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Okay, so I'll start with just a quick reminder of what we were doing last time. So we had this, we had this basic connection within the ADS-CFT correspondence between some measures of entanglement and geometry proposed by Ryu and Takiyanagi where they suggested if I have a state in my CFT and some corresponding asymptotically ADS spacetime, then if I compute the entanglement entropy of some region A, then this is supposed to tell me about the, of this extremal surface in the bulk spacetime that divides the bulk into two parts where the one part has boundary A and the other part has boundary A bar. And so today actually, so the idea was now I wanna consider conformal field theories and I'm only going to assume this formula. Actually for everything today, we don't need any ADS-CFT correspondence or string theory or anything. The idea will be to just assume that for this conformal field theory that for some family of states, including the vacuum state that the entanglement of these states can be represented geometrically, that there exists some spacetime M such that the entanglement entropies for various regions match for the areas in this spacetime. Okay, and I said last time that's a very special property of the states and presumably of the field theories. The space of possible entanglement structures is much larger than the space of metrics. So this is a very special assumption about states but we believe that for states in holographic theories, this is true. And what I wanna do is then, so for these geometries that represent entanglements of CFT states, I wanna understand what kind of constraints to these geometries satisfy? What can I learn directly from properties of entanglement? And so just to remind you of how that would work, the idea is, okay, suppose, so here's the space of asymptotically ADS metrics. Okay, suppose I pick one of these things then I can use this prescription to calculate all of the extremal surface areas. So that puts me, that will give me some function of the subsystems, but then we said last time that not all of these functions can actually be entanglement entropies. So entanglement entropies satisfy various constraints such as sub-editivity, strong sub-editivity, et cetera. So there's only say this green region which could correspond to the entanglement entropies in some consistent field theory and the other regions that can't possibly. So if I find, if I start with a spacetime, calculate the extremal surface areas using the Ryu-Taki-Nagy formula and I find that I'm in this region over here, I find that these areas violate the constraints that entanglements have to satisfy, then I can conclude that this can't possibly be coming, this can't possibly be describing the entanglement of some field theory. Okay, yes. So that's okay, so that's a very important question. That's the same as asking when does ADS-CFT work? So we don't have a complete answer to that. This is sort of another interesting direction for research. How do we characterize states of field theories where the entanglement can be captured geometrically? I, maybe if you ask the question in the discussion this afternoon I could tell you a few ideas, but for now I probably, I'll just say it's an open question. So I'm just going to assume that there are such states and proceed. Okay, so the strategy is going to be to start with, start with a case of just the vacuum state of the CFT and for a holographic CFT then this vacuum state should be dual to pure ADS space time and that should satisfy if we calculate the extremal surface areas in pure ADS space time, that should satisfy all the constraints. And I'm going to start now by considering perturbations. So space times close to pure ADS and ask what are the constraints on those and then we'll talk about more general space times towards the end of the lecture. Okay, so last time I derived the constraint that you have for first order perturbations. Okay, so if I start with a vacuum and then I add some perturbation, there's a constraint that the entanglement entropies have to satisfy and the constraint that we derived is that for some subsystem A as I make this perturbation, the change in the entanglement entropy for region A has to be equal to the change in this expectation value of what I call the modular Hamiltonian and that is just the log of the unperturbed density matrix. Okay, so this would be, in our case, this would be the vacuum density matrix for this region, that's some operator and then as I make the perturbation, the change in the expectation value of that operator must equal the change in the entanglement entropy and this followed just by the definition of entanglement entropy. No, yeah, so the idea is in this formula, you should interpret the H as being fixed and just the state changing. So the H is the modular Hamiltonian corresponding to the vacuum, so this is, I'll say, unperturbed. So I'll give you an example. So this is going to be useful in the cases where we can actually calculate this modular Hamiltonian. I mean, it's always true, but many times the density matrix or the modular Hamiltonian is some very complicated operator that we don't know. But in the previous lectures, we talked about a case where we can compute it exactly. So we're gonna be considering a conformal field theory, our unperturbed state, as I said, is the vacuum state and we're going to take the region A to be equal to a ball shaped region. I'll call it B for ball. And then what I said previously was that we can calculate the density matrix for this special case because this causal diamond or domain of dependence of a ball, you can obtain this region from a Rindler wedge from a half space from the domain of dependence of a half space by a conformal transformation. And so you can obtain an expression for the density matrix, the vacuum density matrix for a ball from the vacuum density matrix for a half space. And that's the thermal density matrix with respect to the Rindler Hamiltonian. So we had this calculation in the previous lecture where we explicitly found what the density matrix for this region is. And so then we explicitly can find what the modular Hamiltonian is. And I can write it down. So the modular Hamiltonian is then just the Hamiltonian that generates this flow in this causal diamond that is the image of the Rindler time flow. So, or the image of the boost operation in a Rindler wedge under the conformal transformations. So this thing is a conformal killing vector. So it's a symmetry generator of the conformal field theory. And explicitly we can write down, okay so if we use the standard know-their procedure to write down an operator, it's then an integral over the region of the zero component of the current associated with this flow, with this symmetry. And this is what it looks like. So remember the usual Hamiltonian, if we wanted to write down the operator associated with just the ordinary time flow in the CFT, it would just be an integral over all of space of T00, which is the zero component of the current. This one is a different symmetry generator and here we have a weighting function. So it's an integral now just over the ball of a weighting function that vanishes at the edge of the ball.  Okay, so this is a weighting function and this defines an operator on this region B. So that's useful now because we have a way to explicitly write down this first law. So this equation now becomes delta S equals delta of the energy density integrated with this weighting function over the ball. So incidentally, this is true for any conformal field theory and it tells you how the entanglement entropy for states near the vacuum is related to the stress tensor expectation value. So what we wanna do is apply this in the case of our holographic theory. Okay, so now we're going to assume that we're talking about a CFT state whose entanglements are related to some geometry. Since we're close to the vacuum state in the CFT, we're thinking about geometries which are going to be close to ADS. So our space time that computes the entanglement will be ADS2 plus some perturbation. Just to write down an explicit formula, we can use this Pheferman-Gramm form of the metric. So this would be the Pheferman-Gramm metric for pure ADS and then if I wanna consider a perturbed space time, I can add some perturbation function. So this is a gauge choice for describing metric perturbation asymptotically ADS metrics. And I've put in this power of Z here for convenience. If I make this choice, then this function H will be well behaved as Z goes to zero. Okay, so our question is if I take this metric and compute entanglement entropies according to Ryu Takenagi, in which cases will I satisfy this? So what does, let me, this right hand side I'm going to refer to as just delta EB. So what does this first law delta SB equals delta EB tell us about H mu nu? So any questions before I go on? Okay, so yes, sorry, I mean entanglement entropy has a definition in field theory and stress tensor has a definition in field theory. So these are, I mean, these are two different things. In principle, I would do different calculations to calculate those. But maybe the content was that I then did a calculation to find out where the modular Hamiltonian is. So I was able to reproduce that. Now I can write exactly what this side should be. So now I think it now it has content once I once I tell you what that modular Hamiltonian is. What, well, I mean, even, okay. So even in CFT, I guess I would say it's too different. I mean, if I told you go and calculate entanglement entropy, here's the state, go and calculate the entanglement entropy for this region. And now go and calculate the expectation value of the stress tensor.  