pl y square root w x w y. So where these are the orthonormal, normal polynomials. Okay, so there is a constant, which we don't care about. And I mentioned, I didn't, again, I left it as an exercise. I mentioned that in fact, all of the correlation functions, that is to say, all of the projections of this measure on all the remaining coordinates also have a determinant form. So they will be determinants. This is determinant from one to n. And all the projections, if I integrate over all variables except five, I will get determinant of size five. Okay, so but today I want to discuss different thing. I want to illustrate on the example of this model a different phenomenon. I want to illustrate the behavior of palm measures. So let us consider conditional measure. Conditional measure, conditional measure by fixing fix x one equals p. And consider the conditional measure. And consider the conditional measure. So, well, the conditional measure is again. So in fact, these are precisely the Christoffel deformations that we saw in talks here in the talk of Pierre Lasag. So the conditional measure, as one can see by direct substitution, will again be orthogonal polynomial ensemble with the weight which is multiplied by p. So let me write xn, xn equals p. So minus one, minus one. So p minus xi square dxi. So, oh, excuse me, w, w. So this is the conditional measure with fixing a particle at p. So now the question arises. Let us consider, let us move this fixed particle. So let's consider, so this is measure. So if this measure is p, then for this measure let me adopt the notation like this. Okay. So, and let me also write the measure by fixing the nth particle, but not at p, but now at q. So this will become very same thing, but this. So now let us compute the ratio. Let's compute the derivative. So the derivative of dpq over d. The configuration x, let me write like this at x where x is x one, xn minus one is precisely the product of p over minus xi. q over minus xi. And well, w of xi just cancels out but there is also the factor. There is the factor. In fact, the factors can be computed. There is the factor, excuse me, let me. Where the w's get canceled for the xi's but there is a factor w of p, w of q. And there is also the factor of normalization. So in fact, normalization, one can see that normalization of this will be by definition the correlation function at p, whereas normalization here will be by definition normalization function at q. So there is also a normalization factor, excuse me. The normalization factor will be here. Knpp and here knqq. Why? Because again in normalizing these measures, so I, excuse me, so just these are two measures on Rn plus one. So these measures are different by multiplication by a function. By which function? By this function. So I could put it like this. pp is equal to psi pq pq, right? So just one measure is obtained. So that is to say that measure of a set with respect to this measure is obtained by integrating this function with respect to this measure. Excuse me, say again. It's just notation. It's derivative. Derivative of one measure with respect to another measure. I'm not sure I understand your question. So derivative of one measure with respect to another measure. Radonnikadim derivative. So just the notation, when I write mu is equal to f mu, it's the same as to write d mu over d mu is equal to f. So it's just, thank you very much. In fact, there are many notational conventions here, but I will just use this one. So this is just Radonnikadim derivative. So one can compute these functions explicitly. So this is just the final formula. So the aim of today's talk is to obtain such formula in scaling limit. And in fact, by the way, this project goes back to work of Olszanski about the gamma kernel. So to the work of Olszanski about the gamma kernel, Olszanski on the gamma kernel. And who obtained such formulas for the gamma kernel. So for a determinant process with the gamma kernel, please allow me not to write it explicitly now. Maybe we will do it later. So for the determinant process with the gamma kernel, in fact, by taking scaling limit in this formula. But let me point out that it is delicate. In fact, there are difficulties in Olszanski's approach. Also for Geniebre ensemble, this approach was later also adopted by Osada and Shirai. So just the difficulties are manifold. And due to the fact that, for example, this function is not bounded, you can see. It's not bounded neither above nor below. So there is a denominator. And in any event, so it is difficult to do limit transition in such formula. Because in fact, limit transition, especially when f is not bounded. If f were bounded, it could be possible. But equivalent measures, when equivalent measures under limit transition can become singular measures. Just think about your favorite sequence of measures with the density converging to a delta mass. Just equivalent, the fact that, so trying to prove such identity by choosing a sequence of approximates mu n, mu n equals fn mu n, creates difficulty because, precisely, it is very possible that such sequence mu n and mu n converge to two measures which are mutually singular. It's very easy to construct examples when this holds and mu n converges to mu and mu n converges to mu. But this is not true. So in fact, the approach that we will adopt is completely different. Approach direct and not using approximation by orthogonal polynomials. Orthogonal polynomials will appear at the end of the day. OK, so before I start, yes? Yes, it is completely relevant also in a discrete orthogonal polynomial case. This is also, the statement is also true. As you say, it is essentially obvious in discrete orthogonal polynomial case because you compare just measures on finite sets, on countable sets, measures on countable sets. But let me point out that when you take the limit transition, when you take limit, then you obtain measures on spaces of infinite binary sequences. For example, the discrete sine process. And such statement, we shall see for discrete sine process. And it is not immediate. So that for discrete sine process, this is not immediate. So let me also say, and this I will address in detail in this talk, that this symbol. So here I wrote conditional measure with respect to part of fix xn equals p and consider conditional measure. But for infinite point process, this is delicate. So what does this mean? This is so-called palm measure. And in fact, I will give detailed definition today. But before I start in this, I have to keep a promise from my first class. And so we shall pursue a digression. So digression from last class promised to prove that the probability of the number of particles being high in a determinational point process decays as e to the minus alpha k square. So this is just a digression. And I pursue it because I can illustrate the concept. I can illustrate the idea precisely very conveniently on the example of orthogonal polynomial ensembles. In fact, if I have an interval of length epsilon, interval i of length epsilon, interval i of length epsilon, then the probability it is clear that the probability is that there are, with this orthogonal polynomial ensemble, that there are k particles in i. Well, let us look at the Van der Monde determinant. This probability is, in fact, at most epsilon to the k square with some constants depending on other parameters. So there we go. So just by looking at the Van der Monde determinant, I get this k square. So my aim now in pursuing a little digression and fulfilling the promise from first class is to prove this statement for general determinational processes and just illustrating the fact that just somehow orthogonal polynomial ensembles are a very convenient model to check, to verify statements about determinational point processes that sometimes often can be proved in great generality. So first manifestation of this we saw in last class when we saw that multiplying by a weight, multiplying by a multiplicative functional, taking product with a multiplicative functional leads to multiplying the range of the point process. This statement, very easy to verify for orthogonal polynomial ensembles, holds in great generality. So let us prove this. So I need some assumption for this. The assumption will be the following. The assumption is that the maximum, so let me only prove this in the case. So to simplify the exposition, let me assume that the length of i is less than 1. The statement holds in general because of negative correlations. But let me just assume this. So assume this. So and let me also assume that they'll assume the following. So OK, I need one more assumption. Let me write the assumptions here. So OK, assume that 1. And second, that the maximum of the case derivative of the kernel. No, yes, that's right, yes. No, case just some fixed number. No, this is excellent question. No, case fixed number. Case fixed number. Case fixed number. And n is very large. Yes, exactly. But in fact, the proof I will give will again not be by limit transition. It will be direct proof from correlation functions. So precisely, this somehow illustrates the convenience of working with correlation functions. OK, so I will assume that the case derivative of the kernel, so the maximum, is Ck factorial. This is convenient assumption which holds in all examples. You can think of, in fact, it's also it wouldn't hurt if I put C to the k or something like this. So I can put C to the k. But let me write like this just for simplicity. But if I put, for example, C to the k, it doesn't matter either. On the interval, on the interval, thank you very much. On the interval, on the interval, thank you very much. On I, yes, thank you very much. On the interval, thank you very much, yes. OK, so with these assumptions I aim to prove this, this is very simple proof. OK, so in fact, this one is equal to 1 over k factorial. So excuse me, excuse me, I misspoke. So it's less or equal to, because it's the expectation, 1 over k factorial integral of rho k x1 xk dx1 dxk. This is just definition of correlation function, if you wish. This is just definition of correlation function. And this is, in fact, 1 over k factorial. So let me continue here. 1 over k factorial integral over i to the k of determinant i xi xj. OK, so then, then, i to k. OK, so then, let us analyze this determinant. And for this, it will be convenient for us to use the formalism of divided differences. Divided differences. Let us recall that the divided difference, given some function f, f divided difference, is defined inductively. So the first divided difference. The first divided difference is what you think it is. And the nth divided difference is plus 1 over x1 minus xn plus 1. So these are the divided differences. OK, so just and, in fact, a divided difference of a function is equal to nth derivative. This is just Lagrange's formula. nth derivative, where xi is in i, is in the interval i. Yes? OK, OK, OK. OK, yes, exactly. I always forget about the blind spot. Yes, excuse me, yes. So this one is OK? The last one is also not OK. OK, OK, OK. I always put the most important formula in the blind spot.  