Good morning, everyone. So yesterday, we tried to explain that if we phrase information paradox from the point of view of an observer sitting at infinity, the question is how can a thermal state, which is predicted by Hawking, be converted to a pure state by small corrections? And we argued that this is actually natural from the point of view of statistical mechanics and can be achieved with exponentially small corrections. On the other hand, we argue that what is more difficult is to reconcile this scenario with the smoothness of the horizon. And the reason for the difficulty is that in order for the horizon to be smooth, we need to have very specific entanglement of the quantum fields between the interior and the exterior, which was actually inconsistent with a previous statement that the radiation is unitary. And today, what we will try to do is to reformulate these questions into questions within the framework of the ADS-FT correspondence and we'll try to address them using the boundary conformal field theory. So before I go on, are there any questions about this? OK. So I suppose that you have some basic familiarity with the ADS-FT correspondence. So we will take the conformal field theory to be defined on a sphere cross time. So we take a CFT on SD-1 cross time. And some of the CFTs are supposed to be holographically dual to string theory on ADS-D plus 1 times some internal manifold. The internal manifold will not play any role in what I'm going to say from now on. So I will ignore it. And we will focus on the ADS part. And the idea is that everything that happens in the bulk is holographically encoded on the boundary. Now, before I go on, I want to remind you of something basic, which is that in ADS, in particular, in the backgrounds of this form, we can classify black holes into small black holes, those whose radius is much smaller than the ADS scale, and large black holes where the radius is larger than of the order of the ADS scale, let's say, and larger. And small black holes in ADS can evaporate. And we can consider the information paradox for evaporating black holes in ADS. While large black holes in ADS do not evaporate, in particular, so they emit Hawkin radiation, but the Hawkin radiation gets reflected by the potential barrier of ADS and the black hole reaches an equilibrium with Hawkin radiation. So large black holes do not evaporate, but as we will explain later, we can phrase similar paradoxes for large black holes. And the point is that small black holes in ADS are not very well understood from the point of view of the CFT, while large black holes are supposed to be dual to thermal states in the conformal field theory. And in particular, at the level of microstates, the black hole microstates of a large black hole in ADS are supposed to be dual to the coagulant plasma microstates of the deconfined theory at high temperatures. And in particular, this correspondence is very successful in explaining the entropy of black holes, because we think of the black hole entropy as being counted by the different microstates of the coagulant plasma. So now if we ask the question about the information paradox in the most basic formulation, in particular, whether a black hole evaporation is unitary, ADSFT predicts that the evaporation is manifestly unitary because the boundary conformal field theory is unitary. So you can imagine creating a black hole in ADS by the collision of two particles that you create on the CFT by some local operators, which will eventually, if the black hole is small enough, it will eventually evaporate into particles. And this process can be described within ADS. And it is equivalent to some process in the conformal field theory. So it is manifestly unitary. And then there's no longer any discussion about information loss. Now, so the question of whether information is preserved or not is settled just from the fact that gravity in ADS is equivalent to a conformal field theory on the boundary which is unitary.  And in particular, we would like to understand whether there is anything singular on the horizon which we discussed yesterday from the point of view of the CFT. So as I already said, we would like to understand whether these black holes in ADS have a smooth horizon. And in particular, we will phrase a question for large black holes in ADS. So at first, you might think that for large black holes in ADS, since those black holes do not evaporate, there is no paradox. There's nothing to worry about. However, in the next few slides, I will show that even for those black holes, large black holes, it is very difficult to reconcile the smoothness of the horizon with unitarity in the dual conformal field theory. And because these black holes are very well understood from the point of view of the boundary, this formulation of the paradox is the most precise from the mathematical point of view. Now, in order to address the question of the spacetime near the horizon of a black hole, we need to understand how to describe local physics in ADS because the question of the study is what happens to an observer crossing the horizon of a black hole. So it is a local question. It has to be phrased in terms of, for example, correlation functions that the infalling observer would measure when crossing the horizon. So the first step is to remind you how we can reconstruct local observables in ADS from the point of view of the boundary. Now, we will be working with a conformal field theory which has a gravity dual and we will always work in the larger limit and also the strong coupling limit. So you can think of the n equals four at large n and large lambda. And then there is a basic understanding of how to represent local fields in ADS, approximately local fields in ADS in terms of the so-called Hamilton-Cabat-Liffes Lore construction, the SQL construction, which is the following idea. Suppose we have a field phi in ADS, let's say a scalar field in ADS, which is dual to an operator O, a single-trace operator in the conformal field theory. Now, this field phi in ADS, in the larger limit, it would behave like a free field because all couplings in the theory are controlled by one over n. So in the larger limit, this field will obey the Klein Gordon equation in ADS with some mass which is related to the conformal dimension of the operator O. And moreover, we have a boundary condition for the field near the boundary of ADS, which is that as we approach the boundary of ADS, the bulk operator should be identified with a boundary operator at the same point x, provided that you multiply by some overall factor of z. So you have some field of being an equation in the interior of ADS, and you have some boundary condition. And this allows you to solve this problem and express the field in the interior in terms of the boundary values of the field, which is the dual operator O. So the most convenient way to solve this problem is by taking the operator of the boundary O and fully transforming it on the sphere. So we expand this field in spherical harmonics on the sphere and in fully emulsion time, thereby introducing these operators O, omega and m. So let me define them here. So these objects are defined as the integral of the boundary of the boundary, the local single trace operator, multiplied by some spherical harmonics. So these are the Fourier modes of the boundary single trace operator. And then the point is that if you take those modes and you multiply them by some wave functions which are solutions of the Klein Gordon equation in ADS, you can write down an operator in the CFT, which can play the role of the local bulk field in the larger limit. So as you can see, this object depends on the coordinates of the omega as well as the coordinates z with the regular direction ADS. So naively you might think that this is an operator in ADS, but the statement is that this is a CFT operator. You can see on the right hand side that we have written down this object in terms of CFT operators times some wave functions. And the point is that this object seems to depend on the coordinates of ADS, but it is a CFT operator. And in particular, you can verify that in the larger limit, if you take two points in ADS, P1 and P2, and if these two points are space-like with respect to the ADS metric, these operators, these two operators will commute. So in some sense, this operator, the CFT operator, can reproduce the locality of the higher dimensional spacetime, the causality structure of the higher dimensional spacetime. Let me emphasize that this, from a CFT point of view, this is a non-local operator because we have taken the local operator O and we have smeared it on the boundary, both in space and in time. So a little bit of, it's a peculiar object where we have to act with the operator at different times, but this allows us to reconstruct the point in ADS at a, a field in ADS at a particular point. Now, this construction is not exact. In particular, it is perturbative in the one-over-n expansion. So if you look at this commutator, and if you consider the one-over-n corrections to correlators on the boundary, you will find that this commutator becomes non-zero by factors of one-over-n, and then you have to go back and correct this definition by one-over-n corrections in order to restore locality in the bulk. So this entire construction is perturbative in one-over-n. So we don't know how to do it non-perturbatively, so we have to live with this construction for now. And also, I would like to emphasize that this construction is not entirely satisfactory because in order to define this object, we have to use the solutions of the Klein-Gorton equation in ADS with sort of assumes that we have a bulk dual with a particular geometry. And in that sense, it sort of uses the bulk equations of motion in order to write down this object. So one would hope that a more fundamental representation of these operators will be found one day where we don't have to put in by hand the fact that the dual geometry is ADS. But for now, and if we want to work in the large limit, this is a good starting point in order to explore local observables in ADS. Another way of thinking about this object is that, so by inserting these wave functions here and replacing this Fourier transform in terms of the local operator, you can change the order of the integrals and you can represent this local operator in ADS in terms of an integral over the boundary operator multiplied by some kernel, which we can write down explicitly in the case of ADS. And roughly speaking, you can see that as the point moves deeper into ADS, you can the support of this kernel of the boundary increases. So in this way, we can reproduce a local physics in empty ADS from the point of view of the boundary. And now we want to do the same thing in the presence of a black hole. Now, before I go on, I would like to say a few things about the types of black holes that we will be considering. So yesterday, there were a few questions about the ensemble, do we fix the temperature, do we fix the mass and so on and so forth? So let me make some comments about that. So one class of black holes that you can consider in ADS are black holes that you can form by gravitational collapse. For example, you throw in some matter in the CFT at some time t equals zero, it collapses into a black hole. If the amount of matter is large enough, it will be a large black hole and it will equilibrate and it will stay there. Now, I want to say that this type of black hole is not the most general state that you can have at a particular energy in the CFT. And if you remember yesterday, we introduced the notion of a typical black hole microstate which I will make a little bit more precise now. So we take all energy eigenstates of the conformal field theory which lie within a particular window of energy. So in the case of energy transport, this E naught would be some energy of order n squared. So we take some energy in the deconfined phase of the theory and this energy window delta E we can take to be something which is, let's say order one or we could even make it smaller but that is sufficient for our purposes. So we take a very small window of energy and there are many microstates, many eigenstates within that window. And then the typical black hole microstate will be a linear