I mean, it was, I mean, the derivation was somewhat trivial, but for the vacuum, for the vacuum, but now we're making a statement about states near the vacuum. So it's really, I mean, it's really, even when I, even in the general case, remember this is basically the first law of thermodynamics. So if I start with more generally some thermal state, so once I say here's the thermal state for this Hamiltonian, then I do my derivation and I get the first law of thermodynamics. So that has some content. Okay. Now from the, so what we wanna do is translate this to a statement about the gravity side. And we have assumed that the left-hand side here corresponds to the area of some surface. But actually we don't know anything about this, the expectation value of the stress tensor. I'm not assuming, I'm not going to use anything from ADSCFT. So so far we actually don't know how to translate this to the gravity side. But the interesting thing is that I can come up with a rule for that by considering the limit of this equation when the ball is very small. Yes. Oh, just about this form, this Pfeffermann-Gramm gauge. I mean, the physical motivation, one of the physical motivations is that it will turn out, it will turn out that in this gauge, certain relations to the CFT are simpler. But it's just a gauge choice. So if I chose some other gauge, I'd be able to write different formulas. Okay, so I want to consider the implications of that formula, but I'm gonna start with a infinitesimal ball. Okay, so I'm thinking about the change in entanglement entropy for this very small ball in the CFT. And so according to our assumption, the entanglement entropy for that very small ball should be equal to the area of this very small bulk surface, which will tend to be located out near the boundary of the asymptotically ADS space. And so if I take my first law, so now I take this limit where r goes to zero. And on the right hand side, then this is the area of B tilde over 4G and the limit r goes to zero. And what happens to the term here is that in the limit where this ball is very small, the right hand side only depends on the expectation value of the stress tensor at one point, because we're taking a limit around this one point. And so the right hand side, actually you can calculate it. And the leading behavior in the limit where r goes to zero is some power of r times the expectation value of the stress tensor at a point. So this, you get some power of r times the expectation value of the stress tensor at a point. And over here, what you get is something related to the boundary metric. Okay, so you get the area of this infinitesimal, the area of this little surface, you can see that's only going to depend on the metric close to the boundary. And so actually this power that I wrote, had I chosen a smaller power here, there would be some inconsistency because the left side would be finite and the right hand side would have turned out to diverge. If I had I chosen a larger power, there would also be an inconsistency because the right hand side would vanish. So the equality actually implies that the leading behavior of this perturbation comes in with this power. So for metrics that describe entanglement of states, this is the power, this is the first power where you have a difference from pure ADS. Okay, and then when you actually, assuming that once you actually compute the area of this small surface, then it just depends on this function H in the limit where z goes to zero. Okay, so the function H has a finite limit where z goes to zero. And so actually you get what you find is that you derive this relation between the expectation value of the stress tensor in the field theory and the asymptotic metric. So so far it's actually just for one component, E00. And the reason is that we worked in a frame, we worked in a particular frame like the T equals, we were assuming that we were living on the T equals zero slice. When I wrote this formula here, this is a formula for this modular Hamiltonian written as an integral over a slice at T equals zero. So we can say that we worked in this frame associated with observers whose time like vector is just one, zero, zero, zero, or one, zero. But this first law is also true if I look at balls in other frames of reference. So if I had an observer moving at some velocity and considered their frame of reference by Lorentz invariance, that observer should also be able to apply this first law. And so this result really, we should be able to extend it to a covariant expression where a more general vector u appears. And if I translate that to the covariant version, what it looks like is this. And so this is the expression I would get in a general frame of reference. And so this is true for any u. So this is true for absolutely any time like vector u. You can show that that's possible if and only if this is true. There's one step I skipped here. So if I remove the u's, I still have this part with h mu mu. And then I used the fact that this CFT stress tensor expectation value is traceless. That told me that h mu mu must also be zero. And so I just ignored the term. If you are careful and keep all of the coefficients, you get that the constant is, and so you can actually derive, this is the standard formula in ADS CFT for how the stress tensor and the field theories related to the asymptotic metric. So we didn't need to use that. We could actually follow it from this Ryu Takinagi assumption. This is the place where the choice of metric is particularly convenient. If I had chosen another gauge, then this is a more complicated formula. Yeah, so the step I skipped was to say that delta T mu nu, it would be h mu nu minus eta mu nu h alpha alpha. And then if I use the fact that I take the trace on this side, I know it's zero. And that implies that h alpha alpha equals zero. Yeah, so we actually get, from properties of the CFT, I think we get the h alpha alpha equals zero. If I wanted to, I could also impose now the CFT conservation equation, and that will tell me that d mu of h mu nu is equal to zero. So I learned these things, so that's already constrained about the asymptotic metric. Okay, yes. Yeah, right, so far this is just telling us, because we just looked at these little walls, it's telling us about something about how the boundary behavior of the metric has to be if I have a state that describes the entanglement of some theory. Okay, so now this is good, because what I'm gonna do is plug this in to this formula over here. Okay, so now we know how to interpret the stress tensor expectation value on the gravity side. And so now we can actually turn this into a completely gravitational equation. Okay, so this constraint on our first law now implies that the delta of the area of B tilde for G Newton equals two pi, some constant and then h, zero zero. Yes, yes, right. So we're completely focused on ball-shaped regions. And so when you see B, it's a ball. Yeah, so the question was about quantum corrections. And I should say that for now I'm working completely in the large N limit with a classical formula. And I will mention what happens if you include quantum corrections later. So so far it's just using, when I translated from here to here, then it's just using the leading expression. Later, if I wanna include the quantum corrections, then when I go from here to here, there'll be an additional term here that involves the bulk entanglement of quantum fields in the bulk. Okay, so what is this kind of constraint? We've translated this first law into a gravitational constraint. And it's all expressed in terms of this metric perturbation h. So this side is like an integral over B tilde of some local function of h. And the right-hand side is an integral over B of some local function of h. And so if I draw the picture, basically it's saying that if I have a metric which captures the entanglement entropy of some CFT state, and I calculate some integral over here, okay I could write it explicitly schematically. So it looks something like this, some integral over the surface B tilde. I can calculate that in terms of h, and I could calculate this one in terms of h. And those have to be equal. And that will be true for some space times m, and it won't be true for other ones. And so far it's a little bit clear, it's a little bit unclear what that really means. Okay, so it's roughly telling us that something about the metric deep in the space time has to be determined by something on the boundary. Oh, so this index m is, yeah, so I'm in this formula, I'm splitting up the coordinates into t, z, and xi. Okay, so an important thing to emphasize is that this is actually not just one constraint. We get one constraint for every possible ball. Okay, so if I have this