So OK, so and then this divided difference is, in fact, equal to nth derivative of xi over n factorial. Yes, so xi is in i. So then, well, let me raise the thing with correlation function. So let me just try that this is less than this. And I continue by taking the divided differences. So I continue, I take the divided differences. So I obtain determinant, so excuse me. So the determinant, determinant pxi xj is equal precisely to the van der moond times the determinant of divided differences. Determinant of divided differences, x1 and so on, xk. So what do I mean by this? So in the first column, I take, so the first column just doesn't change, I take px1 x1 px1 x2 and so on, px1 xn. So in the second column, I take the first divided difference. The divided difference is always taken in the first variable. So yes, so I take the divided difference. So here I have px1, so x1, x2. Yes, so excuse me, x2, x1, x2, and so on, pxn, x1, x2, and so on. So here I will get p, so obviously depending on the xl, so x1, xn. So but then this determinant, I just evaluate as the sum of the terms. So there are n factorial terms, and each term, so this one I evaluate just as the sum of the terms, n factorial terms, and each term is product of the case derivative, which we wrote here. So product of maximum of the case derivative over k factorial. Times, times, excuse me, times obviously the van der moond. So the whole point of taking the divided differences was to get out the van der moond, times the van der moond. So and the van der moond gives me i, the desired i to the power k over k minus 1 over 2. So n factorial means, of course, k factorial. Yes, so and the product is an l from l2. Yes, so there we go. Again, excuse me, f is the kernel pi. f is precisely the kernel pi. f is precisely the kernel pi. So the kernel pi, I take the divided differences of the kernel pi in corresponding points. So here, yes, divided differences of the kernel pi. Precisely, as I said, on the first. So pi is a function of two variables. That is precisely right. Pi is a function of two variables. One of them is fixed. So in the first, that's exactly right. So in the first row, it is the first variable, in the second row, it is the second variable, and so on. In the nth row, it is the nth variable. The second, this is precisely right. Let's, let me say this in greater detail. So in each, in each row of the, of the matrix, I have the following expression. So kth, kth row. So let's say lth row. So I have pi xlx1, pi xlx2, and so on, pi xlxn. So I consider this as function in the variable x1, x2, and so on, xn. L's function, so this is a parameter. I consider it as function in variable x1, xn. So this is the variable. So, and I take these divided differences. Yes, fl of x is equal to pi xl of x. Yes, f depends on row. So in L's row, I take divided difference of fl. Does it make sense? Well, of course there, of course in different rows, I have different f, Igor. I'm not sure I understand your question. Well, it is function of, it is function of two variables. One variable is considered as parameters, and the other variable, the other variable. So wait, let's consider, let's take example two times two if this point creates questions. Just one second, let's, let's consider. So what I, let's consider determinant two times two. Do you, Igor, agree with this? Yes or no? There is no definition. It's called subtracting, subtracting columns in a matrix. Do you agree? So this exactly what is written iteratively. So then, then I write this. So for matrix, please allow me not to write this for three times three and so on. So just I write this for, first I subtract the first column from every column. So I get divided differences of order one and I get products, and I get all these products x2 minus x1, xc minus xc and so on. Then I take divided differences of higher, obviously with the remaining columns, second one, third one and so on. I take divided differences of second order and I develop next, okay, so okay, okay. So any, I think, I hope I managed to convince Igor so does it mean that I have convinced everybody else also? If not, please ask me. This is just maybe, I don't know. I must be confusing you in something very simple because it's very, very, very immediate computation. Does it make sense? Or, sorry, sorry, excuse me, I don't, I don't. Yes? Terminators, excuse me, it's L, the determinators of size K and I'm varying L, this one. It's K, it's K, in fact, excuse me. It's K, yes? I'm varying, I'm varying, so on each row I'm varying this variable which serves as parameter and I'm subtracting in the other variable. Yes, yes, okay, okay, good, perfect. Okay, so we're in good, I hope, we're in good shape, so yes, and then, well, directly we have gotten the Vandermonde here, here it is. Okay, let me subtract, this was auxiliary formula. Yes, so we get Vandermonde here and, okay, let me erase this also, and then, so the Vandermonde comes and the Vandermonde gives this thing. Okay, and so we have obtained the desired estimate. I have assumed that the length of I is less than one, but if the length of I is bigger than one, then one just needs to subdivide it into pieces and observe that there is negative correlations. So I should say that this, please, the experts in the audience correct me. I should say that I don't know which source to quote for this immediate computation. This is easy computation, but I've never seen it done. Please correct me if I'm missing some obvious source and also what is more serious for me, I don't know this constant alpha. So as you can see here, there is a lot of, so this argument is very naive. In particular, I get out only the first, please observe that here I get only the first power of the Vandermonde. So I don't get, in fact, one would expect, so one should expect there to be a square. So this estimate is very crude, but at the same time, so please let me allow me to ask this question. So what is alpha? So I have absolutely no idea. So question, what is alpha? Let's put some constant, let's put some constant, let's put some. Yes, but this you can incorporate into alpha, but this you can incorporate into alpha. K factorial is K to the K, so this is slower than e to the minus alpha k square. Exactly, exactly, yeah, there might be some. Yes, yes, there are, yes. So you can, yes. So if you put K factorial, this just incorporates into alpha. Thank you very much, yes. But so I point out that the probability is less than one anyway, so choosing alpha sufficiently small I can erase this constant. Okay, but you can put a constant in there. Okay, so the point is what is alpha? And this I don't know. What is alpha, what is alpha, this I don't know. How does alpha depend on i? By the way, let me point out that in this argument, one sees that if these estimates are uniform, it only depends on length of i. But how, because I only use length of i here, but how, I don't know. Okay, so closing this digression, so this was a digression about just probability of high accumulation. Oh, by the way, I should say there is another question. So the argument given here directly applies to one real variable and directly applies to one complex variable. But it seems to me that it should also be possible to apply it also in several dimensions, but well, I have not done this. So maybe it's possible to also to have such argument for just not just one complex variable, but also for general process in several dimensions by interpreting divided differences in some good way. Okay, okay, so this much for this, and we proceed with the palm measures. So in fact, I think I erase everything and I start with, I start a new chapter, and it is a beautiful, beautiful chapter, beautiful theory. In fact, with beautiful history, which I like to tell very much. So as I think I mentioned many times, around the turn of the century, the phone companies had a significant problem. Phone companies had a significant problem in that the phone lines were growing out of control. So phone communication was experiencing a rapid boom and just people had to wait in line for very long to place a call. In fact, if you read the literature of the turn of the century, the difficulty of placing a call is prominently mentioned of the beginning of the 20th century, yes. So maybe the analogous difficulty of the 21st is the difficulty of connecting to Wi-Fi or something like this. So just in any event, so the phone lines were growing out of control and so the phone companies were trying to resolve this situation. And in fact, so this led a young engineer in Stockholm working for Ericsson, Konrad Palm, to come up with the concept of the palm distribution. So precisely this is the name of this subsection, palm theory. So one should say that of course, Palm did not write. So Palm's manuscript was written, of course, not even on physical engineering level of rigor. And in fact, the mathematical palm theory was constructed by Alexander Hinchin. So and sometimes one says Palm Hinchin theory also. But in any event, so the idea of Palm was the following that, the idea of Palm was the following that one should consider in a point process. So Palm was obviously just considering the incoming sequence of calls. One should consider the probability distribution of next call arriving provided that the call has just been placed. So the distribution, or in other words, distribution of let's say next particle provided that there is a particle in this position. So this is the whole idea of Palm. So precisely this consideration immediately resolves the well-known waiting time paradox. The waiting time paradox is that if buses departed random times and you leave the ICTP every time at three, then buses have Poisson distribution just with expectation. 10 minutes, then you leave the ICTP at three o'clock every day. But in fact, your waiting time will be, your average waiting time will be 10 minutes. And average time between the bus that just left and you will also be 10 minutes. And it seems a paradox because also the average time between buses is 10 minutes. But precisely the resolution of the paradox, so it seems like 10 is equal to 10 plus 10, but the resolution of the paradox precisely lies in the fact that the expectations are taken into different ways. One is with respect to a measure and one with respect to palm measure. With respect to a measure, one with respect to palm measure. So in fact, or informally the informal explanation is that of course when it is more probable to hit a bigger interval between buses. So that is the informal explanation. However it may be the palm, so this is the palm distribution. So I fix a particle in some position and I am looking at the distribution of the next particle. I'm looking at the distribution of the next particle or of some other event. So and naturally one asks the question, what does it mean to consider conditional measure of a point process, conditional measure of a point process with respect to a particle fixed at a given position? So this question is not obvious for the simple reason that how to say the event there is a particle in this position is not an event with respect to which you can take conditional expectation. The one cannot take conditional expectation with respect to such event. So there is no sigma algebra because there are many events occupying many positions so it is not possible. So the statement conditional expectation with respect to a particle at this position has absolutely no rigorous meaning. It's rigorously completely meaningless. So it has to be endowed with meaning. So there are two ways. So there is a naive way of Hinchin himself which is just take