combination of those states with coefficient Ci which are randomly chosen. Now, the precise definition of randomness is in terms of the harm measure which I introduced yesterday. So remember we think of the Ci's as parameterizing points on the very large sphere. We define the uniform measure on the sphere and this defines the notion of randomness for the Ci's. So this guy here is what we will be calling from now on a typical black hole microstate in the conformal field theory. So the important thing to remember is that the energy of the state is sharply fixed, sharply defined. Okay, so now an important point is that these type of microstates the number of states that you can form by gravitational collapse is much smaller than the total number of typical microstates. This is a simple estimate you can do. You can consider all possible initial conditions, possibly initial microstates for a star of given mass M which can collapse and form a black hole of mass M and if you estimate that entropy which we can do perhaps during the discussion later today you will see that that entropy is parametrically smaller than the Decay-Stein-Hocken entropy. So in particular, the entropy, if we work in ADS-4 the entropy of a star of mass M scales like M to the three over two while the entropy of a black hole scales like the area which goes like M squared. So you notice that there are many more black hole microstates than the microstates that you can start with if you have a star that are going to collapse. So because of this difference, it's important to keep in mind that there is a distinction between black hole which are formed by gravitational collapse in ADS and typical black hole microstates and there are many more microstates of this type that those you can form by gravitational collapse. Some of the states- Kiriakos, can you repeat the question for everybody? In this story, in how many dimensions do we work? Do we work in ADS? Can we do any of this in ADS-2 or ADS-3? Well, ADS-2 and ADS-3 have special properties. So most, I mean, the statements I'm going to make are certainly true in ADS-4 and higher. Some of the statements may have to be refined for ADS-3 and ADS-2. Are there any other questions? Yeah, say that again, please. No, good, the question was, do we have a paced curve for this black hole, a paced curve? Well, these black holes do not evaporate. We have decided to look at large black holes in ADS. So these black holes do not evaporate. They are in a thermal equilibrium with their Hawking radiation, right? So the black hole is sitting there, it emits Hawking radiation, but as you know, in ADS, there is a gravitational potential which is pulling everything towards the center.  So there's no paced curve. I'm sorry, could you maybe rephrase the question a bit? I did not understand. The question is, is this the ADS analog of the picture I was drawing yesterday for flat space? So in flat space, I drew two different pictures. I drew this one. This was a collapsing star. I also drew the one where we take evaporation into account, right? So this black hole does not evaporate, so it is the equivalent of this one. All right, so the rest of my talk will use this notion of a typical black hole microstate quite a lot, so I hope the definition from the CFT point of view is clear. And I want to emphasize an important property of these states. The important property is that if you select this coefficient C i randomly, this stays to be almost time independent. How do we see that? Well, you calculate the time derivative of some operator A, or the state psi, the state psi, and you estimate the size of this time derivative provided that these C i's are selected randomly. Now, let me explain this estimate. So we have this operator A that we will normalize so that we will normalize A so that the expectation value of A squared on the state is of order one. So we take some operator whose two point function on the state psi is of order one. Now, if you take this relationship and you estimate the size of the matrix element of the off diagonal matrix elements of this guy, you can show that these are exponentially small by a factor of e to the minus s over two. The idea is that if you square this guy, you get e to the minus s, and then there are e to the s states that contribute because there are that many eigenstates, and then in order for this to be order one, then the individual matrix elements must be of the order of e to the minus s over two. I will explain this in more detail later if you want. So these matrix elements are of the order of e to the minus s over two, and the coefficients c i are of the order of e to the minus s over two as well because we have e to the s coefficients in that sum and sum of c i squared must be equal to one because the state must have unit norm. So this means that each one of these guys must have magnitude of the order of e to the minus s over two, and since these guys have been chosen randomly and they're complex numbers, the phase of this object will be randomly distributed. So then we have this sum over c i, c i star c j times i j, and we want to estimate the size of the sum. So we get a factor of e to the minus s over two from this coefficient, another factor of e to the s over two from this guy times e to the minus s over two. But then we are summing over i and j, so you would normally think that we get the factor of e to the two s, and then if you multiply all of these guys together, you get something which is of the order of e to the plus s over two. However, you have to take into account that these numbers are complex numbers with random phases, so if you sum e to the two s random phases, the typical size of that object is the square root of e to the two s, so in that way we lose one power of s and the whole thing scales like e to the minus s over two. So this shows that if you take a random superposition of energy eigenstates in this quantum field theory, the states will appear to be time-independent, up to exponentially small corrections. So in other words, what we will be calling typical states can be identified what we would naturally call an equilibrium state in the conformal field theory, which we define by states where the time derivatives of observables are close to zero. Yeah. Hermeser is what I defined yesterday. You think of the CIs as parameterizing points on a sphere, this is an equation for a sphere. You define the uniform measure on the sphere, that is the Hermeser, yeah. Okay, so now let's start thinking of, so these seem to be black holes which are in equilibrium, so if you think about the Penrose diagram in ADS, it will have the following form, it will look like this, at least we will start talking about the exterior and then we'll discuss what happens behind the horizon. So for now, do not pay attention on this part of the diagram, we just want to study this one. So these states seem to be in equilibrium, so we expected the geometry, here will be the ADS-Roschild geometry, then the equation we'll address later is what happens behind the horizon, but this part is expected to be ADS-Roschild. And we want to consider local operators or fields in this region of space-time, and we want to reconstruct them from a boundary. So the starting point will be to analyze this problem in effective theory in gravity and then we will see how to reproduce the same result from the CFT.  You take the field and you expand it in some modes B times some wave functions, which are modes in ADS. So these Fs are the solutions of the Clang-Orton equation on the background of an ADS-Roschild black hole. So you expand the field in a base of modes in the bulk and then you introduce some operators B, which will obey the usual algebra. And as you can imagine, what you find if you do the calculation in effective theory, so it's similar to the calculation of Hawking, is that these modes are thermally populated with a temperature beta, which is determined by the master black hole. So in the bulk we have this mode B, we seem to be thermally populated and they can be used to build up the field phi, describing a Clang-Orton field in the exterior of an ADS black hole. So now we want to see how we can reconstruct this from the CFT point of view. The equation was the spread of energy delta E, how does it enter? The answer is it does not enter. So this statement here is about effective theory in the bulk. So in the next slide I will talk about the boundary CFT where this spread of energy would enter. But let me say that for this calculation that we're doing, it doesn't matter what the spread of the energy is, it can be quite small. And in fact, if the N equals four obeys the Eigenstate Thermalization Hypothesis, which I think it is generally expected that it should, then you can take the spread to be almost zero. So you can even take an energy Eigenstate. Yeah, yeah, so this is what is called the ADS Hartle-Hulking vacuum because we assume that the black hole is in equilibrium. Which follows from the previous statement, right? This typical states, the time independent up to exponentially small corrections. So it is reasonable to assume that the field in the bulk is going to be in an equilibrium state, which is given by the ADS Hartle-Hulking state. Okay, now let's move on to the boundary. So we have this microstate psi, which has energy over the N squared. And then we need to use a property of single trace operators on this state, which is that if you consider a endpoint function, small n, of single trace operators on this typical black hole microstate, then this correlation function factorizes into products of two point functions. Now, is the statement obvious to everyone or should I explain why that is the case? So one way of motivating this expansion is the following. First of all, we consider these objects here. It is a correlation function on a typical state. So we have psi, o, o, o, psi. And as a first step, we can use the results that we presented yesterday. So I wrote down a theorem that any correlation function of this form is going to be very close to the micro-canonical correlation function up to exponentially small corrections. This was a theorem I mentioned yesterday, where rho m is a micro-canonical density matrix centered around the energy of the state psi. Then you can also approximate the micro-canonical ensemble with the canonical ensemble. So this is going to be equal to the trace of rho of e to the minus beta a's over z times o, o, o plus one over s corrections. So this shows that the correlation function of single trace operators on a pure state are going to be equal to the correlation functions on the thermal states plus one over s corrections. Now, these guys, we can argue that they do factorize. For instance, you can think of it in terms of double line diagrams. This thermal correlators you can formulate in Euclidean signature by compactifying the thermal circle and then you can think about it perturbatively in double line diagrams. And then the usual top expansion holds so we expect that this correlated factorize. And then by this reasoning, we conclude that even the correlators on a typical pure state are going to factorize at large n into products of two point functions. This is the usual large n factorization applied to a pure state, a pure heavy state. However, the two point function in which they factorize, so this object here is not the two point function of the operator in the ground state. Rather, it is the two point function of the operator on a thermal state. So this big guy, this correlator factorizes the products of two point functions but each of these objects is actually very complicated and it's not easy to compute it. It is a thermal two point function. So however, even though we cannot really compute it, we can say a few things about it. For instance, we can verify that it obeys the so-called KMS condition which is a statement that if you take the two point function of this operator O at finite temperature and you analytically continue the time argument up to minus high beta, then you get back the same correlator with the order of the operators interchanged which is the result we get this minus two and minus six. So proving this is very simple and we can discuss if you have questions but it's a very standard property which you can think