Voila. Bon dia. So today's language of greeting is Portuguese. All right. I thought I would continue from where we left off yesterday. See, the Lorentz equations were written down in 1963 or thereabouts. And those were the days of very slow computers and so on and so forth. But since in the last 60 or so years, there's been a huge, huge amount of both analytic as well as computational work on a variety of the Lorentz system and various other attractors, which I will talk a little about today. And the Lorentz is like the hydrogen atom of chaos explorations. So a lot is known about it, partly because, A, it's quite simple. And the other is that, you know, as you build up more experience, there is a lot more to understand about the system. All right. So the idea of attraction to some set, which is not a point, not a circle, on which the motion is chaotic, mainly that it shows sensitivity to initial conditions, this is like a crucial idea in complexity. That different initial conditions still give the same final result. Then there are lots of ramifications of that. But the system is simple enough, so one can actually try to look at it from what we were doing for two-dimensional systems. You can find the fixed points. There is one fixed point always, which is stable up till the value rho equals 1. And it will occasionally switch between rho and r. So the second two fixed points, these are two actually, they exist only above rho equals 1 on the real axis. So the behavior of the system has largely been explored as a function of rho, keeping other parameters fixed. And this is a schematic of a very complicated bifurcation diagram. So as you vary r, that is, if you're varying rho, initially 0 is the only fixed point. At r is equal to 1, there is a bifurcation making 0, 0 becomes unstable, and these two fixed points, they're called c plus and c minus, they become stable. So the idea is that there is one branch which is going out from here and another branch which is going out below. I'm just not, this is the symmetry in the system because there is this, the Lorentz system has the symmetry that it is invariant under this transformation. X, Y going to minus X minus Y, Z being, between 0 and 13.926, which is actually a precisely calculable number, there are only fixed points in the system. There's one unstable fixed point and two stable fixed points. If you look, the two stable fixed points have got different basins of attraction and 0 has, I mean, 0, of course, is fixed over here. So the whole of space just collapses into these two fixed points. No matter where you start, you'll go there. Which this one? Yeah. Or just algebraically evident. The y side, though, the rule of change. No, Z is not, you see, it's X, Y, Z going to minus X minus Y, Z. All right. So at 13.926, there is a bifurcation leading to the following situation that there is an unstable limit cycle and this point continues to be stable. So there is this bifurcation that happens over here and this unstable, sorry, the unstable limit cycles, they are actually born out of an unstable fixed point, which then becomes stable. You can see the dashed lines are all unstable. The solid lines all indicate stable. And this is called the hop bifurcation, namely when a stable fixed point crosses a certain, at a particular point, as you change the parameter, the stable fixed point becomes unstable and there is a stable limit cycle that is born. I will consider the Stuart Landau system a little later and I will show you how that happens on the board. So that is actually reversed over here. So you have this fixed point stable up till this value of whatever, R, H for hop and then that becomes unstable. Now, for this particular system, it turns out that up till this value over here, 24.06, I mean these are both important and not important, meaning other systems will obviously have very different kinds of bifurcation diagrams. They will have a whole different zoology to look at. But you have a strange attractor which is born at 24.06 and that goes on. But for a very brief period, the strange attractor coexist with two fixed points. Some initial conditions take you to the fixed point, some initial conditions take you to the strange attractor. And these have very interesting topologies to look at. As I've already told you, this is the values that Lorenz settled on and these were really nice because R is equal to 28. There are no fixed points that are stable. You only have the strange attractor. And if he had chosen a smaller value, there would have been a more complicated kind of... I mean it would have been very difficult to get so much interest in this business. His whole idea was to try to prove that the weather is aperiodic and therefore not predictable, where the forecasting is not an easy science. But I mean there are many things, if you plot them in three dimensions, they settled on to a complicated state. But this strange attractor is not a point, it's not a curve, or even a surface, it is a fractal of some kind. The word fractal is okay with everybody? Yeah? No? Okay. Monday. Small introduction, but Monday. I mean right now I want to do something else. Okay. Yeah. Why there are... What is an unstable limit cycle? Like an unstable fixed point. Okay. Let me look at the following equation. So if I look at this particular... And okay. So here obviously there are three fixed points for this equation in R, which is R is equal to 0, 1, 2. Yeah? R is a radius, always positive. Yeah? Yeah. Is it just by construction? So now if I've got R, if I'm just looking at R, this is 0, this is 1, and that is 2. These are the fixed points just along the radius. Right? Yeah. I'm sorry, I come up with these slightly silly examples, but you can expand it. Yeah. Okay. So here you've got a trajectory which is on some surface. Okay. So let's go just by elimination. Is it... Can it be a one-dimensional... Can the trajectory trace out in one dimension completely? No. Yeah? Important point is that at any point there can be one and only one trajectory. So even though this curve seems to be crossing and crossing and crossing itself all the time, it cannot be crossing itself... It cannot really be crossing itself. So the surface, you know, this flat thing that looks like the wings of a butterfly, right? There's actually many, many, many, many... I mean, there's an infinite number of layers over there. The trajectory goes back onto the same parts of space but without ever intersecting. No, we're looking in 3D. I mean that's perspective 3D. This is a perspective diagram in 3D. When you look at it, this trajectory is never repeating and it is occupying the same part of that space. Right? Yeah. So one thing we know is that it cannot be a two-dimensional surface because if it was a two-dimensional surface it would have to cross itself. You go... I mean it's many steps from there so it is a fractal but I'm just saying it is a fractal. It has that fractal geometry which is why it allows the trajectory to explore many, many... You know, if you cut this in a straight line, right? If you just cut one of those wings of the butterfly by a straight line, you would not see two points only. You'd find actually many, many layers. Yeah? Exactly. Exactly. And then you can measure and whatnot. Some of these things are very difficult to prove mathematically actually. So self-similar... No, you shouldn't. You're seeing it. You know, stop taking what you're taking. It's fractal in the way in which, you know, if you cut it, then when you start looking at it you'll find that it's all going on different layers. Okay? All right. See the last part of it, the Lyapunov exponents can be calculated for this system and as I told you, I just asserted yesterday the three of them. The three come because of the following fact that there are three equations of motion over here. So this entire system starts out in R3. Then there is an attractant. It brings you down to zero volume. Why does it bring you down to zero volume? It's because you can see that the divergence of this vector field over here, right? You've got that vector field over there. You can calculate its divergence. It is just sigma, sorry. It's minus sigma, minus 1, minus beta. Minus sigma, minus 1, minus beta. The sum of those three terms is the divergence which is that. Now in a theorem which has been proved by, you know, a long time ago, the sum of the three Lyapunov exponents has to be that. Right? So it turns out that one of them is positive so long as rho is bigger than 24.74 something. All right? That is, sorry I should, okay. So at least one of them is positive from this point onwards. That is a whole nother story. I mean it is something that for a very, very long time is unrepeating and so on and so forth. And then I'm not even sure what finally happens but that's how long it goes on. Okay. Another system, yeah? Because you're working in three dimensions. No, I didn't say that. There are three Lyapunov exponents because you're working in three dimensions. But it is not as if you can associate one with X, one with Y, one with Z. What happens, I mean what you can show is that you must have three Lyapunov exponents. That's one assertion. The second part is that because there is only beginning now, there's some understanding of what these Lyapunov dimensions are, what are these three of them? Because the transformation between that and the XYZ is not simple. So it's not as if in the X direction if a positive Lyapunov exponent, you're blowing up an X, that's not how it happens. Again, in the Lorenz system, all these three coordinates are all mixed in one into the other. So it's not as if you have evolution only in X, only in Y, only in Z. So the, what's the definition of? Okay. Okay, so a little time out before I come to the other system on the board. Practically how you study this system, you've got these three equations, which gives you the orbit, the ones that I've been writing down, sigma Y minus X, whatever that is. Now, the Lyapunov exponents are computed as I was trained to give you schematically yesterday. You start with the unit vector, right? And see how that grows along the trajectory, right? So to calculate the unit, the, and this unit vector is, you know, is, it is estimating the slope at each point. So it's actually going along the tangent, right? You've got the trajectory itself and the growth of this unit vector that you have is determined by the tangent with some tangent space. So for that, you look at this equation, delta X, delta Y, and delta Z. This is just looking at the linear motion. So if I, see, let me write down the Jacobian. It's minus sigma, sigma 0 and the ZX, what's it? Minus Z plus, I'm sorry, minus Z plus R. It's 1 minus 1 and with Z it is X, right? And the third one is YX and minus beta. So this is the Jacobian. I've just taken, you know, just taken, if I call this F sub X, it's partial of FX with respect to X, partial of FX with respect to Y, partial of FX with Z, and so on and so on. So that's, and then you fill in the others and you get a matrix like this, okay? So what I'm going to be interested in is looking at the dynamics of displacements where delta X dot, delta Y dot, and delta Z dot is given by this Jacobian times, I mean some of this must be familiar, right? Okay? So now I have to start with a unit vector. So this unit vector could be 1, 0, 0. It could be 0, 1, 0 or 0, 0, 1, any of these. So what I do is to start with all three of them. So this is my equation for the Lorentz. Now I come up with three evolution equations, three sets of the tangent vectors. So here I get, let's say the first one, then similarly for the second and similarly for the third. I mean there are many ways of doing this, but I'm just describing the way in which it's computationally the most straightforward to look at. So I start with three unit vectors and as they move along the trajectory, they will change from being the three orthogonal ones to some point over here. At that point you ask, right? What you ask is how much did they change in the direction X1, in the direction Y1, in the direction Z1, etc., etc.  