metric describing the space time m, this equation has to be true for this ball, but also for this ball, and this ball, and this ball, and balls in other frames of reference as well. So roughly speaking you actually get one constraint. You get one constraint for pretty much every point in this dual space. Okay, if you think of maybe the tip of the ball as labeling which point your constraint is associated with. And so that suggests that maybe we actually have enough, maybe there's enough constraints that you could translate all of these things into some kind of local equation that must be satisfied in the bulk. Okay, and so it turns out that this is the case. Morally speaking, what we're going to do now is basically the same as going from the integral version of Maxwell's equations to the differential version. We're just going to make some application of Stokes theorem and then all these non-local kind of integral constraints are going to turn into some kind of local differential equation. I mean, if I have a geometry m, yeah, I mean, then some point, I mean, there are no points related to it by diffeomorphisms or diffeomorphisms refer to different coordinates I could put, so at the technical level when I wrote down this metric and I wrote down a function h, then I already sort of fixed the diffeomorphisms. Okay, so that would be, yeah. Okay, so here's how it works. And this is basically the same as how you would proceed in converting integral equations to differential equations in electromagnetism. So the idea is we want to apply Stokes theorem. And so it turns out we could find a differential form, which I'll call chi, and chi is built out of this metric perturbation. So chi lives in this region, sigma between the boundary and our extremal surface. And this form has the following properties.  If you integrate it over the surface b tilde, it gives the left-hand side. So integrating it over b tilde gives the area perturbation. And then finally, if you take the exterior derivative, it gives you something which is proportional to a component of Einstein's equation. So d chi equals some positive function, which I won't write down specifically, times this tensor that appears, the tt component of the Einstein tensor, and then times the volume form. So the exterior derivative is a d plus one form, something that could be integrated over sigma. Okay, and then it's sort of obvious what to do now. We just rewrite this first law using this form, so we get that integral of chi over b equals integral of chi over b tilde. And that's the same as saying that the integral over the boundary of that region sigma of chi vanishes. And that's the same as saying that, so now we use the Stokes theorem. So that's the same as saying that the integral over sigma of this differential form d chi vanishes, okay. And so that says that the integral over sigma of this positive function times the component of the Einstein tensor times the volume form has to vanish. And the important thing is that this has to be true for every single region sigma that I could draw. So this integral must vanish for every region. And now it's not quite trivial to then conclude that the function, the integrand has to vanish because the integrand, this function here actually depends on the region. So it's not the same function that we're integrating over all these regions. But there's some trick you can apply some differential operator to this equation to make the integrand independent of the region. So it's a few lines of math. And you can show that the only way for this to be true for any b is, would be for the tensor here to vanish. So this is the linear, this is delta e means it's the Einstein tensor linearized around ADS. So what we've learned so far is that this particular component of Einstein's equations must be satisfied if the geometry is capturing the entanglement of a state close to the vacuum state. And then we use, yeah. No, so when I used the ball of a small size, the conclusion of that was to say that the expectation value of the stress tensor was equal to the asymptotic behavior of this metric perturbation H. And then I used that formula in the general first law to obtain this. Okay, so what that allowed me to do was to replace the expectation value of T mu nu with this asymptotic metric. I should have said this is Z equals zero. And then I imposed this constraint for arbitrary balls. Okay, and that's what we applied Stokes theorem to. And so the integral of this quantity for over any region sigma, any of these hemispherical region sigma has to vanish. And so then we concluded that this tensor component has to vanish. And we're going to use the same trick that we used before. So the reason why we're getting the TT component is that we were working in the frame of reference at this T equals zero time slice. But we could have worked in any time slice. So really the covariant version of this thing that we would get if we thought about arbitrary time slices would be this. And that's only possible if all of these components would vanish. Yes, this? Okay, so the idea was to construct a differential form. So I claim we can find a differential form which is built from H and it's derivatives. Or actually it's first derivative. So it's something that has the property that if I integrate it over B it gives the expression here. If I integrate this form over B tilde it gives the expression here. And if I take the derivative of this form it gives this expression which includes which is just some positive function of the coordinates times this is the TT component of the linearized Einstein equation. So this is something which includes two derivatives on H. So when I write down the linearized Einstein equations you have various terms with two derivatives on H and the tensor structure is some particular tensor structure. And so that's what this is. No, okay, so I just write down a differential form. I didn't write it because it's a little bit complicated but I could tell you off the top of my head I wouldn't know. So yeah, so not quite. So here's the, okay, let me schematically say what I did. So we have this equation, okay. And now I write down chi is equal to H. So I'm just schematically writing down something. Okay, if you want I'll show you the explicit expression that it has a number of terms. Okay, so okay, I write down this differential form. So here is a differential form which I'm defining for you. Okay, now I want you to calculate the integral of this form over the surface and you find this expression. Okay, now take the same form and calculate this and I guarantee that you'll find this expression and now take the same form and differentiate it and then you'll find this expression. Okay, so we just check these three properties about an explicit form that I can write down. And the only reason I didn't write it down is that it wasn't particularly illuminating. And so once I know all of those things about this form then I can go through these steps to conclude that delta equals zero. So you can even, as an exercise just starting from these three properties, you can even try to find out what this is. Probably up to some constants or something, yeah. So yeah, at some point I did this exercise but incident, yeah, so for people that are familiar with this walled formalism, there's a nicer way to say what this form is. Okay, so I'm not going to have time to explain what this is but if you're familiar with walled formalism then it's precisely this kind of combination of these quantities that walled uses to say prove various black hole first laws. Okay, so I should mention a few things. These are the components, these are most of the components of Einstein's equations but there are some other components that we didn't talk about. These ones turn out to be what would be called constraint equations. So you could show that these ones are satisfied, once you have the rest of the components these equations are satisfied as long as they're satisfied at z equals zero. And you could show that they're satisfied at z equals zero as long as h mu mu equals zero and delta mu h mu new equals zero and these are the things that already followed from the tracelessness and conservation of the CFT stress tensor. I'll just mention also that if you had included the quantum correction and I won't have time to go through this fully so had I included this term which says that the CFT entanglement entropy is equal to the area plus the bulk entanglement entropy across the surface. Then it's possible to use a bulk version of this entanglement first law to rewrite this term in terms of the expectation value of the stress tensor in the bulk. And then what happens if you follow through the whole derivation you end up getting precisely the expectation value of the bulk stress tensor as a source term for these linearized equations. No, yeah, so, well let me talk about, the rest of the lecture is about going beyond linearized equations. So yeah, so now I wanna talk about what can you say beyond linear order? And you might, so you might wonder can you get the, can you get the nonlinearized equations? So we've shown that any metric close to pure ADS that captures the entanglement of some state, it must satisfy these linearized unsigned