of basically as periodistic Euclidean time. So this is an exact statement even though we cannot calculate this correlator, we know that this has to be true and we will use it in what follows. So as before, we define this boundary Fourier modes of the field. This is what I wrote down there and the KMS condition can be translated into Fourier language and then what it says is that if you calculate O dagger O, then you get this factor into the minus beta omega times O dagger. All these correlators are correlated with finite temperature. So this is a statement about finite temperature correlators in the N equals four. Now, remember we had this expansion in the bulk. This was the field in the bulk which was expanded in terms of this mode B which played the role of creation and inhalation operators of particles around the black hole. And now we will try to identify this B with the boundary operators O, the Fourier modes of the field. Now, when we do this identification we also have to take into account of the normalization of the operators and in particular we will divide this boundary Fourier mode O by the square root of the expectation value of the commutator. And the reason we are doing that is in order to ensure that the commutation relations between the B and the dagger are the canonical ones. The reason that we have to do it is if you define the Fourier mode of the boundary field in this way, then it is not true that O omega, O omega dagger is equal to, well, let's do it precisely. It is not true that this is proportional to delta. There's some function here, G of omega which is not trivial and we cannot calculate it. Because the theory is totally coupled. But by dividing by this factor we get rid of that factor and we can define operators which have canonical commutation relations and can be identified with the creation and inhalation operators in the bulk. Yeah. Yes. Well, here we are working with the primaries which are dual to, so the question was, does this equation hold for all primaries? So here we want to reconstruct the fields in the bulk that you can see at the level of spragravity. So we want to concentrate on primaries whose conformal dimension does not scale with n or with lambda. So the conformal dimension of this guy is taken to be something of order one. Finally, it is a simple algebra then to check that if you define this operators B by identifying them with O then and using the KMS condition you reproduce the expected thermal occupation level for these guys. So remember somebody asked me yesterday whether we are working in the canonical or the micro canonical ensemble? Well, here we see that even though the state is self psi, the state psi is a state in the micro canonical ensemble if you consider the quantum fields in the exterior of the black hole, they seem to be thermally populated with a temperature beta where beta has to be related to the energy of the state in the micro canonical ensemble by the usual relationship between micro canonical and canonical which allows you to translate a particular temperature to a particular energy. Well, so now we identify this B with O which allows us to express the local field in the exterior of the black hole. Sorry, I will repeat the question in a second. So we identify this O with a B's and now we can write down an operator in the CFT by using these O's multiplied by some wave functions and then you can check that this field phi, the correlation function of this phi on the pure microstate reproduce the correlation function that you would calculate in effective field theory in the background of a black hole where you take the quantum state of the field to be the Hartley-Holkman state, right. So did I answer your question? Yes, I'm a massive correlators. I'm trying to reproduce the correlators of the bulk by calculation of the boundary. Yeah, so the question is, is this supposed to be an exact identification? So this identification is supposed to be truly at large N at the level of operators. Stating in please. So the question is, are we making an operator identification or simply the fact that the correlators agree? The answer is that, as I said before, even in empty ADS, when we write down these equations, even without a black hole, even in empty ADS, unfortunately we cannot do something stronger than mass of the correlators. So it's not a full identification of operators because we do not know how to extend this construction to all orders, not even to all orders in all of our N or even what would be even harder to do it non-perturbatively in N. So at this point, the reconstruction of the bulk is perturbative in one of our N. So I can identify the operators only at a particular order in one of our N. But that is okay because the paradox can be perfectly formulated, even working with a leading order at large N. So even to a leading order at large N, there is a paradox that has to be resolved. So the question you're asking is something even more difficult, right? Would be to find the exact operator identification between the boundary and the bulk, which is not something we are able to do right now. So in this way, we can define the CFTO operator which seems to reproduce the correlation functions of the bulk operator around in the exterior of an ADS black hole, evaluated on a typical black hole microstate. Okay, now, so everything is fine in the exterior. I just want to make one small comment that if you follow this reasoning, you can derive some bounds about the variance of this object among different pure states following arguments similar to those that I explained yesterday. And this impose very strong restrictions about the possibility that the geometry outside the horizon is modified on pure microstates. So sometimes there are proposals that the geometry of a given microstate of different black hole microstates may differ depending on the microstate. But this construction impose some restrictions because if different microstates have different geometry, then these correlators will have to have a very large variance among different pure states, which is excluded by some of the arguments that I presented yesterday. Okay, so this was everything I want to say about the exterior of the black hole. And then the question is, how can we move? What happens if we try to move behind the horizon? Yeah, so I think the question, let me repeat the question. The question was that this microstate side that we're talking about is a superposition of many different energy eigenstates. So the question was whether each of the elements of the superposition could be very different from the average, was that the question? Yes, that's the possibility that would contradict what is called the eigenstate thermalization hypothesis which postulates that energy eigenstates look very similar to each other, basically, and to the thermal state. And as I mentioned yesterday, your question is related to something I mentioned yesterday which is that I argued yesterday that typical states look identical. That's what I argued, right? However, it is possible to find a basis of atypical state. So you can find the full basis of the Hilbert space of states where each of the elements of the basis is atypical, that is possible. I can give you an example in terms of a spin chain if you want. It's very simple to see that. So what I wanted to say here is not that you cannot find some atypical states whose geometry will be different, there could even be a basis of states. What I wanted to say is that if you take a random superposition of those states, the geometry will always look like the ADS-Schwartz geometry. Take it, please. I'm sorry, I cannot hear you. Can you speak a bit louder? Yes, it can be completely orthonormal. Okay, let me give you an example. Take a spin chain. So you take n spins, right? So the spins can be up or down, right? So we have n spins, and we want to write down a typical state of this spin chain. The typical state of the spin chain will be a superposition of these states where we have definite spin. Let's call them i. So i is a state where each of the spins is either up or down. So these i's are eigenstates of the spins. And a general state is a superposition of all of those where this i goes from one after two to the n, right? This is a typical state. If you calculate the expectation value of a spin of this state, you will find that it's zero, right? And it's exponentially close to zero based on the theorem that I mentioned earlier. You can really show that if you just randomly select these i's and you compute the expectation value of the first spin, it's going to be exponentially small. However, these guys, they are an orthonormal basis. In each one of those, the spin is either plus one or minus, plus half or minus half. So it's very far from the average in each of those states. So this is a basis of eight typical states for this particular example. Okay, yeah. The question is, do I use regularity at the horizon? Yeah, so this F beta WM, they are constructed in some ADS-Schwarzschild black hole geometry. Using some regularity at the horizon? Yeah, so these were the modes that you would get assuming the naive ADS-Schwarzschild geometry where you quantize the field in the exterior and you get a continuous spectrum, right? In particular, you do not impose any boundary conditions at the horizon. You just impose normalizable boundary conditions at infinity and you get a continuous set of modes. Which I'm using here. So no regularity condition at the horizon? Well, this is a usual calculation. Near the horizon, the field is a linear combination of in-going and out-going modes. I don't know if that answers your question. So the modes, well, each of these modes, if you take a particular frequency, it's highly oscillating near the horizon, but that always happens. Even in regular space, if you expand in base of regular modes, you get these highly oscillating modes, which you can then superimpose to form smooth wave packets that can just go through the horizon without any singularity. So here I am assuming, what I am assuming here is that the classical background is the ADS-Schwarzschild geometry. And these F betas are more like the Rindler modes? Exactly, exactly. Okay, yeah. The question is, is it possible to go beyond semi-classical picture? If you are talking about including one-over-end corrections, it is possible, but it's a little bit difficult because when you start going to sublimiting order in one-over-end, there are two different effects that interfere. One effect is that you have to take into account interactions in the bulk. But at the same time, this difference between the micro-canonical and the canonical ensemble gives you corrections of the order of powers of one-over-end which will mix with the other types of corrections. So there are two sources of corrections. And in general, it's difficult to disentangle the two and to control, in particular, it's not very clear how to control these corrections in a strongly coupled theory. The one-over-end corrections, when you convert from the canonical into the micro-canonical. But as I already said, that is okay for us because the problem is already visible to leading order at large end. So before we even go to the sublimiting orders, we have to resolve a problem. Okay, so now we want to move behind the horizon. And as we discussed yesterday in the context of Rindler space, if you want to be able to cross the horizon smoothly, you need to have modes on the two sides of the horizon which must satisfy particular properties. So these guys which were the Rindler-like modes we were discussing before have to obey the commutation relations that I already wrote. And then we need a new set of modes, B tilde, which must obey similar commutation relations and they have to commute with a Bs because they're space-like separated. So B tilde and B are independent modes so their commutators should be zero. And so in particular, if we want to have a smooth horizon we need to impose, we need to identify some operators B tilde in the conformal field theory which will obey commutation relations of this type. Please notice when I write one, well, to be more precise this should have been a delta function of omega minus omega prime and you can also write down the angular momentum indices M but they