So maybe the material I was asked for to deliver, perhaps a bit foundational for the next to last day, but we'll see as we go, I mean in case it's too, I'll tell you what I've prepared and now we're going to go through it, it'd be just a blackboard talk, well lecture. So the original program was to go through the basic formalism of continuous variables and then introduce Gaussian states and then show something about their entanglement because it's mostly because these are quite old results, like 15, 20 years old, but they're very the seminal in the sense that such techniques are quite far-reaching even in nowadays research and you can still apply them, so they could be beneficial. Alternately, in case we are a bit faster than I thought or you don't want me to go through all the details and such, because that's what I was about to do. So there might be an end of a final lecture on quantum estimation, on how to calculate the future information of, well, again in Gaussian systems because that's the formalism that I'll build up in the first couple of lectures. But maybe we'll see how it goes and then maybe you'll pitch in and tell me whether what you prefer. So, okay, but by continuous variables here we mean mostly in a winter college, though there's no winter anymore, but I mean in a college on quantum optics, obviously, you know, continuous variable just means systems. So continuous variables, this blackboard is so big. It's amazing. Wow. So I'll start from here then. Okay, well, continuous variables that let you know, because quantum, of course, it's quantum optics. So it's a formalism. So it's the systems that underlie quantum optics in the sense of the electromagnetic degrees of freedom in second quantization or any standard quantum mechanics 101 system that behaves like that. Let me just remind myself of what notation I want to use. So that's, of course, something that you are all familiar with. There's a big identity operator there, but you know, we call it a C number like to take on some attitude. Right. So these I'm going to write. And in particular there'll be, I can put these labels because I'm going to talk about a finite set of this. So a discrete set of canonical variables pairs. Yeah. And that's the difference between somehow, it's the difference between quantum optics and quantum field theory. Although quantum optics too is sometimes you get to deal with continuum of modes that maybe interact.  So these are the degrees of freedom. And that's what they're called. They're called continuous variables because as opposed to discrete variables where you have like, you know, quantized levels, stable quantized levels in an atom, you would have operators with continuous spectra. Yeah. That's very trivial. Something that is slightly less, well, it's still trivial, but like the way I'm going to organize my formalism is the following way, which is slightly less standard. I'm going to order all of these operators in a vector of operators. And then, and then I'm going to rewrite the CCR, the canonical commutation relation. This is how mathematicians call them. Even though typically mathematicians will tend to express, mathematical physicists will tend to express them as exponentials because they have problems with the domain of these operators, but we don't care at this stage. Well, certainly not. So the CCR, I'm going to express them this way as, okay, so what I mean here is that I'm going to take the outer product of these two vectors. That's why I write a vector and a row vector, a column vector and a row vector. So you take all possible pairs of commutators between these operators and you'll end up with a matrix. Obviously, technically, this is an operator valued matrix, but there's always the identity, so we don't care. We have to just to bear this in mind. And this matrix there, right, I can't raise this. I can't lift it. So it's this thing. It's, let's say we have n degrees of freedom. This is a direct sum of these blocks. It's an anti-symmetric non-degenerate matrix that's written that way. So this embodies, this sort of represents the canonical commutation relations in this formalism. I like this formalism because it's very powerful and will allow us to prove things rather quickly later on. Well, formalism, there's notation more than formalism. So these are continuous variables.  Well, you know, by the end of these three, two, three weeks, for some of you, you should be familiar with this, but, and I think you are, but just let me repeat. There are many degrees of freedom, obviously, way in quantum optics and other labs. There's a, we have reached a very high level of coherent control. And so they're interesting because, and by these degrees of freedom will be, obviously, in quantum optics, that's, that would be light, you know, the electric and magnetic field. So the, so, so, non-polarization, polarization will be discrete. So we will assume polarization constant or we'll disregard it in terms of optics, but also like as, for instance, trapped ions would be described by such a formalism, emotional degrees of freedom that is for atoms as well. Then there's atomic ensemble of samples of pseudo spins. But mostly now I would say a lot of optomechanics, which you've heard of yesterday from Moriol.  And none, and all the electromechanics that now are getting into the quantum regime plus monics to some super, some superconducting devices. So there's a lot of, of systems that abide by this formalism. So there's an interesting study in the properties of these systems in terms of quantum information, right? And yeah, well, I'll be more specific in a bit. So then obviously solving quantum information problems. So you all know that the CCR algebra cannot be represented in finite dimensions. You just need to take, I don't know, for instance, in finite dimension the trace of this will be zero, but the trace of the identity times something can never be zero, let's say. That's the first, the first and most obvious incongruence that would arise. So, so the, but you all know that this is just, can be represented on an L2 Hilbert space that you're familiar with, a separable Hilbert space that meet a discrete basis that we're going to see in a second. But so the system is infinite dimension in all quantum information problems, I've been, I've been very vague and generic here, but the dimension of the Hilbert space is one of the main parameters and make it more or less difficult. Solving general problems in quantum information for continuous variables would mean to solve them for all systems, yeah? Because you can embed any smaller dimensional Hilbert space into an infinite dimensional one. Up to, you know, there could be some misses with, I don't know, indistinguishable particles from ionic systems, but up to that it's basically all systems. And so it is difficult to solve problems very generally. So there is a description, so there is a restriction then to the Hilbert space, well to the set of states, which is usually, well, which is, which can be adopted, which is the Gaussian restriction. So the first thing we're going to do is introduce what Gaussian states are. And let me comment on this. We're going to see a lot of properties of such states. Why are they relevant though in the first place? I'm about to make it formal, but Gaussian states are nothing but the ground and thermostates. So as in Gibbs thermostate or some temperature of Hamiltonians which are bilinear in X and P. That's the most general definition. It's not the most standard definition. We'll come to that. But these systems are therefore very common whenever you can restrict your interactions, whenever it's relevant to restrict your interaction to second order. And this is very common in quantum optics because it is very difficult to let, to have light interact at higher orders. It's something that one typically wants, strong nonlinearities as well. It's been a holy grail in many senses. But the difficult thing to do for photons, which is one of the reasons why photons are so pure and they're so effective in, for instance, quantum communication. Because they tend not to interact much. I'm being vague, but obviously this is not the same in solid state systems where you have photons that are very dirty, typically. And so in quantum optics, the restriction to bilinear Hamiltonians is often a very good one. And for instance, in optomechanics too, although there's an interest in creating an anharmonicities. I'll come to the point of like assessing the sort of the value of Gaussian states as opposed to having known Gaussian once. But there, but even standard optomechanics can be linearized and it's a good description. Trapped ions typically, given the distances between them, the Coulomb potential can also be linearized typically and they will give you a very good approximate description of the oscillating modes of these ions. And those systems therefore are all described by Gaussian states. So there's quite a lot of interest. And to a theorist, the interest in working with Gaussian states is that they're such a nice playground where you can solve quite a lot of problems that are difficult to solve in general. And they are relevant in practice. So there are many implementation. So there are a couple of caveats obviously. One is that you shouldn't extrapolate because this is a very specific set of states that has certain properties that we will see, but you shouldn't make claims that go beyond the Gaussian realms typically if you are starting with Gaussians. And the second claim which is a bit more controversial and it's something that's been discussed quite a lot within the community is that, is the following. And I'm going to take it, I want to discuss it at the very beginning and then maybe later we'll come to it once more so it'll, in order to reinforce it somehow. And it's the fact that, so a standard critique to Gaussian states is a very old one and it goes as follows. As we will see, Gaussian states are states which have a Gaussian-Vigna function. So you're all familiar with Vigna function and so that's probably part of the lecture that I can just skip altogether. So Gaussian states have Gaussian-Vigna functions. Now the Gaussian-Vigna function and the, well, the Vigna function, so the marginal of the Vigna function, like the, you know, if you have one mode, you'd be, I don't know, the integral along one direction, yeah, of the phase space. It gives you a probability of measuring quadrature outcomes on the orthogonal direction. So integrative of P, you get probability over X, okay? That's a very well known fact. It's about the interpretation, it's the operational interpretation of the Vigna function, if you like. And so in all problems where you're restricted to quadrature measurements, which then, which means all Gaussian measurements, we won't go through Gaussian measurements formally, but they all boil down to homodyne detection, which is essentially measuring X's, P's or combinations, they're off. All problems where you're restricted to such measurements, they allow for a secret, for a hidden variable