But now they are not pointing in, let's say in X, Y, they're not pointing in this direction. They're going to be in some other directions. Then they evolve around the trajectory again. And here again they have changed. Maybe they're looking like whatever. And then again you normalize, bring them back and you follow the trajectory as it goes around, each time going a certain length, seeing how much the length has changed and so on. So when you do that, you will find that there are these three quote unquote directions and initially of course it started out as X, Y and Z. But because of the way in which the evolution takes place, you find that they are just three of them, not particularly with X or Y or Z, because the flow mixes these directions up. See sometimes I mean staring at equations and trying to calculate it is a good way of doing it, of trying to get some intuition about it. So the main point is that if there are only three Lyapunov exponents and one of them is positive, then everything is going to expand along that direction, but that direction keeps changing as you go around the trajectory. Here is another direction which is severely contracting because the divergence of the whole vector field is something like this. It is e to the, what's it? The volume will go as volume naught times e to the 1 plus beta plus sigma times t. And for the parameters that you have chosen, it's sigma is 10, so that's 11 and beta is 8 by 3. So those are the ones that I said we use the calculation. So it's something like 13. So at each time step the volume is decreasing exponentially by a factor of e to the minus 13. That's why the volume is going to zero, but it could go on to zero if it was going into a two-dimensional plane or onto a one-dimensional line. But you can see that it cannot be a two-dimensional plane. So this is sort of the natural place where fractals start making their presence felt. Now there's a simpler set of equations called the Rosler equations which some of you may not have seen before. I mean, Lorenz I think everyone has seen, but Rosler is not quite so common. Although it is much simpler, there's only a single, there's a single term which is nonlinear and that is the xz in the third equation. You have xz. Unlike the other systems we've been looking at, 0, 0, 0 is not a fixed point. There are two fixed points for this system and one of them is the one marked in red over here. And there is another one somewhere out there that doesn't have any interesting dynamics around it. What is nice about the Rosler, and here's this part, the flow actually is not confined to a folded two-dimensional surface. Rather to a folded disk of finite width. There's been a lot of work on the Rosler systems, even though it's relatively less familiar. Now the point about the Rosler is that if I view it from above, that is if I project everything down to the xy plane, that's what it looks like. The motion is always circulating about this point. Of course, this is just a flat projection. It's always circulating about that point. But it's chaotic, even though it's circulating about the point. It is chaotic and I just thought I would show you one little demonstration. Two initial points that start out close enough but slightly differing in z. You can see that the way in which, hopefully this will also give you some intuition of Lyapunov stability. This is not Lyapunov stable. So we started out together, but then the trajectories are really evolving differently. But is it okay? No. See the point is that if you choose your epsilon, you should say how close delta, how close they have to be. And it's not possible to define it this way. And they have to be small in any case. So the point that I was asserting over here, that the orbit keeps circulating around and around and around. Now because it keeps circulating around that point, it is actually possible to think of defining something like a phase. Because this orbit, if I just project it onto the xy plane, is going around some point. And I can just ask what is the value of tan inverse y by x? Supposing I think of this as some polar representation. And people have actually done that. That you define the phase as y by x, the arc tan of y by x. And then ask how does that phase behave? Because the phase would be normally defined for a cyclical orbit. And for that, if you use some kind of polar coordinates, it's always tan inverse y by x. So just taking that, hence, if I just ignore the amplitude variation in these various cycles, this just begins to look like motion around a circle. I've forgotten the radius over there. And if I'm just looking at motion around a circle, it comes back with a little more algebra to the Kuramoto model. So you should not be surprised to know that if I, if instead of taking n-coupled phase oscillators, I take n-coupled Roslars, I will also find something like the Kuramoto system. I mean, it's not obvious that it happens, but it actually does. And the part of the motivation is the, is the fact that it goes around the circle. Just a second. Yeah? Yeah. Yes? Okay. So the argument really is just by visual inspection, you can see that, just one second, let me get this, that was the last of, it's just the following. See, now you're going around some particular curve over here. Now, it never happens, unlike the Lorentz system. In the Lorentz system, we were going back and forth, you know, going in positive x, negative x, positive x, and so on. Similarly, in y, z was always positive, right? But here, z is, I think, always positive as well. But you'll never find the trajectory crossing, changing its orientation or its direction. So now, if I forget about the distance from the point of circulation, I just have something that is moving around a circle. And so I can replace, you know, I can just say, ignore the radial direction. I'm just looking at the circulation. That gives me a phase. And so, if I have only a phase, then, you know, I think about all the other nice systems which have got only a phase. Kuramoto comes up. Yeah? Okay. Yeah? Okay. It doesn't, see, some of it is a little optics over here, in the sense that this distance of where it has to come before it goes further up is, I'll just try to show you what that is. See, just how far it will jump when is not easily determined by the distance from the illusory fixed point. I mean, the fixed point is not actually in that plane. I'm not sure. I don't know the precise scales. But you can see now how erratically it seems to see the z being large or z being small. I mean, that's where the chaos is. No, but, you know, there is probably some region in the three-dimensional space which is more expansive than others. See, these exponents are not uniform all over. I mean, maybe after the lecture, because I want to get some of these other things out of the way. I want to introduce you to the idea of chaos synchrony. But one can discuss, it's not uniform. You couldn't see that. You saw how suddenly it runs up and goes down. That was the point. That's why you can define a phase. Because if it went up and then came down and circulated over there, then you wouldn't be able to define the phase. It goes up and then goes down and goes round and round and up and down. Yeah, it is an interesting question, though. Is there some proper surface that one can... Maybe we can talk a little more with some more calculations. Yeah. All right, so let me get to... Part of the reason I introduced chaos before coming to the idea of synchrony is that you already know to some level what synchronization is. We saw how oscillators of different frequencies can pull each other. They drag each other. And then as you keep increasing the coupling, they have identical motion after a while. Or they can have anti-phase, which was another manifestation that we saw. But we've seen this both for the case of maps. We've seen it for the case of one-dimensional flows, the Koremoto and so on. The real surprise about synchronization as a paradigm came about when it was discovered experimentally and theoretically, more or less the same time, that you could have synchronization in this system. And this was an observation in the 70s and 80s. All right. Now, you've seen this picture before. This is what the Lorentz attractor looks like. A typical orbit in the Lorentz attractor, it looks like that. And one could imagine that regular oscillators can synchronize quite easily. We had all those examples of circle maps and so on and so forth that it could have anything. But it's most commonly known with the name of Pecora and Karel, but it was already done earlier by Fujisaka and Yamada, and also maybe even earlier by Afraimovich and others and so on. I mean, people have been worrying about not precisely synchronization, but interacting oscillators and so on and so forth. Afraimovich was a Russian who lived in Mexico, I think. Large part of his career was in Mexico. Just saying fact of interest. So what Pecora and Karel did was the following. They said, let me take two Lorentz oscillators. One of them got the variables x, y, z. The others got the variables x prime, y prime and z prime. So I'll make two perfect copies, all the parameters identical. And I know that if I start this with one set of initial conditions and this with another set of initial conditions, they're going to just go wherever they go and so on. We saw the example where I showed you that different points are eventually attracted to the same strange attractor. So different initial conditions should not coincide, and they just evolve on their own. But now what they suggested was in the second of these equations, change x prime to x and wherever x prime appears, just say that instead of taking it from this equation, you're going to take your input from the output of that. So the unprimed system becomes the master, and it gives the signal of x to the slave. So this is what is meant by master-slave coupling. It doesn't matter because whatever the x variable does over there just doesn't matter. It also becomes x. So I'm going to sort of show how this is actually, you can put it in the framework of various different things. But when people talk now about master-slave or pecorakarrel, this is what is meant. That some variable or some sets of variables from one system are given unidirectionally to the other system, and that's