don't play any important role so I will skip them from now on. I will just write down the frequency omega. Now these are some of the conditions that we need. In addition to those, we need the condition that both the Bs and the B tilde's have to be thermally populated in order for the horizon to be smooth. Now if you don't understand how to derive these relations the best thing you can do is to go back to Rindler space and work out the similar structure there and you will see that in the Minkowski vacuum these conditions are satisfied of course and these are also satisfied where for Rindler space beta would be equal to two pi so the temperature has a particular value. And you can also verify in the toy model of Rindler space that if you modify any of these conditions you start to see excitations on the horizon. That's what I mentioned yesterday that if you modify, sorry I forgot one more equation. We also want that B omega, B omega tilde to be e to the minus beta omega over two omega, B omega dagger. So we also need the most to be entangled in a very specific way. And if you violate any of these conditions you will generate a stress test on the horizon which will indicate that the horizon is no longer smooth. So the question now is can we identify CFT operators which satisfy these conditions? Yeah. Yes. Yes, yes, yes, yes. Yes, right. We will discuss this point a little bit later. So the question is in Rindler space we drew the diagram yesterday we had the B's defined on this side and the B tilde's on this side and then we said that these B tilde's will propagate in the future like that. So an infalling observer will detect the B tilde's coming from the left side and the B's coming from the right side and they have to be entangled in a specific way for the horizon to be smooth. So the question was can we think of these B tilde's as coming from the analog of the left side? That's a very good question. We will come back to this in maybe in the next lecture. So I will talk about this. Can you say it again please? What do you mean by similar equation? Yeah, yeah, so the question is do we assume that these B tilde's will have similar equations as the ones that I was writing in the previous slides? We're trying to get there. For now what I'm writing down is the minimal set of conditions that we need in order for the horizon to be smooth. So I'm not making any statement at this moment about how this B tilde is realized in the CFT. I'm not saying that this B tilde is related to some single trace operator. I'm just saying that if we want the horizon to be smooth there must be an operator B tilde which has these properties. And we'll try to identify this operator in the next slides. Okay, so now let me make a comment about where these operators B tilde are coming from which is actually related to your question. So if you consider a black hole from bi-gravitational collapse in ADS these B tilde's are nothing else but the guys that you can, as we discussed yesterday, you can trace them back through the collapsing star and see where they came from on the CFT. So they will get reflected on R equals zero and then these modes will go back and hit the boundary. So if you have a black hole from bi-gravitational collapse then you could try to identify these B tilde operators by tracing them back and identifying them by some operators in the CFT at a point which is actually before the moment where the collapse shell was injected into the CFT. However, this type of, this strategy to identify the B tilde's has some problems. The first problem is the so-called transplantion problem which I already discussed yesterday and the problem is that if you want to find these B tilde's at very late times and if you trace them back you find that they get blue shifted so then they collide with a star at very high energies and then it's not clear anymore whether the one of an expansion will be reliable. But apart from this problem, the other issue is that as I explained before the number of states that you can generate bi-gravitational collapse is a small subset of the number of states which is counted by the Beggarstein Hawking Entropy. So these are not typical states. The states you can form bi-gravitational collapse are not typical black hole microstates. So if we want to identify the B tilde's for a typical black hole microstate we cannot do it by starting a black hole which is formed by gravitational collapse. Okay, so let us proceed now and explain what is, explain why it is difficult to identify these operators. Does not, the question was is the collapse matter null matter? It does not have to be null, it could be time like. Okay, so let me now try to explain what is the problem. Now I'll give you a more general argument against the existence of these operators which will make clear why there is a paradox. So before we wrote down the algebra of the B's and the B tilde's, but what I did not write down in the previous slide was the commutator of this guy's B and B tilde with a Hamiltonian. And now I will introduce that commutator for the modes which are outside the horizon. Just by using effective theory you can verify that the commutator of the Hamiltonian with a creation operator B Dagger is equal to omega times B Dagger. That makes sense. This object is a creation operator. It adds one particle outside the horizon and the energy of the CFT increases. That is intuitive, that makes sense. On the other hand, if you look at the commutator between the CFT Hamiltonian and the B tilde Dagger, you find that there's a minus sign relative to that one. So this means that this B tilde Dagger operators have the property that when you act with a creation operator of B tilde Dagger, you're actually lowering the energy of the CFT. So if you add a particle here, you're lowering the energy. If you add two particles, you're lowering the energy even more, so and so forth. So as you can imagine, that is an unstable situation because then you would imagine that the system would thermally produce pairs of particles, B and B tilde without, there's no energy cost in the production of these pairs, but you would get some entropy. So it sounds like an unstable situation that the fact that we can add particles and lower the energy and as I will explain, there's a precise mathematical contradiction in this algebra that I will explain. But just to give you some intuition why we get this minus sign, you can think of the Hamiltonian as being the generator of the killing isometry of the solution. So the killing isometry is time-like in the exterior. So it's time translation in the exterior, but in the interior it becomes space-like. So the killing vector field in the interior of the black hole is space-like, which means that these eigenvalues of the operators with respect to the vector field play the role of momentum so they can be positive or negative from the point of effect theory. And that is the reason that you can find some modes in the interior which have effectively negative momentum with respect to the killing vector field, but when you translate back on the CFT, it becomes negative energy. Okay, so now let me explain why this algebra is inconsistent. So we will try to calculate the expectation value of the number operator for modes behind the horizon using this algebra. And we will take the trace because we want to calculate the average of this quantity over all possible microstates. Now let me call this object a small n. It's the expectation value of this number operator. Now using this algebra, if I use the condition, the commutator is between the dagger is equal to minus omega, the dagger. From this one, we get that e to the minus beta h between the dagger is equal to e to the beta omega times between the dagger e to the minus beta h. Okay, so now I will apply this relation inside the trace. So we will change the order of these two guys which will give us e to the beta omega times trace e to the minus beta h, beta tilde. Now we can use a cyclist of the trace to rewrite this as e to the beta omega trace minus beta h between the dagger. And now I can use the other commutation relation, this one, to rewrite it as e to the beta omega times. Trace e to the minus beta h be tilde dagger, be tilde plus one. Okay, but this quantity here is precisely what we call n in the beginning, right? That's the thing we want to calculate. So looking at this equation, what we found was that n is equal to e to the beta omega n plus one. Now we can solve for n and we find that n is equal to minus e to the beta omega divided by e to the beta omega minus one, which is negative. So we started with an operator which was positive definite because it is, sorry, it's non-negative. It is of the form bit dagger b, bit tilde dagger bit tilde. So this is a non-negative operator. And we're trying to calculate the trace of this operator multiplied by density matrix which has positive eigenvalues. And we get something negative. So this is inconsistent, right? So this shows that postulating this algebra, I mean, this algebra that we wrote down between the dagger is equal to one, h between the dagger is minus omega between the dagger has some sort of inconsistency if you try to evaluate the expectation value of this trace. Yeah, is that stop? Yeah, so just two minutes, right? So we get this inconsistency, which means that that algebra has some issue. So are there any questions about this? Yeah. This Hamiltonian is the safety Hamiltonian. Well, okay. The question is, is there another problem here because the Hamiltonian seems to be unbounded from below? Yeah, so somebody could say that that is not maybe a very big problem because these equations are supposed to hold only at the level of effect field theory, which means that you're allowed to lower the energy only a certain number of times which does not scale with capital N. And remember that the black hole that we started with had energy of order n squared. So we start with the black hole of energy of order n squared. So in order to get to zero, to zero energy, we would have to lower this energy of the order of n squared times, which would not be allowed at the level of effect field theory. But this problem here is present even let's say low point function of this B tilde dagger. So even if you have a small number of times, you run into contradiction with this, because of this argument. Now, you could ask me a question which is you claim that you derive these equations using effect field theory. And now you claim that there is a contradiction that you get this negative trace which is mathematically inconsistent. So this algebra must somehow be problematic. And if everything we have done so far is effect field theory, you could ask why hasn't this problem been noticed many decades ago? Because this problem was actually pointed out by these authors very recently, I mean a few years ago. So you could ask why wasn't this noticed let's say in Geryll and Davis, right? When they analyzed the quantum fields on the background of a black hole. The point is that this inconsistency, we show this inconsistency by using the trace. Which means we try to demand that this algebra is true on a very large number of states which allowed us to replace the typical state by a trace. In Geryll and Davis, there would have been only one state psi of the exterior, for example, the Hartz-Hocken state. And then one of the steps that they used which was a cyclist of the trace would not have gone through. And you would not have been able to derive any inconsistency. So to summarize, this algebra is inconsistent if you demand that the algebra is true on a very large number of states. If you only have one state or a small number of states, there is no intrinsic inconsistency with the algebra. Okay, so to close, the fact that we have this inconsistency suggests that it is impossible to find operators be tilde in the CFT which have the desired algebra for typical states. And hence, typical states will not have a smooth interior because you cannot find these operators in the CFT or perhaps the CFT is not able to describe a black hole interior. So in the next hour today, we will explain some ways of trying to avoid this problem and identify these operators be tilde and we'll explain how this, what's the loophole in this argument. Thanks.