a neighborhood of this particle and so some interval i epsilon of length epsilon condition on the event condition. So Hinchin, Hinchin, Hinchin's elementary approach, Hinchin elementary approach is that condition on the event that there is a particle in this small interval and then take epsilon to zero, take epsilon to zero. So this is the elementary approach of Hinchin. So it has many advantages but it has two important disadvantages. It's very inconvenient to work with this because of this differentiation limit and the second disadvantage is that it is a priori not clear why the limit exists, why the limit exists. Why the limit exists. So in fact, this is not what we will do. This is not what we will do. We will use an approach with through Campbell measures which is due to Olaf Kallenberg. So Kallenberg's formalism through Campbell measures. So we consider the following objects. So Campbell measure. So let me explain the idea of the Campbell measure. The difficulty in conditioning for the palm measure, the difficulty in conditioning for the palm measure is that the particles are not numbered. So when I say there is a particle in this position, if the particles were numbered, I would be able to say the first particle is in this position because the first particle cannot be simultaneously in this position and in that position. So it is possible to have a sigma algebra and to have conditional expectation. But when I say a particle in this position, maybe it's first particle, maybe it's second particle, but these events are not exclusive and so precisely it is not possible to consider it. So Campbell measure is an extension of the point process in which one of the particles is marked. So we consider not just configuration but there is configuration. Configuration is a collection of particles without regard to order. The very idea is that we consider not sequences but configurations, we consider measures not a space of sequences but on spaces of configuration. It's a very important difference. If in finite sequence it does make a difference, ordered or unordered, there is just n factorial in the formula. So in infinite sequence, the difference is very important. So it is not possible to order naturally particles in the unit disk for example. So in fact, Campbell measure is a little bit of ordering. There are particles, they're all indistinguishable but one of them is red. Okay, I proceed to precise definition. So the Campbell measure C is a measure, a measure on E times space of configurations on E. So one should think about it, I will draw it like this. So this is space of configurations on E. This is E. So and one should somehow think that over each configuration, so this is a configuration, over each configuration I place itself as a measure on E and the resulting measure is precisely the Campbell measure. To put it precisely, so C of B times Z, so B is a subset in E and Z is a subset in the space of configurations is just the integral of the occupation, occupation value of X on B over Z. So this is the precise formula that gives this, that gives this Campbell measure and now the Campbell measure, it's an infinite measure but in restriction to any bounded set it is finite. In restriction to any bounded set it's finite. And so I can take conditional measures of the Campbell measure. Conditional measure, so now conditional measure, conditional measure on C, so let me write C, P. Now I can fix a particle, conditional measure of C, P at Q in E is precisely the palm measure. It's precisely the palm measure. It's precisely the palm measure. Okay, so it's precisely the palm measure. So now, it's precisely the palm measure. So now the question is, it is convenient, so this measure as it is defined by definition it has a particle at Q by definition. So we consider the set of those which have a particle at Q. So it is convenient to remove this particle. Convenient to remove the particle. The palm measure by definition has a particle this palm measure, this measure by definition has a particle at Q, by definition has a particle at Q. So it's supported on configurations having a particle at Q configurations X, X such that Q belongs to X. So it is convenient to remove it. So for example, why is it convenient to remove it? I will give very simple illustration. In fact, just already for the determinant measures I will prove that the palm measure of determinant measures is determinant measure. But if I have this particle at Q, I would have to say it's determinant measure plus a particle at Q. So just all the statements would have the form something, something, something, something, something plus a particle at Q. So it's convenient to kick out this particle at Q. So a call, so to speak, a call takes place now but it has already taken place, I forget about it. So what is happening with the phone line? Forgetting the call just took place? Yes, forget about it. So this is the message. And so this is called reduced palm measure. So removing the particle at Q gives the reduced palm measure. Gives the reduced palm measure, used palm, which I denote PQ. And to simplify the exposition even further, let me note the clear proposition. Proposition. So the correlation function, the correlation function of PQ, else correlation function at X1, Excel. So audience participation question, but those who know already don't answer. So what is it, how is it expressed through the correlation functions of the initial point process? You have the else correlation function, meaning that there are particles in positions X1, Excel. So, and also I have this condition that there is a particle at Q. How is it related to correlation functions of the initial process? If you already know it, no. If you know it, if you don't know it, you can try, yes. Seven. No. Okay. So yes, now you can make serious attempt. So what do you think it is? Yes. Precisely, yes. Well, exactly, thank you very much. Yes, so it is precise. You don't need to average or anything. It's just infinitesimal probabilities that there are all these particles and also Q. This is exactly right. So, and from this proposition, there is a corollary, which is the Shirai Takahashi theorem. So the palm measure, the palm measure of a determinant point process, measure of a determinant point process, a determinant point process is again determinant, is determinant, and the formula is, so let me raise this, and Q. So Q, Q. So, again, excuse me. Ah, yes, of course, you're absolutely right. Absolutely right, absolutely right, absolutely right. This is absolutely right. So where should I put row? I should put row one of Q somewhere. You're absolutely right. Over row one of Q. You're absolutely right. Thank you very much. Yes, this was a mistake. Yes, very much. Yes, in fact, thank you very much. Yes. Okay, yes. Very true. Is determinant. So determinant point process, let me write Pk is determinant. Pk Q is equal to Pk Q. So again, the palm measure, by palm measure, I always mean reduced palm measure. So let me write it just once, and I will not write this again, reduced palm measure, and with this formula. So now we are ready to just at least see how one proves the, so the Gibbs property, so Gibbs property for determinant point process, Gibbs property for DPP, for determinant point process. So let us recall, let us recall that we have imposed, we have considered processes satisfying the division axiom. So I consider projection, so K projection onto subspace L, satisfying the weak division property. So if F is in L and F at Q is equal to zero, then F over X minus Q is in L. Why do I care so much about functions assuming value zero at zero? In fact, because Kp, so if K projects, if K projects onto L, onto L, then Kq projects onto Lq being the precisely the set of functions assuming value zero at Q. Assuming value zero at Q. In fact, precisely this is the reproducing kernel at Q. So this is the functional, this is the functional of taking the value at Q. So we subtract from my projection operator the one rank one projection which projects onto the value at Q. So I project on smaller subspace of functions which assume value zero at Q. But now if one looks at this formula attentively, so this is the weak division axiom, let me, weak division axiom, weak division axiom. If one looks at this formula attentively, then one sees that weak division axiom implies that L of Q is equal to X minus Q, X minus P L of P. In fact, if you think about it, it's very natural. Think again about spaces of polynomials. So we all know that what does it mean? Polynomial assumes value zero at Q. It means that polynomial is divisible by X minus Q. So what does it mean that polynomial is assumes value zero at P? It means that polynomial is divisible by X minus P. So precisely L of Q is obtained by X minus Q, by multiplying by X minus Q divided by X minus P and taking L P. Why I can write it like this, also L of Q over X minus Q is equal to L of P over X minus P. So this is just direct corollary of this. Okay, but this implies in turn by the proposition that we proved last time that if the ranges are different by if the ranges are different by multiplication by a function, then the corresponding determinant point processes are different by multiplication by multiplicative functional. So the palm measure of this point process, the palm measures are equivalent and they are in fact different by multiplication by a multiplicative functional. And from this in turn, once I have equivalence of palm measures, once I have equivalence of palm measures, so the corollary precisely is the corollary is that the conditional measure, so the Gibbs property, which I formulated in the first class. So the corollary of this precisely is that the conditional measure if I have some particles inside and with respect to the fixed particles in the exterior, the conditional measure is precisely orthogonal polynomial ensemble. So there is some weight. So there is, of course, normalization constant. There is some weight, some special weight function, and which does not depend on anything. And there is, of course, the product of these factors just in the same way as I wrote in the very beginning in the very beginning of today's class. So just the same formula, the same formula for conditional measure. So fixing the particles in the complement of an interval and considering free particles to be free in the interval itself, I obtain conditional measure as orthogonal polynomial ensemble. This is a weight function, which does not depend on anything. So it's weight function, which only depends on the point process itself. And then there is this product, which has to be understood in principle value. There is this product of interactions between the particles inside and the particles outside. And, of course, there is the Vendremont determinant, which explains that this is an orthogonal polynomial ensemble, and this is essentially a direct measure theoretic. So just Fubini's theorem, if you wish. This is a direct corollary of the equivalence of palm measures by multiplicative function. So this multiplicative function manifests itself here. So by equivalence of palm measure by multiplicative functions, which in turn is a direct corollary of comparability of the palm spaces by multiplication by function, which in turn is a direct corollary of the weak division axiom, which now implies the Gibbs property. Thank you very much.