description naturally. It's provided by the Vigna function, which is a natural probability distribution then for Gaussian states, right? Normally, well, for general Gaussian, for general quantum states, the Vigna function is not a probability distribution because it can be negative. But not so for Gaussian states. So because of this model, you'll never be able to say, violate, well, to prove anything non-local. There'd be no quantum non-locality, you can never violate, you know, Ballina qualities, like with Gaussian states alone, and there's measurements. Now, that may be very well, which is, and that's true. And therefore, so people have questioned that because they can be mimicked, so entirely Gaussian systems can be mimicked therefore with classical systems, and now therefore, they will therefore be useless to quantum technologies. However, there are two, where there's a list, there's a few objections to this. One is that it's still interesting to create Gaussian resources such as entanglement, and then you'll be able to access, and then you need some non-Gaussian key to unlock them, and actually get, you know, sort of harness the quantum potential, as they say. And that could be, I don't know, even measurements like on-off detectors would be enough in principle. Yeah? So, there's still an interest in studying these systems and creating resources, such as entanglement. The second point is, and it's, the second point is the most fundamental one, is that although they can be mimicked, there is still the Eisenberg principle. And the Eisenberg principle limits fundamentally any quantum states, including Gaussian, obviously, as we're going to see. And, but it wouldn't be there in any classical system. Therefore, say QKD, like quantum key distribution security proofs are still fundamentally secure. Well, up to all the problems that security proofs have, but that is independent of the Gaussian character typically, right? So, so there's still the, so there's still an underlying Hilbert space, which a mimicking classical system wouldn't have. So, that's the other element of interest. The third element, I would say, is related to estimation. And it's one of the reasons why in the eighties people went after, well, other than, you know, the standard, sort of the inevitable technological process, but they went after squeezed states. And, you know, you can get squeezing even with Gaussian, well, with Gaussian states too. And the reason was, well, the first observation is, I think, or at least rumor has it, was, was that Braguinsky and co-workers pointed out that in order to detect gravitational waves in this big League of Virgo, you know, apparatus, it would be much more, it'd be more advantageous to use squeeze light. Yeah? When you have a reduction of noise in one quadrature at the expense of the other because of the uncertainty principle. Then again, this claim is enough to motivate interest, because you can do squeezing with Gaussian systems, which are easier to control and describe. So, we're going to see that to some extent. Of course, then gravitational waves were detected without squeezing a few years back. And now then they're redoing the experiments with squeeze light in League of Virgo. I can't remember out there, which one, the successful one, what experiments used that. But this then came to be, in a sense. So, yes. So, how do we introduce Gaussian states? So, let me just call I'll define a quadratic Hamiltonian. This, oh, by the way, the way I'm going to deliver this works that, it's essentially the lectures are drawn from a book that I wrote that you can find anywhere, unless some of you are part of, you know, the publisher, but you can find it anywhere. But I mentioned in my book, because I think it's the best in the many, mostly in quantum optics that they're certainly better books. But like, because it's mine, obviously, I'm taking my lectures from my book, because it's easier. But anyway, I put like, still an average version of the notes, well, of, you know, those parts on the website for the winter school website. Anyway, so everything that I say basically will be there in quite a lot of detail, maybe more detail than you need actually. I'm under the impression. We'll see. But so just in case, and try to follow pretty much it, lest I forget something. So that's what I'm going to do. And so this introduction of Gaussian states is not orthodox in a sense that I don't think you find it elsewhere in this form. But it's still the same. Oh, story. So what I want to say is, so let me call this a quadratic Hamiltonian. And as opposed, so let me see what I mean. Let me, let me explain what I mean. This H is a symmetric, real symmetric matrix 2m by 2n. And half is just, you see why I put up there in a second. And this r is that vector of operators.  So that's what I call a quadratic Hamiltonian. And it's not strictly quadratic. This is the most general polynomial of order 2 in x and p. Yeah. And I can pick H quadratic symmetric because if you look at the commutation relation, you see that all anti-symmetric, any anti-symmetric term will just give you something proportional to the identity in the end. Some operator which is proportional. So it's just changing the zero of the energy if you like. But it is irrelevant to any dynamical or thermo dynamical as well, consideration in a sense. So we don't need that. And then this is what I call H. And then Gaussian states is, is this, is it minus beta H for H quadratic. Okay. And you see there's n squared plus n variables within the H plus another n in the 2n, sorry, 2n in R. Sorry, parameters. I added this fake parameter beta just because I want to describe the situation where if H is finite as non-limiting instances, and beta goes to infinity, then I get all pure Gaussian states. Yeah. You see that this state is pure if and only if beta goes to infinity. Okay.  That's, but, but strictly speaking, beta is, it would be irrelevant. I mean, I could, I could dispense from it. Okay. It's one additional thing that I don't really strictly need. So these are Gaussian states. And, and then the first thing one, one may want to do is, yes. Let's say we want to find the spectrum of these states because a lot of the properties would depend on the spectrum and we'll see that Gaussian states have a very specific spectrum that scales in a certain way. And in this infinite dimensional Hilbert space. Okay. And the first thing I want to do is I want to try and, and sort of handle this bit, which would be instructive in terms of quantum optics. Maybe if this is too basic and you're very, very well acquainted with all this stuff, like, you know, vial operators and shifts and you let me know yelling me and that will, I'll be, you know, I'll fast forward in a sense, say, and then dwell on something else later on, which might be of more interest to you. But otherwise, yes, let me, let me state it. It's easier to just state it. I will call this, what to say? Yeah. So that's a displacement operator. It's easier to put, I put omega. There's a reason why, because it, because this encodes the anti commutation, while the commutation relations are, this can be expressed to respondents. It's convenient to put an omega there at this stage. I'll take it. Sometimes I won't use it. But, and then I just want to show that something that you, you know very well, probably that if you apply this operator, this is a vial or displacement or shift operator, where you want to call it, on R, the vector, then if I, you go the dagger, you get, of course, this will get, so I want a dagger there actually. I want R minus R. And so we want to prove this, that RT omega R. And then you go R. Okay. So how do you prove this? Oh yeah, that is equal to, there are many ways to do it. No, there's at least a couple I can think of to, to prove it. A couple of ways to go about it. But a very quick one is that, and I leave it to you, is that you take the derivative of this operator with respect to R, yeah, all RJs and show that they match. And then you can show that all derivatives match, yeah? Because the second derivative will all be zero and all the further ones. And of course also, and you take them in zero, that's fine. So smooth. So there's only one solution, even if it's, if this is operators, there's no, no, no, nothing else that can happen. So that's the way you prove it. And of course, this means that this, this, this we already knew basically, but that this shift in the first, in the operators is just, can be accounted for, essentially, by applying a displacement operator left and right on the Hamiltonian. It doesn't matter that this is a quadratic function, okay? It's all very well behaved. So, so therefore, yeah, so h equals, oh, no, I want, I want d dagger there, right? The way I wrote it, yeah. So then we're down to just handling this and the quadratic, the purely quadratic part, okay? And then we want to understand this part. And this we're going to do in the following way. They start to be a bit more interesting now. We introduce what's called a symplectic group. We do it that this way. Let's say, yes, let's say I want to describe now instead of using the Hamiltonian to define a state through this like thermal trick, I, we just use the Hamiltonian to describe a dynamics and we do it, we do it in Eisenberg picture. And in this regard, what you want to do is you want to evolve typically the canonical operator. And, and then here I always forget a sign that let me pick it the same way because I keep switching this, okay? Right. So, so let this canonical operator evolve through quadratic RTHR, right? Yeah, so we let, we want this to evolve this vector and see what happens, okay? Because I want to understand, we want to understand what the action on this quadratic polynomial, purely quadratic polynomial is on the canonical operators that defined our whole system in a, in a sense that has been already discussed, okay? So, so our dot equals this. Yeah, so that's something that you, we're all familiar with. So that's a very equation. And, and this is convenient. It's convenient to write these down in components for once. This is the only thing I'm going to do this, the only, the only time I think. And so, so I want to write down this, this Hamiltonian explicitly. I'll have a half, which will be useful later on. And then I take all the possible commutator of commutators. So it will be RK, RJ, and then plus RJ, RK, RL, yes, RK, RJ. So, right? And then you use whatever this, the, the sympletic form. So these are just given by I, those. And then I take into account all the factors. And what you're going to get in the end is that this will be omega JL, JK, R. So, so geometrically, we saw that the equation writes, let me go back to vectors now. The equation writes that way. That's, that's Heisenberg equations for these operators. We drop those. And then we have to use the symmetry of H and the anti-symmetry of omega. And you're going to get that. And that's why I put the two factors because you, you get a single, so the two cancels out because you have two terms. And now then this can be