it. Now, just to show you how beautifully it works. I think this variable is y. And what you see is what I've done is to take the two copies, green and purple, and I make the purple, the master, at some point, t equals 10. See, initially they are independent of each other. They're moving around, and because of sensitivity to initial conditions, the green and the purple are just on the same object but evolving differently. At this point, we mix them, we make one the master, and after that you can see very, very quickly it's just impossible to tell the two apart. The y coordinates becomes identical. The z coordinate also becomes identical. And as a matter of fact, just one second. I don't have that particular curve, but if I look at the distance between z and z prime as a function of time, that just exponentially goes to zero. So the difference between z and z prime just vanishes. The difference between y and y prime here is sort of visually vanishes, and x who cares. But the dynamics is still on the Lorenz attractor because, see, the dynamics of the master is unaffected by whatever is going on in the slave. So the motion is on the Lorenz attractor. It's just that this other attractor has been brought, the x prime, y prime, z prime, they've just been made to coincide. So, right now, the crucial thing that Pecora and Carroll also discovered when they were doing this work was that this system of equations has got three Lyapunov exponents. If I follow this through and go ahead and do it, I'll get three Lyapunov exponents. Effectively, this is now five equations. So there are five Lyapunov exponents. So when they computed the five Lyapunov exponents, what they discovered was that interestingly enough, if you have these five Lyapunov exponents, three of them are the same as the old ones because that dynamics is not changing at all. But then you've got two more. And whether they synchronize or not, depends on the signs of those two extra ones. I've already said that if you have one Lyapunov exponent that is positive, you're going to be chaotic because the distance is going to grow exponentially fast. What goes on when you now couple this in this way and you ask why do they synchronize, there is some other dimension, out of these five dimensions, it's difficult to visualize, but in two of those dimensions, the Lyapunov exponents relevant to those extra dimensions are both negative. If that is so, then you can synchronize. In particular, if you couple them not by making the X signal the master, but if you made Y the master. So that is to say, have these equations, but now with changing this to Y, this again will not matter. And this particular one, make this also Y and X prime Y. So if you make Y the master and in this geometry, it doesn't work because the subsystem, these are called these additional two Lyapunov exponents, are called the subsystem Lyapunov exponents, those are not negative. Totally different. Converged to the chaotic trajectory. Not in Lorentz because Lorentz is globally attracting for all. This is just a phenomenological, part of it was engineering, part of it is there was some idea that you could use this in secure communication because you take a chaotic signal and because it's chaotic, nobody can predict it. You mask a message with this chaotic signal and have it received by somebody and then you tell them, hey, I was using Lorentz with these parameters and eventually they should be able to figure out what's the actual message. Chaos plus message minus chaos is equal to message. It doesn't, I mean it works obviously but it's not good enough.  They know what you're thinking anyhow. But okay, to the point, I just want to say that look, this is something which is a control method. All right, because as, you know, just to see how it goes, but I'd like you to see it a little more in the following way. So here is your master and here is the slave that has come but the master and the copy of the master is these up till here where all the variables are only the primed variables. Now consider that I add these two extra terms. So without these two extra terms, here is your slave and the additional terms that have been added in red over here are like what the, you know, that's the coupling. And it's a coupling with a control objective. Namely, there is this entire branch of engineering called control theory where you say that if I want my objective to be that y is equal to y prime and so on, there is a way of trying to do the calculations and figure out. So, but this is the kind of coupling that will effectively it will do the following. It will give you these equations of what Pekora and Karel wrote down as the slave equations. Or you can say that here is the slave system and I'm going to make a coupling, a vector coupling in three variables. The first term is zero. The second term is what are these two things that you see over there. So if I was to try to think about it as I'm going to do in a little while but let me just give you the idea over here. If I look at these master system and let's just call it x dot is equal to f of x. These are three f of little x is just equal to f is equal to fx, fy, fz. I'm just compressing all the notation and here is master system. Here is my system that is eventually going to become the slave. This is just notation. So what I've written over here, this is the first equation over here.  Capital Y is x prime, y prime, z prime and the right hand side is this is fx and this is fy. Now the question that I'm asking in a control method is let's leave this one untouched. What is the coupling and for later use I'm going to be calling this zeta. So here is my coupling and it is a function of both x and y that I've added over here. And this zeta in our particular case over there is all in suggesting that this is to be seen as 0 x minus x prime plus rho z, sorry not plus, multiplied by rho z prime and x minus x prime times y. So this gives you a coupling and if you want to write, you can also write down over here zeta x of x and y, where this is just 0, 0, 0. So what I'd like you to see in these equations is that both the primed and the unprimed variables have both been changed because of the coupling. If you don't couple them, they're just going independently all over the place. You add two coupling terms and what's the coupling term that you want to add for the x variable or for the sort of unprimed variables you don't add any coupling at all. For the primed variables you have specifically this one. Now the other day I think Thomas was asking is there only one or can there be more or let me just pose the question, how unique is zeta y or zeta x? It turns out actually that it's not unique at all. There are essentially an infinite number of different couplings that can bring you down onto the kind of dynamics that you want to see. But just a little more work before that. So I think it's sort of fair to say that one should be... This was like a huge surprise that you could actually synchronize chaotic systems because everyone said sensitivity to initial conditions they should be pushing you off all the time. But then it turned out that it's actually amazingly trivial to get them to synchronize. But still it had its moment.  No, no, no, it's fine. I teach at a university in India which is known for its protests. Oh, you can, you will.  When you come to 2020, you will have added all sorts of terms. People have just explored all sorts of... See, these are couplings. These are couplings. So people have... If you can think of a coupling, somebody has surely worked on it. And depending on the kind of system, the couplings are different. The simplest one is like what one observes with two pendulums swinging in phase and so on. So that is one simple coupling which then we just take the first term and the sign is just X1 minus X2, something like that. Believe me, there are reams of paper that have been used in writing this. Okay, I want to talk about another kind of synchrony. See, once it was discovered that you could make chaotic oscillators synchronized in this way, you naturally then went on to all the chaotic systems that you knew. And when you looked at the Rosler system over here, and I've just put in some numbers for the constants in this story, this number Y, sorry, omega over here does actually play the role of the phase frequency. So that will tell you how you're moving around, at least in the XY direction. So what they did was to look at this system with two of these systems with whatever. And the coupling between the two systems is just this capital C times X1 minus X2 or X2 minus X1, the other way around. See, the original equation just has got omega Y minus Z, and the coupled equations has got omega Y minus Z. Have I made a mistake there? Yeah, well, one of these Z's is wrong. Right now I don't remember which. Lorentz I recognize instinctively. And then I've got these terms over here. This is the coupling. So the coupling term over there. And then let me describe to you what's going on over here. What's plotted over here is the Rosler oscillator in the XY coordinates, right, for one of them. And here it is in the XZ coordinates, right, same. So we've already seen that in the little demo. Here are the XY and Z variables as a function of time for a single oscillator. If I just plot, if I write down one of these signals as an amplitude times a phase in the way in which I describe the phase, tan inverse Y by X, okay? The difference between the phases when the coupling is small just keeps increasing. The difference between them, the phases just drift away from one another. As you increase the coupling, the phases now take these sort of long passages of being almost identical, but then you have these things which are nowadays called phase slips, okay? So you have a phase slip, slip, slip, and it just goes up in steps. And as you finally increase C to whatever value this is, you find that the phase difference doesn't change. Finally, they are having an identical phase as a function of time. So the amplitudes themselves are highly uncorrelated, but the phase difference actually goes to zero. And what Pikovsky et al. did was to, first of all, give it a name. So this is called phase synchrony. So if you want to think in terms of the oscillators, it's not as if the two trajectories are identical, but these go up and down at essentially the same time, right? And this is actually a very common kind of synchrony which occurs in nature. So it obviously got a lot of attention. For example, when you look at population dynamics, in many cases you have the fact that the populations are highly correlated, but obviously the amplitudes of the two different populations can't be the same or are frequently not the same. So while they go up and down at the same time, as oscillators, the amplitudes are very different, and therefore the idea of phase synchronization is important. I mean, there are many biological, I think breathing, I don't know, there's something to do with the breathing mechanism and the pulse or some, you know, there are all sorts of phase relations between that. Yeah? I don't know. See, the point is that this coupling is somehow trying to, it's trying to alter the dynamics and