So much beauty for people I am back with another out of the ring video and today guys I want to showcase to you an Incredible weapon when I've built a well a short little thought about it I'm gonna talk to you about an hour just to throw something together With a build based around a great weapon, which does amazing damage Now this is a weapon that's been known about for some while people have used it for some while I Haven't really seen anyone cover it since the latest patch Well the patch before that actually because that's your weapons change. It's way more beneficial to the player now It's way more potent way more dangerous much much better And that's why I bring you today guys another build based on this thing How's it going guys? My name's DP Jane if you do enjoy the video leaving a like really helps out to me If you like what you see I want to see more be sure to subscribe Okay guys, so the weapon is the blasphemous blade Mine's a plus 9 could get it even better plus 10 if you want to burn that far It scales with strength a dexterity and faith it requires 22 strength 15 dexterity and 21 faith to actually use this thing and you get it guys from defeating right car that volcano manna which I'm Pretty certain you probably don't at least know about the main boss of this place Once you defeat him you'll get is a remember to take it to two fingers at the round table and you can pick this thing And it is well an absolute beast What's actually better about it now guys is and what makes it much much better than what it was post patch I think this was a 1.0 or 3 patch Now we know it used to heal you Undefeating an enemy. Yep. It used to heal you Undefeating an enemy, but guys it's got way better because now it heals you upon you hitting an enemy Yes, don't believe me. I'm gonna take it to our batch of this destroyer thinking this area Yeah, just testing it a little further.  You know me people.  This is actually pretty good And I show you what I'm using in a quick second and obviously as always guys all put guides in the video description to everything I've got on here in regards to where you get said items from just to make it a lot easier on yourself if you're Thinking about using this build or getting inspiration from the build or whatever.  So yeah, I'm gonna quickly skip to another spot where enemies are a bit tankier Let's go up here. So yeah, I'll catch you back in a quick second people Okay, guys, so I'm at a place that my enemy shouldn't be one hit especially about all the buffs I can apply to this Okay, so I let this guy actually Use some damage to me. Well, I'm a bit more a bit more Okay, so that's actually one more. Don't don't pick me up. Don't pick me up. Don't pick me up No, just hit me one more time. Please come on. There we go. That'll do that'll do And you'll see now guys that sure I'm out of damage. How if you get back upon a hit see that? Absolutely brutal. So if you're just spamming this away like this guys Against the boss against as it don't matter again your health back so fast so fast.  It really does So what I'm actually using with this guys is I'm using the giant seal which boosts a giant flaming contentions I'm obviously using plenty of flaming contentions to you just because it's a fire build I'll show you them in a quick second, but there's one specific one. I'm using there which buffs my damage reducing How me is this impede here which raises faith slightly? So yes, as we know guys faith is important to fire The rest you can just look how you want if you can hold If your equip loads decent enough you probably have tank armor here, but hey use what you can In regards to Talismans, we've got the child of Alexander boosts greatly boost your tap over skills. Nice America social Increases many of those beautiful stats needed for this build. We have the two things a loom increase While raises faith another great one and then we have the fire scorpion charm raises fire attack But lowers damage negation now you can probably switch out one of these For let's say where are you? Where are you? Where are you? I know your peers somewhere When you get one it all they will they will they carry in for the grid crust the slowest fp consumer skills The thing is the world is is kind of heavy on the FP It's not too bad. I guess but it is slightly heavy Nice, you could probably switch that to that is up to you Within my beautiful feisty Flask I'm using the flame shrouding correct here which boosts fire attacks And I'm also using this ruling hidden tier eliminates all fp consumption I believe this is for about 10 seconds, and I use that just because of the actual Heaviness of the special attack, which I actually didn't really showcase it on that So yeah, it uses 30 fp per usage. So yeah within that taker's flames, which is a great weapon art as you've seen So obviously scales with faith you want a more faith develop strength Dexterity as well, you know, I go as guys you don't need to explain this to us Incantations I'm using here we have Let's go down we're using Well, we were well, this is a main one. I'm using here. They raises the physical and fire affinity attack power So this is absolutely great for this. So yeah, just pop this pop my flask game maximum damage for much Or exactly how long it lasts, but it's a good It's a good minute or so. I think this may last three minutes or the flask may last three minutes And this may last a minute. I'm not sure what to be honest There's no real boss. I have left to kill in the game. We can test this on to see who actually puts up a challenge Long or long enough before these wear off. So yeah, most are using flames Sling I'm also using fire deadly sin. I'm also using this one, which is amazing flame of the felt God It's great, but there's many other fire things you can use guys.  I don't know what I don't know what this one's supposed to do I don't know what this one's supposed to do. But yeah, and this one as well. It Increases that fire and a damage negation.  That's basic what I do So I'm going up to an enemy. I'm literally just well, I will pop my My grumpy strength, I'll drink my Physics and then I'll just too handy Main weapon and I'll just go up to enemies lock on to them and just literally Oh Look at the damage that does now It's utterly brutal guys. It really is. Hey, you can't not suppose hit not supposed to hit me Well, I'm trying to demonstrate a video get out of here. Get out of here. You almost killed me And it hit a lot harder here. So it's why I actually test builds a Test amount of lower enemies because I'm used to that with all the weapons and stuff and then come up to that Normally the Giants by the deck test medallion and lift and then I will probably come here because these guys hit hard as well and sometimes the Giants in the The mount tops of the Giants as well. They are pretty tanky. But yeah guys, it's a great build If you can improve on it, I'm pretty sure you can Be my guest if you can help me improve on it Let me know how down below and there we have it guys Like I said, it's mainly based on this weapon here. You could probably incorporate this into your build You already have but it's definitely a great great weapon. It really is but there we have it guys If you enjoyed the video leaving a like really helps out if you like what you see want to see more out of me Be sure to subscribe and hopefully people and we'll see you on that next one


Brain education for our youth means hope. I was very emotional even though I wouldn't always express it. Anything could sway me left or right. I would be excited, I would be depressed, I'd be angry, anxious, whatever it was. And so brain education helped me really ground and center my emotions. I was a scared, angry, up-and-coming fashion designer and I found myself through brain education. I'm Ian Martin. I'm originally from Inglewood, New Jersey. I live in Sedona, Arizona and I'm a program coordinator at Sedona Moggore Street. So the way I found brain education was basically I was designing clothes. I had a fashion brand and to fund the production of the clothes I was working weekends at a country club as a server and I had to wear a tuxedo and I had to get that tuxedo clean. So I went to the cleaners with my friend and she saw a poster for children's yoga on the wall and she had a nephew who was really not in the best shape. He was a little depressed and sad and so we took him to the children's yoga the next day and within five minutes of him going with the brain education instructor in the classroom I looked in the window. He went from total frown to totally laughing doing a hand stand on the wall with his feet up in the air along with the instructor and that's when I thought I'll try this. I need some of that whatever this happiness is. I'll try anything once. So I decided to go to my first class on a Friday which was a vibration class so it moved our body a lot a lot of dancing sweating so much loud music but it felt so good to move without being judged and then I just felt so much energy in the class we laid down felt so much energy and that's when I realized I wanted to keep going with this. I really wanted to keep feeling I wanted other people to feel this energy that I was able to feel. Brain education helped me change a lot in a lot of ways. I was very lost very angry scared very confused narrow minded even though I was open minded the way I did things was very