solved in one line. It's a matrix equation. So this is a matrix equation for operators. This is, these are operators that live inside, you know, matrices and vectors, okay? That's the formalism essentially. And then RT, then the solution is just E omega HT. Yeah. It's an exponential equation that will give us the evolution. Yeah. Do you want to ask? Yeah. Oh yeah. Thank you. Thank you. It should. I forgot, I forgot this. And there too. So it's KL. Yeah, I lost one of these, of these labels as well. So I just wanted to make it a bit quicker because I don't want to dwell on each single line because otherwise, sorry. Well, that was spotted. So yeah, so this is the evolution. And now comes the interesting part to us. Not quite what, well, you know, this is interesting too, but the interesting bit is that this evolution, so what we did is essentially through this Hamiltonian is evolving each component of this vector, which is still written down there thanks to this immense blackboard. We evolved each component with the same unitary evolution. Yeah. Okay. And when you do this, clearly the commutators between any of these cannot be affected. Okay. They must be preserved. But this gives us a non-trivial factoid, which is the fact that this must still preserve the CCR. So if I put it into the CCR and now you see why you start to see why this formalism is so effective. So the CCR were satisfied at time zero. Okay. So we get this non-trivial result that let me call this transpose of that. So this must still be, well, let me write. So this formalism allows me to write this, that I can take this out of the commutator. And the commutator is still whatever it was, which is i omega transposed. And this must still be equal to the initial commutator, which is i. So if you get rid of the i's, we'll find that this operation, well, this transformation, let's call it transformation, yeah. It's a two-end, it's a two-end dimensional real metrics. We'll have to preserve omega. And operation that preserve omega called symplectic, they are actually linear canonical transformation in classical Hamiltonian mechanics. So one is very well familiar with them. And they, well, the symplectic deform a group, obviously. And the symplectic group is one of the three classical groups as they call them, so which would be unitary orthogonal and symplectic. There's some, so let me, I'll get rid of time, that time can be reabsorbed into h. If you look at the algebraic properties of a matrix to be symplectic, you'll find that it must be generated by omega times the symmetric. This you can find, you can derive independently. So this one, we call it s, and it belongs to what we call sp to nr, the real symplectic group. So this will clearly then play a very fundamental role. And we already, with these three lines, we showed that you can sort of represent the group, at least the algebra, through on an L2 space through a quadratic Hamiltonian. And this mapping between infinite dimensional operators, like this h, and this finite dimensional s is, well, this is really technical and I don't really know, but I learned these names by heart. So this is actually a representation of the metaplectic group. You can go on Wikipedia and look up the metaplectic group, which has the same algebra, but it's the same story as SU2 and SO3. One is double covered to the other. And technically, this is a projective representation of the symplectic group. That is, you get a representation times a phase factor that depends on the operation. Whatever. Basically, to all extent, to our purposes, there's a mapping between finite dimensional, two-dimensional, symplectic transformation, and these operators, and e to the i h acting on the Hilbert space. That's what we're going to use. And this is one of the basic tools in this shenanigans. Let me just see the, I haven't forgotten something. All right. So then the first thing then you can do once you have the, okay, then we can solve essentially, what did I want to, oh yes, sure. So in order then to find the spectrum of Gaussian states, which we'll be interested, so that we can write them down in the Hilbert space and then calculate entropies there for other and as well as other quantities which are relevant to quantum information in many different ways. Before, we need one other really basic tools, but this is kind of interesting because sort of, it's very well known to all of you, but maybe not in its most general form. And it's essentially what you do to solve a system of couple harmonic oscillators. So you have all been taught that, taught that, when you have like connected springs, you can solve the system by finding the normal modes, right? So breathing, Egyptian modes, I've always liked those and the center of mass and that. But typically, you've done that in a very simple case where the P's of the momenta were not coupled and often the momenta were the same, were just all the masses of those springs, they tend to be all the same typically, yeah? So that is sort of a simpler case. Of course, you can decompose in normal modes more general quadratic Hamiltonians which have any coupling between X and P as long as they are strictly positive. Oh yes, something that I completely forgot to mention is that Gaussian states are these with h greater than zero because otherwise the operator on the space is not even positive and you have a Hamiltonian which is unbounded from below and so you won't have any well defined Gibbs state, okay? So that I forgot. This we need for Gaussian states, we didn't need this to define states, we didn't need these arguments anywhere here. So in this story, the Hamiltonian could be, so the Hamiltonian matrix could be, it is not necessarily positive and in fact that is the case for squeezing. So normal mode decomposition is just saying that given a certain matrix, you can always, a certain strictly positive matrix, as Stefano knows very well, you can always find, so given any m strictly greater than zero, there exists an s such that s m s t equals d and let me see, how did I call this and this d, okay? Where this d is given by two times two blocks, a direct sum of two times two blocks, all proportional to two times two identities, yeah? And you see why this is called normal modes because typically when you reduce those springs in normal modes, well there you just want to decouple them, it's slightly different but you would also be able with another canonical transformation to bring the coefficients of x squared and p squared to the very same one and then you get what they call the free Hamiltonian in the quantum, in QED, well, when you quantize the electromagnetic field, you have x squared plus p squared, that is the Hamiltonian. So you know, nature doesn't give any squeezing for free and they're always balanced these coefficients. Right, so that's, this statement is, it's kind of interesting to see where it comes from and it's, there's a very simple proof of this, so I'm going to mention it. So what was the proof? Yeah, so you can see that s equals square root of d, these are all, these will all be positives as we see because, and we know it because this is strictly positive and congruences, when you do, when you apply matrix and it's transposed on the left and it transposed on the right, so congruence transformation cannot change the, well if s is known to generate, which is always the case, cannot change the signature. So all the, the positivity of the matrix is preserved. So this will all be positive, we'll have to be positive, m is positive, strictly positive by hypothesis and so I can use the square roots and they'll still be real and then these, this is an orthogonal transformation and then I can read this down. So again, this matrix is well defined and you see that this obviously does the job because you know this action, m is, ah, also symmetric, I forgot that. Well when I, when I write positive I mean diagonalizable and symmetric as well. So this is symmetric and so this will give me the identity out of m acting on left and left and right. The orthogonal doesn't do anything on the identity by definition and then I, I then multiply by what I need to have there. So the, the square root of this squared will give me d, right? And then I want to prove that they're always, they resist a no such that this matrix is simplistic, okay? And it works that way, all transposed. I want to prove that the resistant a no such that this is the case and then, and now I'll cut, I'll cut it short because this is slightly more technical, though very easy. So this is a non-degenerated, so this matrix because of the symmetry of m and the anti-symmetry of omega is still skew symmetric, still anti-symmetric and it's also non-degenerate and there's a little theorem that says that you can always pull, there, there exists a no that puts an anti-symmetric matrix in a standard form. If it's known the general, I can't remember about the generacy there, but, and the standard form is essentially this one times some numbers and then finally d will undo these numbers. So it's, there's always a no that does this, basically. That's what I'm saying. I want to write down all the equations here, but they're written in the notes that I'm going to put up. So, so then, so then we prove that you can always decompose this any, so any strictly positive matrix can always be reduced to the normal form, which is what we refer to the, the sort of matrices in the rest of this left in the remainder of these lectures through a symplatic transformation and you see that, you know, that symplatic transformations are, are unitaries at the Hilbert space level. Yeah, that's what we just said. So this is very relevant to us because in the end everything we are going to need, everything that we, we're going to need, all the information about the spectrum of this Gaussian state, essentially this, will be contained other than beta that, you know, but will be essentially contained in the symplatic eigenvalues of this H. The symplatic eigenvalues are these, these numbers here. There's one per mode and the reason is that of course the spectrum cannot be affected by S. Okay, so we're stripping the, the state sort of down to its essentials and decomposing its form. And this is slightly technical then in the notes there's a slightly technical bit which is a bit boring, more boring than this lecture which is the, which is the, unfortunately for some technicalities the, the Gaussian, the symplatic group is such that if you, okay, so there it's, so it's not always the case that there is a not all element of S of the symplatic group that preserve omega can be written as a single exponential of a generator. Sometimes you need to. Who cares? I mean it's a fact that one might, must take into account if you want to be really technical, but then I'm not going to be, I mentioned it and that's it, but I don't want to get into any sort of swamp based on that. Okay, so then, so these symplatic eigenvalues, what are they? For a, for a Hamiltonian they are the eigen frequencies. Yeah, for a Hamiltonian matrix they are, so you can always write down there's an S that does this essentially or maybe better because the inverse of a symplatic is obviously a symplatic since that is a group so I can do S, yeah, a sum J equal one to N. Okay, so any of these Hamiltonians can be written, Hamiltonian matrices can be written as a symplatic acting left and right on a diagonal matrix with, with doubly degenerate eigenvalues. Okay, and these are called the eigen frequencies. They're the frequencies of the normal modes. For any general Hamiltonian, though, that's the non-trivial bit and there are ways to find them which we're not going to care about but to determine them, but going back to our Hamiltonian there that we're trying to decompose, I want to write it down as, well let me write it down the way I write it down here then, so I want to write it down so H equals the R dagger sum S which will, you know, which will be associated to this S without a hat by this metathletic mapping that we described there and, and this Rt is very simple. So essentially, say we want to know what the entropy of a Gaussian state is. What you need to do is, is that we just need to calculate the entropy of, of this exponential. What's the policy, what's the school's policy as to breaks, what to break, I don't. Yeah, I think it might be, it might be useful to everyone. Yeah, let's take it back in like five minutes maybe, yeah, five minutes then.