it depends on the scales of the problem. So here the omegas, I don't know whether it was taken as one. This is not my calculation, I'm just, you know, reporting from a standard paper. So the coupling will depend on the particular values of these parameters. But these parameters are chosen such that the dynamics is chaotic. In this system actually you can have periodic orbits as you keep changing this number 10. This number 10 is one of the parameters of the game. So when 10 is very small, thinking of 10 as a symbol rather than a number, so you think of that particular, that constant over there is very small, then you have periodic orbits, and once it crosses some value, for example, when it's equal to 10, then you have chaotic orbits. For that, then the range of C may be something else. Meaning that these all depend on a certain amount of analysis that you have to do. That becomes negative. Yeah. You can almost always recognize by looking at the Lyapunov exponent which kind of thing. This system will also, as you keep increasing C, sorry, but as you keep increasing the coupling, you will actually go to complete synchronization also. So phase synchronization is sometimes just called a weaker form of synchronization. Yeah. I'm sorry I didn't get to you. Absolutely they go. So just a little blow-up of the two trajectories. Here is a case when they're not coupled, when 10 is small or zero, when that parameter, when C is zero, the two of them are just totally uncorrelated. When you have phase synchrony, you can see over here that they are essentially in phase, although the amplitude of oscillation is down. And then finally, when you have complete synchronization, the trajectories just coincide. Over here, what I've done is to give you the same information, but now looking at the coordinates of the two oscillators. So this is x1 versus x2. This is just x1 as a function of time and x2 as a function of time, also drawn one on top of the other. So here this results in an uncorrelated mess. Here the fact that they are in phase gives rise to some sort of interesting curve. It's not a mess, but the phase relation between the two sort of plays out because the amplitudes are not correlated. If the amplitudes were the same, then you get this. And I seem to remember that I was reading some paper which has even that. But then it will always be discovered that it's generally observed that you know synchronization, phase synchronization, amplitude synchronization. But like I say, I don't know every fact most. So here is another plot of systems that are completely uncorrelated with one another. So here is a map, a chaotic map, your standard logistic map where x goes from 0 to 1. And here is the other system also going from 0 to 1. And if there is no correlation, the points are the purple ones just all over the place. Now, on the other hand, if the points are in fact correlated, if they are identical, then they'll all just fall on that particular line. And that line, I mean, it's obvious that they will all fall on that line. But I just want to point out that that line is a subspace of the square. Now, if I take two Lorenzes, and now I'm going to just couple them with epsilon x1 minus y1. So this is my, sorry for jumping between notations because I need to have this notation to do it in a little more. So here, x, y, z has just become x1, y1, x1, x2, x3. And then this is x prime, y prime, z prime, which has now just become y1 by 2, y3. I'm not doing Pecora-Carol, but I'm just adding this term epsilon x1 minus y1 to the first equation. And over here, it will be epsilon x2 minus y2, sorry, y1 minus x1. Just flip it around, okay? I mean, there isn't, you know, the coupling doesn't matter in precise form. I'm just saying that I'm coupling the two and I want to look at what the dynamics does. Okay. When they are uncoupled, you get the purple blob. I've just plotted x3 versus y3, right? x3 versus y3. And I'm just looking, they're completely uncorrelated with one another and I just get that mess over there. Okay, it's not uniformly covering that space, but given enough time, it will probably get there, yeah? Okay. Once I couple them and, okay, if I couple them for small values of epsilon, they are still not going to be identical. In fact, that's the orange mess over here. Okay, so I've coupled them, but the motion is not synchronized and you get there. But if I increase the coupling and I finally get synchronized motion, that lies on this thin green line that you see over there, because that is just sort of x3 equals y3, right? I'm sorry, this is the z variable in the primed and unprimed, this thing. So the way to recognize it for me is now just that this is the one which is always positive, right?  Similarly, there is another plot you can make for x1 versus y1 and for x2 versus y2. And again, the fact of synchrony will be a straight line, yeah? We will just come down to that in a moment. I just want you all to... See, this is the same fact of orbits looking, they are the same on top of each other and so on. But now I just say that as far as x3, y3 dynamics is concerned, before synchronization, it's all over the place. After synchronization, it's on a line. The same for the other two variables, x1, y1. So I want to just make this statement. The whole dynamics is taking place in a six-dimensional space, x1, y1, x2, y2, x3, y3. It's a six-dimensional space. But after the whole synchronization process is done, we are on a subspace, which is x1 equals y1, x2 equals y2, x3 equals y3, which is just, if you think about it, there are three requirements out of the six spaces. So the eventual dimension of your flow is three. I'm going to come to how we design coupling.  This is... Okay. This is some little bit of what I do. Yeah. Right now I'm just talking identical. Absolutely. You can make all those variations, but it will still be a lower-dimensional submanifold. All right? The point is that the process of synchronization just... You see, I've talked about how it is a method of control, how it is a fact that you can also talk about it as a method of constraint. All right? So it is reducing things down to a lower-dimensional space. Right? And as far as the manifold business is concerned right now, it's just that the synchronization manifold is just the space on which the eventual motion takes place. That space is given by the coordinates x1... You know, by the condition x1 equals... Sorry, this was... x3 equals y3 times x2 equals y2 times x1 equals y1. Yeah? Don't ask me what the shape of that manifold is, because I mean, we are looking at a subspace of six-dimensional space. I'm already lost at three. But I mean, what I want you to get is the idea that synchronization means confinement to a lower-dimensional subspace. Yeah? Okay. So if one asks the question generally, how do systems synchronize, then the large part of all these says that systems can be mutually coupled to one another, as we've seen in this last example. The term x1 minus y1 adds to all... adds to both the systems. Right? Or as we saw with Pekora and Karel, you've got the master driving the slave. And there's a third interesting paradigm, which is that both these systems can be controlled by one boss. All right? And when you have this condition of both systems being controlled by a third system, this is actually quite... I mean, it's the one that we are most familiar with, namely the circadian. All organisms on this planet have that... get tuned to the circadian rhythm. Right? And we take... All of us take it directly from that satellite there, not satellite, after Copernicus, but... Yeah. But you get the idea, right? Everybody starts looking at their cell phone. That's again coupling to some real satellite up there. Okay. So now I've shown you also how you can have perfect synchronization in many different ways. We can also have variations of synchronization, which is this business of exact synchronization or phase synchronization. So there is a framework for looking at all of them together. It's called generalized synchronization. Surprise, surprise. Right? Okay. So this generalized synchronization, I'm not sure what this is, but anyway, this is complete synchronization, phase synchronization. I don't know why again. And I should change that all to almost all other forms of synchrony that have been seen. People talk in terms of lag synchrony. Because things are exactly the same, but at a small difference in time. Okay. There's also... Oh, there's this relay synchrony. You name it, there's probably a version of synchronization. Okay. So I just want to point out that force systems are a very fruitful way of thinking in terms of different types of synchrony. So if you think of a forced oscillator, for example, okay, exercise in elementary mechanics. So here is an oscillator with frequency omega naught. And if I force it with another oscillator of frequency omega, you know what solutions are obtained. These solutions are, depending on whether omega is equal to omega naught or not, then you just find behavior of one kind. You have beats and so on and so forth. Now, I just want to point out that f cosine omega t can itself be seen as the... It can be seen as the solution of this equation. This equation for a specified initial condition, right? This equation equation over here is another oscillator equation. And this solution is just a cosine omega t, right? So if I were to go back to this equation over here, look at f cosine omega t, right? a is equal to f, right? This is just q double dot plus what omega naught squared q equals y. That is, I've got two equations of motion. One is independent of the other. This is just the mathematics called skew product, right? Or you can think in terms of master, well, not quite master and slave, but this is your drive which is not affected by the response. This is a drive response system. So you have a drive and a response, okay? But now both these systems are not the same. I can't say why is the master, because the way in which I think of master and slave is that democracy, master and slave without the coupling are identical or very close to identical, right? So here I'm not... I couldn't care what omega naught is. I could even have a nonlinear oscillator being forced. I mean, this methodology would still go through, but there'd be just two different systems. One is the drive, the other is the response, yeah? Okay, so the idea here is that we have for a long time been studying these drive response systems as interesting examples of dynamical systems, right? Okay, now when systems are non... Now the thing is to go back and what I want to think of is the following. I've got my drive system which is giving some oscillations. Here it's a harmonic oscillator, but it could be any old... any equation that has some kind of oscillatory solutions. And I take that and put it back. Here again it's driving a harmonic oscillator, but it could be any other equation and it would be the output from here driving that. In the extreme example, one can think of having, let's say, one Lorentz oscillator. That's giving rise to some oscillations which give you some kind of chaotic forcing. And that could be fed into, let's say, the Rosler or another Lorentz