narrow minded. I was very emotional even though I wouldn't always express it anything could sway me left or right I would be excited I'd be depressed I'd be angry anxious whatever it was and so brain education helped me really ground and center my emotions really focused my mind to be a lot more flexible of course I'm still working at it but it's helped me so much. I couldn't smile when I started brain education they had I was reminded maybe 10 times a day to keep smiling when I would ever go to the brain education center and now I can smile whenever I want and physically it's helped me relieve a lot of tension that I held here I think I tried to protect myself a lot a lot of tension in my back and shoulders has released my breathing my intestines internal organs my brain everything is you know feeling a lot better I couldn't touch my toes before my back is a lot more flexible now so overall I feel much better much healthier my energy feels cleaner brighter. Brain education for our youth means hope I use that word a lot hope because I feel like we're given a lot of information now a lot of Instagram personalities influencers entertainers and we have formal education a classic education system in America which is kind of outdated and so brain education not neuroscience but teaching us how to use our brain how to control our emotions use our bodies that are connected to our brains our brain really controls everything in our life and so I feel brain education through all the different principles and methods can really help us to take control of our lives especially as youth as the future leaders of this world we should really have that down pack before we start making big decisions like guiding other people or putting systems in place we should really know ourselves know our brains my favorite part of brain education would have to be sleeping tiger or donjon tapping anything that has to do with donjon your second chakra lower abdomen grounding your energy that has been like my lifesaver so anything that helps you really ground yourself and grow the energy in your second chakra I'm all for it I tell everybody who I teach who I work with my friends if you don't do anything else at least ground your energy bring it to your second chakra everything will make sense from there any exercise that has to do with grounding helped me so much I was very creative but thinking a lot not always in my body now I would worry about my physical body I was in shape I'd lift weights but I wasn't inside my body taking care of my organs my joints my everything and so grounding really helped me to snap out of it snap out of my my thoughts and come back to reality and that helped me be a lot happier be a lot more compassionate more empathetic with my family with my friends treat people better treat myself better and so I think any any positive change you want to make really starts with grounding and coming back to like this kind of zero point right in the center from there you can create anything any kind of change you want if I could give a message to my teenage self who was lost confused emotional lonely I would definitely say look for help ask for help ask the questions that you may be afraid to ask keep your hope that you'll get help and then from there you can begin to become the person who you want to become I hope everybody watching this can find a passion and not just something that they've been doing for a long time but something that really connects with them don't be afraid to try a bunch of new things and be open-minded live your life open and then find that thing that really connects with your heart with your soul and then from there you can begin to create the life that you want I was a scared angry up-and-coming fashion designer and I found myself through brain education


We found the three most burning Hey Arnold questions that are haunting your dreams. Hey Grandpa, whose glasses are these? How did Helga keep a shrine to Arnold in her closet? Oh, Arnold! Who is the resident in apartment 16? Mr. Smith. How do the residents of the boarding house all share one bathroom? 13 boarders, one bathroom, what do you expect? Let's start with Helga Pataki, the blonde bully of PS118 who is super obsessed with Arnold. Trying to make me pat and get out of here. Okay, thanks again Helga. I'll never wash these clothes again. Which leads us to this burning question. What is the deal with her closet shrine to Arnold? My sultry pretty. Why must I hold you only whilst I dream? As seen here, Helga moves her clothes out of the way to get to her statue of Arnold. So how did Helga manage to construct this shrine without alerting her parents? Okay, well sleep well. Yes! And speaking of alerting her parents, did they not notice that she was bringing a bunch of random fruit to her room? Helga! The door's locked honey, what are you doing in there?  Will I be forever enslaved by your spell? How in the world did she manage to get that to her room unnoticed? Being a fruit, wouldn't that make her closet stink?  What's the amount of time fruit can stay in a closet without rotting? And what about fruit flies? Wouldn't they make an appearance due to all the rotting produce? How is she able to make all of this happen? And in her closet! Why must I worship you? We are left totally stumped by this one and cannot find a reasonable explanation as to how this can possibly happen. I dance divinely. My eyes are lovely. Let's move on to the question that has left us stumped since 1996. Who is Mr. Smith? What do we know about Mr. Smith? Arnold, we know nothing about Mr. Smith. Some people say he works for the government. Satellite Industries? Sounds like the name of some covert cover-up operation for the CIA. I knew it!  Let's take a look at what we do know about him. One, he lives in apartment 16. Two, he works for satellite industries. Three, he wears bowler hats. Four, he has quick and easy access to a helicopter. Five, he is technologically inclined. I don't know about you, but I don't think these five facts tell us anything about who he is. What does satellite industries do? Sounds like the name of some covert cover-up operation for the CIA. Is it a government agency? I knew it!  It has got to be a government agency, right? Why does he have access to a helicopter? Does this mean the boarding house has a helicopter pad? That guy is unbelievable. And what's with all the gadgets and technology he installed around the boarding house? Now that's pride. Speaking of the boarding house, how is it possible none of his neighbors have seen him? Tip, tip, tip. The guy's lived here three years, he's never said a word. And I mean nobody. He's creepy. He gives me the creepies. Didn't grandpa and grandma have to see him when he rented the room? Well, he does pay extra, Mr. Kagashka, hand on time. What does he do when he isn't working at his, maybe, possibly government job? Does he have a partner? Kids? Maybe a pet. Why is it that in five seasons of Hey Arnold, we only get about a one-second glimpse of him? And why is he wearing a trench coat? It isn't raining out. What's in his briefcase? Is it important? Why bowler hats? We know he always wears one of those weird bowler derbies. Unfortunately, we have more questions than answers when it comes to this elusive resident. Okay, so two situations left us with more questions than answers. But maybe we can solve this last one. How in the world do all the residents of the boarding house share one communal bathroom?  The less-than-ideal bathroom situation was first mentioned in the episode Apartment 16. 13 borders. One bathroom. What do you expect? And has been making us scratch our heads since. I mean, think about it. You have Arnold, Ernie, Mr. Wynn, Oscar, Susie, Grandma, and Grandpa, and Mr. Smith living in the house. Good morning. The thickest are back down. And these are just the residents they interact with the most. New borders. Need to take a number? Do they coordinate their bathroom times? What if someone really has to go? Hey, Gramps, did you try to nail what? Do they ever run out of hot water? Or worse, toilet paper? How can such a big place only have one bathroom? 13 borders. One bathroom. What do you expect? Or maybe they don't. When looking at the episode Four Eye Jack, we discover there is a hidden bathroom in the basement. Hey, didn't Val use the downstairs bathroom in peace? I didn't know we had a downstairs bathroom. But unfortunately, Grandpa keeps it all to himself. You think I want everyone finding out about my extra bathroom? And Mr. Smith. Let's go back to him. How has nobody seen him going to or from the bathroom? What about Mr. Smith? He has his own private shower and a great big split-level suite. Okay, that explains it. So there are actually three bathrooms. But one is private and one is hidden. Secret sound. Well, this one is partially solved. It still leaves us with the issue of the majority of the boarding house residents all having to use the same one bathroom available to them. Hey, Gramps, did you try to nail what? Maybe there's another hidden bathroom in the house we don't know about. Three questions asked. Three questions left unanswered. Actually, we're left with more questions than we even started with. I don't know if anyone can answer these head-scratching questions. But one thing we do know, Mr. Smith looks awesome in his bowler hat. Where do they sell bowler derbies?