My name is Sam Baknin, I'm the author of Malignan Self-Love, Narcissism Revisited and a series of other books and e-books about personality disorders and other topics. I'm also a professor of psychology and a professor of finance in several universities. In October of this year I'm going to publish a very long paper in a prestigious academic journal in the field of psychology and in this paper I'm going to make a claim which is bound to be controversial because I never make claims that are not controversial, it's not fun. So this controversial claim is that all narcissists are both overt and covert, there's no type constancy. Narcissists oscillate between being overt and covert and they do so in reaction to changing life circumstances and especially to incidents of extreme narcissistic injury leading usually to modification. And so that's the first claim and the second claim I'm going to make has to do with the behaviors of coverts who are predominantly classic. In other words when the classic narcissist or overt narcissist becomes covert, he is not fully covert. There's a kind of sub-variant of covert which I call collapsed covert narcissist. There every personality disorder has a collapsed state. There's a collapsed narcissist. I have a video on this channel which deals with collapsed histrionics. There is a collapsed borderline. I will dedicate a video to this a bit later this week. And there is a collapsed covert narcissist. Now this gives me the opportunity to teach you a useful tool. If anyone confuses failed narcissist with collapsed narcissist, they are not the experts they claim to be. And I don't know the first thing about narcissism. Failed narcissism is a phase in the development of borderline personality disorder. It was first discovered, discovered, suggested and described by a scholar of great importance. His name was Grotstein, G-R-O-T-S-T-E-I-N, Grotstein. Grotstein said that borderlines are actually failed narcissists. As children they had tried to develop narcissistic defenses in the face of extreme abuse and trauma, but they had failed. And instead they remain exposed, they remain without a skin, they remain vulnerable to their own emotions and to pain emanating from the outside. Consequently they become hyper vigilant, they anticipate rejection and humiliation and abandonment and they react with decompensation, they lose it and they act out. They misbehave, recklessly, defiantly if they are antisocial. So today we are trying to unify the diagnosis of borderline personality disorder and secondary psychopathy. That's a topic that I've dealt with in at least three separate videos on this channel. Failed narcissism is a stage in development of borderline. When we talk about a narcissist who fails, a narcissist who does not succeed to obtain narcissistic supply on a regular, predictable and repetitive basis, a narcissist with deficient narcissistic supply, that's not a failed narcissist, that's a collapsed narcissist. And any self-styled expert with or without the title doctor who confuses the two simply never read the literature and is exactly that, a self-proclaimed wannabe expert. Be very careful, there are a lot of fakes out there, out for your money and nothing else. So the collapsed narcissist, either too we thought that the collapsed narcissist simply goes through a phase of withdrawal, a schizoid phase, or becomes antisocial, becomes a bit psychopathic or delusional, reframes situations in a grandiose way and so on and so forth. I'm suggesting that one of the main strategies of the collapsed classic narcissist is to become for a while a covert narcissist. He becomes a covert narcissist and he in this way coaxes with his collapse. Now, this would mean that there is no type constancy, that every overt or classic narcissist can be covert and essentially every covert can be overt. To test this hypothesis, I conducted two studies and this is the paper that will be published in October, it's being peer reviewed right now. I conducted two studies to remind you I have the world's largest database of people diagnosed with narcissistic personality disorder and this database comprises 1,800 people. The first one in my database dates back to 1997, so it's a longitudinal database, it's very long. And I've also interviewed an average of five family members, colleagues and so on of each of these narcissists. So the database in totality has something like 15,000 people. Now, each of these people had responded to a questionnaire comprised of 683 questions modeled roughly on the MMPI2. And so it's a database with a gigantic number of data points and allows me to data mine at my leisure using tools that are off the shelf, so statistical tools. So I conducted two studies, the first study I simply data mined the database and found out the patterns, the patterns of conversion from collapse to covert and back. And then I administered a questionnaire to close to 3,000 family members who had agreed to participate, about 70% of them women, 30% of them men. And I asked them a series of questions about how they had experienced this switching between overt or classic and covert. And I'm using the word switching very judiciously because switching is how we describe the word that we use to refer to a change in personalities in multiple personality disorder. Shifting from one personality to another for one alter alternative personality to another in multiple personality disorder. Today known as dissociative identity disorder, this shifting is called switching. And I think the narcissist switching from classic to covert is exactly a dissociative state. It's a self state exactly like borderline. In general the picture emerging is that all these personality disorders are forms of multiple personalities. They all involve multiple self states which approximate and are asymptotic to full fledged personalities. And they all involve switching. So there I was with this majority of the 3,000 to my good surprise responded. And now I had a complete picture of how people experienced the narcissist when he switches from overt to covert and I incorporated it in the paper. Now in this particular video, I don't want to be too academic or too dry. Maybe it's too late for this and so on. And what I did instead, I had rewritten the paper with the first person pronoun. It's like I've rewritten the paper as though it were a personal testimony. Now, I am a classic overt malignant psychopathic narcissist. So I am 99% of the time I'm not covert. So the majority of what you're about to hear has nothing to do with me. Even though I will be using I, my mind, most of it doesn't have anything to do with me. But it is a composite, a collage and agglomeration and aggregation of all the information provided in the two separate studies. Bear that in mind before you bombard me with comments about my personal life and so on and so forth. Some of it applies to me of course. I have gone through covert states. I now realize. But the bulk of it describes hundreds of narcissists and their family and thousands of their family members. So it's a valuable, I think, contribution to interpersonal dynamics within the experience of switching from overt to covert. First of all, when the overt becomes covert, he develops immediately conflict aversion. Conflict aversion is in every possible situation in business, at work with family members in romantic or interpersonal relationships. Such narcissists would suddenly lose boundaries, not enforce boundaries. They will not fight for their rights. They will allow other people to pilfer their ideas. They will never protest. They will never take action. They will never fight back. They don't stand up for themselves, not because they're cowards, but because of other reasons. So I asked these people, why don't you stand up for yourself when you become covert? What happens to you when you become covert? So the question of shyness or vulnerability or fragility is none of these have to do with not fighting back. It seemed to involve other psychodynamic processes and motivations. And this is what these people told me. I don't fight back. I don't protest or stand up for myself, not because I'm a coward, but because I am just or because I'm practical or because I'm indifferent or because I'm grandiose. And I broke it down this way, just. Many narcissists said, I cannot satisfy the emotional, sexual or business needs or whatever. I cannot satisfy needs. In the case of interpersonal relationships, I cannot satisfy the emotional and sexual needs of my women. So I have no right to set boundaries. I have no right to make demands or to enforce rules of conduct. I encourage women in my life to look after themselves and to outsource their needs. That's in interpersonal relationships. Same in the workplace or in business. I cannot provide the goods. So I encourage outsourcing. The second reason covert narcissists gave to becoming dormats, to becoming submissive, to becoming reticent, to withdrawing, to not fighting, to not standing up for themselves, to not enforcing their rights. The second reason was practical. Many narcissists said, there is no point in fighting back. Some of them said, my reputation is so short that no one will ever believe any of my claims or intentions, not even my so-called nearest, dearest, intimate friends and significant others. So for practical reasons, I'm not fighting back. And then there was a very big group, which we will focus on today, of narcissists who had switched from classic to covert. And they said that their character had changed. They became indifferent. They say, I easily switch off. I tune out. I repress. I dissociate. I reframe. I move on. I sometimes mind some things, but I never care