or whatever, you know what I mean? Because the interaction between different systems is very important, right? Okay, now then what does one get? Okay, so this is the general methodology that has been applied. I mean what I was suggesting was just this, that I have some equations which oscillate and you notice that this equation doesn't involve Q. Here I've got another equation which has its own dynamics and then it gets affected by Y. We'll see other ways of writing such equations momentarily. Okay, so the point that I've already made is that eventually when we see some kind of resulting dynamics occurring on a lower-dimensional invariant sub-manifold of M of the phase space which is the synchronization manifold, all this means is that you come on to this lower-dimensional subspace and then you stay there. If your synchronization is stable, if your subsystem Lyapunov exponents are negative, then once you have come on to that sub-manifold, you're going to just stay on that sub-manifold. There's another way of thinking about it which says that if I've got these two systems, X and Y which are coupled to one another, again with an abuse of notation, X and Y refer to the variables of these two other systems. So it could be X1, X2, X3, Y1, Y2, Y3. When this happens, the implication is that Y is uniquely determined by X. So I have Y which is some functional of X. So this is the paradigm of generalized synchronization that two systems could be dissimilar. You couple them. It's not perfect synchronization, but if it's going on to a lower-dimensional sub-manifold over there, it's possible to think of one of the systems as being uniquely determined by the other. So the one way in which you would think about it is the following. If you have some drive which is affecting the response, let's just consider this case that you have a drive which you then apply on to the response and you get something that looks like a complete mess, meaning you've got some chaotic drive or an aperiodic drive, it doesn't matter. You've got a response, whatever it is, and you look at what is the output. Pecora-Carol, the drive was identical to the response, and so if you had a chaotic drive over here, your response was identical. It was on that diagonal line. So the way in which people discovered and then discussed generalized synchronization in the 90s was to say that let me make another copy of the response system. Because the response systems intrinsically are chaotic, they are evolving any which way. But after the drive has been applied to this response system and comes up with one output like that, when it applies on to the copy of the response system, it should come out with the same function because of that functional relationship, which means that the two responses should be in perfect synchrony. Drive hits response one, you get some output. It hits response two, you get the same output. So this is the basic idea of generalized synchrony and let me just show you how that works in a very simple system. Now this is the logistic map which I presume is boringly familiar to everybody. So for the case of the logistic map, I'm taking Mr. X as the drive and the response is Y and this function is this little function over here because even I got tired of just saying 4X into 1-X. This is 4 square root of X into 1-square root of X. It doesn't matter. So your response is the same and here is the additional driving term. So when epsilon is equal to zero, these two are just completely uncorrelated. Well, not completely because things tend to concentrate at various points but it fills up almost this entire space over there. This is X on this axis and Y on that axis. If I take another copy of Y which I have now indicated by Y prime, I also get if I look at Y versus Y prime, see X versus Y or Y prime is going to look something like this. Y versus Y prime is uncorrelated. So it's just filling up that space. For increasing this coupling epsilon over here, let me just describe what happens to X and Y. X and Y go from being this space to this. Some complicated thing which I don't know. This is not a simple function but then I increase the coupling even more and then lo and behold, I'm on that synchronization manifold. X is equal to Y. But now let's look at Y versus Y prime. When this value of the coupling has been reached, Y versus Y prime is identical. So X versus Y is this mess. X versus Y prime is the same mess. So the two messes are on this synchronization sub-manifold over here. Increase the coupling more. X is exactly equal to Y. X is exactly equal to Y prime. Y prime is equal to X prime. Everything is equal on this slide. So it's this intermediate picture that will give you an idea of what is generalized synchronization. Response is complicated. We don't know what it is. But any two systems will have the same identical response because there is a unique functional. I mean implicit. I don't know what this functional is because I mean who can tell what gives that. So one drive, many responses. There is a regime when all the responses give you the same output and that is in a sense in the next class. We'll discuss why it's called generalized synchronization. Okay. I'll give you a preview of what is to come. Okay. Just some fact, let me mention. This coupling actually turns out also to replace the coupling by noise. So you have noise acting on one system, noise acting on another copy of the same system. If the noise is identical, the response will become identical. Okay. This has got important applications, especially in things like ecology and so on and so forth. Something called the Moran effect and so on. But what I'm saying is that this is actually a very general framework. If I think of two systems, here they are subject to similar coupling. But if I make them subject to noise or to periodic oscillations or to quasi-periodic oscillations or whatever, the responses becomes identical after a while. Yeah. Exactly identical. These are usually called common noise. So if you think of two nonlinear systems in a common bath, heat bath or something, they're all given the same fluctuations. Not the same spectrum of fluctuations, the same. Okay. All right. So this is it. But usually for most couplings, it's not very long. It just goes quickly. So this is the point that I just made, that the so-called external drive can be even a stochastic drive in many applications in, you know, at least current kinds of applications and complexity. This is actually an important thing. Okay. What I want to do is to now go back and say that if synchronization is sort of bringing everything onto a common sub-manifold, I choose my manifold. Does it always have to be either this line which is diagonal or we saw some example of anti-diagonal? Maybe I can have my own sub-manifold of choice. Will I still call it synchronization? And how do I make sure that it happens? So I want to now think of all of synchronization as basically going onto a sub-manifold in your phase space. Okay. One day. Now we take, we have a group photo. So please.


Alright, now in this JSON file, can you tell me what kind of mistakes I did? Well, you can pause this video for a while to observe the mistake which I committed in this file. Okay, now let me help you over here. Let me show you one mistake which I did say by mistake. You can say, so over here you can see that I forget to add the comma like this. Okay. So, let's go through all these mistakes and fix it using our online JSON validator tool provided by ByteScout. Okay. So, here I have pasted our DC history JSON file content and when I past that JSON file in this tool, it immediately started throwing this type of error and here it is telling me that I have forgotten the comma. So, let me add this comma. Now after adding the comma, it started showing me the next error over here at line number 10. So, now can you identify this? What kind of mistake is this? Well, consider a situation like if you have a control character within a string literal in your JSON file. For example, this literal string contains a new line fit character. So, now what to do in this situation? How you can fix this issue? Well, for that, you have to use new line character, which is backward slash and n and let me arrange in one line. So, now you can see that we have fixed this new line character issue and it started showing me the another issue, which is at line number 16. All right. Now, again consider a situation where what if any of this JSON property value contained a literal backward slash character like this? Well, right now it is giving a syntax error because it is trying to parse a string with backward slash and dot. Okay. So, how we can fix this issue? Well, to fix this issue, you need to escape it by using one more backward slash character like this. So, now it is showing me the next error, which is at line number 17. So, what is the error at line number 17? Can you identify it? Yes, you are right. I have added the extra comma over here. So, let me remove this extra comma and that error is gone and now it is showing me the next error, which is at line number 23. So, let me scroll down. So, now over here at line number 23, can you identify what I have forget something? Yes, I have forget the colon. So instead of dash, I need to add colon over here and if I scroll up, then that error is gone and it started showing me the next error, which is at line number 27. So, now let's see what is at line number 27. So, now again, can you tell me what mistake I did over here? Okay. Now, let me remind you one thing once again. In JSON, you have to have double quotes around the key name and this is the thumb rule. I guess now you got it. Yes, I forget the double quotes over here and now it is showing the next error at line number 29. So, let us scroll down again. So, now can you help me what kind of mistake I did over here? Now, as we know that in JSON, array is always start and end with square bracket. So, we have opened the square bracket over here, but instead of adding the square bracket, I have added the curly brace. So, to fix this issue, I need to add closing square bracket. So, over here, now you can see that our JSON file is become a complete valid JSON. Okay. Now, let's move ahead. So, now consider a situation. What? My JSON file contain any comment like this. Well, as you can see that this tool are now started throwing this type of exception. So what it means is comments are not allowed in the JSON file. Now let me show you one stake overflow thread for this. So, over here, you can see that comments were removed from JSON by design. According to this answer, JSON does not support comments and it was also never intended to be used for configuration files where comments would be needed. But let me show you another stake overflow thread. Well, according to this stake overflow threads, nowadays some of the libraries like JSON.net started supporting comments in JSON file. So, in this answer, as you can see that JSON.net 6.0 supports single line comments. Alright. So, now after seeing this video, hope you will take care of all these points which we have learned when working with JSON and with this we have reached the end of the module. Now, it's time to wrap up the course.