Hi, I'm Mary Harrell for Tan Books. More is at stake in the music we listen to or perform than most people realize. So what are you listening to in your car? What hymns are you hearing at Mass? And are you ever without those ubiquitous little airpods in your ears day in and day out? It's time to face the truth of what we're hearing every day. And here to discuss his new book on this topic is Dr. Peter Questnisky. He is the author of Good Music, Sacred Music, and Silence, Three Gifts of God for Liturgy and Life. Peter, thank you for being here today. Thank you, Mary, for having me.  So let's go ahead and start with what the problem is. Do you love a somewhat startling claim early on in the book that you say that just as great classical music is morally and intellectually good for us? Conversely, certain forms of music can actually be harmful and downright sinful. Tell us why you make that claim. Yes, so in the moral life, there are many, many influences on us and music is one of them, not the only one. However, it's a particularly important influence on our moral life because music as all of the philosophers from ancient times through modern times have recognized has a peculiar power to get under our skin, so to speak, and get right into our emotions, our feelings, our passions and form them in a likeness of the character of the music itself. We see this because dance music makes people wanna dance, march music makes them wanna march, church music at its best makes them want to pray. The way the music itself is, and I don't just mean the words, I mean the music really shapes our character. And that's a truth that nobody has ever denied, but a lot of people become very uncomfortable when you emphasize that point to them. And yet it's really kind of obvious, if you look at the people who listen to heavy metal music, they dress and they act and they talk a certain way, the people who listen to jazz, dress and talk and act a certain way, the people who listen to classical music perhaps, there could be some stereotypes in there, but there's also just a truth that we see about the formative power of music. And there are definitely types of music, I would say heavy metal is one of them, rap is another one, where there are serious ethical questions here about what kind of spiritual food are we taking into our souls when we listen to this music? We're asking it to shape us to make us like itself. And the sentiments conveyed in the lyrics especially, they kind of drill into the soul even more deeply when they're combined with music. I think parents find that when they maybe turn on a song that they listen to in their youth or even currently, and then you turn it on and your children are listening and you think, oh my gosh, this is wildly inappropriate and I just have heard it for so many years, I didn't even notice anymore, absolutely true. And I don't wanna paint that with too broad of a brush, you do make allowances for folk music, for music that is appropriate to certain instances or cultures, right? It's not just totally its Mozart all the time, even though that wouldn't be a bad thing. Yes, I would say that part of my goal in the book is to encourage people to broaden and deepen their musical culture, their musical experience because we as Western Christians, Catholics, we inherit the greatest musical and artistic culture that the human race has ever seen. There isn't even anything close to what Christendom has given us. And I'm talking now about everything from Gregorian chant and Byzantine chant through the polyphony of the Middle Ages and of the Renaissance, Palestrina, Victoria, Bird, Talas, these wonderful composers, unequaled at writing sacred music. And into Bach, Handel, Vivaldi, Mozart, Beethoven, Haydn, Mahler, Bruckner, Brahms, I mean, there are so many great composers, each one of these you could devote your entire life to because they left a corpus, a body of work that is comparable, say, to the work of Leonardo da Vinci or Michelangelo or Shakespeare or Dante, right? So these are, this is a great heritage we have. And yet the musical taste or the musical habits of most people is like a tiny thin line of this whole heritage. And in fact, when you look at it, that is when you look at a lot of contemporary or popular music, it's extremely simplistic as music. It has very repetitious rhythms.  The melodies are not at all interesting. Sometimes there isn't even a melody. And oftentimes the styles are one of sort of grinding almost bestial repetition. This is what you hear thumping out of the woofers of so many cars in cities. And this is like people eating a musical diet only of sugar candy or worse, even poison perhaps. Fast food, I compare it at one point to fast food. If all you ever ate was Burger King, you're gonna be a very unhealthy person, right? And this is true psychologically and spiritually as well. Well, and so let's go to the converse of that. The opposite of that would be Gregorian chant. You go into great detail in the book about the incomparable art form. And I love that you call it an art form. I don't think people always look at a musical category and say, yes, that is art as well. So what about Gregorian chant? It sets it apart as being uniquely suited to divine worship. You go through eight points that I thought were wonderful. Yes, exactly. Well, I do talk a lot about chant in the second part of the book. The first part is about classical music. Although as you say, I talk about folk music there too, which I think is a very important genre or genres multiple. But in part two, where I'm looking at sacred music, what's appropriate for the liturgy? There I really, I just start where the church herself starts in so many magisterial documents that Gregorian chant is the norm, is the perfect exemplar and example of sacred music. Why is that the case? Well, as you said, there are eight characteristics. The first is the primacy of the word. Gregorian chant gives primacy to the word of God, to the word of God in scripture. It's a musical lexiodivina, a musical interpretation of the word of God as given to us through the liturgy. In other words, the music doesn't draw attention to itself, but it draws attention to the sacred words that are being sung. And it does though, because of the, in a sense, the purity or the chastity of the melodies. It's not music that jumps up and down and says, pay attention to me. It's music that says, submit yourself to the holy word of God and let it form you and penetrate deeply into you. And the chant, the peacefulness, the tranquility of the chat helps that word to penetrate into our hearts. This is something that happens over a long period of time. We're meant to be hearing this over a long period of time, not just once. If you hear chat once, you might think, oh, that's strange and interesting, but it won't really have an effect on you. It's supposed to be a habitual exposure. The second characteristic is free rhythm. The chant doesn't fit into a system of beats, like duple or triple time. You can't put a meter to it, like three, four or four, four. If you have musical training, you know what I'm talking about. It's not like a waltz or a march or a dance. It has a free rhythm that follows the rhythm of the words themselves, usually from scripture. And this gives chat, it's sort of ethereal, free-floating character, right? It sort of meanders and almost soars like a bird in the sky, right? And that's part of the, it has this effect on us then of liberating and freeing us from worldly concerns. That's very much the effect of this free rhythm. Unison singing, typically Grimory and chant is sung, everybody is singing the same melody at the same time. It's not music in parts, like polyphony or just about every other later form of music, but it's music, it's unharmonized, unaccompanied often, and just one unison voice. Well, what's important about that? That represents the one holy Catholic and apostolic church speaking and praying una voce with one voice, right? And that means everybody can sing along with the chant either in the choir or even in the congregation. So that's important, the unison singing. The unaccompanied vocalization, I kind of touched on that. The fact that oftentimes there are no instruments involved. It's just the God given instrument of the human voice that is meant to be emitting the chant. And that's how it was for many, many centuries. There was no organ accompaniment. And still to this day, I would say in most churches when the chants are sung, there's not organ accompaniment. It's just the sound of the human voice. The only instrument God created every one of us with, right? I'll just mention the others briefly. Modality is unusual about chant. Chant isn't written in major keys or minor keys, but it uses an older system of tonality by which the melodies themselves have a unique set of shapes that we call the modes. And major and minor keys are like modes, but there are eight modes, not just two. And so a chant then has a kind of strange sound to the modern ear because for hundreds of years, we've been using only major and minor keys in Western music. But chant comes from an ancient culture that used eight different scales for the music. So that gives it a unique aspect or frame. And these modes have different emotional characters as well. Some of them are more bright. Others are darker. Some of them seem very incomplete. They frustrate in a way our musical expectations. And so what they actually lend themselves to is conveying something like the longing for eternity or the longing for the divine, precisely because the chant doesn't end in a sort of neat and tidy cadence, the way that a lot of later music does. You know, anonymity is a trait of Goraine chant. We don't know the names of, well, with very few exceptions, we don't know the names of any of these composers who wrote thousands of these gorgeous chant melodies, right? So there's no cult of personality. There's no celebrity status that somebody gets to have as a performer or as a composer of chant. It's just a big anonymous body of work produced by countless monks over all of these centuries. And what a wonderful thing that is too. It's like the liturgy itself. So much of the liturgy, we don't know where it came from. It just sort of, it was there. It emerged from faith and from prayer. Emotional moderation, this is very important about chant too, that it is emotional, it's not devoid of emotion, but the emotions are subtle and calm and pure. It does express joy, it does express sorrow, but it doesn't express, the extremes that say a romantic opera or perhaps a modern pop song is trying to get at, right? It's more subtle. And the last thing is maybe the most important in a way, the last trait of chant, which is that it's unambiguously sacred. And the reason I say that is the chant arose exclusively for use in the sacred liturgy of the church. It's never had any other purpose than that for its entire history. And we're going on now, we were talking about a heritage that's at least 1,500 years old. We don't even know when the chants began. They just suddenly show up in the historical record. As long as people have been liturgizing, they've been singing. Well, that leads me to the next question then of another part you had in your book that I wasn't something I hadn't even considered before that we sing liturgical texts. We don't just speak them. And there is a strange disconnected one. If you attend a Nova's Ordo Mass, sometimes the mass parts just spoken if there's not musical accompaniment for the day, the pianist is not there or whatnot. And it sounds rather strange. And I never thought about that, but why do we sing liturgical texts and not just speak them? Could you go into that for a little bit? Yes, for sure. Well, there are many reasons for doing this. And it's important to note that for the first 1,000 years of Christianity in East and West, when there was an undivided church before the Great Schism, that tragic event, all liturgy was sung. Public liturgy was always chanted. And it was only in the second millennium in the West that the idea of a private or a low mass developed. And it developed mainly because in monasteries that had dozens or even hundreds of monks who were priests, they could only do one collective mass per day as a community, one chanted mass. There was no such thing as a celebration, that's a novelty. And so these priests, they wanted to offer the holy mass as a personal devotional act and as an act on behalf of the church living and dead. And so that's how the low mass developed as an opportunity for these monks to pray a private quiet mass in the morning prior to their communal sung liturgy. But why do we sing the texts? Why is that the norm? First of all, it's because it elevates the text to a higher level. Whenever we sing something, we are elevating it. When we sing a song, a ballad, we're elevating the topic of that ballad. When we sing a mass, we're giving a sort of consecrated and ornamented and beautiful costume in a way to the words, we're treating them with even greater love and respect and they move us more deeply when they're sung. They're more memorable to us. People, there have been studies that show that people memorize things 10 or 20 times faster when they're sung as opposed to when they're just merely recited, right? This is why the advertisers love jingles.  