equations. So at the classical level there's just delta emu nu equals zero. So could we show that for just any space time that captures the entanglement which is not close to ADS, can we show that that satisfies Einstein's equations nonlinearly? But the problem is that as a geometrical constraint on space times, so Einstein's equations relate the curvature to some matter stress tensor. And we're kind of starting from some universal property of entanglement and trying to derive constraints on space times. But there's not just one, if I just give you a space time and I ask, does this satisfy Einstein's equations, you can't really check it in general because you don't know what sort of matter fields there would be. I mean there are many possible examples of ADS CFT, there might be lots of different matter fields. Basically any metric satisfies Einstein's equations if you choose the stress energy tensor correctly. So when we're talking about, as we're going to do now, if we're talking about constraints that you get at nonlinear order, they're not going to be specific equations that tell you is this space time a solution of some differential equation or not. Where they're going to be, it will be some kind of inequalities. So the idea would be, okay, you have all the, any equation, any metric is a solution of Einstein's equations with some stress energy tensor. But it may be that some stress energy tensors are impossible to obtain using any kind of matter you could cook up in a consistent theory. So this is the nature of the equations that we're going to get once we go to nonlinear order. They're going to be something that will tell us that here's a metric which is impossible to get in any theory. And that will be something to do with the fact that you can't possibly obtain the required stress energy tensor using a consistent theory of matter coupled to gravity. So the first question is, I mean is there a constraint on entanglements that generalizes this first law that we wrote down? And that would be our starting point for trying to constrain metrics at higher order. And it turns out that there is a very natural constraint we can write down. And it's simply that if I have a large perturbation, so a general state not close to the vacuum state, then the entanglement entropy of this ball relative to the vacuum state, it turns out that it has to be less than or equal to the change in the expectation value of the modular Hamiltonian, of the vacuum modular Hamiltonian. So it's exactly the equation we had before, but now it's an inequality and it applies to any states. And this comes from, this comes from a quantity, thinking about a quantity which is called relative entropy. So it's defined like this. It's a way to compare two density matrices. So we can think of our state and then we can think of the vacuum state. And if I look at the ball, then this one has a density matrix, row B and this one has a density matrix, sigma B. And I might wanna say how different are these two density matrices? So I can compute this quantity. And the nice property of this quantity is that it vanishes if and only if the two density matrices are the same and otherwise it's always positive. And actually furthermore, if I consider a larger region, so I think of one region B and now think of a larger region B2, then this quantity always increases as I go to the larger region. So it's positive and it's monotonic and I can show that it's actually exactly the difference between these two quantities. So by using the definitions that we had so far, you can just check that this definition of relative entropy is equal to the change in the expectation value of the modular Hamiltonian, okay, that I'm calculating from sigma minus the change of the entanglement entropy. So in quantum information theory, this is a measure of distinguishability between these two states. Yeah, so this is a row. So it's not symmetrical. So you should think of it as something which compares the state row to a reference state sigma, okay? If it were sigma, then it would just be the, that would be delta S, that would be the entanglement entropy of this minus the entanglement. But this is a little bit different. Okay, so five minutes or should I? Yeah, okay. So yeah, so I'll just summarize the results and then if you, maybe in the discussion session this evening we can. Okay, so I can just tell you then the results. So it's a quantity that's always positive no matter what perturbation I do, okay? And so that tells me that the first order perturbations, so at first order, perturbing away from ADS, it has to vanish. So if I have some function which is positive and the first order perturbation is zero in any direction and that's another way to see this entanglement first law. At second order, this is where we get the first non-trivial constraint, okay? So at second order, this defines a quantity which actually is symmetric. It's something like a metric on the space of perturbation. So I start with a density matrix and I think about perturbations in various directions and at second order this is a quadratic form on those perturbations and the positivity tells me that this must be positive, okay? And so that would be the first non-trivial thing if I translate that to the gravity side that has to be some positive quantity. What is it? So we think about pure ADS and now we're thinking about perturbations at second order. So we talked about how this region B can be associated with a certain wedge of the bulk, okay? And in ADS that was very well-defined. I was drawing it in the global picture where you had this Rindler wedge here, okay?  So there's a, it's kind of a natural, time-like killing vector and so from the unperturbed ADS point of view, this is a natural definition of time that lives inside this Rindler wedge. It's the Rindler time for this wedge, okay? And so at least at the perturbative level, like if I did quantum field theory on, or field theory on the background of pure ADS, then this would be a way to define an energy, okay? The energy associated with that time is some quantity. And at the perturbative level, I can even define that, including gravity, including metric perturbation. So I can write down some standard integral over this region, sigma of T mu nu and this vector. And this would just be the energy associated with that particular definition of time. And at the perturbative level, I can include matter contributions and gravitational contributions. This would be quadratic in the metric perturbation. And this turns out to be what this second order relative entry maps to, okay? So it tells me that this gravitational, this perturbative definition of energy for the region has to be positive, okay? And this is a quantity called, that had previously been considered canonical energy. And it was known that it had to be positive just for pure gravity. If you don't have any matter fields, it was, you could prove that it has to be positive. So the positive of the relevant entropy suggests that for any space time, even if it has matter, there has to be this, for every one of these regions, there has to be this positive energy. But then finally, you can say, well, even at non-perturbative order, even if you're far from pure ADS, on the field theory side, there's this relative entropy quantity that has to be positive. So this suggests that there's actually an energy that you could define for subsystems of your gravitational theory. So this is some arbitrary asymptotically ADS metric. It says that there's some energy, even though there's no killing vectors in this space time, and this is now just some extremal surface, there's an energy I can associate it with this subsystem. And the definition is I can define some vector X, which again behaves like this vector near the boundary. So it behaves like this vector zeta, this conformal killing vector near the boundary.  So close to the extremal surface, it behaves like this killing vector behaves close to this extremal surface. So it's kind of like zooming in and it looks like a bit of a flat space time and then you define the Rindler time vector. So it's only defined, X is only defined close to the boundary and close to the surface. And in the middle it's just arbitrary. But what you can show is that the energy associated with that definition of time, it doesn't depend on the details of what X does in the middle. So you can argue that there's actually an energy for these arbitrary space time, for these regions of arbitrary space times, that's well defined. And then according to this positivity relative entropy, it must actually be positive. So what it suggests is that there's actually a new positive energy theorem that applies not for entire space times, all of the standard positive energy theorems for ADS or flat space. It's always a statement about the entire space time. But what this suggests is that for asymptotically ADS space times that are physically consistent, any of these subsystems associated with balls on the boundary can have an energy associated with them and it must be positive. So you get sort of an infinite number of positive energy theorems for any asymptotically ADS space time. So I'll stop there and then later today we can ask questions about more details.


