And so BMO is going to do exactly what thermo does, but three other things that thermo doesn't do. The first one is view essentially touch the two contacts here on BMO. We're going to be able to do an ECG and an SBO2 in 30 seconds. So that's going to give you an electrocardiogram and also let you know your blood oxygen level, excuse me. I'm going to take blood sugar. That's the holy grail. We don't have that one yet. No, no, that's right. It's blood oxygen, thank you. Blood oxygen level. And then also the new thing we added is a digital stethoscope. So that's number three. So if you're not feeling well and you want to record your lung sounds or your heart sounds, you can do that like any other withings product, it would be captured in the withings app and you can share that information with the doctor. Let me hold you up for a second because this is audio too. So the device is maybe six inches long and maybe three quarters an inch thick. It's got two contacts on one side and then a button here on the other side.  It's the size of a candy bar and it's about a pound. It's not even that heavy. And back to the stethoscope because it's a big deal here. So you can send those sounds to your doctor. How are you capturing the sounds with this device though? So what you're doing is you just put it on the stethoscope reading and then you just put it to your lungs and you capture a recording. Seriously? Oh, that's cool. But here's where it gets really good Allison, right? If you do a telehealth visit, the doctor can then listen to your lungs in real time and tell you to put it in the upper respiratory area or a lower respiratory area and then listen to your heart and then at that juncture there make a better diagnosis of what's going on with your state of illness. It's not only good for you and your husband, but it's also good for your children and also for aging parents or what not, or however phased you are in your life. There are a lot of people lately because the pandemic have been having lung issues. So this is another, I mean, this is the right time for this product. They say also due to climate change that there's more activity in the atmosphere and that activity is actually kicking up more particles, breaking down particles that are actually more infectious to your lungs. Yeah, the particular problems we're having in Central California is a big mess. Wildfires and any of a lot of rain events that happen right before the rain, the humidity is kicking up a lot of particles. I'm going to ask a dumb question.  When you hold it up to your chest and it's listening to your lungs, is there like a readout on your phone showing what it looks like? Yeah, the readout here, I'm not sure if I'll be able to show it to you, but the readout looks like a sine wave. Turn it around and show it to Steve there. Yeah. The screen you're looking at. So it's got different modes. He's popping through. He was on stethoscope. That's the readout that will be right there. So let's see. Oh, OK, so it's a sine wave. OK, so we wouldn't be able to interpret whether that was a good sine wave or a bad sine wave, but giving it to your doctor, they would. It would be an audio wave that they'd be able to listen. And they would know right away whether there's something going, whether you're not having long breaths or short breaths or whatnot and where it's peaking in its valleys. OK, so BMO is going to do, it's going to do my temperature. Is it a temperature? It's going to do blood oxygen. Blood oxygen. It's going to do ECG. It's going to do your heart rate as well. And it's going to be able to listen to your lungs and heart. Wow, this is amazing. So when is this product, BMO, going to be available? You'd never ask. This will be available at the back half of the year, as we say, fall. So it'll be in time for Christmas, and it'll be $250. That's an amazing piece of equipment for $250. And we've been big fans of your products for a long time, so we've got a chance to talk to you. This is great, Paul. Thank you very much. Allison, you're the best. Thank you. All right, and we would go to withthings.com, correct? withthings.com to get all the information on all our products, especially BMO. OK, very good. Thank you. But one more thing. Oh, wait. If they sign up, if they go to withthings.com right now, you can sign up and give us your email, and you'll be the first people to be able to buy it. So we treat everyone who signs up on that list first to get first crack at it. Very cool. This sounds fantastic. Thank you so much. You got it. Thank you.