You'll never forget it for as long as you live. Also, when words are sung, they actually have a way of carrying through a space more. If somebody just says at mass, the Lord be with you and with your spirit, it's kind of stale. The words just sort of drop there like you're just dropping something. But if the priest says, and the whole church chants, that's come spirit to do, very simple. Anybody can chant that. But suddenly it has this monumentality to it, right? It has a real solidity and strength and power that you're not going to get when you merely recite the words. Absolutely. I keep going back to children just cause I have so many of them, but that sticks with them too. When we want our children to memorize something or learn it, we often give it to them in a song. And in the same way, my kids will come home from mass and I'll hear them chanting in the living room. And I love that because something has stuck with them. The book is not totally about music. It is about silence as well. And I think any Catholic reader today is probably familiar with Cardinal Robert Sarah's book, The Power of Silence. And so what is the context of the silence you're writing about in this book and was his book any influence on your own work or thinking on the topic? Yes, absolutely. Well, Cardinal Sarah is certainly an influence, I think on any of us who love the liturgy and who treasure silence in particular. Silence in the liturgy is something that is more distinctive to the Western or Latin tradition. The East, which I love, I'm very familiar with Eastern Christian liturgies, especially the Ukrainian Greek Catholic Church and its liturgical rites, they sing everything. It's very extroverted. There's hardly any silence. You don't have a moment to think to yourself. And that's fine. That's their tradition. That's their custom. It's very effective because they're leisurely about it and they take lots of time and they sing, they repeat all kinds of songs. And it's like you sort of get steeped in it. You're simmered and stewed in all this chanting. And I think that that has a kind of mesmerizing mystical effect as well. It works within their own heritage. In the West, for various reasons, which I won't go into right now, the liturgy developed more room, more space for silence, for sometimes quite considerable periods of time in which the ministers at the altar, let's say the priest, deacon, sub-deacon, they're busy doing something. They're praying their own prayers quietly. And in the rest of the church, everybody is kneeling and praying silently and uniting themselves in a very deep and fervent way with the overall offering of the liturgy that's taking place. We've all experienced this if we've attended the traditional Latin Mass and we've seen or we've heard, if you can put it that way, the not only the chants and the readings, the antiphons, the prayers, but also this great silence during the canon, during the Roman canon. So from the point when the sanctus dies out to all the way through the peromnia secola secolorum and the amen at the end, it's this oasis of silence. And in that oasis, we find ourselves, I think, drawn even more deeply into the mystery of the sacrifice of Christ on the cross and the love and the mercy with which he offered himself on the cross and the adoration that we owe him in his real presence in the most holy sacrament. All of that is heavily accentuated paradoxically by the absence of speaking and the absence of singing. It's what I call a sonic iconostasis. There's a kind of veil that we lower over this awesome mystery in order, because we almost have a sense that no words could do justice to this and no music either. Even though the Roman canon is full of beautiful and majestic language, we can follow that language if we want to in the missile and I do sometimes and I hope everybody does, but there's something about the experience of that cavernous, awesome silence around the cross at Calvary with Mary and John that I think it's so poignant. And it's one of the things that I think it prompts people to pray with deeper fervor at that point in the mass. You have a line on silence in the book, which I absolutely loved. It said that silence is music's necessary counterpart and prayer's inseparable companion. And I love that dichotomy. Have you always cherished silence in your life and in the liturgy or was it something you came to later on in life when you had a greater appreciation for the Latin mass? That's a good question. And I always want to be careful not to reconstruct past events, to sort of read into the past what I've figured out later. And so I won't pretend that I've always appreciated silence. I don't think, and I actually don't think that human beings can appreciate silence until they've become more mature and had more life experience. Just like little children are squirmy all the time and it's hard for them to sit still and they have to learn how to sit still and then later on going beyond that they have to learn to read a short book then a middle-sized book then a long book and then they need to go from literature to non-fiction and maybe even philosophy. So I mean, human, our education takes place over a long time and it goes from phase to phase to phase and really the sky's the limit because you can keep moving. And I think something similar happens with regard to music and silence and prayer, all of those, in that we start with rather simple maybe almost even animal habits or tastes or inclinations and we have to grow through good habits, through habituation and a good environment to a greater and greater appreciation of beautiful music, of the value of silence, of prayer forms that are not merely vocal. Everybody starts by memorizing the Our Father, the Hail Mary, et cetera, we pray the rosary but we're supposed to eventually without leaving that behind, of course we're supposed to graduate also to being able to sit still in church and not be saying words but just sit there and just be in God's presence and sort of shut, almost to shut off the talking and just be in God's presence. And that's what happens often in adoration and Eucharistic adoration that people can reach a point where they're just content to be there like that wonderful story where the Curie of ours asked that old man, what are you doing here for so long in church? And he just says, I look at him and he looks at me. And so that's why I think all of, that's what my experience has been that it's taken a long time to appreciate certain things in life, including silence. And yet we all need to strive for that. So true and as we wrap up here it's been a wonderful conversation but you attend a strikingly beautiful church in Lincoln, Nebraska. I've been there myself. It's such a beautiful, holy, calm, quiet place to pray. So beautiful. It's served by the priests of the fraternity of the FSSP and it's striking that it's filled every Sunday, every mass with young families. And if you took an average of the attendance of the average age, it would be like five because there's so many babies. There's so many little kids too. So what do you see for the future of the church, for the hope of these families attending the Latin mass and of being simmered in that silence, in that holy music, in that chant, every single weekend and holy day? Does that give you hope for our future as a church? Yes, it does because in fact, what we're seeing in a place like St. Francis of Ceci or any of the parishes run by the fraternity of St. Peter, the Institute of Christ the King or Diocesan priests who offer the Latin mass. What we're seeing there is a rediscovery, a recovery of some of the church's most powerful, evangelistic and missionary and cataclysm and spiritually formative tools. These are tools that the church under the guidance of the Holy Spirit developed over centuries and centuries and they're tested, they're time tested, they've been proved sevenfold like silver in the fire and they work, they work very well. These are the tools with which the Catholic church conquered the world, the Roman Empire, the barbarian kingdoms and all of the continents with the missions, right? So of course they're effective, of course they work. We just have to persevere in prayer, in fidelity and in patience because we're living at a time when there are people who just don't, they have psychological barriers to the recovery of Catholic tradition. They see it as something which is completely passe, something that belongs to the past, that has nothing to say to us anymore. The opposite is the truth, is the truth but they have these barriers or impediments inside to seeing that and we need to pray for them and for ourselves and just keep doing what we're doing, brick by brick, chant by chant, child by child, right? This is how Catholicism will be rebuilt in the future. Amen to that. Again, the book is good music, sacred music and silence, three gifts of God for liturgy and for life. You can find it here on tanbooks.com or at your local Catholic bookstore, a wonderful addition to any home Catholic library and totally accessible to even a regular reader and a mom just like me. Encourage everyone to pick up a copy. Dr. Krasnicki, thank you so much. Thank you, Mary, I appreciate it.


Hello everyone, welcome to Oxmer Toyota. I'm Gabrielle and I wanted to take a minute, talk about this vehicle. It is a 2024 Toyota Sequoia. Now this is the SR5 hybrid, but it does have the TRD Sport package. So this color is pretty rare. You're not gonna see a whole lot of them. It is the Lunar Rock, absolutely beautiful. Now with it being a hybrid, you are going to have the blue in the Toyota symbol in the front. You have that big front grille, really aggressive looking. There's going to be LED headlights. You do have your fog lights as well up here. Now going on to the side, you're gonna have the 20 inch alloys. So they are black and you are gonna have the TRD in the red in the very middle.  And then we will show the back as well. So back here you're going to have the Sequoia in the bold black lettering. Again, with your hybrid, the blue within that Toyota symbol. And then let's go ahead and open it. So you can see the spacing back here. This is a very large SUV. You are going to have your third row. It is currently lying down. You're gonna have an all-weather floor liner back here. Another couple of things that are back here, you're gonna have your 120 volt. You are gonna have some charging ports back here for your third row, cupholders.  Now going into the interior, it's beautiful.  The seats are really neat. Kind of has like a white underneath, really cool like diamond-esque pattern. Now your shift knob is going to have the TRD on it. Then looking up, you are gonna have your 14 inch audio multimedia. You have all-weather floor liners.  There's a digital display. There's also gonna be a digital rubber mirror. And then also let's look up and we have a sunroof.  There's gonna be an all-weather floor liner back here.  And there's also 120 volt back here as well. Now to get to the third row, it is pretty easy. All you do is lift that up just like that and you can get to the third row. Now guys, speaking of the third row, there's a button that's right back here that you can lift up these seats. So if it is down for whatever reason, you are, you know, groceries, but now you've got kiddos, that button, and then people can go right back in. All right guys, if you have any questions, let us know all of our contact info is listed right here. Thanks for watching and I'll see you soon. Bye.