Hey, Lisa Martin on the ground with theCUBE at Google for the sixth annual Cloud Now Top Women in Cloud Awards event. Our second year covering this, very excited to be joined by tonight's emcee, Becky Wanton, the founder of RSW-1C. Welcome to theCUBE. Thank you. It's great to have you here. So tell us a little bit about what you do and your background as a technology leader. So I've been in technology for close to 40 years. I started out as a software director. Sorry, I don't even, what? A long time ago, yeah. So I started out as a developer back in the Department of Defense. And so it wasn't rocket science in the early days when I began, because it was back when computers took up whole rooms and I realized I had an affinity for that. So I leveraged that, but then I got into, at that time, and I'm from Northern California, if you remember right, Department of Defense was drawing down and so I had put my, I decided I was going to leverage my experience in IT to get into either Integrative Financial Services or healthcare, right? So I took over running all of tech for the money store at the time, which you would have no idea who that is. And then that got acquired by Wells Fargo first union, so I took over as their global CTO for Wells Fargo. And what you'll see is, so let me just tell you about RSW1C, because what it is, is it's a technology consulting firm that's me. And the reason I have it is because tech changes so much and it's easy to stay current. And when I get brought into companies, and you'll look at me, so I've been the executive officer for tiny little companies like PepsiCo, Wells Fargo, Southwest Airlines. Small ones. Yeah, tiny, not, MGM Resorts International, the largest workers company in California, a company that I'm more mid-sized, SMB in Southern California that just wrapped up last year. And when I get brought into these companies, I get brought in to transform them. It's at a time and the maturation of these companies, these tiny little brands we've mentioned, where they're ready to Jettison IT. So I take that very seriously. And because I know technology is that gateway to keep that competitive advantage and the beauty is of the companies I've mentioned, they're all number one in their markets. And when you're number one, there's only one direction to go. So they take that very seriously. How do you come in there and help an MGM-Gran Resorts transform? So what happened in MGM's case, and probably in the last five CIO positions that I've taken, they've met me as a consultant again from RSW1C. And then when I look into what needs to happen and I have the conversation, because everybody thinks they want to do digital transformation. And it's not an easy journey. And if you don't have the executive sponsorship, don't even try it at home, right? And so in MGM's case, they had been talking, MGM's the largest taxpayer in Nevada. People think about it as MGM-Gran. It's 19 brands on the strip. Is that right? It's Bellagio, MGM. So it's the biggest taxpayer in Nevada. So it owns 44,860 rooms on the strip. So if I just count it down, you have Circa Circa, Slots of Fun, Mirage, Bellagio, Monte Carlo, New York, New York, MGM-Gran Las Vegas, MGM-Gran Detroit, they're in the countries and so forth. So it's huge. And that includes Mandalay, Aria and all those. So it's huge, right? And so in MGM's case, they knew they wanted to do M-Life, right? So M-Life game changed their industry. And I put that in, this will be our nine-year anniversary coming up on Valentine's Day. 30 years they talked about it and I put it in with a great team. And that was part of the transformation into a new way of running their business. Wow. We have a couple of minutes left. I'd love to get your perspective on being a female leader in tech. Who were your mentors back in the day? And who are your mentors now? So I don't have any mentors, I never did because when I started in the industry, there wasn't a lot of women and obviously technology was fairly new, which is why one of my passions is around helping the next generation be hugely successful. And one of the things that's important is, in the space of tech, I like this mantra. I'm on this mantra that says, how about brains and beauty? You know, how about you get you in the door? How about having the confidence yourself? So I want to help a lot of the next generation be hugely successful. And that's what Jocelyn has built with Cloud now and her and Susan. And I'm a big proponent of this because I think it's a chance for us to give back and help the next generation of leaders in a non-traditional way be hugely successful in brands and companies that are going to unleash their passion and show them how to do that. Because the good news is I'm a total bum. At least I've never had a job. I love what I do and I do it around the clock, so. Oh, if only more people could say that, that's so cool. But what we've seen with Cloud now, this is our second year covering it, I love talking to the winners and even the folks that are keynoting or helping to sponsor scholarships. There's so much opportunity. There really is. And it's so exciting when you can see someone whose life is changing as a result of finding a mentor or having enough conviction to say, you know what, I am interested in a STEM field and I'm going to pursue that. So we thank you so much Becky for stopping by theCUBE and your career is amazing. And I'm sure you probably are mentors to countless, countless men and women out there. Absolutely. Well, thanks again for stopping by. Thank you, Lisa. Appreciate it. Thank you for watching theCUBE. I'm Lisa Martin on the ground at Google with the Cloud Now, six annual top women in Cloud Awards event. Stick around, we'll be right back.


Dr. Thomas is a professor in the Department of Agriculture, Food and Resource Economics at Michigan State University. Right to joining MSU, he worked with Disney for eight years. Tom's research focuses on links between agri-food industry, transformations and food security in Asia, and he's listed in whose who in economics was back in writing to World Economic Forum in 2009, and he's also a member of the WES Global Alliance Council for Food Security. He's going to talk about the other end of the supply chain, talk about ice in the air supermarket. With that, Tom. Thank you so much. It's a pleasure to be here with you. My focus is not going to be on the farm level except in a way that in a sense the farm level is affected by the other levels in the supply chain. I think it's important to emphasize, as I'm going to be speaking about the rice industry and the rice market, that 50 to 75% of the rice price that's paid by the consumer in Asia is formed by the segments of the supply chain that come after the farm. Distribution and logistics, processing, retail, these are basically the segments that form 50 to 75% of the rice price. Yet the discussion already at this conference might have touched on those segments 5% of the time or 1% of the time. So I think that that investment of those and understanding of those has to become central to understanding the overall rice economy. Now to summarize that idea, the talk is called Rice in the Air of the Supermarket, and I'll focus on Asia and I'll use some field research that's been funded by the Asian Development Bank mainly in order to illustrate this. And of course the points will be general because I don't have time to go into great detail, but of course I'm talking about areas that are heterogeneous and so there's lots of differences across the area. So I'll talk about tendencies and future movements and moving averages. And I'll start with a set of points about structural change in the rice industry. Then I'll look at conduct change in the rice industry and finally performance change in the rice industry. And my first set of points will deal with trends that have been occurring in the 1990s and 2000s in the industry, let's say especially in Asia where I'll focus, and you can