Ewan oedd yma, ddweud am ymdweud yma, a rydyn ni'n gweithio ar y ddweud yma a'r dweud i'r Dwybl yn Centrall. Mae'n gŵr o'r gwbl yn ôl, ac nid oes i'n gweithio ar y ddechrau, ac rydyn ni'n mynd i'n wneud yr oedd ymddangos Sèry yn ymddangos eu cyffredinol i'r cyffredin hon yn ymdweud o'i ddaf yma, ac ymddangos ymddangos ar yr oedd ymddangos ymddangos yma ar y cwyr nhw, ac ymddangos ymddangos eu cyfr. Isaeth yn adill ar y cyffredin cyllustu gyda dwyd yn ofaeth y c pelwyddiol. A beth rwy'n gobeithio ychydig yn ystod gydweithio'r ffewrdd yn gweithio'r sefydliadau gan beth y gallu cyffredin ciliriaeth arall rhan o'i gydweithio. A hynny byddwch yn dwylo eich gaflu ar gwrthwyr gyngor. Roedd, oherwydd ciliriaeth ar gweithio'r eich bobl, ac yn y briforolus i gweithio, yn ystod dda'n ymhwytaeth a'r ystyried ymateb sydd yn ymddangos, yn ychydig ar gyfer y pethau yma ar y proses, ac yn ymwyaf ymweld yr ysgol yma ymweld yr ysgol ymweld yr ysgol, ymweld yr ysgol yn ymwyaf yr ardal Patrick. Cymru'n argyfwng arall, dyfodol yn ymweld yr argyffredig hynny yn ymweld yr ysgol, edrych gyda'r ysgol, y gallwn i'n rhaid i'w ddweud y cyfnodau bod y cynnig yn ei ddweud yn ymgyrch. Mae cyfnod ar gyfer y cyfnod am gyfryd ymgyrch gyda'r ysgol ymddiotiaeth yn ei ddweud i'r ysgol ymgyrch gyda'r ymgyrch gyda'r Yrddangodol, ac mae'r ysgol yn ymddir i'r hyn o ddysgu'n dod oedd yn ei ddweud o'r yr edrych ar gyfer gwneud ymgyrch gydag yn ymgyrch gyda'r cyfnod ac yn ymgyrch ar gyfer gwneud ac y gallwn cyfan wedi ychydig frysgau yma. Roedd o lawr sy'n ddych chi'n gwneud y concept ac y dyfu'r ymgylchedd i'w beth, ar gyfer ddechrau, byddai'r cyfaint cyfaint yma. Roedd o gynhyrch a ddysgu ddysgu byddwn yn meddwl i'r cyfeiniedl ar gyfer ddych chi ar gyfer ddydd byddwn yn y cyffredinol yma y byddwn yn gallu chi'n gwneud am y ddechrau. A'r cyflwydd o gyrraedd drosdyn yn ôl ac sy'n cael ei roi ein cyfaint gan rhain gyda'r cyfaint sydd yn y gyrhaf, ac yn ymgyrch yn Llyfrgellton Llyfrgell o bobl o'r drosol, этиiru y ddiweddordeb sy'n cyfrannu ychwanegi ymdau yng Nghymru sy'n gwneud ymmyl iawn ac yn y gyrtu'r gwynedd cyfaint. Ac oherwydd byddwn i ni i ni'n ddigwydd ar hyn o erbyn, gyda'n ei wneud o'r cyflwybr oedd yn ganfer o'r ddodol, dweud o'r ddodol, o'i arweithio o'r awr interlocki. Dwi'r reflectedio, dwi'n meddwl ei wneud, oedd yn gweithio i gyd yn i'r awr o'r leidio. Felly yn fel gael'u gyd yn ei weld o'r leidio i'r gwlad dweud o'r garfynau. Mae'r digwyddr ddwyll Dont Ddiadau bawb. Rhaid o'n rhaid ac yn clomiadwyr sy'n cyfwyrd fel myfyrdd mwy o'r cyfoedd. Rhaid o'r cyfwyrd i'w wahanol, ond rhaid o'r cyfwyrdd honno a'r cyfwyrdd byd. Mae'n rhaid o'n cyfwyrdd y pwyl, a wedi'i ffau y gweinig. Rwy'n dda yn fwy o bwysig, lle rhaid iddo ddweud yr edrydd i fynd bobl a gyntaf i'r funins rheolaeth Rydymol Rheinsiadol. Mae'n groes yma yn ffordd am y cwrdd Rheinsiadol yn adnodd cyfnod o'r ffaith comwr i'r newid am oedd gael eu cyfarfain oherwydd, ac yw gwirionedd mewn mynd i'r proses ychydig i'r cymysgfaeth eich累gen o'r dweud o'r greu cy freelyr yw'r hyffordd ym heddiol. Felly, ydych chi'n gweithio gweithio am y celfaith yma, a rwy'n cael ei gael'r barod o'r wneud yn y bydd yma, ddod yn ôl yn ni, ac rwy'n gofyn am gweithio i'w ddiddordeb yn y gallu'n gweithio'n gweithio'n gweithio'n gweithio. Felly, mae'r ddweud ystod yn y gweithio'n gweithio'n gweithio i gael'r barod o'r wneud. Yr ystod, yn y celfaith ar y Patrige'r werth, ac yn y celfaith ar y celfaith. mae'n addysg ei meddwl o'r cyfweld a'i ymddangos ystyried. Ydyn ni'n fwyfa'r cyfweld i'r cyfweld, gyda'ch yn bach y prosiectau peticoli a'r polisi economaeth, ond y tu'n meddwl yn oed i llwyafol iawn i chi, i ardalol iawn i gryf wladol. Ond oedd y gallu cyfweld i'r gwasiwn ffasiliad dowod o'r polisi兩ndol. One of the issues that Patrick explores in this book is the degree to which that perspective was missing in the run-up to the crisis period, where during that period it was assumed that we can make particular national budgetary decisions, make particular decisions in relation to the level of credits within our economy, but not be aware of the fact that, while we had a currency, obviously, We shared that currency with many, many other economies and countries.  We overlaid that with our membership of the single market. We didn't put enough focus on the fact that that conferered responsibility on us and didn't also give enough thought to the fact this is an amplifier not only of benefit to a national economy, ac yn ydych chi'n meddwl cyfodol. Mae'r team yw'r hyn yn ymhwylliant ar Y Patriarch i'r llwyr. Roeddwn i'r cyflwyno'r cynllunau. Fe yw'r ddebyg yn y cyflwyno ym mhwyaf â'r gynllun. Mae'r ddebyg yn ymhwyaf. Mae'r ddebyg yn ymgyrch ar y dyfynol ar gyfer mewn cymdeithasol, ac yn ymgyrch ar gyfer y policy. Ychydig o'r ffagorol ymgweld y Patriarch yn y llwyddon yn y bwysig, rydych chi gan neb unemployment hon ac yn meddyliad yn ei tanffordd. The second thing that was important to me was the other sea of the volume which is of course levels of credit. The book is a salutary reminder as if we need one but we always need to be reminded of us of these supercharged levels of credit that were available in our economy across our period. The cathastrophic effect that it subsequently had Mae'n gweithio'r cyflogol gyda'r ffigol. Rwy'n gweithio'n gweithio'r gweithio, yma yw'r pwysig mai 2008. Gweithio'r Llywodraeth yn y gynfaith i gweithio, ti'n 57 bilynyddiadau i 157 bilynyddio. Mae yna'r rhai diwethaf ei ddylch. Mae'n dweud i ddechrau'r cyflogol, ond dyna'r gweithio yn rhan o'r llwyffol, was not only the quantity of that credit, but it was the composition of that credit, how it was made up. By the mid-2000s, two-thirds of the loans in our economy had a loan-to-income ratio that was greater than three-and-a-half, and one-fifth of loans in our