What's going on everybody welcome back to another draw preview and we have the BMW open in Munich this week It's an ATB 250 event and some players are pulled out of this event So let's go to the withdrawal list Okay So we have some big names that have played well over the clay season so far that are pulled out Dan Evans He's pulled out foot you bitches out her catch Nishioca Yannick Sinner has pulled out Sonny go and Vessely has also pulled out of this event starting at the top of the draw We have eight seeds in this one and the top four seeds get a buy Alexander's Vera He is the number one seed he gets a buy in the first round He'll take on the winner of a qualifier versus the wild card Marta in the second round and we have Russa very versus Quan winner That's going to take on either a qualifier or the number six seed Lyovic in the second round then we have the number four seed Cranovich He gets a buy in the first round he would take on the winner of Daniel or the wild card halfman in the second round They may have more Germans taking on each other with copper and coal stribert going at it winner That's going to take on either a qualifier or the number seven seed Strouf in the second round So you can see lots of Germans in the top half of the draw We've got Alexander's Vera of course the top German also the number seven seed Strouf It's the players to watch out for this week the big seeds of course It's very of in Cranovich definitely need to watch out for them But also keep an eye on Daniel who had a great week last week in Serbia and Russa very he is a good little clay Court player as well bottom half of the draw now We have the number five seed Basilash Vili takes on Monteiro in the first round winner That's going to take on either Travalier or quarter in the second round Then we have the qualifier versus Korya winner of that's going to take on number three seed Carrots of who has had a great week in Serbia this week beating Djokovic in the semi-final So he's going to be full of confidence going into this tournament Then we've got two Aussies going at it with John Milman the eight seed taking on Alexey Popperin winner That's going to take on either Pella or Jerissimov in the second round Then we have Quaibos versus Sangren winner That's going to take on number two seed Kasparud who just like Carrots of is in a little bit of form at the moment Especially on clay and he'll be feeling good going into this tournament But the names to watch out for obviously Carrots of you've got to watch out for him after a huge win over Djokovic last week Kasparud as well But also keep an eye out for quarter because he's had some great wins on the hard courts so far in 2021 But he really made a breakthrough on the clay last year at Roland Garros So keep an eye on quarter in this one as well So there it is the BMW open in Munich this week and there are a lot of good players playing obviously Carrots of Definitely want to watch out for after such an impressive week last week and Kasparud after a couple of weeks back in Monte Carlo He played great there as well and Alexander Zverev really hasn't started his clay court season yet Maybe he can do it in front of his home crowd. Let me know down the comments below Who's gonna win this event? It's very wide open for me Even though Zverev's the top seed is a lot of good clay quarters in the mix. All right, so going through the draw I think I'm gonna go with Kasparud to win this one I think Carrots of probably gonna be a lot of people's choices But I think after such a big week last week Carrots of might have a dip this week and I think Kasparud is gonna Tate the title he's been very consistent on clay over the last six months again Let me know down the comments below. Who do you think's gonna win this one? So the BMW open it's back again in 2021


I know you're all excited, but settle down. We better get started before any more people come on the fire marshal makes his move. So thank you all for being here. Obviously, Father Tom knows how to pull a crowd in. I know most of you, but in case I don't know some of you, my name's Paul Lakeland. I direct the Center for Catholic Studies here. And this is one of the many events we are putting on this semester, I think about 12. And for those of you who haven't been here before, all our events are offered at no charge. So there's literature over there on the table. We pick it up when you leave and see what else we are doing. There are other almost as spectacular events as this one later in the semester. So it's just my job to introduce Father Tom, although most of you don't need the introduction, but you're going to get it anyway. It's a short introduction. He will speak for a while and then take some comments, conversation, et cetera, for a little while. So like many Jesuits of his generation, Father Tom entered the Jesuits at the age of 18. So he did all his education sort of within the walls of the society. He told me he did his undergraduate and master's degree from Boston College, but they never went to the college. They were always at the seminary, which, again, is typical of the time. He's been a Jesuit for 64 years, and he's been ordained for 51 years. He has a doctorate in theology from the University of Innsbruck in Austria, which is a remarkable university that has trained many of the great European theologians. So he knows whereof he speaks. You know that he works here at Fairfield University, and he works with the Center for Ignatian Spirituality and guiding people in the exercises. In his past, he has taught at Fairfield Prep, at Fairfield University, at Boston College, at the University of Notre Dame, at Western School of Theology, and at the University of the West Indies. I think all of those were short appointments. I don't think he was rejected from each one in turn. But the part that many of us, I certainly didn't know, is how long, how much of his life he spent in the Middle East. So he was the founder and director of the Jesuit Center in Amman in Jordan. For 14 years, he worked there. Then he became director of the Pontifical Biblical Institute in Jerusalem for 10 years, which is an amazingly prestigious appointment, where he founded the Cardinal Martini Leader Institute at Bethlehem University. He's written, and then he came back to us. He's written numerous articles. You can find them in all sorts of periodicals throughout the states. And of course, Sir Jordan and Jamaica. And I think he'll tell you more about this, so I won't say much about the last line I have here. But he is also a playwright. And there may be something coming up soon, but I'll let him talk to you about that. So will you please join me in welcoming Father Tom to talk about sexuality and prayer? Thank you very much, Paul, for that generous introduction. The title is actually Sexuality in Prayer, not sexuality and prayer. But who was going to notice that on an advertising? OK, Sexuality in Prayer, the title of this presentation. What does sexuality mean? Perhaps some other word would be more appropriate. Because of the ambiguity about the term sexuality, I could perhaps call this lecture affectivity or intimacy in prayer. But no.  But then the word sex is used in another way. We check off when asked our sex, whether we are male, female, or neither preferred. Sexuality is much more ambiguous. The Collins English the Tsarist lists as synonyms for sexuality the following words. Desire, lust, eroticism, sensuality, virility, sexiness, voluptuousness, carnality, body, appetites. I stay with the word sexuality because there has been a strain in Christianity to put spirituality over here and sexuality over there. It is somehow dangerous. With the term sexuality, I am bringing us as body front and center into the whole consideration of prayer, presence of God. With all the ambiguity of the term, I expect we would know at least generally what area of human life we are talking about. And I hope that by the end of this presentation, you would have an idea how I am using the term. These ideas that I will present have for me developed over a good number of decades. And I stress the word sexuality has always been central in my long extended pondering. Further, I stay with the title sexuality in prayer because the whole area of human sexuality is widely avoided in church presentations because of sensitivity and contentious issues. People do not want to get into the mess. I am happy to raise the issue of sexuality in the context of prayer. In my reflections, what I say, even inadequately, is a way for us to look upon human sexuality in a very positive way. I do not claim the reflections I present are unique, but I do claim that how I present these reflections are my own. I expect that I will continue to develop these reflections and that the presentation tonight may be a challenge to deepen them further, sharpen them. Desire. In our human experience, we express desires continuously, smaller ones, larger ones. You arrive at the breakfast table, you choose oatmeal rather than raisin bran. That is no big choice, no big desire. It is done without a lot of energy. But then, there are other desires that are deeper, more significant. I use to illustrate at the levels of desiring the metaphor of the onion, a humble vegetable. The onion serves as a good metaphor because there are identifiable layers that can be peeled away. Let us think of all the desires on the outer level that fill much of our day. You go to your office early because you want to be well-prepared for a meeting. You close the door of your office because you do not want to be disturbed. We make constant choices throughout our days, which are the expressions of our desires on this surface layer of the onion. I do not want to say that these surface desires are unimportant. They are very much the stuff of our days, how our days are structured, how we keep our world going. But then, there are those deeper desires. So for example, you want to be a good parent. This is a much deeper layer of the onion. Now, the deeper the desire, the more that desire influences the layers above it. All the desires on the surface are informed by the deeper desire for the good of your family, for example.  We raised the question, what is the deepest layer of desiring? What is that level beyond which there is no deeper level? The level that is the very core of the onion, the very center of yourself, the bedrock foundation of all your desiring, all your longing. I suggest that desire is the desire for God. This deepest layer of the desire for God may not be conscious and could be a challenge to unwrap. For this, we are invited to pray, to contemplate. I spend much of my occupation guiding people in the Ignatian spiritual exercises. And I offer the challenge, what are your deepest desires? You have to be careful in asking that question. If you asked it in a singles bar, it would have a rather different nuance than when I would ask it as a stimulus for prayer. On this core level of ourselves, this deepest desire is implanted in us by God in creating us, another simple metaphor. We make things and they have a purpose. We make chairs because we want to sit down. We give the chair a purpose. God made us with a purpose. And this purpose is embedded in us. And in contrast to a chair, we can discover, unwrap this purpose. Uncovering this longing, we become conscious of the desire of God for us. Our desire for God and God's desire for us coalesce. Could I just invite you to come in, please? This deep desire for God informs every other desire. It expresses your purpose in life, why you are doing anything at all. We live in a culture that would easily have us live very much on the surface. The very busyness of our lives has the danger of keeping us on a rather superficial layer of ourselves. In the Ignatian exercises, I invite the retreatant to put the embedded longing for God into a verbal expression in their own words. I try not to lead them into what my words would be. When this happens, individuals say, God be with me. I want you