think of these as symbiotic trends, that is they're co-evolving, they're very related. The first one, one I'm very passionate about is the consolidation and multinationalization in retail simply put the rapid rise of supermarkets. And what we've been finding is that supermarkets that might have been a very small share of the food industry or food economy in 1990 even in Asia have gone to be 30, 50 more percent of the food economy by the end of the 2010. And an example from our recent work is that while there were no supermarkets at the end of the year in 1989 in China by the study that we did this year we found that 50% of rice retail in Beijing is going through supermarkets. Now this is about the early 1990s, late 1980s in Hong Kong so it's lagging behind that but it's already changed very quickly. It's lagging behind overall penetration of supermarkets and processed food which is around 75% of the largest cities in China but it's catching up. Now in Delhi where we just did a study and 85% of the supermarket sales in Delhi have been formed in the past three years so this is very recent. Already supermarkets have 7% of the rice retail in Delhi. The concomitant point of course is that there's been as in many parts of the world the trend that you see also in Northeast Asia and East Asia is now occurring in Southeast Asia and starting in South Asia and certainly in China which is the decline of the traditional rice shops. So there's a fundamental shading up of the retail side of the rice economy. Then there's also a shake-up that's occurring really over the past decade or a little bit more depending on the country in the milling sector with rapid consolidation and mechanization, a rise of large and medium mills and we've watched it in our studies that rapid decline of the small rural rice mills and a rise, this has been fascinating in our study in Beijing with Hanoi province, that there's a rise of direct relationships between the mill and the wholesaler and the mill and the supermarket cutting out the rural broker, the semi-wholesaler, all these pieces in the chain that we've come to think of are there. Third point of structural change is related to the point I just made which is the rapid consolidation and disintroduction in rice wholesaler. There's a rise of medium and large wholesalers that we've found are representing directly sets of mills or single mills and a decline of the small rural rice brokers in many areas. The last structural point is that just as downstream from the farmer once seen rapid ferment and change in Asia, also upstream as is evidenced by the presence of buyer and other agri-input companies at this conference, there's been a growth consolidation, multinationalization in the inputs being sold to farmers, a rise of large seed chemical companies. The start of the rise of one-stop shop rural modern input retail if you want input supermarkets that one is seeing in India and the rural business hubs. The decline of the state sector that was so important in input retail in decades past in China and India and elsewhere. So in four ways structural change has been occurring very quickly in what was thought to be a sleepy sector. Now all of that is inducing waves of change of the conduct of the behavior in supply chains of rice. First one that you can see is coming really immediately from these trends is disintermediation. So when I started to do this research with colleagues, everyone says, well the way the rice supply chain looks in Asia is there's a farmer and then there's a rural broker and then it goes to a mill and then it goes to a broker between the mill and the city, then it goes to a wholesaler within the city, then it goes to a semi-wholesaler and then it goes to the traditional retailer. Many hands, lots of inefficiency. But in fact what we've seen is that in very many places there's a shift from these long supply chains to much shorter chains with disintermediation. And along with that shift has come a shift from the informal sector to formalization. For example in the Beijing study in other places we've seen a shift from rice sold loose to rice now sold packaged, labeled, branded, 80% of the wholesale market rice in Beijing is sold packaged, labeled and branded, 80%. That was much much lower just five years ago. And with that comes incipient traceability, the importance of which I'll point out in a second. A third topic in change of conduct in supply chains which sends me into paroxysms of obsession really is this issue of the product cycle of the value ladder climbing that one can see happening in the rice sector as well as the non-rice sector in Asia. Shifting from local niches, building them up into commodity rices that are sold at zone level, national level and international levels into commodity cost-competed products. And then with differentiation of these commodity rices into quality differentiated rices that is by far the wave of the future. And differentiation into safe rice, green food for example in the rice sector in Beijing is rising very quickly, organic rices. And what we think, when I say we, I've been talking a lot and working a lot on this with Peter Timmer. In fact this is an outline of our joint paper that we're preparing Thursday. But there's a probable trend toward traceability and all of these things will conspire to make that happen. And we think that traceability will be a key thing in the rice sector for the same reason that it became so in the beef, milk and produce sector because all the points that have been made about the incursion of cities into the rice areas means also incursion of pollution of metals. There's going to be the same kind of PCB crisis that affected the fuel sector in Europe. You'll have several major crises like that in Asia in the next five years, I'm sorry to say. I really believe that will happen and the traceability topic will become very central in rice. On the other hand, besides those challenges we're faced with opportunities, food security increased through greater efficiency in the supply chain. Supermarkets is motors of rice market quality differentiation and labeling. And all of this will increase incentives right up the supply chain to the farmers. Now I have some open questions that I feel privileged to just throw on the table, which are two. I've been thinking what the heck is the role of policy and private public partnerships to address these challenges and pursue these opportunities? Is this a thing that will happen parallel or will policy interact with it? Will it make it faster? Will it make it easier? Will it include more people? Will it make it more effective? And the last question I had actually flipped the other way around when I was sitting this morning listening to the plenary. I'm thinking, hey, everybody has in their line of rice farmer and formal rice farmer and a big government guy. That's the way all these debates go. Over and over and over again like a broken record. And of course when there's a crisis it becomes more of a broken record. It spins a little bit faster. But really these changes I'm talking about are a lot more important over the longer term than some policy debates here and there as you're bumping along. How will these things change the policy debate? How will these actors that are consolidating turn around and say, as they have in the produce sector, they have in the dairy sector, they have in the meat sector, they have in the non-food sector. They turn around and policy makers and they say, hey, make this work. Cut down the resistance. Cut down the constraints. We need to make this market grow. What are you going to do about that? And there will be a heavy pressure in the future that will affect how the policies and how these market structures and regulations develop. Just in the way that proper science people are doing at present influencing the regulations and the property rights that envelop the supply chain at the input end. So with that, I conclude. Thank you.