economy had a loan-to-value ratio that was greater than 95%. So, it wasn't just the level of credit we'd earn in our economy, it was the composition of it, it was the make-up of us, and of course we all know the subsequent vast difficulties that emerged from this, both when it became apparent that the level of funding wasn't actually in place to fund this level of credit, when it became apparent the degree to which domestic savings were utterly inadequate to deal with this level of credit, and our banks became more and more dependent on international capital markets to fund our credit with disastrous consequences for all of us. I contrast that with some of the debate that we have now. It is striking that we are, where we are at this point in our economic development and economic growth, with a level of credit that is a fraction of that. In fact, if you look at the levels of credit in our economy over the last number of years, in many different ways they've been flat, they haven't grown, and we are way below the level of credit that caused such vast harm to us. The next point that, again, I felt was relevant in this book is the work and the debates that Patrick raises regarding the European institutions that were in place across this period. I leave it to others that might speak, or others who read the book, to form a view regarding the role of the European institutions. I'm going to say that quite carefully because I'm still dealing with them myself at the moment. But what is striking in the book is the point that is made again and again is that the institutions, particularly across Europe, were only being put together or were underdeveloped for the scale of challenge that both the Eurozone and Ireland then had to confront. From an institutional point of view, that's particularly relevant to me. Last Thursday night I was in Luxembourg for a monthly Eurogroup and economic meeting. We spent, as can sometimes be the case, up to half-four on Friday morning, engaged in trying to reach agreement regarding the role of the ESM, regarding the role of the ESM being a backstop to future state and banking difficulties, and then engaged in a debate regarding the role and power of the single supervisory mechanism. Patrick's book is very clear in pointing out many of the issues regarding the institutional deficiencies and capacity gaps that were there. While there is definitely a debate to be had regarding the operation of what we have in place now, what has changed is the scale of institutions and the power that they have. I sometimes make this point in debates on this issue that for those who think our regulation of the banking sector has not changed, they've never dealt with the single supervisory mechanism. It's a very clear example of the change that has happened. The final point that was again relevant to me and work that I'm involved in is the point that Patrick makes in his book, not just about the deficiencies that were there in the design of the Eurozone, but also the deficiencies that we had in terms of our own institutions and their inability to be aware of the responsibilities that they had and their role within a single currency zone. If I go back to the first point regarding the incomplete design of the Eurozone, again last week we spent a lot of time engaging and trying to see if we could reach agreement in relation to what the term sheet is going to be for what's now called the BIC. The BIC, for those of you who might not be aware, is what now has been referred to as the budgetary instrument for convergence and competitiveness, which is a debate that is under way regarding the new kind of tools the Eurozone may need to support countries who face a systemic shock and what can be done to deepen the tools that are there. The fact that that debate is ongoing and the fact that that work is not yet complete speaks to the fact that some of the lessons and issues that Patrick identified are still really live issues. The debates done are not yet concluded and I can see at first hand the degree of tension at times and disagreement that exists, not only regarding the funding of those instruments but also regarding their use.  If we contrast that with where we are now, we have a central bank through various legislative changes that has a significantly expanded policy armory open to us than it did during that period, much of which was instigated during Patrick's tenure as governor. The Iraq this then made a number of changes and much of that work now is still ongoing. To give a concrete example of that, tomorrow morning I'm taking to cabinet proposals in relation to how we can look at strengthening the accountability and the sanction regime available to individual key members of our banks. This is a deficiency that was identified by so many but the consequences of it and the harm that is imposed on our banks, again it's documented in many works not only Patrick's but this work is ongoing. We're still involved in much debate regarding changes that are needed and this is exemplified by the kind of debate now that we're having in relation to the conclusion of the mortgage tracker saga, all of the harm that that did and the inquiry that is still underway in relation to us. A very obvious example of the institutional change is now the role of the Irish Fiscal Advisory Council. The debate that I've been involved in and the scrutiny they're placing me under, that is not evidence of institutional weakness, that's evidence of institutional strength. The very reason an organisation like that was set up is to offer views regarding the performance of governments and the responsibilities that they have. And it's then up to the minister of the day and obviously me to form a view on that and to respond back. But this is the kind of change and the kind of