about them. Everything and everyone becomes meaningless to me, imbued with no emotions. They were describing the process called decafaxis, imbued with no emotions. They admitted that I'm quoting these confuses people, especially women, and drives them to test me and to test my boundaries in an attempt to ascertain the extent of my involvement. But it doesn't work. I remain indifferent. And finally, some of them admitted that one of the reasons they're not fighting back is because they are grandiose. Fighting back means that I care. Caring is vulnerability. I don't want people to see that I care. Not caring is the ultimate form of personal strength. It enhances my feeling of omnipotence. So they're not fighting back. They're not imposing rules. They are not enforcing boundaries because they're grandiose. That's for the lesser more. It's all for them. So the only times switched covert narcissists, collapsed, collapsed covert narcissists engage in conflict is when they are afforded the opportunity to statistically humiliate other people, preferably in public. Covert narcissists are very insidious, very pernicious, very subterranean, very passive aggressive, and if they can't humiliate in public, they will give them statistic supply. So it is only then that they may suddenly come alive and erupt in conflict. And I focused in my study on the issue of sexual exclusivity. And the reason I chose the issue of sexual exclusivity in a diet, in a couple, in an intimate interpersonal relationship is that sexual exclusivity provokes our most primordial defensive instincts. Like if someone homes in or zeroes in on the woman with me, I would become an animal. I would be romantically jealous. I would act out. I may even become violent. Nothing, nothing provokes more basic reflexes, instincts, drives, urges, and reactions.  That's why people react to cheating, for example, with extreme trauma. So I decided to choose this because it combines the intellect, primordial, basic, primitive drives, the body, body, and the mind. So it's like a package deal. And I focused on this and I tried to see how the behavior of the overt or classic narcissist would change if he were to become a collapsed covert narcissist. So I'm going to use the first person singular, although I remind you that this is not about me. This is a composite or a collage of hundreds of testimonies by narcissists and thousands by their family members.   Though she can be present in my life in other functions, she is not a woman to me and I do not care.  I sometimes even encourage the woman in my life to be with other men in order to get rid of the relationship altogether or to transform it into a sexless, sexless companionship. Women interpret it, so now I'm drawing on the study of the family members. Women interpret it as proof that I do not care about them. They want to test me and my boundaries and to see if I would mind when they misbehave with other men.  We recreate our childhood with each other, of course. So, the first sign of switching from classic narcissism to corrupt, covert narcissists is losing interest, losing interest in difference. This indifference, I have described indifference within sexual, romantic, interpersonal relationship, but this indifference extends to all realms of life. And so, I'm continuing with the collapsed covert narcissists. I have a feeling that I don't know how to be a man. I switch between hero, macho, all women be damned and zero, resistance is futile. Any passing male is more men than I am and is going to beg and beg the woman in my life. And here I took experiences described by hundreds of narcissists and amalgamated them. I put them together as a first person testimony. Men just walk to women who are with me, lovers, girlfriends, wives, and they pick them up in my presence. This is because when we are in public, I show zero interest in the woman with me and I give no hint of intimacy of any kind with her. I ignore the woman completely or if I pay any attention to the woman at all, it is briefly just to mock and to berate her painfully. And this sometimes arouses the other man's saviour, protective damsel or princes and distressed instincts. I've been told by men, you don't protect your women. Men talk to me about my women disrespectfully. Men don't respect me. They disrespect me. They misbehave with the woman who is with me and they know it, but they think that I do not mind. They think I do not care. So they see an opportunity to take advantage of my sad and mad partners and of my blatant indifference. Showing an utter lack of interest is tantamount to communicating a license to proceed. It's like saying to the other men, you're not disrespecting or offending me by absconding with my woman. Go ahead. Go with her. Do with her whatever you want. When I make clear that their behaviour bothers me, they explain, they apologise, they minimise and they all stop immediately. And of course, this is a collapsed covert narcissist, describing his behaviour when he becomes a classic overt narcissist again. So the same collapse, the same narcissist can go through periods of total indifference. Encouraging actually his woman or giving her license or giving other men license to misbehave, to slip around, to cheat. And then suddenly, having switched back from collapsed covert narcissist to overt narcissist to classic narcissist, he regains his sense of possessiveness, ownership, romantic jealousy and he demands sexual exclusivity. It can be extremely disorienting. It's like two personalities. One could even argue these are two personalities. One of them doesn't care about sexual exclusivity at all, doesn't care about the intimate partner at all, is unable actually to have any kind of intimacy. And the other one is very possessive, very jealous. It's the same person. We are not talking about two people. We're talking about an overt classic narcissist who goes through a phase of collapse and becomes covert narcissist. These men don't take the woman away from me. They don't do anything against my will. They don't do anything against her will. I give up on the woman. I discard her publicly. And she wants the other men. There's no underhandedness. There's no coercion or expropriation. It's all out in the open with full knowledge and consent, consent of everyone involved. And so I cannot really claim innocence. I cannot say I didn't know that they're going to have sex. I didn't know he was going to have sex with them.  I know that they're going to spend the night together. I know they're going to drink together. They're going on a vacation together. And I realize that when they get drunk or when they are isolated on an island in a vacation, when she flirts with him, shamelessly in my presence, I realize what's going to happen. I decline to force myself on them. I don't insist to join them. I don't insist even when I'm invited. I withdraw. I withdraw and give them full freedom. I have only myself to so-called blame. Men don't abscond with my woman property. I give my woman to the men because I'm not interested in her in any way. This is how this is the inner experience of a collapsed covert narcissist. If he experiences indifference, whether it's real indifference or feigned indifference, it's an open question because when the collapsed covert narcissist reverts to classic form, he experiences horrible pain, horrible agony over what had happened. So it's like he's leading himself to modification. It's like in a classic narcissist, modification leads to enlightenment and self-awareness. But in a covert narcissist, modification leads to classic narcissism. Modification is the way the covert narcissist awakens himself and becomes a full-fledged, overt classic narcissist. And the classic narcissist, when he experiences modification, he experiences self-awareness and then a covert phase. Modification, therefore, is the bridge between overt and covert and back. That is the mechanism we've been missing. We've been racking our brains for the last at least 30 years, asking ourselves, how is it possible that an overt narcissist can become covert? They are so such diametrically opposed types. How can a single individual be both? Well, through the process of modification, which shuts down the false self for a while and allows the covert, indifferent, withdrawn, schizoid, self-effacing, passive-aggressive mode to emerge. Classic narcissists say, I'm immersed in interacting with a male company, trying to impress them. I usually meet in groups. So the role of the woman by my side is very unclear. Is she a hanger-all? Is she an admirer, a student, a guest, a strange wife, an ex? Did we have a lover's quarrel? I leave that hanging in the air. I never protest when a man floods with the woman next to me, when he picks her up. I give the impression that I couldn't care less, that I'm not bothered at all, that I have better, more important things to do than to get involved. In truth, I'm kind of afraid of confrontation. I feel weaker, much less of a man than the other man. I'm also certain that the woman will mock me and humiliate me in front of the other men, and still abscond with him, still go with him. I don't have the power, I don't have the right to stop her, and that's already a classic narcissism. Actually, he's not aware, but he's describing a covert mindset. I never stand up for my woman. I never protect the woman in my life, even when I know that she is vulnerable, very drunk, unhappy, sad, depressed, or sick.  