Good afternoon and welcome to our talk with Phenobs through the Cloudcast jungle. Today we'll talk about how you can achieve transparency in your cloud to optimize custom usage within the Phenobs framework. We will also take you on a little journey through a real jungle, so stick with us. My name is Viviane and I'm here with my lovely colleague Vanessa. We both work at Liquid Reply. I have a background in media informatics and I'm specialized on data analysis and Phenobs. With a focus on knowledge sharing because there are still enough people out there who don't know how to save money in the cloud and how to optimize it. I'm Vanessa. I ended up doing Phenobs like two years ago and before that I did I was a technical project manager and also a cloud consultant and what I really like about Phenobs that it brings all of those dimensions together and even more there is one one topic I need to talk about and it's green ups because that's I would say is my new passion and green ups is all all about optimizing your cloud environment for sustainability. So measuring the carbon footprint and optimizing that one but I guess that's a topic for another day. So let's start our expedition through the cloudcast jungle. This is our agenda for today. First of all we will talk about the problem and we will introduce you to Phenobs. We will enable you to become your own guide and achieve transparency and in the end we will give you an outlook into the future. Okay let's start with the problem. Why do we even need that Phenobs? Previously pre-cloud and the old on-prem days there was a super easy and straightforward process. At least it was easy for the finance people right? It's on the left side here on the slides you can see an engineering team or a project team and that team had a demand maybe a demand for some piece of hardware let's say a standard on-prem server and they communicated that demand to their project manager maybe to the team lead that's the person in the middle and that person verified it, planned his or her budget accordingly, approved it and then forwarded it to the procurement department. The person on the right side the procurement person and then purchased a piece of hardware the server and yeah that's it pretty straightforward and six to eight weeks later a beautiful server arrived and with it came the invoice. The controlling department or finance department on the right side of the slide they processed the invoice and that was pretty easy because the costs were already planned before and it's just standard capital expenditure they were able to amortize it everything is fine purchase done and the engineering team used the server and usually quickly the server was over or underutilized hopefully overutilized and so that started the whole procurement purchasing process all over again. To stay in jungle terms because that's what it's all about today that old process was all like planting one tree after another now the present the cloud days you see it's a lot more complex than before now engineers can buy the resources by the push of a button but it's not only with one cloud provider but with all of them and at the same time it's not only about infrastructure but service anymore maybe you've heard about past SAS and fast whatever else is out there and so they can buy it just whatever cloud resource they want and wish for by the push of a button without waiting for any approval of our team lead of a project manager or else. The difficulty with that is that also nobody planned in the budget so at the end of the month an invoice more than one invoice typically arrives and the controlling department on the right side with the question mark were asking themselves okay where did that came from all of these variable costs we haven't planned them what's happening so they're diving deeper into the invoice and quickly they stumble upon a huge amount of data so you can see like in the back of that slide that's AWS curfile that's short for cost and usage report and that curfile is a huge CSV full of rows and rows of rows and each row shows the purchasing of one resource in one hour one time unit and you can imagine that curfile has like a million rows for a short amount of time and yeah it's just not human readable anymore and so in the present what does the finance department do in the best case they go back to the engineering people and just ask them but then the engineering people have to continuously justify them about every single line item of that curfile that's annoying right I mean in the worst case that the finance department wants to go back to the old on-prem processes meaning they again try to get a debt approval process or maybe they can or allowed to apply some policies but that hinders innovation because the engineering people then can't buy those resources super quick anymore so the time to market is not as fast as it would be with the cloud and yeah it's not working well and at the end of the day also silos start building up so the people are annoyed of each other obviously and so they don't they stop talking to each other angry and things are not working properly yeah so what can we do about that baby this is where FinOps comes in to save the day so what is FinOps exactly FinOps is a cloud financial management discipline it's a cultural practice to break down the silos between the different departments this is the issue and as I mentioned before about the current process FinOps is a combination of DevOps and finance and FinOps is not something you do alone so you could see the collaboration between the different departments as the engine for the FinOps practice the goal here is to get the most value out of the cloud usage with constant usage optimizations and if all the stakeholders work together they can collaborate on data-driven spending decisions and they can leverage all the promised benefits of the public cloud and this is how the future looks like first of all you take all the data of the cloud so not just the builds or not just the cost of usage report you just saw you take all the data from all the different cloud providers you use and then you normalize them you make them readable and usable you put them into useful KPIs for all the different stakeholders to work with and this breaks down the silos so they start working together and they can make cloud-based innovation and this whole process contributes to transparency and transparency is very essential especially to efficiently optimize costs and save costs and without transparency people stay confused in their cloud and with the collaboration they can manage the cloud cost jungle together so how to achieve transparency that's our main topic for the day and we'll demonstrate that by using a wild tropical jungle so imagine you're stranded there in that beautiful some color the green hell and some of these plans maybe you you've stranded there with a few strangers you don't know yet and of course you need to survive and so you look at your surroundings you see all of those plants maybe you see some plants that look familiar others do not we are not biologists I'm not I'm an IT person but you need to make sense out of this jungle because I mean you want to survive now so what do you do next how do you start yeah just getting familiar with your environment well you guessed it it starts with transparency and mapping that to the cloud before we come back to our jungle I'm talking about the account structure the account structure is the first step in achieving transparency and accounts themselves are like isolated units they're like units where you can group resources or accounts are also units just like a logical kind of grouping and when you have an account it's not only beneficial for billing because the invoices at the end of the month are an on an on account basis but it's also beneficial for other things like for example security because when one account gets compromised it doesn't automatically mean the other one is so there are a few different benefits to that how to decide the account structure is heavily dependent on your organizational structure and on the right side of the slide you see an example of proposed account structure and that could start with the company on top then you have like different departments below that different products and at the end you have staging for each of the products or in that example just for product that and in that example the in in none of these so in in the staging accounts there are the cloud resources then so you would see a VM or maybe a EC2 instance if you were working with AWS under one of these dev product that accounts but you will probably not encounter one of these cloud resources and at any other account because the others are just used for logical yeah grouping of resources and just as a means to make sense of your invoicing at the end of the month so for the account structure to define that in your company you really need again the involvement of the different stakeholders because the finance people can tell you okay what are the cost centers that are relevant how does the invoicing process work at your company but you also need the business department and of course also the engineers and all together you can finally define a strategy about your account structure and going back to our jungle let's make it easy let's divide our jungle into three areas so maybe on on the top left you see some trees let's make it super easy and call that the tree area and then on the right we have some bushes and plants let's call it the perennial area and then on the bottom we have weeds and small plants let's make it easy and call it a small plants area so now stranded in our jungle we finally kind of know maybe where we are looking around but we still don't know okay which of these small plants can I eat or which trees can I use to buy to buy to build a house and so we need to go one level deeper and make a bit more sense and get a few more details in our jungle and that's where we have to talk about tagging so what is tagging tagging is essential to optimize costs and you do that by assigning useful information to any resource of an account or to an account itself and this information consists of a key and a value and this provides an extra layer of granularity for the cost allocation and in this whole tagging process of course you need to involve all the different stakeholders like we said a thousand times before and your tagging strategy need to be aligned with your company and if you look at our example here you can see that we added another layer we added the resources and if you question yourself okay when do I need to tag and when do I need to create an extra account for resources you can see that we have on the right side of our example we have the database a and the database b and here we have the tag owner and if you think about it you wouldn't create extra accounts for all the different owners that exist because then you would have a lot of different accounts and it would be just too much or if you just look at pot a and pot b here we have the tag team so we have a front end and a back end team and you wouldn't tag these services either you wouldn't create an extra account for these services either you would just tag them because in the end you would just know which team is producing which costs of an account and if we map that back to our jungle we can see now that we added some tags here we have the tag tree for example and with the value rubber tree we have the tag perennial with the value banana and we have the usage tag so we can see now that we can but that we can have some trees for manufacturing we have trees for food and we have some plans for medicine so we know a lot now about our jungle but there are still some resources that are hard to allocate or that we cannot tag here in our example would be something like the sun or the water because we know that all of our plants use water but we don't know how much and we need to