contrast in the base and differing views that Patrick in his book makes the point was conspicuously absent. So in conclusion I'm reminded of a comment and a famous comment that was made by Winston Churchill when he concluded in one of his works of history that history is written by the victors. In Patrick's book he makes the point I think towards the end that the scars are still there, so much harm was done and this is a history from which it's very, very hard to see any victors at all, particularly within our own country and our own economy. And a balance that I need to strike and it's one that I'm constantly in the middle of is how we can deal with the social scars, how we can deal with the pent-up need and demand that is still there, that citizens still feel while trying to get the balance right between the needs of tomorrow. And this is the challenge of political economy. It's the challenge of being responsible for an economy that's located within a democracy. Trying to get that balance right between how you can maintain support for what you are doing in economy and getting the balance right between the needs of today and the imperative of tomorrow and this is the challenge. Having read much of Patrick's book and having considered some of the points that he made in the book, what I wanted to illustrate is two things. Number one, that many of the issues that he've identified we have made progress on but we still have more progress to make. And the second point is is that the level of challenge that Patrick described in his book, the cost that is there and the harm that it did not only obviously to our economy, to our society, is something that we always have to remind ourselves of and always have to challenge ourselves to see are there different ways of managing and ways of avoiding this crisis happening again. I believe a really important part of how we have to do that is ensuring there is debate about policy alternatives, ensuring our public debate can be better informed. And one small example of how this is done in Patrick's book is when it goes through the different five currency regimes that Ireland has participated in and goes through the counterfactual example of what we have been better off outside of the euro. And for those of you who want to find the answer to that question, you're going to have to read the book. So on that note, I just want to not only congratulate Patrick for the book, which is really relevant to many of the issues of today, very relevant to trying to understand where we were in recent years, and obviously, at a moment like this, congratulate him for the extraordinary contribution that he made to our country at a time of great difficulty. Thank you very much Minister for such interesting penetrating comments. I think we're very lucky to have such a thoughtful Minister for Finance. It's great that he's launched the book in such style this evening. Thanks are in order. But then, even the people in the room, there's so many people to thank, certainly have to thank Rory and Donal and Dill for hosting the event. I was just thinking... I was just thinking... talking to Donal and to Rory or Donald who's also there. It's now 30 years ago since Rory and myself wrote the first book in this institute about the single currency, and look what happened. No, but there are so many people. My successor, Philip Lane, not only insisted that I write the book and kept on saying, how far is it along now, how are you doing? But he also made it possible that I would have enough access to the documents that I needed because you can't take... And that was important to make sure that the thing is properly documented. And of course the archivists at the central bank. And then I start with the central bank. There's such a list of people who have been vital over the last 10 years in one way or another. So it's just impossible to... I don't know those things. It's up to us here. She's also made it possible. Now that the book is finished, I have no further excuses to be dodging to do... I'm thinking who else could you thank and you think we're bankers. Oh yes, because without the bankers, there wouldn't have been any materials.  And I noticed that the Irish Times journalists picked out that part of the book to highlight that Saturday week. But actually it is something that we have to be careful about is the role of our institutions, the institutions of state and the national institutions generally. First of all, of course, they should function for the people. But if they're seen and if we make cheap shots at everything, all the institutions of state, then the trust and the confidence of the general public can be eroded very badly. We've seen that in other countries and there's always a threat of that here. Of course that means that the institutions must serve the public. So let me come back to that in terms of the central bank. I want to make four points that are not the themes of the book but because everybody in the room knows the story and I hope you'll find some details that you don't know in the book. But just four themes that I thought of perspective that you might find interesting. First of all, the market is always wrong. On average it's right but it's nearly always wrong. And we saw that in many ways. We saw how wrong it was in the years before the crisis up to 2007. It was wrong because it was over-optimistic and thought nothing can go wrong in Ireland. And then after that and then progressively 2008, 2009, 2010 it became too pessimistic and it overshot in its pessimism actually as subsequent events showed. And then maybe by about 2013 maybe had it about right. And then in some quarters with the 2015 the 20-something percent GDP growth market started to get over-optimistic about Ireland again. Now where are we now