abide with me. And similar phrases. And it is mutual. God's desire is for us. He created us as an expression of sharing what is happening in his core. The eternal mutual sharing of a desire that has come to full expression in the love of the Father and Son. The joy in God flows over to us. God creates us because he wants us humans to know his deep divine love within himself and to invite us to share that love. He wants us to want him in a way similar to how the Father and Son express and live out their love. God's radical desire for us could be expressed in phrases like, I want you, and I want you to want me. Be with me in your radical self. I relate desire, desiring to sexuality. The whole thrust of the human person outward toward another person, person's God, and as we shall see to all creation. Sex, physical genital intercourse, is certainly an expression of sexuality. But as I have said, I am using sexuality in a broader way, a term describing the thrust of a person in a whole and entire way to another person. In prayer, when our hearts are open and we are in intimacy with God, we can speak of these moments as instances of knowing God, first of all, but then knowing the very meaning and purpose of our lives. There is no deeper meaning. Everything comes together. This is what our sexuality is all about, being whole and entire before and with God. There is a strain in some thinking that without genital intercourse, we are not sexually whole. That would imply that without physical penetration, full human-healthy sexual relationships would not be possible. Let me point out that if lacking genital intercourse, a human could not be in full communion, we would have to say that vowed celibates and all those others who do not have sex could not possibly be whole. Please let me be personal. I know myself as this happy, rather well-integrated, old, sexually alive celibate. More about this later. Body. Let us talk about ourselves as body. We are body. In Christianity, there is a strain over the centuries of negativity toward the body. Very briefly, and perhaps too simply, Plato says that the body is like a cage for the soul, and the soul like a bird wants to be free of the cage so as to be united with the really real. This kind of thinking has woven its way through much spirituality in the last several thousand years. I raise one specific example out of my experience. A good number of years ago, a gentleman came to me eager to develop his prayer life. In Ignatian spirituality, remembering is a very important activity to appreciate how God has created us. I asked this gentleman to remember events of his life so he could appreciate God's creation and give thanks for the reality of his life. He responded immediately that he could not do that. He was trained not to remember, because in remembering events of his life, there was always the danger of bodily, sexual memories and that these could easily become temptations again foreseen. I do not know what happened to this person after I met him. I never saw him again. I would like to have been a help in his recognizing the beauty of his life, his body through memory. We are body. There are various aspects through which we are able to talk about ourselves. I am rational. I am heart. I am feeling. I am mind. I am spirit. I am body. I am not attracted to speak of having a body. This could imply that the really real me is some person in my body. I stress that we are this one person with these different ways of talking about ourselves. The negativity towards the body then is negativity towards my whole self and very expressly toward myself as sexual. In the strain of negativity toward the body, we meet a paradox. How do we express our love of God, our desires deep within ourselves, deep within us as bodies? If we think that our bodies as bodies have to be rejected, in the church, we have a longstanding feast of Corpus Christi, the body of Christ. We celebrate in this feast Christ as body. Let me tell you a little fun I have with God in celebrating this feast. You may remember the song that goes like this.  Maybe you have to be a certain age to remember this.  A nice thought. Well, I play with God and say, God, you were a nobody until you became somebody in Christ. God is not body, but he has become body in his son Jesus. One implication of this is that now God knows sexuality as a human. And another implication is that because a specific body is divine, all bodies have the capacity to be divine. We spoke of the lowly onion serving as a metaphor for different layers of desiring and emphasize that the deeper the desire, the more that desire informs the desires above it. The deepest desire penetrates up through the more surface desires. All desires above the deepest desire become lived metaphors, reflections of the deepest desire. So desiring Cheerios for breakfast is a thrust toward desiring God in a specific lived situation. My very speaking with you tonight is itself an implicit but real expression of desire for God. And this is body to body because Jesus, the Son of God, is body. Communication between ourselves bodily is a lived metaphor of bodily communion with Jesus. Human and divine communion come together bodily. There is a beautiful meditation and the Ignatian exercises of God looking at the creation He has made, looking at us humans, and the mess we have gotten ourselves into by our own misguided desiring, our own free choice, and He laments, but does not simply let us go to hell. He decides to intervene, tries to help by becoming one of us, by becoming body like us. He reinvents himself in and through the creation He has made. And so Jesus, the Son of God, is born among us as somebody. The ongoing challenging question for me has been, how is it? How is God a help for us just by becoming body like ourselves? How is God a help for us just by becoming body like ourselves? God now is in communion with us not only in a divine way, but in a human way. I suggest that God and Jesus knows human sexuality in a way before the incarnation as body He did not. We can speak only in space and time. For us, there was a time when Jesus was not this divine person bodily with us. Jesus bodily joins us because of the mess we are in. He joins us in our brokenness, in our fractured relationships, in our pain, in order to bring us to wholeness, to human, and divine communion, divine communion. And at the risk of going too far, let me be very personal. Much of this presentation is the fruit of my prayer life over years. And the phrase that I know myself as this happy, rather well integrated, old, fully alive sexual celibate needs a fuller development in order to have a deeper sense of this whole lecture. I will do that by telling you several stories. Several years ago, I participated in the inauguration ceremony of Lynn Balmington as president of Chaminade University in Honolulu. I could not conceive of traveling to Honolulu for just a few days. I managed to arrange to make my eight-day retreat, annual retreat, in a beach house of the university while I was there. It was literally on a beach.  I was for the week a hermit on a beach. For a good many years now, I have made my retreat in solitude. It may take a few days for me to be able mentally to get away from the busyness of my life. I pray to God at the beginning of retreats that I am seeking his presence, that I am not looking for drama, about that I hope I could know God's presence and love. The retreat began peacefully enough, and things were quiet for several days. And then it happened. I was walking on a road parallel to the beach. And I was taken very quickly by the experience that God was hugging me. God in everything she, he, is, but also in his whole creation.  This included parallel universes if there are such things. This was a total moment for me, a singularity. Initially, a very brief moment, an infinitesimal moment. Then, very quickly, that moment began to unfold through my whole person, every layer of myself. One result was that God appeared blue. That does not mean blue as sad, but the color blue. The vision of God was blue. You figure that out. One meaning that has had for me is that the initial experience in flowing over into everything I am, every layer, influenced my sight through color, the color blue. I have pointed out to God in the meantime that in a similar experience the year before, God appeared as green. For the rest of the retreat in Honolulu, I dwelt upon that event of being hugged and just let it unfold through my whole person. That event was whole and entire for me. That means it permeated all that I am. The encounter with God happened on the deepest layer of myself and permeated every other layer, all the layers of desire, all the layers of purpose, mind, spirit, heart, body. That event took over. The phenomenon of blue I would highlight is one of the physical bodily aspects of the experience. Out of such experiences, I know myself as integrated. All the various aspects of myself brought into harmony because of this touch of God on the deepest level of myself, the deepest desire for and thrust outward for God, being met by God's hug and everything with God, God's desire for me. This is my sexuality coming into full bloom. Speaking this out seems strange, but it is the only way I have of bringing it to words. This story in Hawaii touches the core of this presentation, an experience of wholeness. I was there complete and entire as full communion as it may be possible to me in this life. This is what I mean by sexuality, yet another story. I spent 20, 24 years in the Middle East working in Amman Jordan, where I helped found the Jesuit Center of Religious Education, and then in Jerusalem, where I was the director of the Pontifical Biblical Institute. As the time came for me to leave the Middle East, I was feeling down because I thought I had not done very much in my 20 years there. This was misguided. I was feeling that in the overall social mess of the Middle East, I had done little. My heart was breaking because of the extreme violence, hatred, hopelessness. But one day some months before I left, I had a particularly strong encounter with God. God said to me, Tom, thank you. That was startling for me. I had never heard anyone say or read anything that God thanks us. We want to live in a spirit of gratitude to God, thanking him for all his blessings. Now in that experience of God's gratitude to me, he was not listing specific works that I had done. He did not say thanks for founding the Cardinal Martini Leadership Institute at Bethlehem University. He thanked me on a deeper level. He thanked me for not losing heart, for being faithful, for staying with it. What does this have to do with sexuality? God was saying, within, over, above, through all of the frustrations, failures, successes, he loves me. That dominates over everything else. That is godly communion, human communion. Genital expression, we would hope, is a help for human communion. But sadly, we know that it is not the case more often than what we would want to think. In rape, there is not only not the movement toward fuller human exchange, but the exact opposite, violent disruption of human communion. Also, the hookup culture describes encounters of sex that are superficial, not in context of deepening human life. Genital activity, then, is an important component of human life, but is not the only factor bringing people to human communion and not the most important. Again, we would hope intercourse could be in the context of helping people come to rich, full, deep human communion. I tell you a story that may help in understanding what I mean by human communion. I taught here at Fairfield in the Prep and the University for three years, beginning in 1962, perhaps before most of the people, if not everybody in this room, was born. It was a time of formation for me as a Jesuit. In 1965, I went to Innsbruck, Austria to study theology in preparation for ordination as a priest. And I also earned a doctorate in theology in the process. 