I let the woman go with him. I let her get hurt. I don't care if my intimate partner is mocked, physically attacked, falls ill, is depressed, sexually assaulted, or needs me in any way. Except if helping her generates narcissistic supply as a guru, a psychologist, an advisor, a wise man, a father figure. So this is a description of the transition back from covert to overt. We have the two sides. We are dealing with sexual exclusivity in interpersonal relationships to remind you, because they evoke and provoke the most intense emotions. And these emotions are partly primitive, reptilian, if you wish, and partly civilized, and partly intellectual, and partly bodily. There's no other realm of life which provokes this concoction. So that's why I decided to study this. And so many, many narcissists used a phrase that I invented, virtual single. They say, my women behave like virtual singles. In my presence, they always prefer to communicate with other men, aggressively pick them up, flirt with them, spend long stretches of time with them. Days, sometimes whole nights, go to bars, go to nightclubs alone, and pick up men there. They have emotional affairs. They cheat repeatedly. They become so desperate that they signal to men, in my presence, they give them their phone numbers. They flirt with them, even when they are having an evening out with me. They feel no real bond with me. They start for sex and intimacy to be wanted, to be cherished. They feel used and abused by me. They want out by any means. They feel exploited. Cheating and ostentatious infidelity is their exit strategy, as you have said in your videos, writes one. By the way, this puts paid to the myth that narcissists are not self-aware. Had narcissists been totally not self-aware, processes like narcissistic injury and modification would not have been possible. It would not have been possible to penetrate the narcissist mind. It requires a modicum of standing out outside yourself and looking at yourself, of introspection. The narcissist continues, When asked directly, the woman with me lets the other men know that I don't care, that I don't mind her misbehavior, and that I have no interest in her. I don't care about her whereabouts or who they are spending the time with, or when and if they will return to me and how she chooses to act. The woman in my life is likely to say he is busy with his work or he rejects and abuses me. He is very sick. He has mother issues. He told me, he told me I can sleep with others. They would use a variety, a monopoly of excuses and explanations. Some of the narcissists feel this, experience the covert phase following the collapse, experience the covert phase as deeply humiliating. Men disrespect me completely into my face for letting them have my women, in whom presumably I am invested as my property. So, they imply that I am a doormat. Some of them say that I am not involved in my intimate partner's life, and I don't involve her in mine, that I am not human. Even men who admire and value what I have to give, intellect or contributions to business, pity and mock me as a pompous fool, a deranged freak, a doormat, non-men in other realms of life. Okay, so this was an example of the collapse, covert experience of indifference in a field, an area of life, where we would have thought indifference is impossible.  Even there, he is rendered totally indifferent. But this is an aspect and dimension of a larger phenomenon, which is a form of people-pleasing. And we must contrast people-pleasing with primary psychopathy. So, many of the narcissists say, men have been taking away what's rightfully mine all my life, my time, my ideas, my money, my reputation, my history, my women, my contacts. Based on my indifference and collusion in this plunder, all men have reached two conclusions. One, as a people-pleaser, I have no boundaries, no dignity, no self-respect and no sanity. I'm defenseless. What they can do to me and to mine is limited only by their own pity, compassion, morality, and sense that there is nothing more to take or that the maintenance cost is becoming too high. And this makes people in my life feel unsafe and unprotected and makes my partner feel disillusioned. And the second conclusion that people reach when they observe the covert phase, the collapsed covert phase is that the person who is undergoing this switch is very mentally ill, utterly dysfunctional, incapable of maintaining even the rudiments of a relationship or capable of having sex, gauge reality, or act in reality self-efficaciously, even if only to the extent of holding on to what's and who's his. So many narcissists describe the moment of loss, the moment where they had lost their spouse, their family, their money, their business, their freedom. They describe the moment of loss as intimately connected to a phase of modification followed by collapsed covert narcissism. It is then having been observed from the outside that people got alarmed, got frightened and walked away because it is then that the underbelly of the narcissists, the hidden black hole like deep space void and darkness, the totally empty Hall of Mirrors, it is then that the non-existence, the absence of the narcissist in his own life and in his own mind became glaringly apparent and it's a terrifying sight. It's like confronting an alien.  As long as the overt of the classic narcissists maintains the show, as long as the show goes on, there will be people charmed by him, succumb to his charisma, play along with his stratogens, collude, co-opt and co-lob collaborate with his plans, etc. As long as it keeps it together, but when it disintegrates and switches and transitions via the modification bridge to a collapsed covert state, it is then that they see the true face of the narcissists, the nothingness, the absence. They see that there's no one there. It's a most terrifying experience. So narcissists say, gradually everyone comes to regard me the same way with a mixture of weariness, pity, revulsion and contempt. Some are envious of my gifts and project their envy and their sense of guilt and shame for having abused me by becoming even more aggressive. They compensate. I mean they feel guilty and ashamed. When they see the narcissists disintegrating, there's an immediately an empathic reaction, like you feel bad. And some people feel guilty and ashamed. They think that they had caused, they had caused this integration. They pushed the narcissists over the edge.  But some people, if they're immature, if they're narcissistic themselves, they would react to their own discomfort, to their own shame and guilt with extended and enhanced aggression. The majority would just walk away, having squeezed the narcissist's drive of any usefulness. Narcissists say, from time to time I try to fight back. But when I asked the narcissists in the sample to tell me how do they fight back? How do they extricate themselves? Like the Baron Minkhausen lifting themselves by their own hair? How do they extricate themselves from the pit, the cesspool of covert narcissism? How do they restore themselves back into an overt or classic state? I found out that they do it by conning people, cheating people, deceiving, making false promises, lying, or engendering the fantasy and then drawing people into the fantasy. For example, drawing women into the fantasy via the process of grooming. There's a series of videos I made about this shared fantasy. So they con people, they cheat people, out of money, out of love, out of compassion, out of, they simply pretend to be who they are not. They assert themselves by taking instead of giving. And at that point, gradually they regain their classic narcissism, their overt narcissism. And suddenly, with the same intimate part, they would make a new list of demands, boundaries, and rules, which include, for example, sexual exclusivity. Some narcissists said, even when I failed, even when I failed, I still tried to con people. But even there, as a con artist, I failed time and again. People saw right through me. People walked away. Women cheated on me repeatedly. Their needs unmet. And the hope that I will set these people free, let them go, once they make me aware of their betrayals. That is the force that drove all of them. In other words, what these narcissists are saying is that when people discovered that he is conning them, that he's lying to them, that he's deceiving and cheating, they transgressed against him, they betrayed him, and they did it ostentatiously, openly, so that he would let them go. Conning people, said these narcissists, was setting boundaries for and asserting not myself, but the fictitious character that I had created for the con. So again, it defeated the purpose. Again, I ended up giving everything of myself freely to another entity, albeit an entity that I myself had conjured up. It's a very, very fascinating observation. This narcissist says that when he felt himself transitioning from classic through modification to collapse and from collapse to covert narcissism, he wanted to go back. He wanted to be classic again. And he felt that the only way he could do this is by calling people, cheating, deceiving, taking from them. So he tried to do this. But in order to do this, he had to come up with a fictitious figure, with a false self, with an act. And then he suddenly realized that whatever he's taking from other people, it's not he who does the taking. It's the false self. It's the invented character. It's the conjured up entity. It's again not him. Whoever is calling other people, deceiving them, cheating them, stealing from them, taking from them. It's not him. It's the character he had invented. Again, he has been usurped. Again, he has been replaced, displeased, and substituted for. And similarly, I make woman fall in love with a false apparition. A fespian project, a role play, never with a real me. The grooming phase over, upon entering the shared fantasy, all my women discovered to their dismay, that I had combed them into a relationship with a complete, abusive, and mentally disabled stranger, which is the real me. Of course, the most fervent wish of these women is to up and walk away, by any and all means necessary, including by having casual sex with strangers ostentatiously. So grooming is like making women fall in love, not with the narcissist or the psychopath, but with another person he had created, a facade, a potemkin person, a fictitious entity. So they fall in love with this, and then they discover the real thing, the real McCoy, and they walk away. Again, by luring women into my lair, I am giving myself abundantly to another man. That other man is a fictitious character. In my case, for example, it's the irresistible genius. I am doing the dirty work of this fictitious man. I am doing his dirty work for him. I am satisfying his grandiose and sadistic needs to uphold and prove his irresistibility, and then to taunt, frustrate, humiliate, and dispoil the women he captivates. Those are his needs, not mine. I dedicate all my resources to cater into these needs on his behalf. Again, there's a situation of exploitation and gullibility. Again, the real narcissist is not catered to, is not satisfied.  They often complain about their relationship and how its dysfunction is brought on the adultery. So in a typical, classic relationship, women complain about their relationship and say, well, their relationship is not working well. That's why I'm fornicating. That's why I'm cheating. But the intimate partners of the narcissist don't describe the relationship as the problem. They describe the narcissist as the problem. They actually like many elements of the relationship. They miss these elements, but there's no way they could countenance the narcissist himself. It's a mirror image of normal reality. In normal reality, you love the person you're with, but you're having difficulties in the relationship. When you're with the narcissist, you love some elements of the relationship. It's exciting, it's thrilling, it's adventurous, but you have serious problems with the person you're with. Something is seriously all right with the narcissist, which makes even the greatest rewards and gifts he can offer and incommensurate compensation. And so these are the only two modes the narcissist has. The doormat and the psychopath.  One of them is comatose. One of them is recessive. One of them is dominant at any given time. At some points, the narcissist becomes avoidant, celibate, and a con artist.  