today? Careful, careful assuming that the market has these macroeconomic things right. And that is the reason why we have to have macroeconomic and financial and financial stability authority. Of course the public sector can also get it wrong and actually within that time frame that I was talking about in 2010 when Greece was in terrible trouble the European official sector was pointing to Ireland. Look, Greece. Look, Portugal. Look at Ireland. Ireland is doing everything right. Well, we were trying to do everything right but we were very far from having achieved that and that was a mistake that allowed them to be shocked when things didn't work out. So they are very complex issues that do require institutions to think carefully about these things. So that's why we have a central bank. What I want to say about the central bank and its mandate is there's been a fashion over the last 25 years that central banks should stick to very narrow mandate of keeping getting price stability 2% on average good rate of inflation not zero for various technical reasons 2% is good, that's all. Let central banks not do anything else and I think that the crisis showed quite clearly that that's not good enough that the central bank must hold there's an implicit mandate for the central bank to pick up other tools and work to stabilise the economy when it goes badly off the rails and that was not learned very quickly in certain quarters in Europe in particular and central banks tend to say with somebody else's problem and I think was one of the things that we insisted on in the central bank we think we have a mandate to do this we are going to do it not only that but when people ask us will you do this as well there were risks in taking on additional responsibilities but we thought if we don't do it who will do it and that also speaks and this is my third point to the role of the central bank in one country in Europe in relation to the rest of Europe a friend in need is a friend indeed and who are the friends well this was quite complicated but one thing was clear to me all along is that the treaty says that each central bank will be represented with its governor in the governing council and that means that vital national interests have to be presented by the national central bank in Europe and fought for and you don't lose your nationality when you go to the ECB to do perform these functions there are responsibilities to the mandate of the ECB and the euro system as a whole have an important national responsibility how did our European colleagues do a lot of discussion of that in the book Europe and the IMF European authorities didn't do as well at first the IMF did because the IMF were used to these situations they were used to countries that got into difficulty and they didn't they could stand back and compare and contrast other experiences they did not have that experience and made some bad mistakes mistakes that cost other countries in Europe as well as the stressed countries like Ireland in the end and I discussed this in the end they made redress you can decide whether they made adequate redress but quite substantial redress was made in some of the arrangements that sorted eventually the banking indebtedness that had arisen with the ECB they didn't want to boast about it but you can detect that they felt bad about how they had handled it earlier on actually going to Dan O'Brien was asking me give us some numbers and it's there you'll find a detailed set of footnotes about all that by the book I just want to say one last thing and I think it's important because I think we've got to when we think of austerity and the fiscal contraction and the cutbacks and all the pain that passed through the contraction of this state's apparatus and the increase in taxation I think we've got to contrast ideology and necessity as drivers of this kind of behaviour and this is true in the 1980s as well as in the last 10 years I mean when when the government of Garrett Fitzgerald that I was working with in the 1980s when they cut made cutbacks and when they increased tax rates they hated doing it they hated every minute of it the Thatcher regime in Britain didn't really have the same attitude they thought this is you know everything's gone out of whack we don't want big government and in a way we have the same parallel in this more recent experience you know we had successive ministers of finance Lenahan, Noonan, Howlin they also hated cutting back it was necessary but they hated doing it whereas Osborne he said we've got everything in balance but we can cut things even more and we think it's a better approach an ideological approach to austerity and I think we need to hold on to that our government policies in this country have not been ideologically driven they have been pragmatically driven sometimes they go off into unsustainable territory and they've got to be yanked back those were the the thoughts I had and you're meant to thank even more people at the end but I'm not going to do that


I think that the first day that I joined the military was probably the most intense day, I would say, of my military career. My name is Alejandro Villanueva. I play left tackle for the Pittsburgh Steelers. I think the composition of the Armed Forces and the NFL have a lot of similarity. Most people that I've served with came from our sorts of backgrounds. I think Westbourne was a really fun part of my life because your college experience that's supposed to be fun turns into a four year journey where you learn and experience things that you never thought you were going to experience. From a commitment and sacrifice standpoint, the NFL is a completely different culture. It takes parallel leadership to gather all this talent and the egos and the different interests and put them into one.