1965 was exactly 20 years after the Second World War. I lived in a very large community of German and Austrian Jesuits, most the same age as I. I was sensitive about being an American and hesitated to talk about the war. After all, we had been enemies. I made friends, and time went on, and there was no reference made of the war until. One evening, I and an Austrian Jesuit went out for supper in a local restaurant. I remember I had Wienerschnitzel und Pumphrit. We talked about classes and teachers, and then suddenly we shifted into memories we had of the war. We had both been small children during the war. The conversation was like opening of a dam. We spoke of the war for several hours. That evening, we too young adults spoke as we had not before. With an animation, mutual affection, freedom, and even a sense of reconciliation. Compared to his experiences, mine were trivial. I remembered waiting in lines for gasoline and some foods. He remembered fleeing with his whole family, abandoning their ancestral farm in order to land up in what would be the American occupation rather than falling into the Russian sector. The power of the human exchange that night, and its continuing power these many years later, I describe as an example of human communion. I go further and consciously describing that exchange as sexual. That is a mutual expression of affection, sharing of life, total presence, breaking down of barriers. I introduce a metaphor that may be of further help in reflecting about human communion. As the lowly onion was a globe, I introduce another globe, the whole earth.  We are separated by space. We are distributed on the circumference of the globe. Now if in our imagination, we all dig down into the earth, we would all come closer to one another. The circle would become smaller. Progressing further inward, we would progress deeper and deeper, become closer and closer. This is a metaphor of our progressing in human communion as we go deeper and deeper in our knowledge, our consciousness, our love of one another. Then as we reach the center, we reach what we could call complete human communion. At some point along the way, we as humans in our communication would be relating more from the inside than the outside, the interior than the surface. I offer another experience as an example of human communion. I spend much of my time on this campus leading people in the Ignatian exercises. I as a guide am helping people to come to as clear a consciousness as possible of how God is with them and they are with God at this time in their lives. In each session, there is invariably a deep human presence between me and the retreatant. We are there in as much wholeness as possible. This is human communion. But then because of the topic, God, there is a godly presence. God washes over us as a wave. Human communion and divine communion come together. Human desire and God's desire coalesce. Our human sexuality and may I say divine sexuality are alive. When I ask people I am leading in the Ignatian exercises to unwrap their deepest desires, rather regularly, people would say the desire for the good of their children are their spouse. I have found that there is a very little distance between desire for people and desire for God. I gently guide people from an awareness of their desire for their loved ones to an awareness of the deeper level of the desire for God. And this is often a help for people to deepen their desire for their family. The deeper the desire, the more every desire above it attains another dimension. So the love of God becomes united with love for family, and this easily overflows to everybody. This thought brings to mind the two great commandments, love of God and love of neighbor. For as believers, these two are inseparable, desire for God and desire for neighbor. Human communion and divine communion again coalesce. Communion with creation. I introduce into our reflection the notion of beauty. Beauty beautifully enters into the discussion on sexuality. Beauty is again one of those concepts that's difficult to pin down. I hope that in how I am talking about it here may make sense in our discussion of sexuality. Beauty is an attractor of desire. Let me tell you yet another story. Regularly, when I would be driving through a forest rich in trees with sun piercing through and some distant opening, I have the movement in myself to jump in. Over the years, this experience has been the stimulus for much reflection and prayer. What is going on here? What does it mean to want to jump into a forest? My reflection is that I want to become more a part of the beauty, just not be an observer. I want to be covered by it, immersed in it. I want to be identified with this beauty, get inside it, be overwhelmed by it, overcome by it. Beauty is an invitation. This is the language of love, the language of desire, the language of sexuality. Yet another story. You're getting it all. When I lived in Amman, Jordan, I regularly walked early in the morning to the Jesuit Center two miles away. One clear morning in this desert area, I was walking in the direction of the sunrise. There was nothing happening in the streets of the Arab city. I was alone. As I walked, I felt that the rhythm of my walking was physically in sync with nature and the rising of the sun. The colors captured me, especially the swath of sea foam green. I prayed God was present. Then the physicality took over. And I was not only responding to the invitation to enter the color, the beauty, but with the very motion of my body, with every step I took, I was helping God to raise the sun. I was helping God to create His creation. My communion with nature was at once communion with God. Now, every time I see the color sea foam green, this episode is reenacted. That we experienced beauty through the experience of nature means that we now include all God's creation to talk about communion. Communion with God, communion with humans, communions with nature all come together. God is the beautiful, the great attractor. There is a strange, deep in our tradition about, this is a strange, deep in our tradition about God. My experience is that wherever I experience beauty, there is the breaking through of God. All beauty is the reflection of God, the mirror of God. It is there whether I am taking notice or not, but in the awareness of it, the consciousness of it, there is a communication. God is the beauty. God is communicating His beauty and throwing out to us His hand. He is inviting us into Himself. He is saying, jump in. We are at the root of our being. We are at the root of our desiring. We are at the root of our sexuality. Passion, death, resurrection. God is among us in Jesus' Son in order to be a help. Jesus joins us in our brokenness and all our fractured relationships and our pain in order to bring us to wholeness, to human and divine communion. Some humans reacted by trying to crush this dream by crushing Jesus. Human sexuality in the passion and death of Jesus is perverted by the desire to destroy the dream of God for wholeness, intimacy, love. A great horror of the story of the passion and death of Jesus is that it is so much body. It is not abstract. Jesus is torn apart, nailed on a cross, naked. Sexuality gone awry in the extreme. In our meditation on the passion and death of Jesus, we ask for the grace to identify with Jesus. We ask God to place us with His Son. We desire to be present with Jesus in His pain. We need to meditate on the passion and death of Jesus because although the historical Jesus is no longer in His passion and death, we are. Jesus is no longer in the time of death and suffering. We are. The only Jesus who lives now is the Jesus bodily resurrected from the dead. Jesus is not eternally slaughtered on the cross. The only Jesus now we encounter is the resurrected Jesus. The aspect of Jesus resurrected from the dead as body is unavoidable in the resurrection stories in the gospels. In story after story, the bodily presence of Jesus is stressed. He walks with people, he talks, he eats, he shows his wounds. The whole person Jesus is resurrected from the dead, but what very significantly the disciples experience is this person Jesus as body. Whenever we encounter Jesus, we encounter this somebody, Jesus whole and entire. We do not have the privilege of encountering Jesus as body in the way the first disciples did at His resurrection, but there is no other Jesus now than Jesus as body resurrected. A major point of the resurrection of Jesus is that we are invited to be with Him forever, also as resurrected body. In that circumstance, we will be in full and complete human and divine communion. Desire will be ever expressed and ever fulfilled. Our whole thrust outward toward other human beings and God, our sexual longing will be complete. We have this now in a mirror, darkly, but then face to face body to body, there will be only complete and everlasting human and divine communion. Thank you. And the rest of this will continue. So one minute on your feet, sit down again. Great stuff. Thanks so much.  So what did you tell me? Next summer, about in Chicago, maybe for 300 people, but I'd be happy to do it anyway. I have to think about that. That's the one you told me. Oh, yes. Just get a few students a chance to leave if they have to without Jesus. Oh, thank you. Okay, sit down.  Am I talking to sit down? Is it okay? I said, do you hear it? Well, it was on mute. You need to unmute. I thought I did. Oh, maybe you did. It's not on mute. I think they, can you hear me okay? Okay. Okay, now, how do we do this? It's Marcy, Marcy, where are you, Marcy? Marcy has been a very great help to me in putting this talk together and very, very encouraging about being more personal than I really want it to be. And Marcy is the assistant director of the Ignatian Spirituality Center. Marcy, would you have a few remarks or three remarks? Something forward when I was, when I was being raised. So this, the way that you talk about human desire just is a gift and a challenge. Thank you. Do you have anything to say? Do you have anything to say? This is Paula, Paula, get a little pen. I just really love the way. Could you stand up if you didn't think I might know? I just really, I'm just gonna talk to you.  But it makes sense and I can relate to your encounters with God in nature and in color and in just breaking through. And I can relate, it is, it's orgasmic when that happens. So yeah. Okay, thank you. Yes. I just have a question, Paula. I thought you did a phenomenal job portraying this longing and desire that we have for God. And then I love how you tied it in that. In contrast, God has this long desire for me. My question is as a poor human being, do you believe that through continual prayer in this life that we'll be able to fully experience this desire and love that God has for us? Okay. I feel safe in saying no, we never get there completely in this life. Even though I talked about some very powerful experiences for myself, the next day was another day. And it takes on a new nuance, maybe it may get deeper and whatnot. And so ending, that's one reason I ended the way I did on the resurrection where we have this longing and we do believe that with the resurrected Jesus forever with the Father, it will be complete. We may not be able to know exactly what all of that is and what are we gonna be doing for all of that time? We can only speak in time. Let me tell you a little story though. This may be a little bit tangential. I hope I've answered in some way. That in thinking about God and the afterlife, again, I play with God, I have fun with God and I'll say, okay, God, what is it gonna be like there? Are we gonna get bored? Will there be too many people? And so I said, okay, what I'd like to do because over the ages, people have often imagined what heaven is gonna be like. And so I remember reading some time many, many years ago that this family living in late Victorian times, they imagined heaven, they were gonna have the best possible stand up piano.  