At some points, and the psychopath micromanages the shared fantasy, at some points the doormat is the one who is modified. You remember that modification leads from covert to overt. And so sometimes the doormat is modified. It's when we force two alternative self-states to encounter each other and to communicate. But even as the doormat continues to process the modification, the psychopath continues apace with his exploits, forcefully dissociating the doormat in order to function. So when the overt transitions via collapse and modification to the covert, when the covert transitions via collapse and modification to the overt, there is a short period of dissociation where the dominant personality at that moment is fighting back, doesn't want to go away. So if you're covert, you're modified, you're about to become overt, the covert will reassert himself.  This is part of, again, a bigger problem of delusionality. One of the main management problems in narcissism, both in a therapeutic setting and for the narcissist himself, when he tries to manage his life, his cognitions, his emotions, is this delusionality. It's not only a lack of self-awareness, it's taking the information available and then reframing it in a way that supports grandiosity, grandiosity or other misconceptions. It's delusionality in the sense that the reality testing is impaired. The narcissist is divorced from reality at any time. And so, for example, in the vast majority of cases of narcissists, everyone who comes in contact with the narcissist shuns him and ultimately flees, runs away. I mean, look at, for example, Donald Trump. He's a president of the United States, but look how many hundreds of people have abandoned him already in the last three years. Men do it one way and women do it another, but all of them flee, all of them run away, all of them escape, all of them scatter, all of them don't want anything further to do with narcissists, all of them. Men don't mind or even relish being seen as assertive and decisive, so they just vanish or they tell the narcissist off. Women prefer to be thought of as sluts rather than heartless, traitorous bitches, so they cheat ostentatiously to get rid of the narcissist. So each gender has its own coping mechanisms and so on and so forth. If you're online, people will avoid the narcissist, like the virus of the mind which can cause systemic infection. Even when people recover from exposure to the narcissist, there are always multiple organ long-term damage like the COVID-19, but the narcissist doesn't see all this.  His compensatory grandiosity compels him to reframe everything counterfactually, counterfactually and delusionally. Let's take a few examples. Narcissists might tell you, everyone is addicted to me, everyone misses me horribly and it is their loss that I'm out of their lives. And the reality is people, especially women, can't wait to get away from the narcissist. They do anything. They do everything. They even go to extremes to set themselves free to immediately go no contact with the narcissist unless and until the narcissist can be of use. And they proceed with their lives happily after the narcissist and profitably and they decline the narcissist's attempts to over or renew contact and sometimes they do this aggressively and hatefully. And yet all of this doesn't affect the narcissist's perception that people are addicted to him, that they miss him, that they want him in their lives. And so Narciss doesn't realize that it's 100% his loss that people flee and abhor him having crossed paths with him. He doesn't realize, think it's their loss. And he's very traumatized. The reason for modifications that he's traumatized when he realizes that he can be humiliated, he can be made unsafe even by non-core issues, not important issues, even by useless people. When the narcissist goes through modification, he feels unsafe, disoriented. The whole situation looks like marriage and surrealistic because his grandiosity impairs his reality testing. He is inside the delusion. He has selective attention. He filters out things. And this renders him dangerously unaware of his environment. Gullible to a frightening extent. The narcissist is delusionally, for example, considers himself witty or funny, fascinating, authoritative, omniscient, transformative, addictive, irresistible, hyper-intelligent or hypersexual.  And yet very few narcissists would use these terms to describe themselves. On the other end of grandiosity there's paranoia. Persecretary delusions. Everyone, especially women, tried to deceive me, to manipulate me, to lie to me, to get away with abusive misbehavior. I am such a treasure. I have so much to give.  But actually people perceive the narcissists as histrionic, as provocative. And they don't respect him. They don't admire him. They are not old by him. They're not afraid of him. None of this is true. Actually they loathe the narcissists. They pity him. They deride him. They're exasperated. They ignore the narcissists on many occasions. They often conspire to hurt the narcissists. But they do so in extremes when the narcissists are sadistic or bullying or threatening. And even then when there is a real conspiracy, a real collusion to hurt the narcissists, the narcissists will fail to notice it because of his grandiosity, cognitive deficit. The thing is that it's all based on cognitive dissonance. When the overt or classic narcissist fails, he rejects reality. He rejects life. And he rejects... He refuses to accept his responsibility for his own life. He becomes, therefore, covert in the shadows, hiding a reflection. So it's rejection which is intended to settle the dissonance, to resolve the dissonance, and to ameliorate the anxiety that comes with dissonance. The narcissist deludes himself that he provides value-added. I don't know what analysis, money, insight, healing, support, support. He convinces himself that he is so unique that people will never give up on him. Never mind how negativistic, passive-aggressive, aggressive, sadistic, frustrating, withholding and hurtful he is. They will never give up on him. Because what he has to give is unique, can't be found anywhere else. And invaluable, has no price. Worth every price, priceless. In reality, the narcissist provides value-added that sometimes is a bit unique, but it's not indispensable. It's not irreplaceable. It's definitely not worth the emotional price that people have to pay for his abuse. So people, men and women, give up on the narcissist with lackrity. They go no contact, post-haste. People may respect the narcissist for some accomplishments or for his intelligence but this is also very misleading. It's false advertising because an intelligent, charming, magnetic, charismatic narcissist, it implies that his wives are mature and narcissists are not wise or mature. When people get to know the narcissist up close, they lose all respect for him and coupled with their envy and revolt at his obnoxious and pompous personality. It sometimes leads, if there are narcissists, if there are psychopaths, if there are victims of abuse who are vindictive and vengeful, sometimes this confluence of disrespect, envy and revolt, revulsion, leads them to virulent displays of public humiliation, shaming, narcissists shaming and passive-aggressive or punitive acts which in turn lead to modification and collapsed covert state. Such disrespect is also communicable. Contagious. People catch it from each other, you know? And this contagion is exacerbated by the narcissist's own behaviors. Ironically, when he feigns indifference in a covert state, it increases the incentive and the motivation to hurt him even more, to get through his firewall of apathy. And when he is reactant, when there's reactance and defiance, when he's antisocial or psychopathic, of course you want to put you down like a rabid dog. The apathy of the narcissist in the collapsed covert state is not perceived as a sign of strength, but on the contrary, it's perceived as a doormat, cowardice, weakness, absence of enforceable boundaries. The narcissist opens himself up to contempt, abuse and derision exactly by becoming covert. When alternatively, people perceive the narcissist's feigned and ostentatious disinterest as passive aggression. The narcissist disrespects for an ostentatious disinterest in his intimate partners, is interpreted by extension as a lack of dignity, lack of strength, lack of resilience and lack of self-respect. Who doesn't care for his property, for his intimate partners? Who doesn't protect people he loves?  So similarly, if the narcissist switches from covert, collapsed covert state to a psychopathic, antisocial, defiant, overt, narcissistic state, if he then pendulates, if he swings, if he switches from covert to malignant, his reactance, his defiance, his aggression, they're not perceived as credible. He's about as intimidating and deterring as a spoiled brat and equally repulsive and antagonized. It's one of the few points where I fully agree with Jordan Peterson. Nothing more repulsive than a spoiled brat. And the narcissist's conspicuous attempts to men up, to deter, to intimidate, they provoke the offended parties to escalate into egregious territory. Narcissist induces escalation in a war he can never win. People, men and much more so, perhaps women, they have very, very little to, very few strategic options in such cases. They have to become aggressive and they have to hurt the narcissist. In a way, they have to modify him. He's like in a, in a daze, in a trance. They have to wake him up. They have to bring him back to reality, screaming and kicking and, you know, there's no other way. He can go into deep space. He can, he's, you know, he's in a trip. He's high on his own grandiosity. Even as a covert, he is high on his own grandiosity because the covert feigned indifference. The form of grandiosity, I mean different. I don't care. See if I care. I don't mind. You can do anything. Who are you?  It's grandiosity. And so this is, this is the dynamic that the switching from overt to covert provoke. And the inner dialogue of the narcissist, both classic and covert, they share a single template. It's a little like Microsoft Word. With the same software, you can write this novel or that novel. You can write a novel or a poem with the same template. You get overt classic narcissist and covert. So the dialogue goes like this. People says the narcissist to himself, men and much more so women. They have very little to offer me. Compared to alternatives like books or films, people are bore me to death. They can teach me nothing, of course. Nothing relevant or useful. I know everything. They are wasteful. They're inefficient. They're entitled. They're inflated. In other words, the narcissist projects. He says everyone is a narcissist. Everyone is grandiose. To maximize return on investment because narcissists like to thinking, like to thinking objective terms. They consider themselves optimizing machines, optimizing devices, all wise, all knowing robots. And everything is dictated by ultimate supreme rationality. Unless they play the spiritual guru or the public intellectual, philosopher, psychologist who has all the answers. Unless they play this game, majority of narcissists would pretend to be optimizing machines. So to maximize return on investment, the bottom line in the balance sheet, the narcissist says to himself, I need people to adhere to strict standards and rules and to obey me. It is my way or the highway. Take it or leave it. This is not flexible. And so this insistence on following the narcissist's rules of conduct. This has the added bonus of gratifying the narcissist's sadistic impulses because it frustrates and hurts other people. And that's fun.  