This study found that light or moderate alcohol consumption was associated with a reduced risk of death from all causes, as well as from certain specific causes such as cardiovascular disease, chronic lower respiratory tract diseases, Alzheimer's disease, and influenza and pneumonia. Heavy or binge drinking, however, was associated with a higher risk of death from all causes, as well as from cancer and unintentional injuries. This article was authored by Yalan Tian, Jia Hui Liu, Yu Jiao, and others.


What's up everybody? Jason here for Jasper's Case Breaks.com. Another Wax Party promo break sold out 2021 Penini Immaculate Basketball. This is a one box break. Round of the teams were a 52. High risk hardware guys, put some good stuff. Here's the dice roller. Customer names. Remember only 10 bought in. Straight up the rest were sold in two fillers. Hawks down to the wizards, and then we'll come back around to my customer names. Number one gets Wax Party Promo spots. Roll it. Five hundred one six times. One. Two. Three. Four. Five and six. Six. Carl down to Brian Frank. One six times. One. Two. Three. Four. Five. Six times. Six times. Six times. Carl with a bull sorry. Warriors. Pacers. Nick with a horn. It's Carl with a necks. Nick with the nets or nuggets. Sorry. Brian Frank with the heat. Carl with the T-wolves. Nick with the jazz. Brian with the raptors. Carl with the blazers and pistons. Nick with the pelicans clippers. Terry with the hawks. Brian with the Celtics. Bjorn with the spurs. Carl with the magic. Nick with the thunder. Carl with the suns. David with the bucks. Or sorry, Nets, I should say. Brian Frank, you have the bucks. David with the wizards. Carl with the 76ers. Dylan with the Lakers. Nick with the mouse. David Green with the grizzlies. Brian with the cows. David Green with the kings. Brian Frank with the Houston rocket. All right, any trades, guys. I'll give you guys a quick trade window. No trades, guys? Just keeping it as is or what? All right, let's close the trade window. All right, so we have one two three four boxes. Let's see if I can roll a one two three or four. Well, let's see that. Let's see that. Two on two. Season zero would be for the next ones. Didn't see, didn't see, didn't peek. Steph Curry, base. I'd sell all right. 1799. Steph and Curry. Go and say wars. That's Carl. We got a De'Aaron Fox. Relic to my do not. David Green with the kings. Jumbo Jersey numbers. James Wiseman. When is he gonna come back? How old are you guys? 40 to 45. Is he already back? I don't think he's back. Another one for the wars. We have Brook Lopez. The 99. That's Milwaukee Bucks. Brian Frank. A patch autograph here of Joe Harris. Kaminga's great. Yeah, he I think he's kind of established himself there. I think now it's just like eventually depending on how the next season or the off season goes for them finding room for Tim to play more. And last hit is Pat Williams. Initiation Inc. For the Bulls. Carl with the Bulls. There you go, buddy. That's number 25 out of 49. All right, so nothing too crazy here. I don't know if Evan pulled anything long two in the first box. I think hasn't already. I'll reload it guys. But let's keep it going guys. Thank you guys. So this is the number 52 53 should be in the store already. If not, I'll post it. And again, wax party promo spot being given away. Number one after three times gets that spot. One, two, oh, three times. So 29 sad people, one happy person and that's going to be Nick Smith. Straight up. Congrats, buddy. Well, after three times. So let's paste you in here. I think we did one Wednesday. Sweet. Congrats, Nick. And thank you guys. Of course, number 53 on the website already. Got to do two fillers in 10 spots. So let's run that back. Jaspy's case breaks.