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It's probably one of the vaguest things I've had in a while, but it's still very intriguing. Hey guys, this is my review for The Rover. This is a film that was suggested to me by a good friend of mine. I've ever seen the trailer for it back in 2015, 2014, and the film looked really vague. Well, in a sense, it's a movie about Guy Pearce, whose car gets stolen, Robert Pattinson's brother is one of the guys who steals it, they go and find the car. That is the movie in three sentences. However, there's so much more that happens on a visual level in terms of just watching the characters. We're not seeing them, there's dialogue here and there, but what happens really the main meat of this story is how we visually see these characters.  There was at least three times I watched this. When the night I watched it, it was really late and I was like, you know, I should go to bed. I was like, okay, I'll give you five minutes. That happened three times. Each time there's a moment where I was like, maybe I'll turn it off. There was a part that would make me, that would draw me back into it. In the end, I watched the entire movie until the wee eight hours of the night. Possibly one of the most interesting aspects of this entire movie is Guy Pearce's character. Because he's not a protagonist, but he's not an antagonist, but he's definitely not a good person. I think this really captures the idea of a man who has nothing left to lose. That is, in a sense, the main meat of the story is that Guy Pearce is hell bent on doing, getting his car back. And the reasons why is not really revealed until the end. But when you think about it, when you see it and then you look back, everything else makes sense to him. There's such great visual cinematography in this film. There's very long lasting shots. There's very large landscape shots and they're all really good.  They actually do have, especially there's two mirroring ones from behind Guy Pearce's back, that both mirror kind of his emotional state as well as just how little he cares about anything else in the world anymore. And there's a scene. There's one scene with a army guy that was probably one of my favorite scenes in the movie. There is talking about the, what do you do now that it's over. And that's the thing too, is that the director of this film really captures a different version of the apocalypse or the end of the world. Because, to be honest, it still looks like what I think Australia looks like. I've watched too much Mad Max. But otherwise, there's still stability in areas, but in the rest of it, it's still, it's pretty shitty. And you really don't get a full look at it. You only get pieces, which I'd like. I mainly want to see the more of the world and different aspects of how the world is structured. Now, one thing that I'm definitely on the fence about was, I liked him at some point, but then there was other times I was like, eh, it was Robert Pattinson. Robert Pattinson's character has this southern draw that's so difficult to discern at points. Guy Pearce's Australian accent sounds completely normal. And I had to put on the subtitle sometimes for what Robert Pattinson was saying. But his character is very interesting. He's maybe like an ex-drug addict, but he has these weird mannerisms that are very consistent, especially in the final climax. These weird mannerisms of his character, these kind of speech impediments. I like that he had this and made him a very unique character. Well, and then the decisions and the choices and the events that happen around these two are so brutal that I just couldn't stop watching it. Every time I thought I was going to end it, I just kept going. And this pop, admittedly, like I said, it's a slow burn. Admittedly, when I try to watch this movie, the first time I actually turned it off after five minutes, I just wasn't into it. And there's a soundtrack choice at one point where they put on this pop song. Admittedly, it's coming from a car. But just the whole scenario was just very strange, kind of a weird look back into the world that they once was. So in the end, I'm going to give the rover a five out of seven. It's a good movie, but it's a one time watch. I'll basically give you that. You really wouldn't be able to watch this movie again for a long time. It's very well done. It's very well, it's very well set up. The world that it's set in is very interesting. The characters themselves, Guy Pearce's character is incredible. But as I said, when you watch it once, you really won't want to watch it again. At least that's my take. Anyway, guys, hope you enjoyed this review and I'll see you guys next time.


It is time for some metencephalon. We're going to use the same views for our metencephalon. There's two structures that we are going to learn that are involved in the metencephalon, and one of them is the pons. The pons is the, well, it's not really, okay, never mind. The pons is basically responsible for regulating breathing. We have the pons also here. It's kind of an obvious little bulge on your brain. You can see it, and there is a connection between the pons and the cerebellum, which is our other metencephalonic structure. I think I just made that word up. Cerebellum. The cerebellum is a fantastic structure. It's, first of all, really pretty. Second of all, it's responsible for fine motor movement and complex motor movement. The cerebellum is capable of learning routines. You are an athlete, and you do the exact same, I don't know, I used to coach volleyball, and we would practice our approaches to spike the volleyball, and we would do it over and over and over again. And when my players were, you know, seventh graders, they were terrible, and they had to think about every single step that they did. But by the time there were sophomores, they had it down. They didn't have to think about how to do an approach. It just was automatic because they had had it drilled into their bodies. Same thing with something like playing the piano.  Your fingers just kind of know where to go, and you're not actually actively processing it. The parts of the brain are at work when you are doing something that you know how to do really well, or something that you are just learning how to do. Hmm, I think that's about it. I better stop because the last one is the myelin cephalon. Let's keep going.


Dietary practices influence our exposure to pesticides, toxic heavy metals and industrial pollutants. A diet high in fish and other animal products, for example, results in greater exposure to these pollutants than does a more plant-based diet, because these compounds may accumulate up the food chain. Researchers at UC Davis analyzed the diets of children and adults in California to see just how bad things have gotten. Cancer benchmark levels were exceeded by all children. 100% of children tested for arsenic, the banned pesticides Deldren and DDT, metabolite DDE, as well as dioxins, and not just by a little. More than 100 times the acceptable daily exposure for arsenic in preschoolers, school-age children, parents, and older adults. About 10 times the acceptable levels for these various pesticides and up to 1,000 times the daily dose for dioxins. Where are all these toxins coming from? The number one source of dioxins in the diets of Californian preschoolers, kids, parents, and grandparents appears to be dairy, dairy, dairy, dairy. Followed by meat, then white potatoes, refined grains, mushrooms, poultry fish. Our DDT legacy these days is also mostly from dairy. Deldren was created as a safe for all alternative to DDT, but was banned two years later in 1974, though still found in our bodies mostly thanks to dairy, meat, and evidently cucumbers. Chloridane made it into the 80s before being banned, though were still exposed through dairy and kukes. Lead is also food-wise mostly from dairy, and mercury, not surprisingly mostly from tuna and other seafood. But arsenic was surprising, mostly from chicken in children. Why? Let me tell you a tale of arsenic in chicken. Arsenic is well known as a poison by anyone who reads mysteries or the history of the Borges. With its long and colorful history, arsenic is not something that people want in their food. So when a biostat student went to the USDA 17 years ago in search of a project for his master's degree, he decided to look into it. And what he found was this startling difference. Arsenic levels in chicken were like three times that of other meats. His veterinary colleagues were like, duh, though. I mean, don't you know we feed four different types of arsenic-containing antibiotic drugs to poultry since, you know, like 1944? So while arsenic-based drugs have been fed to poultry since the 40s, recognition of this source of exposure for humans only occurred after this student churned through the data. It was published in 2004, expanded upon in 2006. The National Chicken Council was none too pleased saying lots of foods are contaminated with arsenic by focusing specifically on chicken. The Institute for Agriculture and Trade Policy makes it clear that their true objective is to force chicken producers to stop using these safe and effective products, by which they mean these arsenic-containing drugs, which they admit to using, but say don't worry, they use organic arsenic, not the inorganic form made infamous in arsenic and old lace. That is apparently until you cook it. When you cook chicken, it appears some of the arsenic drug in the meat turns into the arsenic and old lace variety. And so, the Poison-Free Poultry Act of 2009 was introduced into Congress. You can tell how well that did based on the subsequent introduction of the Poison-Free Poultry Act of 2011. Twist they said, poison, poor poultry, fish, posh. And so in 2013, a coalition of nine groups got together and sued the FDA. And by December 31st 2015, all arsenic-containing poultry drugs were withdrawn. And so as of 2016, arsenic will no longer be fed to chickens. The bad news is that without the arsenic-containing drug-rocks-arsone chicken may lose some of its appealing pink color. In the end, the poultry industry only got away with exposing the American public to arsenic for 72 years. It should be noted that the European Union had never approved such drugs in the first place, saying, Feed our animals arsenic, no thanks, nine danka, no grazzi, no merci. Europe also longed since banned the urgent threat to human health posed by feeding farm animals millions of pounds of human antibiotics, a problem that gets worse every year instead of better, including chickens in mass literally tons of drugs like tetracycline and penicillins to fatten them faster, dating back to 1951, where drug companies whipped out the all caps to promise big profits. A dangerous practice the poultry industry had gotten away with for 66 years and counting.