allocate this to get a full picture of our jungle and it's the same in the cloud we have here untaggable resources at all we have two different kinds we have the shared costs these are shared by different teams and used by different teams for example network charges support charges or shared storage then we have public cloud resources that are not taggable at all these are most of the time special services like the AW app mesh there are three different split cost models which help us to allocate these shared costs first of all we have the even split here the shared costs are distributed evenly among the different business units next we have the proportional split here it depends on the raw spend of the business unit so if business unit A has the most raw spend they will pay the most of the shared costs and we have the fixed split this is a fixed percentage and it's determined by the evaluated past spent and we go back to our jungle now and we have here the percentage share of the water consumption so we added 20 percent to the small plants area because there are a lot of weeds and they don't need that much of water and for the other two parts we added 40 percent so we know a lot of our jungle now looks pretty good right and I think we can survive now and we can live in our jungle but we want to evolve with our jungle we want to know when is the next time we can harvest our plants or how do our grand plants grow and how is our jungle and we want to live in it and for that we need monitoring and it's the same with the cloud we need cloud monitoring cloud monitoring assesses the elements of the cloud for example health checks and it's not enough to just look at the total costs of the cloud because it's not specific enough and you don't know where to optimising our cloud and the account structure and the tagging helps us to know where the costs come from but there are still a lot of parameters we can monitor and to know which are the right ones for us we need individual FinOps KPIs aligned with the companies and the different stakeholders in our example here you can see a Grafana dashboard and for this company they have KPIs like the CPU cost the memory cost the utilization the requests so a lot of different things and not just the total costs and you may ask now okay but why do I need a third-party tool why can I just use my existing cost monitoring tool from AWS Azure or GCP there are two answers so on the one hand if you use more than one cloud and you can see with a third-party tool you can see all the data from all your different cloud providers in one dashboard together and on the other hand if you just use one cloud provider third-party tool is still good because it helps you with a KPI definition and it provides special stakeholder views for you we brought some monitoring KPIs with us so these are more technical KPIs but these are also an insight for the other departments so first of all we have the average price of compute for our power you want to decrease that number over time and you can do that through right sizing and reservations Vanessa will talk about that in a few slides we have the count of anomalies anomalies are something like a spike in your costs and here it's about the consistent identification of the anomalies and the time it takes to address them we have the percentage of the tax resources and of the untact resources and we have the percentage of idle resources and here listen carefully here you can achieve the biggest cost savings just by shutting down idle resources so it's not that hard just shut down what you don't need and in our jungle scenario we have now a beautiful dashboard so we have the growth rate we have the count of ripe bananas and we have the weeds coverage and in our case these are the right KPIs for us because we want to survive in the jungle so these are right maybe a biologist would have different KPIs regarding the animals that live in the jungle or other ones but for us these are the right ones and we can survive and live in our jungle so in a nutshell collaboration is key and one of the first steps of phenox so you really need the involvement and maybe even a buy-in from people of finance of IT teams of business maybe your C-level people and you need to create a strategy for all of the topics we mentioned before you start your journey speaking of accounts and tagging it's great if you already have that strategy or if you've created it but you need to implement it consistently because it doesn't make a lot of sense as you might know if you apply it just once and then forget about it it's not of great use to you same for tagging and regarding the untaggable costs it really pays off if you revisit the untaggable costs from time to time so it's awesome if you've decided for one of the cost models maybe explained before but from time to time the cloud providers have of course features they're working on their products and so it might make sense to revisit those untaggable costs because some of them might not be untaggable anymore for example Vivi mentioned the AWS app mesh might be in the future that it's somehow a taggable fourth point is monitoring we now okay all of us all of us that work somehow in IT so I guess all of us are already doing monitoring on a performance level but we also need that finance monitoring we engineers are now responsible also for costs but at the same time we need to enable the finance people and the business people to work with us to get their buy-in and their understanding of how the cloud works and what they need to consider when they define their user stories or plan the budget so we've talked a lot about transparency and we survived in our general because it's transparent and yeah achieving transparency or those concepts that we have we've explained those are not rocket science at all but from our experience most companies most people struggle with these topics because usually they work in there just within their teams for example they've great tagging but just in their project in their isolated world here again you really need to involve the whole company because phenops is all about change about a cultural mindset okay so we've achieved transparency now we can finally start optimizing paying and using less for our cloud resources so the way forward you see that's us the green people there with the lantern transparency we can now finally start for example with processes there are a few strategies with the cloud where it can save a lot of money for example by committing to instance types or instance families it's called commitment based discounts you can save up to 60% but it pays of course off if you before that know which machine types you really need you could also work on implementing phenops in the agile culture or in the agile framework of your company maybe you're already working in sprints and with user stories and you might know the definition of done and so you could add thinking of phenops so you could add in the definition of done one sentence about you're having the costs in mind or making that even a bit stricter after or in parallel to the to the process dimension you can now really start optimizing and lowering the costs usually when companies start out with phenops they have about 30% of well waste so you can reduce 30% of your costs as soon as you know where to look as soon as you have to transparency optimizing means on the one side shutting down idle resources of course shut down what you don't need on the other hand it could mean yeah right sizing so choosing the right instance size for your workload typically it's the lazy way to just use an over provision and just use a larger instance and with right sizing you reduce that size you take a look at your monitoring and see okay just 5% of the CPU of that machine is being used I can definitely make that a bit smaller and the third point that we've mentioned here is out of scaling so scaling is really one of the benefits of the cloud but a lot of people don't use the out of scaling functionality at all and so that's really something you could look into and then at the end of the road there is redesigning your applications so they are architectural patterns like for example containers or server less that might reduce your costs even further but I would say that's really a topic you shouldn't look into right away except if it's a greenfield project of course because coming back to a not greenfield project because typically it's a lot of it takes a bit of effort or a lot of effort to redesign the applications so that's something you can then tackle as soon as you you've already reduced the cost and I know that whole jungle metaphor we are talking about it's super cheesy I think it's a great way that you can remember what we were talked about today the bottom line FinOps as it is in the jungle FinOps is a continuously evolving system FinOps is all about accountability it's all about the engineers that spin up the resources they need to be accountable we need to be accountable for the costs we incur when we deploy a resource but at the same time FinOps is about enabling other people and about the mindset change in the company because it doesn't work like in the ancient times with the on-prem times that old process that's outdated so we don't we need to look not only at us as engineers and think of costs but we also have the more or less duty to enable the other departments and explain the finance people why the cloud incurs variable costs why it's not about capital expenditure anymore so FinOps really is about yeah a community of people and cultural mindset change for your whole company and there is nothing more left to say than go out there be your own jungle guide and guide others in your company or at home thank you


All right in the interest of showing you how I use my brain I Collected together some things that I just put in over the last three or four days Now each of these came in from some different vector meaning one of them was an article in the New York Times one of them was A meeting I had with a friend where we got into a conversation about the history of Portland and highways Another one was a video that I ran across About things I care about about healing of trauma. So each of these is very different I just created a node here called 1606 new notes, which means 2016 June I do things a lot by by a year month because they sort nicely then when I go someplace So for example, if you we see my event schedule up here We'll see a few different things that are on year month orientation There we go. So these are different things that I've done this year. So let's go back to Where we just were and I'll start with Carl Safina who I actually had never heard of before and I already had a thought in my brain called do animals have feelings so one of the things about all the things that I'm going to show you now is that these nodes and the books and Twitter account so here's a book beyond words Which is what prompted this whole inquest into Carl Safina somebody mentioned on a conference call that I host The book I didn't even know it was a book. They mentioned beyond words So I googled beyond words and that brought me to all of this. So Carl Safina turns out it isn't is an ecologist He's at Sonny Stony Brook And he cares a lot about this notion about animals and feelings and he's you know Do animals actually have feelings and I had the topic animal well-being and a couple other things in here Also, I thought do insects have feelings believe it or not all these of course under feelings and animals so here's Carl and He wrote the book beyond words, but he also was He also gave a Ted talk which I then watched So I'm annotated the talk by saying that Elephants for example can distinguish between tourists and herders Safina Describes an experiment where they recorded tourist voices and they recorded herder hunter voices and they put the speaker out near elephants and When the speakers had tourist voices the elephants