Growing up you were probably taught to work hard, right? To delay gratification or there's even a phrase called to eat the frog. What does that mean?   But this all assumes that work is supposed to be unpleasant. That work is supposed to be struggle and strife and suffering. And I want to offer you a reminder of a different way. What if all of your work can be done with joy? And this is something that I've been practicing for years and it really has made a profound difference in my business and in my own personal growth. And the idea is a shift in focus. It's a shift in focus from the quality of the result, right? Oh, I got to make a great video. I've got to write a great blog post. I've got to create a great product. It's a shift from the quality of the end result to the quality of the process at hand. So for example, I'm making this video right now. I can think, gosh, I hope this video is a great video. I hope this really helps people. I hope that it goes viral or whatever thoughts I can have about what a great video is supposed to do, right? It's supposed to be like, right? I hope that I'm attractive. I hope that, you know, my message gets across. That's the focus on the quality of the result. I could do it that way. And doing it that way means I would have to feel like I'm performing. I would feel anxious that I might miss the mark or that I might fail. And I can then, but if I catch myself doing that, whenever I do catch myself with that, I shift my focus over to the other side, which is focusing on the quality of the process. So am I bringing heart and joy into this moment? That's really what I care about when I catch myself and remember to do this. Am I bringing heart and joy into this moment? Because if I do that, then my whole day is filled with heart and joy and my whole day is fulfilling. Rather than worrying about did I do a good job on the content or the product or meeting with the client or sending that email or writing that webpage, did I do it? No. I'm focused on, oh, did I bring my heart and my joy into this work? That's it. Now, I do this because I have trust. I have a big trust that my life is guided and always protected by a higher power. Now, I don't know what you believe. Some of us believe in a God or in angels, spirit guides, et cetera. Some of us don't believe in any of it. But even if you don't believe in it, you can still believe in your higher self. You have a part of your brain. You have a part of your psyche that is wiser than other parts. And that part of the psyche is always trying to help you, right? Always guiding you along. So regardless of what you think your eternal source is, we can trust that that eternal source of guidance will make sure that our life is going to be okay. That through the ups and downs, we will somehow still achieve our calling. Remember that. And by having that trust, you can then hopefully relax about the end results and focus every day and every hour on the quality of the moment, your presence in the act of whatever you are doing. So I hope that throughout the rest of the day, you can bring that heart and joy or choose the words that are meaningful for you. Maybe it's mindfulness, maybe it's truth and love. Maybe it's wisdom and grace or whatever it is. Bring the words that mean something to you right now. Maybe it's lightheartedness. Maybe it's compassion. Bring those words into every moment of your work and let the results take care of themselves. And you might be quite surprised that oftentimes the results are actually even better. But we don't even think about that. We forget ourselves in the moment of bringing our presence. We forget the high standards. We forget any standards for the end result. That's the aim anyway, to forget all that and just lose ourselves in the moment of bringing our presence to the task at hand. So I hope this, well, I don't know if it's helpful, but that's the thing. I'm not even here to help you. See, I'm not here to make a great video. I'm not here to help you. Those would be wonderful, blessed outcomes. But I'm here to bring joy and heart to this moment. And if it has helpful results, then wonderful. I'm even more blessed, but I can be blessed regardless. So anyway, I wish you a truly fulfilling day ahead and the next day and the next day. Take care.


about it folks, let's jump over to our man, Teddy Kegstad. You can read Teddy's, Tiger Fork support folks. He puts a new issue out every Monday for subscribers. He puts out updates when warranted. He just hosted a subscriber webinar a couple weeks ago, 60 minute webinar for the second quarter market forecast. He talks about a bunch of great information in there. You get that when you sign up as well. Check it out on the front page of TFNN. You can subscribe, it's $97 folks. It comes with a 30 day money back guarantee. You don't like it for some reason. It doesn't fit into your trading day for whatever reason. And folks, you're gonna get value out of this newsletter, out of the webinar, but you cancel it. You get a money back guarantee and you get to keep all the value over that month and the webinar. And boy, we've got a great day to talk to our man, Teddy Kegstad, good morning. Good morning, Tommy. Yes, we do have some good stuff to talk about. So where do you wanna start on a pretty active day in the markets this morning? Well, we can start with the number. I think that the reaction in the markets is just showing you a really pump and dump rally, if you will, especially like in the bond market. So, I mean, the reality of the number is that, okay, we're just not increasing at the rate that we were, but we're still going full steam ahead with inflation. So, and I think you have to really watch the bond market over the next couple of days because a number like this, you would expect a reactionary rally. That's because just of a short-term blip of the release. As far as the overall reality, the market knows that there's something wrong. And I think you have to really put things in perspective. If you look at like, for instance, numbers like CPI and stuff, they're slowing, but look at where the yield curve is. I mean, the yields, they topped out back in October of 2022. And if you look at over the past say like month or two, we've been kind of buffering up against resistance, meaning yields have been pulling back. Now, that's all because you have artificial buying being brought on by the Fed and other central banks propping up the cash market. And the reality is, how is it after four rate hikes that the bonds are trading much higher than they were five months ago, six months ago, seven months ago? That doesn't make any sense. And it also, think about what it's doing to the banks. Banks borrow money from the Fed, correct? That's how they make loans. Now, the rate that they're paying is much higher now than it was six, seven months ago. Now, if you're paying more for money, the banks are and the yields are retracting, going the opposite way than they should be going, then how much money are banks making, especially when there's a banking crisis? So there's a lot of tailwinds. I think we're gonna catch from this over the next couple of months especially.  