And so I'm thinking about what we would do there. So I thought with God, what I'd like to do, God. I said, I'd like to help you to make another universe. If there are multiple universes, you're continuing to make them. I would like to be an advisor. And I would suggest to God to avoid some of the mistakes of this one. Like Brussels sprouts. And a few other things. And so that's one way that I have fun and imagining myself with God completely resurrected. What are we going to do for all of that time? But in a way, there's a certain seriousness that I get to that and thinking about my own life in here. But the whole experience of God now for us is not over. It's not complete. Even though there might be very high moments along the way. I use that, I think somewhere along the way, the one where God was hugging me, I don't know of a more, of a deeper experience I've had. So in this human life, I think I talked about that. I could not imagine having anything deeper. Maybe something will. I don't know, I don't know. God plays with me too, okay? I think that would be very similar. It might touch similar experiences of people in this room. The sense of oneness, of wholeness. With everything. With everything. Notice how that all of creation was in everything. Everybody was there. You were there, you know? Yes. That it's if I can just try to be present, I'd notice afterwards just in daily life that maybe he's worked a little bit on my spirit in darkness and silence. And I am not aware of communicating with him. Okay, along the way, we do have to be aware in our spiritual journey. There will be moments, down moments in darkness. I had a very long period in my life of real painful darkness. I thought I was crazy. Maybe I was, maybe I am. But we know that, yes, in our life, often the whole journey with God is very, very rough. And sometimes we have to ask God, why have you made it so difficult?  But that's so right. It's a combination.  A play that I've written, a young person comes back and says to this person who talks about God that, well, what about creating a universe without pain? And that stops the conversation. And the elder of the Jesuit, you can only guess who that is in the play, says, well, if we do away with all pain, do we do away with beauty? So we live in this mystery of combination, side by side, pain and beauty. And maybe we only know beauty because out of the pain of our lives, but this is a big mystery. I want to recognize Janus, but I'd like to, it's appropriate at this point for me to make an announcement. There's a very exciting announcement for me that I would like to tell you. And I got this information just this afternoon. I have written a play and it will be produced at the Westport Country Playhouse. Remember this because this is an audience that I think would enjoy this play now. There will be two performances on December the 7th in the afternoon at three, at two, and the evening at seven. And the idea of this, that this is a jumping off place for further productions of the play. And of course I have my eyes set eventually on New York City and I'd like to be alive if that happened. And so that's gonna be on December the 7th. And preparing for this talk, I was well along in the preparation where it dawned on me that the themes of the play and the theme of this tonight's lecture are the same. Tonight was a more philosophical, theological reflection, spiritual reflection, the play is a story. It's a very dramatic story. It's an adult play. So I don't think it would be appropriate for people under 18. It's all about divine communion, human communion, communion with nature. The title of the play touches the last phrase I said. The title of the play is the gentle whisper of trees. There's a lot of woods in this story. And so I invite you to think about it. I'd love if you could go. The good news is that the box office is opening up a week from today at 10 o'clock in the morning. It'll, tickets will be available online through the Westport Country Playhouse. I'd just like to point out maybe to her embarrassment that one of the producers is here tonight, Christine Brown over here at the end of the second row. There are two producers. The other could not come tonight. He will be looking at the video, though. So I'm very happy to announce that this is all a part of a dream at my own age that is kind of unbelievable. It's another miracle that I'm doing this tonight. It's a miracle in my life. The play is another one. And we will see what happens after that. I do have a second play. And do you know what the name of that one is? C-Foam Green. I don't know. I don't know. C-Foam Green. I don't know. I don't know. I don't know.  Now, Janice, I owe a lot to Janice for this presentation this evening because I gave a homily at St. Anthony's Parish on the Feast of Corpus Christi, June 30th, this last June.  And I said a few things about human sexuality. And Janice picked that up and wrote me a wonderfully gracious long letter by hand and sent it by mail. And I was very touched by that. And she ended by saying, I wish, I hope this is the first homily of number two and number three. And so I wrote back to her immediately. I said, you caught me. I've been thinking about years, wanting to do something like this. And so this has resulted in this evening. So Janice, do you have? Spirituality, this idea that is floating in my head that body and spirit promulgated through not just the Catholic Church, but churches in general, would there be a deeper integration in secular society where sexuality is not cut off from our entire and just experienced for its own sake rather than experiencing it as part of our totality? That is a very large question. And really honestly, it's right on the point. I feel incompetent to answer it. What would happen if this would happen? I think along the way we as human beings don't come to a final, complete, peaceful solution for ourselves on the whole difficult issue of human sexuality. I mentioned there's a strong strain of negativity in the last couple of thousand years in spirituality about negativity towards the body, towards sexuality. But at the very same time, there are very beautiful documents, official documents in the church of the beauty of sexuality, of intercourse. You can look in the catechism under marriage. Vatican II has some very powerful, beautiful stuff. But at the same time, and also all along the way with all kinds of movements that arose within the church and churches of negativity towards the body, and some of them were very, very strong. But with that, there was always official positions, no, there's something wrong with this. But it's never really contained. And I think a part of it is that sexuality is a frightening thing, the sex part of it can be very frightening. And so we never get to a complete balance in it all. We pray all of the time. I had a very upbeat presentation tonight on human sexuality and one reason was very deliberate because one, as I said, there's not much talk out there about it because of all of the very, very difficult issues. And so I said, okay, I present this very upbeat, but I hope you could see this is the way I see life. This is the way in my work that I see I'm relating to people and that I use that phrase, I see myself as a happy, integrated, sexually alive celibate, I mean that. And now that doesn't mean there are the down times with all of this. But so I tended deliberately to be very upbeat and talk about sexuality in a very positive way and in a kind of broad way too. When I looked up the Thasaris on synonyms, those were presented as synonyms of sexuality, virility, voluptuousness, sexiness. And you say, wow, how do we pin this down, you know? I hope by the end of the talk, you at least had some idea, it seems the way you were responding, yes, some idea to how I was using the word sexual. Anybody else, yes? Just to cover a quick thought, well I thought on the question. So the thought would be, you know, as you talked about all this, I was waiting for you to mention the song of Psalms. Yes, okay. There is a perfect example of what you're talking about. Right. But the question has to do with the relationship between ordered desire and disordered desire and discernment relative to the desire for death. You end this catalogically, so have you got a word about that? Yeah, I am 82 years old, do I desire for death? No, I do desire for life, but the life that I believe in that is complete is going through the portals of death. And as an older person, for all of you younger people, you tend to think more about death as you get older. It becomes more a part of almost the naturalness of it. But I don't pray for it. I think it's a part of God's, I think it's a part of the natural aspect of God's creation. And that I hope in praying to be with Jesus in this passion, which I hope is sincere, I hope not to die that way. This brings up a whole theology of what God desired in the death of Jesus that takes us in another direction. But I don't know if I feel competent of giving you a complete satisfactory answer to that. Can we talk around it? December 7th at two or seven.


Odd little moment here when Cummins gets Rizwan with the bouncer, at least they want it. They're like, yep, come on, we caught it. Nah, nah, so it hits something. And then Cummins reluctantly like, we gotta get this guy out. He's pointing to his arm. I hope he's not pointing to that white spot. It seems like he might be pointing to that white spot. I hope he's not, because he showed up to the crease with that white spot on his arm. You can see it when he shows up. You can see it the whole time.  And in review, it shows that it hit his wristband, which is part of the glove, which means it's part of the bat, which means he's out. Same as baseball, hands part of the bat. The sound says he had hit the wristband, but he was showing that spot on his arm, thinking it hit there, but he had that spot when he showed up. He's like, what? Australia's excited. I don't know about that. What was he pointing at? Was he tricking?


Brilliant's Audio presents Adventures in Memory, the Science and Secrets of Remembering and Forgetting by Hilda Östby and Ilva Östby. Translated into English by Marianne Lindwall. Performed by Christel Lewis. Forward. Sam Keane. In one of Plutarch's lives, he mentions an old philosophical conundrum now called the Ship of Theseus Paradox. After slaying the minotaur in the labyrinth, the Greek hero Theseus sails home, and the people of Athens are so overjoyed that they preserve his ship as a memorial. Being a material object, however, the ship shows somewhere in terror as the years pass, and every so often the caretakers have to replace a piece of it. A board here, a plank there. Eventually, after several centuries, they've replaced every last original piece of wood. So is it still the same ship now that it was at the beginning? You can ask a similar question about our own bodies. We're three fourths water, molecules of which cycle into and out of us in a constant flow, never sticking around long. And because our DNA and other biomolecules break down, we swap in new parts all the time to repair them.  Over the course of a decade or so, every last atom in your body gets replaced. So are you still you at the end? Most of us feel intuitively that we do remain the same person from decade to decade. But how can that be if our bodies aren't the same? Why do we feel this continuity so strongly? One big reason is because of our memories. The bio bits come and go, but the pattern of information coursing through our brains remains largely consistent. In a fundamental way then, we are our memories. Yet few of us really understand how memory works. We rely on misleading analogies or folk theories, or we simply remain oblivious and take it all for granted. Memories bubble up so easily inside us, so effortlessly, that we rarely pause to consider just what a miracle they are. Well, no more. After reading Adventures in Memory, you'll fully appreciate what a compli... Sample complete. Ready to continue?