All right, first hockey breakdown in a while. Thanks to whoever suggested this. I appreciate it. It's brought to you by DraftKings. Download the number one sports book app. Use promo code, Johnboy, when you do. Bet on the wild to win everything. I know a lot about hockey, and you can trust me. Kaprisov, I believe is his name. Little Dude from Russia, number 97. He's going to skate up on the big dude, number 64, and kind of jump at him, throws the elbow up. It doesn't even really hit him that bad, but Stanley's a big guy. Big guy falls hard. Little guy falls easy. All cool, he gets up, says, fall again, because I didn't like that. Kaprisov is going to turn around and say, oh, hi, what's up? And then the ref's going to say, you're both going to the penalty box, mad at both of you. Oh, coach, looking on real. Confused, ah, what the hell's going on? Now they're John, so this is our guy who does the big punch we're going to see later. Felino, is that how you pronounce it?  And he says, oh, yeah, he's fucking, yeah, I think he's talking tough.  Oh, ha, ha, ha, ha, in there talking and they're John and they're laughing.  And then we're going to speed this up. We're going to go two minutes into the future and we get our next little hullabaloo where we're going around here. They're going to wrap that around. Number 97 again, little dude. Kaprisov, is that how you say it? He's going to get in trouble again.  Our dude, Felino's on the ice, number 17. He's been looking for a fight. Everyone's looking for a fight, so he's just finding his partner. He says, you, no, no, no, no, not you. Get out of here. You're done, bye. Now he's going to challenge someone. He's like, yeah, blah, blah, blah. Let's drop him, I think. So he's been invited and not invited to drop him twice later on. We're going to get a goal and now's the perfect time. A center ice face off, the perfect time to drop your gloves and put on a show for the people. So that's what happens. Number 17, Felino versus number five. Dylan, haven't seen him before. They're squaring up, they're squaring up. Ref says, hey, get that puck out of here. Other ref says, okay, got it, back to the fight. Now, a little shimmy shake here and now he's going to jump into the Superman jump punch. Get some air, lines it up and misses. But the crowd goes wild. They don't care where the punch landed. They just saw that he jumped up to punch and they loved it. I actually like this. When he jumps up with his left hand, he takes the other dude's hand and says, get this out of the way. Don't block this punch. And then he just misses it completely. And you can see from both angles here, jumps up, misses right into that window and bam, misses it. But moving forward, he does land some more. This was a big fight that everyone liked. They said, oh, we got a lot of good punches landed. So they're dancing, they're dancing and now they're in and bam. I think that's the best punch landed unless there are some inside jabs I didn't see. But they're trading big blows. Everyone's enjoying it. It's only the first period. Kaboom, kabam, kabah, kaboom, ooh, bam. Helmets off so the rest are like, hey, stop. Hey guys, stop, stop.  Show everyone how good you look with your hair. And he says, okay, that's my second favorite thing to do. Throws the elbow pads on the ice. Dylan gets high five. Felino gets high fives. This guy, yeah! Everyone is loved.  Superman punch, how about that? DraftKings Sportsbook, how about them? Number one sportsbook in the world.


23-year-old mother's pregnancy only happens once every 480 years. Young couples cannot be more than happy when they learn that their family will get bigger. It's a powerful feeling of elation to learn you'll become a parent. For a young couple from the Czech Republic, being parents wasn't out of the ordinary. They already had a boy, but the mother soon learned she would have a very special pregnancy. Blessed with a son. Alexandra and her husband Antonin Kainova were already blessed with a son. When Alexandra learned she was pregnant again, they were all happy since they had already planned for a second child. However, her pregnancy would soon make headlines around the world. A pregnancy like Alexandra's is said to only happen once every 480 years. Alexandra and Antonin would learn it all on their own once they went to the doctor's office. As soon as Alexandra realized she was pregnant, she went to have a checkup to make sure her baby was fine. As the couple was looking on the monitor to see their baby, the doctor had a news that brought tears of joy to the parents. You see, Alexandra and Antonin were planning to have a big family, with three children. Little did they know that the doctor was about to tell them they would have twins. But this was just the beginning of a very strange pregnancy. Both Alexandra and Antonin had a history of twins in the family, so it was like they carried the tradition. But a month later at a second checkup, the doctor was stunned to see that the mother wasn't really carrying twins. Alexandra was overjoyed learning that she'd have three kids in total, reaching her goal. However, she'd soon learn that the surprise of twins would soon be just a little slice of what was about to come. The first visit to the doctor ended with the surprise of twins, but as Alexandra and Antonin were preparing for twins, they got a call from the doctor to go back and get a re-diagnose. What was wrong? Alexandra was nervous and emotional, worrying about her babies. She had never expected to learn what the doctor was about to tell her. To say it was some shocking news was definitely an understatement. At the second checkup, the doctor looked on the monitor and told Alexandra she was actually having triplets. A few moments later, the skin revealed something that shocked the young parents. The ultrasound revealed one more baby. Alexandra wasn't really expecting twins or triplets, she was carrying four babies. We can all agree that it was shocking news, considering she thought she was having a baby, not four. But that's just the beginning of her story. The pregnant mother went home knowing she was carrying four babies instead of one, two or three. Alexandra had to tell everyone that already knew she was pregnant the amazing news. It was overwhelming, but surprises kept coming. The young mother saw her belly kept growing. She didn't know how much it was supposed to grow, so she once again went for an ultrasound to see if everything was all right. That's when the doctor told her something that made history. Believe it or not, but at the last checkup, the doctor was able to better see the fetuses which grew bigger and were easier to spot and count. As he examined the image on the monitor, he counted one, two, three, four, five. When we finally found a fifth head, I started to cry, recalled Alexandra in an interview before giving birth. A pregnancy like Alexandra only occurs once every 7 million. Two of the baby's sex was a mystery since they were hidden from the ultrasound, so they just had to wait for them to be born. In the Czech Republic, this kind of pregnancy is very rare, explained Dr Elena Makurova in an interview with the website news.com.au, in this specific country, we have been actively recording statistics of birth ever since 1949 and in that time, there has never once been a mention of quintuplets. As a matter of fact, quintuplets are birthed in the Czech Republic once in every 480 years on an average. Quintuplets are very rare, and they can be all male, all female, or a combination of the two. Identical quintuplets will always have the same gender, but most quintuplets are a combination of boys and girls. Alexandra and Antonin just had to wait and see what this miracle pregnancy would bring. As weeks passed, the family struggled to take in the shocking news. Alexandra recalls that her first baby boy was nursed for a year and a half and she planned to breastfeed all of her five babies. That would be challenging. First, she had to go through the few months of pregnancy. I look very much forward to seeing how they will look, said the happy mother who struggled to move around with her huge belly. When the day of birth came, she was rolled into the delivery room where a small army of doctors and nurses waited to bring the quintuplets to the world. Almost 40 people were inside the delivery room. The doctors performed a C-section to deliver the babies. Each of the quintuplets had designated doctors and nurses. Then, the head doctor of the neonatal unit announced the family the babies were healthy. Alexandra and Antonin were blessed with healthy babies. Antonin nearly missed the big moment when the quintuplets were born because the train was late. He finally got at the right time to greet the babies and kiss his wife. The family has grown quite a lot. The boys were named Deeniel, Michael, Alex and Martin, and the girl was named Teresa. They all bear the names of saints. Here they are as happy toddlers. The quintuplets are now six years old and are healthy and happy together with their older brother who must have been overwhelmed by so many new family members all at once.


Good morning, my name is Nyam Gul Aghaji. This is the News Update. The president of the academic staff union of universities, ASU, Professor Emmanuel Ossotike, has said members of the body may find it difficult to get to their respective schools today as they do not have money for transport. Professor Ossotike, who disclosed this while speaking about the suspension of ASU strikes, said that unlike those days when lecturers lived in staff quarters very close to campuses, most lecturers now live far away from the school campuses as most schools could not provide accommodation for them. They said that since they have not been paid for eight months, it would be difficult for them to afford the transport fares to their respective schools to teach students, and so the union expects the government to pay the money so that lecturers would be able to go back to work while other issues are being negotiated.