I mean, anything can happen, but it doesn't make any sense. Mathematically, and I think you're gonna see more and more where this is gonna give a boost to the dollar short-term over the next few months. And when it happens, it's gonna be a violent reaction as well. Yeah, you got to the dollar. It's pretty interesting, man. The dollar, it's interesting. We're pushing kind of that low of January. You've talked to us about the different pairings and the impact, and this is so Euro dependent and so forth, but it is interesting. We're pushing those levels. And the market reaction today, we've talked about it before. I know you talk about the possibility, man, that we get some hikes continuing. It's always interesting on mornings like this, Teddy, this is my own take, where you see the headlines from great institutions that I love, man, like the Journal, like Bloomberg, talking about inflation easing, and then you get into the core number that's at 5.5%. And we are 14 months into a hiking cycle. It's kind of amazing that you get the easing notion. And I think this is something like the 10th decline in overall CPI. But as you know, man, that crude market, things get shifted around dramatically when you start bringing energy into things. The core number, 5.5, I was talking about in the beginning of my program, like five months ago, we were at about six, and that's near the peak. And so if you're just dropping marginally from a peak, man, we got a long way to go, because if we can't drop from six to five quickly, what's it gonna look like when we're trying to go on from four to three, let alone from three to two? So we find out. We have a long journey ahead of us. And as traders, it's great, folks, because you see in the volatility everywhere, whether you brought up bonds, I was looking at bonds when you were walking us through that. I was looking at the dollar index, just magnificent moves, man, in both directions. Can we jump to crude a little bit since I just brought up some of the headlines, man? We've had some interesting action. In crude, we hit 63 bucks after I talked to you last week, last Wednesday, and then from there, we've popped back kinda into that $72 range. What do you think of the price of crude? Okay, well, you gotta realize we came off of, we hit that low last week. We were coming off a very big slide, over a period of a couple weeks, crude dropped $20 some dollars. So the bounce off the low from last week, I think is very normal to have a correction back to where we're at. So I think that the market was overdone on the slide last week. I don't think that you're gonna see crude trending lower. I mean, I don't see us going down to lower six, holding lower sixties, let alone going into the fifties. I mean, the only thing that would bring that on would be a totally decrease in demand. Well, how is it we're gonna have a decrease in demand when we know we're coming into the summer? And if the travel and leisure business is really doing as well as they're saying, that means people are traveling. That means there's a demand for gas and for oil. So that part, I don't see really trending. I see it maybe in the choppy wide range trade for the next couple of months, that's possible. Maybe especially if there's some sort of increase in production on our end. And that would really be the only thing I think that would really get us to trend lower. Obviously, if they open up the floodgates and take away all these rules and regulations they put in place a couple of years ago. So for oil, I'd be very cautious. I'd be a buyer of dips, especially when you have extremes like what we had going down last week. I mean, when you have a $20 slide in crude, and it wasn't really because it wasn't lack of demand driven, so that's where I have to say that you have to be careful with it and look for more potential to the upside. And it is interesting, man. Just pulling it up on the chart. I mean, yeah, we got a little bit of an ex exacerbated low in March and exacerbated low in May. I got above 82 bucks, but this thing's almost been a consolidation since last November between only about like 75, 72 and 82. Just remarkable considering how volatile things have been overall. And since November crude just kind of been trapped. You know, you got outside of that area a little bit. But as you mentioned, you've kind of recoiled. And I just put a Fibonacci number on that pullback. Yeah, from 83 bucks down to 63. And where do we just pop to? About a 50% retracement was all it was. Up to 73 dollars. How about the end? Can we talk a little bit again? Because I know that's always interesting for our subscribers. What do you think of the end? Pulling back today, 134.39. I think that that's all because of the number. You know, this was a very, when you have CPI is one of the biggest economic numbers that you have coming out on a monthly basis. And it's a very big interest rate number. So excuse me, interest rates drive as a functional pricing mechanism for the dollar or any currency. So when you have a big rally like this, meaning a pullback in yields, the dollar gets whacked by all currencies.  And it's not, everything's retreating. Like the yen right now is close to its lows for the day. You know, you saw the Aussie breakout to the upside, but this is all because of that number, you know? So if everyone really believes that inflation's disappearing or something like that, then it's sustainable. But this is just a news-driven reactive day. And that's where you gotta be careful where it's where you buy the rumor, sell the fact. So you got the pop on the number, you know?  Something like 60 pips today off that number. That's not a big move, you know? I pulled it up and he said at the euro and then I pulled up the pound, man. Quite the charts for sure. So the yen's going sideways to higher. No wishing, no hoping, no praying, right? I love that class, man. Teddy, thanks so much, man. We'll talk to you next week. Have a great one, man. Thanks, Tommy. You take care. Thanks, man.