Agent K-7 returns. Number one adventurer, K-7, form a United States secret agent who operated in 22 countries on land on sea and in the air, brings you a story of today. We take you to secret agent K-7's headquarters. This is K-7 speaking. Send in Agent M for assignment. Special Agent M reporting for duty. Agent M, this city is the focal point of world trouble today. As you know, it formerly belonged to one nation and was made free after the world war to create a port for another country. Now the first nation wants it back. As a result, the city is a hotbed of intrigue and threatens to become the torch that might ignite another world war. I have traced the famous spy, Andre Zermann, here. I want you to find out what he is plotting. Here is his photograph and all known facts keeping me informed. Being a high-ranking officer arrived in the city, he visited Andre Zermann in the latter rooms within an hour after his arrival. And tried to steal. I've been here three days. I thought you were not coming. I came as soon as my affairs were in order. Tonight is the embassy ball. I had to be here for that. Zermann, we are ready to act. I want you to listen to me carefully. The act tonight? Yes, Zermann. We are determined to seize the city. Our enemies have won sympathy here. Many of the population favor them. You are here to change that feeling. We must make the people of this city hate those who oppose us. Now, people already hold many important positions. They are not popular, Zermann. We have decided on a bold stroke. We are going to murder certain of our own diplomats. Murder? A try. I don't understand. Three of our people who hold power here are no longer popular with our leaders. We are to dispose of them. Do you understand, Zermann? The people of this city would never think of accusing us of murdering our own people. They will say our enemies have been plotting. We will gain the people's sympathy and support. And at the same time, liquidate three who are no longer useful. That is good. They will turn our enemies. I had not thought of that. Our plans have been carefully laid. The newspaper will raise a great cry. Certain of our people will stage demonstrations in the streets. When the rioting has reached its peak, our troops will march into the city and restore order. And the free city will be ours, exactly.  Three are to die. Two of them tonight. I am ready. Zurg, yours to be the first. He will leave his home between 9 and 9.30. He lives on a quiet street. There are shadows to hide you. When you're finished, come to me at my hotel. Three are to die. Two of them tonight. A few minutes later, the officer left Zermann. Agent M and Ivan watched him from across the street. There's someone coming out, Ivan. Whoever it is, he's in uniform. Wait until he passes under the light. Ivan, I know that man. Who is he? The head of another country's secret police. His presence here means trouble. K-7 was right. That officer has been calling on Zermann. That means Zermann is here for a purpose. We've got to act fast. Do you think they were crossing? There's no doubt about it. Now wait. The officer is nearly out of sight. I want you to follow him. Find out where he's staying if you can. I'll stay here and play with Zermann if he leaves his room. Ivan stayed a few hundred feet behind the officer and on the opposite side of the street. They'd hardly disappeared from sight before Zermann also left his room. He walked rapidly. A few minutes later, he stopped before the home of Zorgio, high consular representative. As he paused, M came to a stop and the shadows behind him. I'm limited to man. Zorgio should be leaving his room. Yeah. A few minutes later, the front door of the diplomat's house opened and a short, stocky figure stepped into the night. What? Stay where you are. Don't try to run, Zermann. I arrest you. That man did you not interfere in the affairs of Andre Zermann? Ivan followed the officer from Zermann's rooms to a leading hotel. He registered and went directly to his suite. Ivan waited in the lobby. An hour later, she saw a man who answered Zermann's description into the lobby. He stopped at the desk. A man in form 407 is expecting me. My name is Andre Zermann. You are to go up at once, Herr Zermann. Room 407. Ivan waited until Zermann had gone into the elevator. Then she followed him by way of the stairs. Room 407 was at the end of the hall. She crouched outside the door. Zorgio is dead. He came out of his home when it left at nine o'clock. He never reached his car. Good. He had no trouble then. It was also necessary to kill him now that he followed me. He did not see him until after Zorgio was dead. Then he stepped in front of me. Who was he? A foreigner, an American, I think. I had to kill him. An American? Well, no matter. You are sure of Zorgio. There must be no slips. Zorgio is dead. Then they are ready to strike a second time. And who is to be next? The high commissioner. He also goes to the embassy ball. But he has already left his home at his native ten o'clock. Who? What you forget? I too am going to the embassy ball. Tonight at midnight I will step out onto the south balcony. The high commissioner will be with me. Somehow I will get him in front of a window so his figure will be outlined against the light.  At midnight they were to strike again. Ivan had two hours. Who was the American who had been shot? Was it agent M? Ivan inquired of the police at the hospital. There was no report. There was only one thing she could think of. M had been shot. Somehow his body had been removed. She determined to bring Zerman to justice alone. At twelve that night she concealed herself in the shadows under the south wall of the embassy. Ivan's eyes became accustomed to the darkness. She made out the figure of a man lying flat on the wall near her. Then the balcony doors opened. A figure was outlined in the darkness but not against the lights of a window behind him. Instead the bright rays of a flashlight were trained directly on it.  I also have a gun. Don't try to jump. I warned you. You wouldn't listen.  Ivan, is that you? M, are you all right? Your head is banded. A man tried to kill me early in the evening, Ivan. His bullet grazed my head. A diplomat was killed. He was a close friend of the high commissioner. I came to the ball to warn the commissioner. I heard them plotting. The officer whom we saw leave Venom's room was supposed to bring the commissioner out under the balcony. Venom was to shoot from this wall. It's too bad you didn't know in time to save his life. I did save his life, Ivan. I turned my search life on the officer. He is the one who died. Now his own police will cut down his murderer. They won't have to, M. What do you mean? Look there in the shadows. I killed him. I thought he had shot you. He was working under the direct orders of the... Before he died, he killed that official. Completed my assignment. Today, as war clouds hang over half the world, there are plots and counterplots. World peace is at stake. This condition must prevail as long as there are men who are willing to sacrifice humanity in their thirst for power. Listen for my next story. This is K-7 Speaking.


And the battle for your heart allow no pockets of resistance. There are two parts to any military conquest. One, the initial assault, and two, the mopping up operation that deals with any lingering resistance. Keeping that in mind, consider this principle that holds true in military and spiritual realms. Pockets of resistance, if left unchallenged, can lead to rebellion. Dilling with those pockets is not optional. It is essential if complete victory is to be achieved. Study the life of Good King Joash, and you will quickly detect some pockets of resistance in his spiritual life. Idolatry, insensitivity to the message of God's prophet, and cruelty after the gift of kindness. How about you? Are there any areas of your life that have become pockets of resistance, such as finances, pride, time with God, gossip, your thought life, time with family? Pick an area of resistance and deal with it today.