It's even more fun than sex. Of course, the reality is other people are not inferior to the narcissist. I would even say as a general rule, the overwhelming vast majority of people are way superior to the narcissist in almost every conceivable way, perhaps with the exception of intelligence or intellect in some isolated cases. The narcissist is deficient, cognitively deficient, emotionally non-existent, is as clueless in social situations and in sex as the most autistic person. Women cheat on the narcissist because as he is, he is not lovable. And this creates in them a frustrating and infuriating, tantalizing dissonance. They love an unlovable person.  And so men equally reject the narcissist because of this incongruence, lack of cohesion and coherence between what he promises and what he shows, the appearance and the substance or actually the lack of substance. There's nobody there. It's a zero in the fullest sense of the word, not to mention the lack of substance. It's a zero in the fullest sense of the word, not as a value judgment but as a mathematical description. The narcissist is a zero. There's nobody there. And when a woman cheats on the narcissist, the narcissist tells him so, how could she have chosen? How could she have opted for such an inferior man? Look at me, intelligent, I'm irresistible, handsome, I'm rich, I'm powerful. How could she have ended up with him? They don't understand.  They bring normalcy into the life of the narcissist's intimate partner. His abuse creates claustrophobic, suffocating, hypervigilant bubble with no atmosphere.  Women don't perceive the narcissist's absence in their lives after the breakup. It's a punishment or a loss. They perceive it as wonderful liberation, as a relief, as a reward. Of course they miss, his intimate partners miss some aspects. Some narcissists are very insightful. So they miss maybe the psychological insights. Are the narcissists reasonably good lovers? Maybe they miss the sex. You always miss something in someone. So generally, most intimate partners would miss something. But largely and overwhelmingly, they are relieved. They are relieved, they are liberated, they are happy. They are happy to have gotten rid of the narcissist and his sick shared fantasy. They are much happier when the narcissist is away. And even when they are together ostensibly, they try to avoid the narcissist. And all women, if the narcissist allows them closure or closure dialogue, they compile this long and exhaustive list of the narcissist's shortcomings, deficiencies, disadvantages, et cetera, et cetera. And these lists are very, very, very long, almost interminable, almost endless. So this by itself proves that all other men alternatives are vastly superior to the narcissist and way more attractive to his intimate partners. You see, what the narcissist fails to understand is that women first connect to a man as a person. And they want a person who loves to be with people or more specifically loves women. They want someone who is kind, who is interesting, who is passionate, who is horny. They want openness, gregariousness. They want safe acceptance, a core, a good time. So they end up being with other men. And what I'm saying here applies to business as well, applies to the workplace, applies to organizations the narcissist belongs to. I don't know, church, political party. People want, people, people want human beings. People want persons to be with. They don't want to be with pale and dysfunctional and glitchy imitation of humans like the narcissist. Other people allow for intimacy to develop patiently and attentively. And so when the narcissist's intimate partner betrays him, cheats on him with another man, it's because they see in that other man, the man, the person.  Women are attracted to other men because of the person, the personality, the sex is a derivative. Many narcissists are functional schizoids. In other words, even if they socialize a lot, they don't really socialize. They are averse to people. They hate men.    Except when and for as long as other people are of some use to the narcissist. I don't know, give him supply, money, access, sex, services. In this sense, all narcissists are very psychopathic. They are out to get narcissistic supply. And it's a goal. And they will instrumentally use other people to obtain this goal. But otherwise, they are very averse to humanity.  Sex is not a sufficient compensation as far as the narcissist is concerned. Anyhow, narcissists never have sex. Women are no exception. They are useful to the narcissist in his pursuit of sadism, to despondent, to degraded, to humiliate. They're useful to him to providing with services. The three Ss, supply, services, statistic sex. He's willing to invest in order to extract benefits, but only when there is an immediate specific and high return on his investment. It's not gratification, entitlement, or one of the other goals that I mentioned. And with women, the investment horizon is longer. Women demand reciprocity in some respects, sexually, emotionally, time-wise.  So it's a bargain. And if the bargain is not kept, women end up being with other men. They cheat and deceive. When the investment tap is, the faucet is closed, or when there is asymmetry or imbalance. And women could, the narcissist intimate partner could even end up with other men who are as abusive, grandiose, entitled or sadistic as the narcissist is. But these men give them something, attention, decor, money, children, stability, reliability, goals, sex, good time, socializing, something. The narcissist only takes. Even the narcissist's sex is autoerotic, sadistic, using the woman's body. There's no reciprocity there. Narcissists can give insights. Narcissists can be entertaining. But even these can be overbearing, meandering, compulsive, pompous, wrong, aggressive, sadistic. And ultimately, he degeneration into unwanted rants, ramblings. He's too much. The narcissist is a caricature of a human being. He's too much, too emphasized. And so when a woman has to make the comparison between the narcissist and any other man, I mean, narcissists usually end up losing. End up losing the game.  It's where everything is revealed. There's maximum intimacy, maximum emotions, primordial and contemporary, civilized, bodily and mental, intellectual, and emotional, cognitive and feelings. I mean, everything is there. It's a microcosm and a microcosm. It's the cosmos itself. The workplace has a subset of these features. Frenchy has another subset of these features. But only an intimate relationship with an intimate partner, an interpersonal, prolonged interaction. Only there, the true face of everyone involved gets revealed. And only there, the narcissist can transition via modification from one state, self-state to another, from overt to covert, from covert to overt. And now to round it up, to sum it up, I want to discuss the issue of whether anyone is preferable to the narcissist. Because this seems to be the behavior of the narcissist's intimate partners, the narcissist's business partners, the narcissist's friends. They all seem to give up on the narcissist and then proceed to develop relationships, sometimes instant relationships, sometimes one-night relationships, with perfect strangers. Does it make sense? If you have known the narcissist for years, does it make sense for you to replace him with a total stranger overnight? If you have worked with the narcissist for years, does it make sense for you to dump the narcissist and start something with someone totally new? The answer is yes. It's a rational choice. Consider, for example, dating a perfect stranger. When you're dating a perfect stranger, there is a 1-3% chance of ending up with a narcissist or a psychopath. 1-3% of a population are narcissists and psychopaths. So when you are with a stranger, these are your chances.  So it's much better to take the odds of 3% than to take the odds of 100%. It is rational to trust and to take chances with strangers and not with a narcissist or the psychopath. And it's wrong to think that spending time with a narcissist, having a relationship with a narcissist, having a previous acquaintance with a narcissist, regardless of length and intensity, should change these calculus. Because it doesn't.  So his self-reporting is very suspect. Can't learn much by spending time with you. And second thing, from the very first moment, he abuses, lies, tortures, manipulates, openly throughout any relationship, business, personal. So you gain nothing by spending time with a narcissist. You gain nothing. Narcissism is a guarantee of ultimate loss and abuse. Why take the chances? So this is what I wanted to tell you. That there is no type constancy. Narcissists switch from classic to covert when they go through collapse and modification. They switch back from covert to overt when they go again through collapse and modification. And I wanted to reassure you as victims of narcissists, survivors of narcissistic abuse or people who contemplate being in relationship with narcissists or exposed to people you suspect are narcissists. It's very rational to walk away. And it's very rational to prefer even relationships, even one-night stands, even dating, even with perfect strangers than with the narcissists you know. Because you don't know. There's no such thing as being in relationship with narcissists. Because you don't know. There's no such thing as knowing the narcissists. I just demonstrated to you that narcissists have self-states exactly like motor lights. Exactly like people with dissociative identity disorder. There's nobody there and because there's nobody there anyone can be there and everyone is there. The narcissists you think you know can suddenly experience narcissistic injury, modification, a collapse and he becomes covert. And that's a narcissist you don't know. Surreptitious, undermining, underground, passive-aggressive, maliciously dangerous. And then it goes back to being covert by another collapse, another modification and you have a grandiose abuser with sadistic overtones. Why do you need this? Why do you need any of this? No contact. In 1995 I suggested a coherent strategy of no contact in a series of papers. The no contact strategy is not simply going no contact. It has dozens of steps of what you should do to ascertain that you are in a real no contact state. I'm going to continue to watch the videos on my channel which deal with no contact. These transitions it's a new way of looking at the narcissistic dynamic. But it doesn't really add any meaningful insight to the question. It doesn't really provide a new answer to the question, should I be with him or not? Not.