were just fine. They just kept on walking because tourists aren't annoying They don't hurt you When they played the herder voices the elephants started running the other way away from the speakers So they understood that Etc. Etc. So I Have this under what makes us human and also that we are very unaware of our relationships in nature Which I think I need to make more profound He talks a bit about the cruelty we inflict on animals So I put it under cruelty to animals and as you'll see I've got quite a few things under cruelty to animals and then also I connected it to Ted talks because this is a Ted talk and I Been doing this for a while, but these are all Ted talks all of these are Ted talks And in fact there's another thought for Ted X talks So this is just the Ted talks and I differentiate between Ted talks and Ted X talks So that's very funny Clay Shurkey has apparently done five different Ted appearances And I love clay. He's a great great speaker so if I go back to curl and Connect back up to curl by the way anywhere you see a link next to a thought That means that if I click on that link it'll launch my browser to that page So here we are going to cross a penis Wikipedia page I use Wikipedia pages when somebody has one as their sort of canonical starting point and it turned out Carl did so That's what I did. So that's just curl and all of that probably except for listening to his Ted talk Which is itself an 18-minute adventure more often than not But all of that probably took me 15 20 minutes to do Granted I it wasn't central to anything I was doing that day And it was a distraction as all these things are But in some strange way, I'm busy weaving the context of life. So on from there So I had a conversation and learned that Portland the city of Portland back in the days of the national the Federal Highway Act of 1956 and the interstate highway system that resulted Robert Moses and his team went around the country basically basically showing cities What they should do to install freeways which would meant Knocking down housing in different places and had lots of ill effects as well as some good effects And then they offered the Federal Highway Act offered funding for this So they said we'll cover 90% of the cost of installing freeways around your city Portland has a couple of freeways that cut through it But then they said no and what I what I didn't know and that was really interesting was that there had been a series of highway revolts That many cities around the country actually said no including Sydney and Australia It wasn't all in the US But cities that that had planners come in and say you need these kinds of freeways in this many in some cases Not all we have many cities that were really really cut up by freeways And the famous instance of this is Jane Jacobs standing up in New York for a freeway that was going to go through the village the The part of New York that's sort of actually organic shaped in different ways So what was really interesting about the jiu-jitsu part though was that? Portland managed to change some wording or use some wording In the funds they were offered to use the funding that was supposed to go to freeways Originally it was going to be the Mount Hood Expressway To fund their light rail system So Portland actually funded their max system and some of their other Tram system with money that was supposed to go to federal highways that is a tremendous irony because There's something known as the great American streetcar scandal now all of this existed before the last four or five days In fact this these nodes are pretty old because I've heard about this for a long time But if you've seen the movie who framed Roger Rabbit, which is right here in 1988 it's a movie actually based on historic events. It's a cartoon Directed by Robert Zemeckis has Bob Hoskins and Christopher Lloyd in it But there was actually a great American streetcar scandal where General Motors Firestone and others Invented national city lines, which was just a fake company and then proceeded to buy up streetcar systems around the country and shut them down There's a lot more to it But basically 80 cities around the US had delightful light rail systems in Los Angeles it was known as the red the red line was the famous one and amazingly they Burned the cars and dug up the rails knowing full well their goal was to sell bus fleets to all these cities, which they did There but but they knew that once you've pulled up the lines and burned the cars How's somebody going to reinstall a light rail system? So the irony that Portland manages to use highway funds to font or fund a Tram system is delicious Even though I don't believe that Portland had a tram system that got pulled up before that all of that from Conversation where I learned about that on Portland and just came back did a little bit of googling and put all that in Then I had never heard of a woman named Vivian Ming So I watched her Ted talk. It's actually a Ted med talk about incentive insensitivity and about the fact that Fanatics people who really care about stuff are are insensitive to incentives They will stay on something regardless what the motivation is in fact I connected that to a thought I already had before that extrinsic motivation often erodes intrinsic motivation and That rewards and measurements often don't really work Which is tied up to a really important thought that's up here on my On my pinboard called my beliefs. So this is part of my belief snapshot So we're kind of linking up to that from this whole notion about intrinsic and extrinsic or endogenous and exogenous rewards So that was the paradox of insensitive sensitivity I'll do a couple more Then there was a terrific Op-ed in the New York Times actually not an op-ed Judith Chulovitz is actually a New York Times correspondent. I believe so I put her under New York Times correspondent and a journalist married to Nicholas layman And here's her Twitter account. She's written a couple of different really interesting things about Parenthood and The role of moms and so forth also a book about the Sabbath about looking at time differently But this one on how to fix feminism was really interesting It had a lot to do with valuing Homemaking and about work work life balance women balancing career and family Which is a topic I have under work life balance Which is a topic I have next to women in the workplace So there's you know, Hollywood ageism against women Rosie the Riveter career women Rosie the Riveter of course should connect us to World War two Let's see if it does that there it is World War two But if I go back to how to fix feminism It's also linked to articles about feminism and she coins the term caregiver ism And she says that givers of care really are under underappreciated in many different ways points to some really interesting books Finding time is one of them which I had not heard of so I put Heather Boucher and Finding time in the book in in my brain, which I didn't have before and then also The time bind is another good book and one thing I didn't realize was how really crippling Tan F was the temporary assistance for needy families program which passed under the Clinton administration under welfare reform And it replaced the aid to families with dependent children AFDC, which had been doing a pretty good job Protecting Families and children so they they made sure oops. I made a mistake there. I wanted to put a parentheses in at the end So they made a mistake there Anyway, let's go back to I'm clicking on the breadcrumb trail down below here to go back to where we were Then there's going to be Published any day now, which is one reason why I'm making these videos an episode of the cool tools podcast about me and my brain Mark Fraunfelder and Kevin Kelly are the guys who run the cool tools podcast I've had them in my brain for years and years know them both personally oops, and that was my brain crashing So let's reopen it. I'm using the brain 9 beta So It crashes a little bit now and then I was just thinking I should close it and reopen it because that usually clears things up And it doesn't crash So if I go back to the cool tools podcast That will take us back to 1606 cool tools on me and my brain And I was just going to show you how much I had on Kevin Kelly, which the fetching that might have been what caused it to barf on us right then So here's Kevin Kelly the books. He's written In fact, in fact, sorry I have so many things connected to Kevin Kelly that I have a separate note that I colored So it would stand out on the list of just his books And I'm not I'm not guaranteeing that these are all the books. He's written in fact I know that he's he's written more than this, but these are the ones I have in my brain where possible There's an Amazon link so you can go buy it and the year of of its initial publication So he recently put in a whole bunch of work Publishing the silver cord with Steve Massaroni, which is a graphic novel Which is really quite outstanding In fact, it was a Crowdwritten science fiction work that he then turned into a graphic novel in different ways anyway There should be a cool tools episode out pretty soon and those of you who follow that far enough will end up right here and Then finally I will go to I'm not going to do all of these But in fact, I'm gonna do most of them But I'm gonna go to the American Slave Coast, which is the book. I've been reading and probably 40% through it Now I don't know how thick books are anymore because I read them in my Kindle app on my phone But this book is really tremendous. It's blown my brain and I mean this one not this one he Ned sublet who my wife and I met in Havana on a trip recently where we went to speak at a conference He was also a speaker at the same event He wrote this book and talks about the slave breeding industry, which is much darker than I thought America's past was and he really he really talks about the the economy of the south and he refers he Among the many many interesting things he says which have really stuck in my head. He says that the US Revolutionary war should really be seen as a successful civil war It was the colonies splitting away from the UK and establishing their own governance So they broke away in a civil war and created their own governance, but the motivation was really mostly a slave Dependent economy preserving slavery because the UK Went toward abolitionism first British ships could no longer carry slaves. They blockaded Africa. There's a whole bunch of interesting history here Americans saw that coming and the south in particular But the north also completely complicit were so mixed into this that they couldn't they couldn't go that way It's really quite amazing Then he says look at the US civil war as an actually functional more or less Revolution because that's what broke the back of slavery and of course a hundred years after the civil war We had the civil rights movement and we still don't have equality But the history here is very difficult. All the founding fathers are completely complicit the documentation about in particular South Carolina what is up with you South Carolina But Virginia all these different states what they were doing how they handled it Explicitly what was going on in in Congress and before that in the Constitutional Convention and and so forth is really quite incredible so This thought 1606 new notes. I just made so I could tell you the story I think I'll end here, but I wanted to give you a flavor for what happened over four or five days Each of these probably took me a half hour to do the slave coast I've been reading now for a couple weeks so every now and then I'll add a little something to it But this is what it's like to annotate things in your brain and then have them connect up to Things you've already put in before and don't worry. You don't have to have as many thoughts as I do for that to start happening Thanks for listening and keep coming back subscribe if you like this